Volume 1: Logical Foundations

Global Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | : | _ | (1163 entries)
Notation Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | : | _ | (79 entries)
Module Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (23 entries)
Library Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (19 entries)
Lemma Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (343 entries)
Constructor Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (201 entries)
Axiom Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (1 entry)
Inductive Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (71 entries)
Definition Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (426 entries)

# Global Index

## A

add1 [definition, in Top.ProofObjects]
aeval [definition, in Top.Imp]
aevalR_division [module, in Top.Imp]
aevalR_division.ADiv [constructor, in Top.Imp]
aevalR_division.aevalR [inductive, in Top.Imp]
aevalR_division.aexp [inductive, in Top.Imp]
aevalR_division.AMinus [constructor, in Top.Imp]
aevalR_division.AMult [constructor, in Top.Imp]
aevalR_division.ANum [constructor, in Top.Imp]
aevalR_division.APlus [constructor, in Top.Imp]
aevalR_division.E_ADiv [constructor, in Top.Imp]
aevalR_division.E_AMinus [constructor, in Top.Imp]
aevalR_division.E_AMult [constructor, in Top.Imp]
aevalR_division.E_ANum [constructor, in Top.Imp]
aevalR_division.E_APlus [constructor, in Top.Imp]
aevalR_division.:type_scope:x_'\\'_x [notation, in Top.Imp]
aevalR_extended [module, in Top.Imp]
aevalR_extended.AAny [constructor, in Top.Imp]
aevalR_extended.aevalR [inductive, in Top.Imp]
aevalR_extended.aexp [inductive, in Top.Imp]
aevalR_extended.AMinus [constructor, in Top.Imp]
aevalR_extended.AMult [constructor, in Top.Imp]
aevalR_extended.ANum [constructor, in Top.Imp]
aevalR_extended.APlus [constructor, in Top.Imp]
aevalR_extended.E_AMinus [constructor, in Top.Imp]
aevalR_extended.E_AMult [constructor, in Top.Imp]
aevalR_extended.E_ANum [constructor, in Top.Imp]
aevalR_extended.E_Any [constructor, in Top.Imp]
aevalR_extended.E_APlus [constructor, in Top.Imp]
aevalR_extended.:type_scope:x_'\\'_x [notation, in Top.Imp]
AExp [module, in Top.Imp]
aexp [inductive, in Top.Imp]
AExp.aeval [definition, in Top.Imp]
AExp.aevalR [inductive, in Top.Imp]
AExp.aevalR_first_try [module, in Top.Imp]
AExp.aevalR_first_try.aevalR [inductive, in Top.Imp]
AExp.aevalR_first_try.E_AMinus [constructor, in Top.Imp]
AExp.aevalR_first_try.E_AMult [constructor, in Top.Imp]
AExp.aevalR_first_try.E_ANum [constructor, in Top.Imp]
AExp.aevalR_first_try.E_APlus [constructor, in Top.Imp]
AExp.aevalR_first_try.:type_scope:x_'\\'_x [notation, in Top.Imp]
AExp.aeval_iff_aevalR [lemma, in Top.Imp]
AExp.aeval_iff_aevalR' [lemma, in Top.Imp]
AExp.aexp [inductive, in Top.Imp]
AExp.AMinus [constructor, in Top.Imp]
AExp.AMult [constructor, in Top.Imp]
AExp.ANum [constructor, in Top.Imp]
AExp.APlus [constructor, in Top.Imp]
AExp.BAnd [constructor, in Top.Imp]
AExp.BEq [constructor, in Top.Imp]
AExp.beval [definition, in Top.Imp]
AExp.bevalR [inductive, in Top.Imp]
AExp.beval_iff_bevalR [lemma, in Top.Imp]
AExp.bexp [inductive, in Top.Imp]
AExp.BFalse [constructor, in Top.Imp]
AExp.BLe [constructor, in Top.Imp]
AExp.BNot [constructor, in Top.Imp]
AExp.BTrue [constructor, in Top.Imp]
AExp.E_AMinus [constructor, in Top.Imp]
AExp.E_AMult [constructor, in Top.Imp]
AExp.E_ANum [constructor, in Top.Imp]
AExp.E_APlus [constructor, in Top.Imp]
AExp.foo [lemma, in Top.Imp]
AExp.foo' [lemma, in Top.Imp]
AExp.In10 [lemma, in Top.Imp]
AExp.In10' [lemma, in Top.Imp]
AExp.optimize_0plus [definition, in Top.Imp]
AExp.optimize_0plus_b [definition, in Top.Imp]
AExp.optimize_0plus_b_sound [lemma, in Top.Imp]
AExp.optimize_0plus_sound [lemma, in Top.Imp]
AExp.optimize_0plus_sound' [lemma, in Top.Imp]
AExp.optimize_0plus_sound'' [lemma, in Top.Imp]
AExp.silly1 [lemma, in Top.Imp]
AExp.silly2 [lemma, in Top.Imp]
AExp.silly_presburger_example [definition, in Top.Imp]
AExp.test_aeval1 [definition, in Top.Imp]
AExp.test_optimize_0plus [definition, in Top.Imp]
AExp.:type_scope:x_'\\'_x [notation, in Top.Imp]
aexp1 [definition, in Top.Imp]
AId [constructor, in Top.Imp]
All [definition, in Top.Logic]
all3_spec [lemma, in Top.Induction]
All_In [lemma, in Top.Logic]
alpha [constructor, in Top.ImpParser]
AMinus [constructor, in Top.Imp]
AMult [constructor, in Top.Imp]
andb [definition, in Top.Basics]
andb3 [definition, in Top.Basics]
andb3_exchange [lemma, in Top.Basics]
andb_commutative [lemma, in Top.Basics]
andb_commutative' [lemma, in Top.Basics]
andb_commutative'' [lemma, in Top.Basics]
andb_eq_orb [lemma, in Top.Basics]
andb_false_r [lemma, in Top.Induction]
andb_true_elim2 [lemma, in Top.Basics]
andb_true_iff [lemma, in Top.Logic]
and_assoc [lemma, in Top.Logic]
and_commut [lemma, in Top.Logic]
and_example [definition, in Top.Logic]
and_example' [definition, in Top.Logic]
and_example2 [lemma, in Top.Logic]
and_example2' [lemma, in Top.Logic]
and_example2'' [lemma, in Top.Logic]
and_example3 [lemma, in Top.Logic]
and_exercise [definition, in Top.Logic]
and_intro [lemma, in Top.Logic]
antisymmetric [definition, in Top.Rel]
ANum [constructor, in Top.Imp]
APlus [constructor, in Top.Imp]
app [definition, in Top.Poly]
App [constructor, in Top.IndProp]
apply_empty [lemma, in Top.Maps]
apply_iff_example [lemma, in Top.Logic]
app_assoc [lemma, in Top.Poly]
app_exists [lemma, in Top.IndProp]
app_length [lemma, in Top.Poly]
app_ne [lemma, in Top.IndProp]
app_nil_r [lemma, in Top.Poly]
Auto [library]
auto_example_1 [definition, in Top.Auto]
auto_example_1' [definition, in Top.Auto]
auto_example_2 [definition, in Top.Auto]
auto_example_3 [definition, in Top.Auto]
auto_example_4 [definition, in Top.Auto]
auto_example_6 [definition, in Top.Auto]
auto_example_6' [definition, in Top.Auto]
auto_example_7 [definition, in Top.Auto]
auto_example_7' [definition, in Top.Auto]

## B

BAnd [constructor, in Top.Imp]
bar [definition, in Top.Tactics]
Basics [library]
baz [inductive, in Top.Lists]
Baz1 [constructor, in Top.Lists]
Baz2 [constructor, in Top.Lists]
bempty [constructor, in Top.IndPrinciples]
BEq [constructor, in Top.Imp]
beq_id [definition, in Top.Lists]
beq_id_refl [lemma, in Top.Lists]
beq_id_true [lemma, in Top.Tactics]
beq_list [definition, in Top.Logic]
beq_list_true_iff [lemma, in Top.Logic]
beq_nat [definition, in Top.Basics]
beq_natP [lemma, in Top.IndProp]
beq_natP_practice [lemma, in Top.IndProp]
beq_nat_false_iff [lemma, in Top.Logic]
beq_nat_refl [lemma, in Top.Induction]
beq_nat_sym [lemma, in Top.Tactics]
beq_nat_trans [lemma, in Top.Tactics]
beq_nat_true [lemma, in Top.Tactics]
beq_nat_true_iff [lemma, in Top.Logic]
beq_nat_0_l [lemma, in Top.Tactics]
beq_string [definition, in Top.Maps]
beq_stringP [lemma, in Top.Maps]
beq_string_false_iff [lemma, in Top.Maps]
beq_string_refl [lemma, in Top.Maps]
beq_string_true_iff [lemma, in Top.Maps]
beval [definition, in Top.Imp]
bexp [inductive, in Top.Imp]
bexp1 [definition, in Top.Imp]
BFalse [constructor, in Top.Imp]
Bib [library]
bignumber [definition, in Top.ImpParser]
black [constructor, in Top.Basics]
BLe [constructor, in Top.Imp]
bleaf [constructor, in Top.IndPrinciples]
blt_nat [definition, in Top.Basics]
blue [constructor, in Top.IndPrinciples]
blue [constructor, in Top.Basics]
BNot [constructor, in Top.Imp]
bool [inductive, in Top.Basics]
boollist [inductive, in Top.Poly]
bool_cons [constructor, in Top.Poly]
bool_fn_applied_thrice [lemma, in Top.Tactics]
bool_nil [constructor, in Top.Poly]
bool_to_bexp [definition, in Top.Imp]
BreakImp [module, in Top.Imp]
BreakImp.break_ignore [lemma, in Top.Imp]
BreakImp.CAss [constructor, in Top.Imp]
BreakImp.CBreak [constructor, in Top.Imp]
BreakImp.ceval [inductive, in Top.Imp]
BreakImp.ceval_deterministic [lemma, in Top.Imp]
BreakImp.CIf [constructor, in Top.Imp]
BreakImp.com [inductive, in Top.Imp]
BreakImp.CSeq [constructor, in Top.Imp]
BreakImp.CSkip [constructor, in Top.Imp]
BreakImp.CWhile [constructor, in Top.Imp]
BreakImp.E_Skip [constructor, in Top.Imp]
BreakImp.result [inductive, in Top.Imp]
BreakImp.SBreak [constructor, in Top.Imp]
BreakImp.SContinue [constructor, in Top.Imp]
BreakImp.while_break_true [lemma, in Top.Imp]
BreakImp.while_continue [lemma, in Top.Imp]
BreakImp.while_stops_on_break [lemma, in Top.Imp]
BreakImp.::x_'/'_x_'\\'_x_'/'_x [notation, in Top.Imp]
BreakImp.::x_'::='_x [notation, in Top.Imp]
BreakImp.::x_';;'_x [notation, in Top.Imp]
BreakImp.::'BREAK' [notation, in Top.Imp]
BreakImp.::'IFB'_x_'THEN'_x_'ELSE'_x_'FI' [notation, in Top.Imp]
BreakImp.::'SKIP' [notation, in Top.Imp]
BreakImp.::'WHILE'_x_'DO'_x_'END' [notation, in Top.Imp]
BTrue [constructor, in Top.Imp]
byntree [inductive, in Top.IndPrinciples]

## C

c [definition, in Top.IndProp]
CAss [constructor, in Top.Imp]
ceval [inductive, in Top.Imp]
ceval'_example1 [definition, in Top.Auto]
ceval_and_ceval_step_coincide [lemma, in Top.ImpCEvalFun]
ceval_deterministic [lemma, in Top.Imp]
ceval_deterministic [lemma, in Top.Auto]
ceval_deterministic' [lemma, in Top.Auto]
ceval_deterministic' [lemma, in Top.ImpCEvalFun]
ceval_deterministic'' [lemma, in Top.Auto]
ceval_deterministic''' [lemma, in Top.Auto]
ceval_deterministic'''' [lemma, in Top.Auto]
ceval_deterministic''''' [lemma, in Top.Auto]
ceval_deterministic'_alt [lemma, in Top.Auto]
ceval_example1 [definition, in Top.Auto]
ceval_example1 [definition, in Top.Imp]
ceval_example2 [definition, in Top.Imp]
ceval_fun_no_while [definition, in Top.Imp]
ceval_step [definition, in Top.ImpCEvalFun]
ceval_step1 [definition, in Top.ImpCEvalFun]
ceval_step2 [definition, in Top.ImpCEvalFun]
ceval_step3 [definition, in Top.ImpCEvalFun]
ceval_step_more [lemma, in Top.ImpCEvalFun]
ceval_step__ceval [lemma, in Top.ImpCEvalFun]
ceval__ceval_step [lemma, in Top.ImpCEvalFun]
Char [constructor, in Top.IndProp]
chartype [inductive, in Top.ImpParser]
char_eps_suffix [lemma, in Top.IndProp]
char_nomatch_char [lemma, in Top.IndProp]
CIf [constructor, in Top.Imp]
classifyChar [definition, in Top.ImpParser]
clos_refl_trans [inductive, in Top.Rel]
clos_refl_trans_1n [inductive, in Top.Rel]
color [inductive, in Top.Basics]
com [inductive, in Top.Imp]
combine [definition, in Top.Poly]
combine_odd_even [definition, in Top.Logic]
combine_odd_even_elim_even [lemma, in Top.Logic]
combine_odd_even_elim_odd [lemma, in Top.Logic]
combine_odd_even_intro [lemma, in Top.Logic]
combine_split [lemma, in Top.Tactics]
cons [constructor, in Top.Poly]
constfun [definition, in Top.Poly]
constfun_example1 [definition, in Top.Poly]
constfun_example2 [definition, in Top.Poly]
cons' [constructor, in Top.Poly]
contradiction_implies_anything [lemma, in Top.Logic]
contrapositive [lemma, in Top.Logic]
count [definition, in Top.IndProp]
countoddmembers' [definition, in Top.Poly]
CSeq [constructor, in Top.Imp]
CSkip [constructor, in Top.Imp]
CWhile [constructor, in Top.Imp]
C1 [constructor, in Top.IndPrinciples]
C2 [constructor, in Top.IndPrinciples]

## D

d [definition, in Top.IndProp]
day [inductive, in Top.Basics]
derive [definition, in Top.IndProp]
derives [definition, in Top.IndProp]
derive_corr [lemma, in Top.IndProp]
de_morgan_not_and_not [definition, in Top.Logic]
digit [constructor, in Top.ImpParser]
dist_exists_or [lemma, in Top.Logic]
dist_not_exists [lemma, in Top.Logic]
doit3times [definition, in Top.Poly]
double [definition, in Top.Induction]
double_injective [lemma, in Top.Tactics]
double_injective_FAILED [lemma, in Top.Tactics]
double_injective_take2 [lemma, in Top.Tactics]
double_injective_take2_FAILED [lemma, in Top.Tactics]
double_neg [lemma, in Top.Logic]
double_negation_elimination [definition, in Top.Logic]
double_plus [lemma, in Top.Induction]

## E

eauto_example [definition, in Top.Auto]
eg1 [definition, in Top.ImpParser]
empty [definition, in Top.Maps]
EmptySet [constructor, in Top.IndProp]
EmptyStr [constructor, in Top.IndProp]
empty_is_empty [lemma, in Top.IndProp]
empty_matches_eps [lemma, in Top.IndProp]
empty_nomatch_ne [lemma, in Top.IndProp]
empty_state [definition, in Top.Extraction]
equality__leibniz_equality [lemma, in Top.ProofObjects]
equivalence [definition, in Top.Rel]
ev [inductive, in Top.IndProp]
evenb [definition, in Top.Basics]
evenb_double [lemma, in Top.Logic]
evenb_double_conv [lemma, in Top.Logic]
evenb_S [lemma, in Top.Induction]
even5_nonsense [lemma, in Top.IndProp]
even_bool_prop [lemma, in Top.Logic]
even_1000 [definition, in Top.Logic]
even_1000' [definition, in Top.Logic]
even_1000'' [definition, in Top.Logic]
evSS_ev [lemma, in Top.IndProp]
evSS_ev [lemma, in Top.IndProp]
ev' [inductive, in Top.IndProp]
ev'_ev [lemma, in Top.IndProp]
ev'_sum [constructor, in Top.IndProp]
ev'_0 [constructor, in Top.IndProp]
ev'_2 [constructor, in Top.IndProp]
ev_double [lemma, in Top.IndProp]
ev_even [lemma, in Top.IndProp]
ev_even_firsttry [lemma, in Top.IndProp]
ev_even_iff [lemma, in Top.IndProp]
ev_ev' [lemma, in Top.IndPrinciples]
ev_ev__ev [lemma, in Top.IndProp]
ev_minus2 [lemma, in Top.IndProp]
ev_minus2' [lemma, in Top.IndProp]
ev_plus2 [definition, in Top.ProofObjects]
ev_plus2' [definition, in Top.ProofObjects]
ev_plus2'' [definition, in Top.ProofObjects]
ev_plus4 [lemma, in Top.ProofObjects]
ev_plus4 [lemma, in Top.IndProp]
ev_plus4' [definition, in Top.ProofObjects]
ev_plus4'' [definition, in Top.ProofObjects]
ev_plus_plus [lemma, in Top.IndProp]
ev_SS [constructor, in Top.IndProp]
ev_sum [lemma, in Top.IndProp]
ev_0 [constructor, in Top.IndProp]
ev_4 [lemma, in Top.ProofObjects]
ev_4 [lemma, in Top.IndProp]
ev_4' [lemma, in Top.ProofObjects]
ev_4' [lemma, in Top.IndProp]
ev_4'' [lemma, in Top.ProofObjects]
ev_4''' [definition, in Top.ProofObjects]
ev_8 [lemma, in Top.ProofObjects]
ev_8' [definition, in Top.ProofObjects]
examplemap [definition, in Top.Maps]
examplemap' [definition, in Top.Maps]
excluded_middle [definition, in Top.Logic]
excluded_middle_irrefutable [lemma, in Top.Logic]
Exercises [module, in Top.Poly]
Exercises.Church [module, in Top.Poly]
Exercises.Church.exp [definition, in Top.Poly]
Exercises.Church.exp_1 [definition, in Top.Poly]
Exercises.Church.exp_2 [definition, in Top.Poly]
Exercises.Church.exp_3 [definition, in Top.Poly]
Exercises.Church.mult [definition, in Top.Poly]
Exercises.Church.mult_1 [definition, in Top.Poly]
Exercises.Church.mult_2 [definition, in Top.Poly]
Exercises.Church.mult_3 [definition, in Top.Poly]
Exercises.Church.nat [definition, in Top.Poly]
Exercises.Church.one [definition, in Top.Poly]
Exercises.Church.plus [definition, in Top.Poly]
Exercises.Church.plus_1 [definition, in Top.Poly]
Exercises.Church.plus_2 [definition, in Top.Poly]
Exercises.Church.plus_3 [definition, in Top.Poly]
Exercises.Church.succ [definition, in Top.Poly]
Exercises.Church.succ_1 [definition, in Top.Poly]
Exercises.Church.succ_2 [definition, in Top.Poly]
Exercises.Church.succ_3 [definition, in Top.Poly]
Exercises.Church.three [definition, in Top.Poly]
Exercises.Church.two [definition, in Top.Poly]
Exercises.Church.zero [definition, in Top.Poly]
Exercises.curry_uncurry [lemma, in Top.Poly]
Exercises.fold_length [definition, in Top.Poly]
Exercises.fold_length_correct [lemma, in Top.Poly]
Exercises.fold_map [definition, in Top.Poly]
Exercises.prod_curry [definition, in Top.Poly]
Exercises.prod_uncurry [definition, in Top.Poly]
Exercises.test_fold_length1 [definition, in Top.Poly]
Exercises.test_map1' [definition, in Top.Poly]
Exercises.uncurry_curry [lemma, in Top.Poly]
exists_example_2 [lemma, in Top.Logic]
exp [definition, in Top.Basics]
expect [definition, in Top.ImpParser]
exp_match [inductive, in Top.IndProp]
ExSet [inductive, in Top.IndPrinciples]
Extraction [library]
ex_falso_quodlibet [lemma, in Top.Logic]
E_Ass [constructor, in Top.Imp]
E_IfFalse [constructor, in Top.Imp]
E_IfTrue [constructor, in Top.Imp]
E_Seq [constructor, in Top.Imp]
E_Skip [constructor, in Top.Imp]
E_WhileFalse [constructor, in Top.Imp]
E_WhileTrue [constructor, in Top.Imp]

## F

factorial [definition, in Top.Basics]
fact_in_coq [definition, in Top.Imp]
false [constructor, in Top.Basics]
false_beq_string [lemma, in Top.Maps]
filter [definition, in Top.Poly]
filter_even_gt7 [definition, in Top.Poly]
filter_exercise [lemma, in Top.Tactics]
filter_not_empty_In [lemma, in Top.IndProp]
filter_not_empty_In' [lemma, in Top.IndProp]
firstExpect [definition, in Top.ImpParser]
flat_map [definition, in Top.Poly]
fold [definition, in Top.Poly]
fold_example1 [definition, in Top.Poly]
fold_example2 [definition, in Top.Poly]
fold_example3 [definition, in Top.Poly]
foo [definition, in Top.Tactics]
foo' [inductive, in Top.IndPrinciples]
forallb [definition, in Top.Logic]
forallb_true_iff [lemma, in Top.Logic]
four_is_even [lemma, in Top.Logic]
friday [constructor, in Top.Basics]
fst [definition, in Top.Poly]
ftrue [definition, in Top.Poly]
functional_extensionality [axiom, in Top.Logic]
function_equality_ex1 [definition, in Top.Logic]
function_equality_ex2 [definition, in Top.Logic]
function_equality_ex2 [definition, in Top.Logic]
f_equal [lemma, in Top.Tactics]

## G

green [constructor, in Top.Basics]
green [constructor, in Top.IndPrinciples]

## H

hd_error [definition, in Top.Poly]

## I

id [inductive, in Top.Lists]
Id [constructor, in Top.Lists]
identity_fn_applied_twice [lemma, in Top.Basics]
iff_refl [lemma, in Top.Logic]
iff_reflect [lemma, in Top.IndProp]
iff_sym [lemma, in Top.Logic]
iff_trans [lemma, in Top.Logic]
Imp [library]
ImpCEvalFun [library]
implies_to_or [definition, in Top.Logic]
ImpParser [library]
In [definition, in Top.Logic]
IndPrinciples [library]
IndProp [library]
Induction [library]
informal_not_PNP_TODO [definition, in Top.Logic]
injective [definition, in Top.Logic]
inversion_ex1 [lemma, in Top.Tactics]
inversion_ex2 [lemma, in Top.Tactics]
inversion_ex3 [definition, in Top.Tactics]
inversion_ex4 [lemma, in Top.Tactics]
inversion_ex5 [lemma, in Top.Tactics]
inversion_ex6 [definition, in Top.Tactics]
In_app_iff [lemma, in Top.Logic]
In_example_1 [definition, in Top.Logic]
In_example_2 [definition, in Top.Logic]
In_map [lemma, in Top.Logic]
In_map_iff [lemma, in Top.Logic]
in_re_match [lemma, in Top.IndProp]
in_split [lemma, in Top.IndProp]
isAlpha [definition, in Top.ImpParser]
isDigit [definition, in Top.ImpParser]
isLowerAlpha [definition, in Top.ImpParser]
isred [definition, in Top.Basics]
isWhite [definition, in Top.ImpParser]
is_der [definition, in Top.IndProp]
is_even_prime [definition, in Top.Logic]
is_fortytwo [definition, in Top.Auto]
is_three [definition, in Top.Logic]

## L

le [inductive, in Top.IndPrinciples]
leaf [constructor, in Top.IndPrinciples]
leb [definition, in Top.Basics]
leb_complete [lemma, in Top.IndProp]
leb_correct [lemma, in Top.IndProp]
leb_iff [lemma, in Top.IndProp]
leb_refl [lemma, in Top.Induction]
leb_true_trans [lemma, in Top.IndProp]
leibniz_equality__equality [lemma, in Top.ProofObjects]
lemma_application_ex [definition, in Top.Logic]
length [definition, in Top.Poly]
length_is_1 [definition, in Top.Poly]
le_antisym [lemma, in Top.Auto]
le_antisymmetric [lemma, in Top.Rel]
le_n [constructor, in Top.IndPrinciples]
le_not_a_partial_function [lemma, in Top.Rel]
le_not_symmetric [lemma, in Top.Rel]
le_order [lemma, in Top.Rel]
le_plus_l [lemma, in Top.IndProp]
le_reflexive [lemma, in Top.Rel]
le_S [constructor, in Top.IndPrinciples]
le_Sn_le [lemma, in Top.Rel]
le_Sn_n [lemma, in Top.Rel]
le_step [lemma, in Top.Rel]
le_S_n [lemma, in Top.Rel]
le_trans [lemma, in Top.Rel]
le_trans [lemma, in Top.IndProp]
list [inductive, in Top.Poly]
Lists [library]
list' [inductive, in Top.Poly]
list123 [definition, in Top.Poly]
list123' [definition, in Top.Poly]
list123'' [definition, in Top.Poly]
list123''' [definition, in Top.Poly]
list_of_string [definition, in Top.ImpParser]
Logic [library]
loop [definition, in Top.Imp]
loop_never_stops [lemma, in Top.Imp]
lt [definition, in Top.IndProp]
lt_S [lemma, in Top.IndProp]
lt_trans [lemma, in Top.Rel]
lt_trans' [lemma, in Top.Rel]
lt_trans'' [lemma, in Top.Rel]

## M

many [definition, in Top.ImpParser]
many_helper [definition, in Top.ImpParser]
map [definition, in Top.Poly]
MApp [constructor, in Top.IndProp]
Maps [library]
map_rev [lemma, in Top.Poly]
matches_regex [definition, in Top.IndProp]
match_eps [definition, in Top.IndProp]
match_eps_refl [lemma, in Top.IndProp]
MChar [constructor, in Top.IndProp]
MEmpty [constructor, in Top.IndProp]
minustwo [definition, in Top.Basics]
minus_diag [lemma, in Top.Induction]
monday [constructor, in Top.Basics]
monochrome [definition, in Top.Basics]
MStarApp [constructor, in Top.IndProp]
MStar' [lemma, in Top.IndProp]
MStar'' [lemma, in Top.IndProp]
MStar0 [constructor, in Top.IndProp]
MStar1 [lemma, in Top.IndProp]
mult_assoc [lemma, in Top.Induction]
mult_comm [lemma, in Top.Induction]
mult_eq_0 [lemma, in Top.Logic]
mult_plus_distr_r [lemma, in Top.Induction]
mult_S_1 [lemma, in Top.Basics]
mult_0 [lemma, in Top.Logic]
mult_0_l [lemma, in Top.Basics]
mult_0_plus [lemma, in Top.Basics]
mult_0_plus' [lemma, in Top.Induction]
mult_0_r [lemma, in Top.Induction]
mult_0_r' [lemma, in Top.IndPrinciples]
mult_0_r'' [lemma, in Top.IndPrinciples]
mult_0_3 [lemma, in Top.Logic]
mult_1_l [lemma, in Top.Induction]
MumbleGrumble [module, in Top.Poly]
MumbleGrumble.a [constructor, in Top.Poly]
MumbleGrumble.b [constructor, in Top.Poly]
MumbleGrumble.c [constructor, in Top.Poly]
MumbleGrumble.d [constructor, in Top.Poly]
MumbleGrumble.e [constructor, in Top.Poly]
MumbleGrumble.grumble [inductive, in Top.Poly]
MumbleGrumble.mumble [inductive, in Top.Poly]
MUnionL [constructor, in Top.IndProp]
MUnionR [constructor, in Top.IndProp]
MUnion' [lemma, in Top.IndProp]
MyEquality [module, in Top.ProofObjects]
MyEquality.eq [inductive, in Top.ProofObjects]
MyEquality.eq_refl [constructor, in Top.ProofObjects]
MyEquality.four [lemma, in Top.ProofObjects]
MyEquality.four' [definition, in Top.ProofObjects]
MyEquality.singleton [definition, in Top.ProofObjects]
MyEquality.:type_scope:x_'='_x [notation, in Top.ProofObjects]
MyIff [module, in Top.Logic]
MyIff.iff [definition, in Top.Logic]
MyIff.:type_scope:x_'<->'_x [notation, in Top.Logic]
mynil [definition, in Top.Poly]
mynil [definition, in Top.Poly]
mynil' [definition, in Top.Poly]
MyNot [module, in Top.Logic]
MyNot.not [definition, in Top.Logic]
MyNot.:type_scope:'~'_x [notation, in Top.Logic]

## N

nandb [definition, in Top.Basics]
NatList [module, in Top.Lists]
natlist [inductive, in Top.IndPrinciples]
NatList.add [definition, in Top.Lists]
NatList.alternate [definition, in Top.Lists]
NatList.app [definition, in Top.Lists]
NatList.app_assoc [lemma, in Top.Lists]
NatList.app_assoc4 [lemma, in Top.Lists]
NatList.app_length [lemma, in Top.Lists]
NatList.app_nil_r [lemma, in Top.Lists]
NatList.bag [definition, in Top.Lists]
NatList.beq_natlist [definition, in Top.Lists]
NatList.beq_natlist_refl [lemma, in Top.Lists]
NatList.ble_n_Sn [lemma, in Top.Lists]
NatList.cons [constructor, in Top.Lists]
NatList.count [definition, in Top.Lists]
NatList.countoddmembers [definition, in Top.Lists]
NatList.count_member_nonzero [lemma, in Top.Lists]
NatList.fst [definition, in Top.Lists]
NatList.fst' [definition, in Top.Lists]
NatList.fst_swap_is_snd [lemma, in Top.Lists]
NatList.hd [definition, in Top.Lists]
NatList.hd_error [definition, in Top.Lists]
NatList.length [definition, in Top.Lists]
NatList.member [definition, in Top.Lists]
NatList.mylist [definition, in Top.Lists]
NatList.mylist1 [definition, in Top.Lists]
NatList.mylist2 [definition, in Top.Lists]
NatList.mylist3 [definition, in Top.Lists]
NatList.natlist [inductive, in Top.Lists]
NatList.natoption [inductive, in Top.Lists]
NatList.natprod [inductive, in Top.Lists]
NatList.nil [constructor, in Top.Lists]
NatList.nil_app [lemma, in Top.Lists]
NatList.None [constructor, in Top.Lists]
NatList.nonzeros [definition, in Top.Lists]
NatList.nonzeros_app [lemma, in Top.Lists]
NatList.nth_bad [definition, in Top.Lists]
NatList.nth_error [definition, in Top.Lists]
NatList.nth_error' [definition, in Top.Lists]
NatList.oddmembers [definition, in Top.Lists]
NatList.option_elim [definition, in Top.Lists]
NatList.option_elim_hd [lemma, in Top.Lists]
NatList.pair [constructor, in Top.Lists]
NatList.remove_all [definition, in Top.Lists]
NatList.remove_decreases_count [lemma, in Top.Lists]
NatList.remove_one [definition, in Top.Lists]
NatList.repeat [definition, in Top.Lists]
NatList.rev [definition, in Top.Lists]
NatList.rev_app_distr [lemma, in Top.Lists]
NatList.rev_involutive [lemma, in Top.Lists]
NatList.rev_length [lemma, in Top.Lists]
NatList.rev_length_firsttry [lemma, in Top.Lists]
NatList.snd [definition, in Top.Lists]
NatList.snd' [definition, in Top.Lists]
NatList.snd_fst_is_swap [lemma, in Top.Lists]
NatList.Some [constructor, in Top.Lists]
NatList.subset [definition, in Top.Lists]
NatList.sum [definition, in Top.Lists]
NatList.surjective_pairing [lemma, in Top.Lists]
NatList.surjective_pairing' [lemma, in Top.Lists]
NatList.surjective_pairing_stuck [lemma, in Top.Lists]
NatList.swap_pair [definition, in Top.Lists]
NatList.test_add1 [definition, in Top.Lists]
NatList.test_add2 [definition, in Top.Lists]
NatList.test_alternate1 [definition, in Top.Lists]
NatList.test_alternate2 [definition, in Top.Lists]
NatList.test_alternate3 [definition, in Top.Lists]
NatList.test_alternate4 [definition, in Top.Lists]
NatList.test_app1 [definition, in Top.Lists]
NatList.test_app2 [definition, in Top.Lists]
NatList.test_app3 [definition, in Top.Lists]
NatList.test_beq_natlist1 [definition, in Top.Lists]
NatList.test_beq_natlist2 [definition, in Top.Lists]
NatList.test_beq_natlist3 [definition, in Top.Lists]
NatList.test_countoddmembers1 [definition, in Top.Lists]
NatList.test_countoddmembers2 [definition, in Top.Lists]
NatList.test_countoddmembers3 [definition, in Top.Lists]
NatList.test_count1 [definition, in Top.Lists]
NatList.test_count2 [definition, in Top.Lists]
NatList.test_hd1 [definition, in Top.Lists]
NatList.test_hd2 [definition, in Top.Lists]
NatList.test_hd_error1 [definition, in Top.Lists]
NatList.test_hd_error2 [definition, in Top.Lists]
NatList.test_hd_error3 [definition, in Top.Lists]
NatList.test_member1 [definition, in Top.Lists]
NatList.test_member2 [definition, in Top.Lists]
NatList.test_nonzeros [definition, in Top.Lists]
NatList.test_nth_error1 [definition, in Top.Lists]
NatList.test_nth_error2 [definition, in Top.Lists]
NatList.test_nth_error3 [definition, in Top.Lists]
NatList.test_oddmembers [definition, in Top.Lists]
NatList.test_remove_all1 [definition, in Top.Lists]
NatList.test_remove_all2 [definition, in Top.Lists]
NatList.test_remove_all3 [definition, in Top.Lists]
NatList.test_remove_all4 [definition, in Top.Lists]
NatList.test_remove_one1 [definition, in Top.Lists]
NatList.test_remove_one2 [definition, in Top.Lists]
NatList.test_remove_one3 [definition, in Top.Lists]
NatList.test_remove_one4 [definition, in Top.Lists]
NatList.test_rev1 [definition, in Top.Lists]
NatList.test_rev2 [definition, in Top.Lists]
NatList.test_subset1 [definition, in Top.Lists]
NatList.test_subset2 [definition, in Top.Lists]
NatList.test_sum1 [definition, in Top.Lists]
NatList.test_tl [definition, in Top.Lists]
NatList.tl [definition, in Top.Lists]
NatList.tl_length_pred [lemma, in Top.Lists]
NatList.::x_'++'_x [notation, in Top.Lists]
NatList.::x_'::'_x [notation, in Top.Lists]
NatList.::'('_x_','_x_')' [notation, in Top.Lists]
NatList.::'['_x_';'_'..'_';'_x_']' [notation, in Top.Lists]
NatList.::'['_']' [notation, in Top.Lists]
natlist1 [inductive, in Top.IndPrinciples]
NatPlayground [module, in Top.Basics]
NatPlayground.nat [inductive, in Top.Basics]
NatPlayground.nat' [inductive, in Top.Basics]
NatPlayground.O [constructor, in Top.Basics]
NatPlayground.pred [definition, in Top.Basics]
NatPlayground.S [constructor, in Top.Basics]
NatPlayground.stop [constructor, in Top.Basics]
NatPlayground.tick [constructor, in Top.Basics]
NatPlayground2 [module, in Top.Basics]
NatPlayground2.minus [definition, in Top.Basics]
NatPlayground2.mult [definition, in Top.Basics]
NatPlayground2.plus [definition, in Top.Basics]
NatPlayground2.test_mult1 [definition, in Top.Basics]
nbranch [constructor, in Top.IndPrinciples]
ncons [constructor, in Top.IndPrinciples]
negb [definition, in Top.Basics]
negb_involutive [lemma, in Top.Basics]
next_even [inductive, in Top.IndProp]
next_nat [inductive, in Top.IndProp]
next_nat_closure_is_le [lemma, in Top.Rel]
next_nat_partial_function [lemma, in Top.Rel]
next_weekday [definition, in Top.Basics]
ne_1 [constructor, in Top.IndProp]
ne_2 [constructor, in Top.IndProp]
nil [constructor, in Top.Poly]
nil' [constructor, in Top.Poly]
nn [constructor, in Top.IndProp]
nnil [constructor, in Top.IndPrinciples]
nnil1 [constructor, in Top.IndPrinciples]
no [constructor, in Top.IndPrinciples]
node [constructor, in Top.IndPrinciples]
None [constructor, in Top.Poly]
NoneE [constructor, in Top.ImpParser]
nostutter [inductive, in Top.IndProp]
not_both_true_and_false [lemma, in Top.Logic]
not_equiv_false [lemma, in Top.IndProp]
not_exists_dist [lemma, in Top.Logic]
not_False [lemma, in Top.Logic]
not_implies_our_not [lemma, in Top.Logic]
not_true_iff_false [lemma, in Top.Logic]
not_true_is_false [lemma, in Top.Logic]
not_true_is_false' [lemma, in Top.Logic]
no_whiles [definition, in Top.Imp]
no_whilesR [inductive, in Top.Imp]
no_whiles_eqv [lemma, in Top.Imp]
nsnoc1 [constructor, in Top.IndPrinciples]
nth_error [definition, in Top.Poly]
nth_error_after_last [lemma, in Top.Tactics]
null_matches_none [lemma, in Top.IndProp]
n_le_m__Sn_le_Sm [lemma, in Top.IndProp]

## O

oddb [definition, in Top.Basics]
one_not_even [lemma, in Top.IndProp]
option [inductive, in Top.Poly]
optionE [inductive, in Top.ImpParser]
option_map [definition, in Top.Poly]
orb [definition, in Top.Basics]
orb_true_iff [lemma, in Top.Logic]
order [definition, in Top.Rel]
or_assoc [lemma, in Top.Logic]
or_commut [lemma, in Top.Logic]
or_distributes_over_and [lemma, in Top.Logic]
or_example [lemma, in Top.Logic]
or_intro [lemma, in Top.Logic]
other [constructor, in Top.ImpParser]
O_le_n [lemma, in Top.IndProp]

## P

pair [constructor, in Top.Poly]
parse [definition, in Top.ImpParser]
parseAExp [definition, in Top.ImpParser]
parseAtomicExp [definition, in Top.ImpParser]
parseBExp [definition, in Top.ImpParser]
parseConjunctionExp [definition, in Top.ImpParser]
parseIdentifier [definition, in Top.ImpParser]
parseNumber [definition, in Top.ImpParser]
parsePrimaryExp [definition, in Top.ImpParser]
parseProductExp [definition, in Top.ImpParser]
parser [definition, in Top.ImpParser]
parseSequencedCommand [definition, in Top.ImpParser]
parseSimpleCommand [definition, in Top.ImpParser]
parseSumExp [definition, in Top.ImpParser]
PartialMap [module, in Top.Lists]
PartialMap.empty [constructor, in Top.Lists]
PartialMap.find [definition, in Top.Lists]
PartialMap.partial_map [inductive, in Top.Lists]
PartialMap.record [constructor, in Top.Lists]
PartialMap.update [definition, in Top.Lists]
PartialMap.update_eq [lemma, in Top.Lists]
PartialMap.update_neq [lemma, in Top.Lists]
partial_function [definition, in Top.Rel]
partial_map [definition, in Top.Maps]
partition [definition, in Top.Poly]
peirce [definition, in Top.Logic]
pigeonhole_principle [lemma, in Top.IndProp]
Playground [module, in Top.IndProp]
Playground.le [inductive, in Top.IndProp]
Playground.le_n [constructor, in Top.IndProp]
Playground.le_S [constructor, in Top.IndProp]
Playground.test_le1 [lemma, in Top.IndProp]
Playground.test_le2 [lemma, in Top.IndProp]
Playground.test_le3 [lemma, in Top.IndProp]
Playground.::x_'<='_x [notation, in Top.IndProp]
plus' [definition, in Top.Basics]
plus2 [definition, in Top.Imp]
plus2_spec [lemma, in Top.Imp]
plus3 [definition, in Top.Poly]
plus_assoc [lemma, in Top.Induction]
plus_assoc' [lemma, in Top.IndPrinciples]
plus_assoc' [lemma, in Top.Induction]
plus_assoc'' [lemma, in Top.Induction]
plus_ble_compat_l [lemma, in Top.Induction]
plus_comm [lemma, in Top.Induction]
plus_comm' [lemma, in Top.IndPrinciples]
plus_comm'' [lemma, in Top.IndPrinciples]
plus_comm3 [lemma, in Top.Logic]
plus_comm3_take2 [lemma, in Top.Logic]
plus_comm3_take3 [lemma, in Top.Logic]
plus_fact [definition, in Top.Logic]
plus_fact_is_true [lemma, in Top.Logic]
plus_id_example [lemma, in Top.Basics]
plus_id_exercise [lemma, in Top.Basics]
plus_lt [lemma, in Top.IndProp]
plus_n_n_injective [lemma, in Top.Tactics]
plus_n_O [lemma, in Top.Induction]
plus_n_O_firsttry [lemma, in Top.Induction]
plus_n_O_secondtry [lemma, in Top.Induction]
plus_n_Sm [lemma, in Top.Induction]
plus_one_r' [lemma, in Top.IndPrinciples]
plus_O_n [lemma, in Top.Basics]
plus_O_n' [lemma, in Top.Basics]
plus_rearrange [lemma, in Top.Induction]
plus_rearrange_firsttry [lemma, in Top.Induction]
plus_swap [lemma, in Top.Induction]
plus_swap' [lemma, in Top.Induction]
plus_1_l [lemma, in Top.Basics]
plus_1_neq_0 [lemma, in Top.Basics]
plus_1_neq_0' [lemma, in Top.Basics]
plus_1_neq_0_firsttry [lemma, in Top.Basics]
plus_2_2_is_4 [lemma, in Top.Logic]
Poly [library]
Postscript [library]
Preface [library]
preorder [definition, in Top.Rel]
primary [constructor, in Top.Basics]
prod [inductive, in Top.Poly]
proj1 [lemma, in Top.Logic]
proj2 [lemma, in Top.Logic]
ProofObjects [library]
Props [module, in Top.ProofObjects]
Props.And [module, in Top.ProofObjects]
Props.And.and [inductive, in Top.ProofObjects]
Props.And.conj [constructor, in Top.ProofObjects]
Props.and_comm [lemma, in Top.ProofObjects]
Props.and_comm' [definition, in Top.ProofObjects]
Props.and_comm'_aux [definition, in Top.ProofObjects]
Props.conj_fact [definition, in Top.ProofObjects]
Props.Ex [module, in Top.ProofObjects]
Props.Ex.ex [inductive, in Top.ProofObjects]
Props.Ex.ex_intro [constructor, in Top.ProofObjects]
Props.ex_ev_Sn [definition, in Top.ProofObjects]
Props.False [inductive, in Top.ProofObjects]
Props.I [constructor, in Top.ProofObjects]
Props.Or [module, in Top.ProofObjects]
Props.Or.or [inductive, in Top.ProofObjects]
Props.Or.or_introl [constructor, in Top.ProofObjects]
Props.Or.or_intror [constructor, in Top.ProofObjects]
Props.or_comm [definition, in Top.ProofObjects]
Props.some_nat_is_even [definition, in Top.ProofObjects]
Props.True [inductive, in Top.ProofObjects]
provable_equiv_true [lemma, in Top.IndProp]
Pumping [module, in Top.IndProp]
Pumping.napp [definition, in Top.IndProp]
Pumping.napp_plus [lemma, in Top.IndProp]
Pumping.pumping [lemma, in Top.IndProp]
Pumping.pumping_constant [definition, in Top.IndProp]
pup_to_n [definition, in Top.ImpCEvalFun]
pup_to_n [definition, in Top.Imp]
pup_to_2_ceval [lemma, in Top.Imp]
P_m0r [definition, in Top.IndPrinciples]
P_m0r' [definition, in Top.IndPrinciples]

## R

R [module, in Top.IndProp]
red [constructor, in Top.Basics]
red [constructor, in Top.IndPrinciples]
reflect [inductive, in Top.IndProp]
ReflectF [constructor, in Top.IndProp]
ReflectT [constructor, in Top.IndProp]
reflect_iff [lemma, in Top.IndProp]
reflexive [definition, in Top.Rel]
refl_matches_eps [definition, in Top.IndProp]
regex_match [definition, in Top.IndProp]
regex_refl [lemma, in Top.IndProp]
reg_exp [inductive, in Top.IndProp]
reg_exp_ex1 [definition, in Top.IndProp]
reg_exp_ex2 [definition, in Top.IndProp]
reg_exp_ex3 [definition, in Top.IndProp]
reg_exp_ex4 [definition, in Top.IndProp]
reg_exp_of_list [definition, in Top.IndProp]
reg_exp_of_list_spec [lemma, in Top.IndProp]
Rel [library]
relation [definition, in Top.Rel]
Repeat [module, in Top.Auto]
repeat [definition, in Top.Poly]
repeats [inductive, in Top.IndProp]
repeat' [definition, in Top.Poly]
repeat'' [definition, in Top.Poly]
repeat''' [definition, in Top.Poly]
Repeat.CAsgn [constructor, in Top.Auto]
Repeat.ceval [inductive, in Top.Auto]
Repeat.ceval_deterministic [lemma, in Top.Auto]
Repeat.ceval_deterministic' [lemma, in Top.Auto]
Repeat.CIf [constructor, in Top.Auto]
Repeat.com [inductive, in Top.Auto]
Repeat.CRepeat [constructor, in Top.Auto]
Repeat.CSeq [constructor, in Top.Auto]
Repeat.CSkip [constructor, in Top.Auto]
Repeat.CWhile [constructor, in Top.Auto]
Repeat.E_Ass [constructor, in Top.Auto]
Repeat.E_IfFalse [constructor, in Top.Auto]
Repeat.E_IfTrue [constructor, in Top.Auto]
Repeat.E_RepeatEnd [constructor, in Top.Auto]
Repeat.E_RepeatLoop [constructor, in Top.Auto]
Repeat.E_Seq [constructor, in Top.Auto]
Repeat.E_Skip [constructor, in Top.Auto]
Repeat.E_WhileFalse [constructor, in Top.Auto]
Repeat.E_WhileTrue [constructor, in Top.Auto]
Repeat.::x_'/'_x_'\\'_x [notation, in Top.Auto]
Repeat.::x_'::='_x [notation, in Top.Auto]
Repeat.::x_';'_x [notation, in Top.Auto]
Repeat.::'IFB'_x_'THEN'_x_'ELSE'_x_'FI' [notation, in Top.Auto]
Repeat.::'REPEAT'_x_'UNTIL'_x_'END' [notation, in Top.Auto]
Repeat.::'SKIP' [notation, in Top.Auto]
Repeat.::'WHILE'_x_'DO'_x_'END' [notation, in Top.Auto]
restricted_excluded_middle [lemma, in Top.Logic]
restricted_excluded_middle_eq [lemma, in Top.Logic]
rev [definition, in Top.Poly]
rev_append [definition, in Top.Logic]
rev_app_distr [lemma, in Top.Poly]
rev_exercise1 [lemma, in Top.Tactics]
rev_involutive [lemma, in Top.Poly]
re_chars [definition, in Top.IndProp]
re_not_empty [definition, in Top.IndProp]
re_not_empty_correct [lemma, in Top.IndProp]
rgb [inductive, in Top.Basics]
rgb [inductive, in Top.IndPrinciples]
rsc_R [lemma, in Top.Rel]
rsc_trans [lemma, in Top.Rel]
rtc_rsc_coincide [lemma, in Top.Rel]
rt1n_refl [constructor, in Top.Rel]
rt1n_trans [constructor, in Top.Rel]
rt_refl [constructor, in Top.Rel]
rt_step [constructor, in Top.Rel]
rt_trans [constructor, in Top.Rel]
R.c1 [constructor, in Top.IndProp]
R.c2 [constructor, in Top.IndProp]
R.c3 [constructor, in Top.IndProp]
R.c4 [constructor, in Top.IndProp]
R.c5 [constructor, in Top.IndProp]
R.fR [definition, in Top.IndProp]
R.R [inductive, in Top.IndProp]
R.R_equiv_fR [lemma, in Top.IndProp]

## S

saturday [constructor, in Top.Basics]
sillyfun [definition, in Top.Tactics]
sillyfun1 [definition, in Top.Tactics]
sillyfun1_odd [lemma, in Top.Tactics]
sillyfun1_odd_FAILED [lemma, in Top.Tactics]
sillyfun_false [lemma, in Top.Tactics]
silly1 [lemma, in Top.Tactics]
silly2 [lemma, in Top.Tactics]
silly2a [lemma, in Top.Tactics]
silly3' [lemma, in Top.Tactics]
silly3_firsttry [lemma, in Top.Tactics]
silly_ex [lemma, in Top.Tactics]
silly_fact_1 [lemma, in Top.Tactics]
silly_fact_2 [lemma, in Top.Tactics]
silly_fact_2' [lemma, in Top.Tactics]
silly_fact_2_FAILED [lemma, in Top.Tactics]
sinstr [inductive, in Top.Imp]
SLoad [constructor, in Top.Imp]
SMinus [constructor, in Top.Imp]
SMult [constructor, in Top.Imp]
snd [definition, in Top.Poly]
Sn_le_Sm__n_le_m [lemma, in Top.IndProp]
Some [constructor, in Top.Poly]
SomeE [constructor, in Top.ImpParser]
split [definition, in Top.Poly]
split [definition, in Top.Tactics]
split_combine [lemma, in Top.Tactics]
split_combine_statement [definition, in Top.Tactics]
SPlus [constructor, in Top.Imp]
SPush [constructor, in Top.Imp]
sq [constructor, in Top.IndProp]
square [definition, in Top.Tactics]
square_mult [lemma, in Top.Tactics]
square_of [inductive, in Top.IndProp]
SSSSev__even [lemma, in Top.IndProp]
Star [constructor, in Top.IndProp]
star_app [lemma, in Top.IndProp]
star_app [lemma, in Top.IndProp]
star_app [lemma, in Top.IndProp]
star_ne [lemma, in Top.IndProp]
state [definition, in Top.Imp]
string [definition, in Top.IndProp]
string_of_list [definition, in Top.ImpParser]
st12 [definition, in Top.Auto]
st21 [definition, in Top.Auto]
subtract_slowly [definition, in Top.Imp]
subtract_slowly_body [definition, in Top.Imp]
subtract_3_from_5_slowly [definition, in Top.Imp]
succ_inj [lemma, in Top.Logic]
sunday [constructor, in Top.Basics]
symmetric [definition, in Top.Rel]
s_compile [definition, in Top.Imp]
s_compile1 [definition, in Top.Imp]
s_compile_correct [lemma, in Top.Imp]
s_execute [definition, in Top.Imp]
s_execute1 [definition, in Top.Imp]
s_execute2 [definition, in Top.Imp]
S_inj [lemma, in Top.Tactics]
S_injective [lemma, in Top.Tactics]
S_nbeq_0 [lemma, in Top.Induction]

## T

Tactics [library]
testParsing [definition, in Top.ImpParser]
test_andb31 [definition, in Top.Basics]
test_andb32 [definition, in Top.Basics]
test_andb33 [definition, in Top.Basics]
test_andb34 [definition, in Top.Basics]
test_anon_fun' [definition, in Top.Poly]
test_blt_nat1 [definition, in Top.Basics]
test_blt_nat2 [definition, in Top.Basics]
test_blt_nat3 [definition, in Top.Basics]
test_ceval [definition, in Top.ImpCEvalFun]
test_countoddmembers'1 [definition, in Top.Poly]
test_countoddmembers'2 [definition, in Top.Poly]
test_countoddmembers'3 [definition, in Top.Poly]
test_der0 [definition, in Top.IndProp]
test_der1 [definition, in Top.IndProp]
test_der2 [definition, in Top.IndProp]
test_der3 [definition, in Top.IndProp]
test_der4 [definition, in Top.IndProp]
test_der5 [definition, in Top.IndProp]
test_der6 [definition, in Top.IndProp]
test_der7 [definition, in Top.IndProp]
test_doit3times [definition, in Top.Poly]
test_doit3times' [definition, in Top.Poly]
test_factorial1 [definition, in Top.Basics]
test_factorial2 [definition, in Top.Basics]
test_filter1 [definition, in Top.Poly]
test_filter2 [definition, in Top.Poly]
test_filter2' [definition, in Top.Poly]
test_filter_even_gt7_1 [definition, in Top.Poly]
test_filter_even_gt7_2 [definition, in Top.Poly]
test_flat_map1 [definition, in Top.Poly]
test_hd_error1 [definition, in Top.Poly]
test_hd_error2 [definition, in Top.Poly]
test_leb1 [definition, in Top.Basics]
test_leb2 [definition, in Top.Basics]
test_leb3 [definition, in Top.Basics]
test_length1 [definition, in Top.Poly]
test_map1 [definition, in Top.Poly]
test_map2 [definition, in Top.Poly]
test_map3 [definition, in Top.Poly]
test_nandb1 [definition, in Top.Basics]
test_nandb2 [definition, in Top.Basics]
test_nandb3 [definition, in Top.Basics]
test_nandb4 [definition, in Top.Basics]
test_next_weekday [definition, in Top.Basics]
test_nostutter_1 [definition, in Top.IndProp]
test_nostutter_2 [definition, in Top.IndProp]
test_nostutter_3 [definition, in Top.IndProp]
test_nostutter_4 [definition, in Top.IndProp]
test_nth_error1 [definition, in Top.Poly]
test_nth_error2 [definition, in Top.Poly]
test_nth_error3 [definition, in Top.Poly]
test_oddb1 [definition, in Top.Basics]
test_oddb2 [definition, in Top.Basics]
test_orb1 [definition, in Top.Basics]
test_orb2 [definition, in Top.Basics]
test_orb3 [definition, in Top.Basics]
test_orb4 [definition, in Top.Basics]
test_orb5 [definition, in Top.Basics]
test_partition1 [definition, in Top.Poly]
test_partition2 [definition, in Top.Poly]
test_plus3 [definition, in Top.Poly]
test_plus3' [definition, in Top.Poly]
test_plus3'' [definition, in Top.Poly]
test_repeat1 [definition, in Top.Poly]
test_repeat2 [definition, in Top.Poly]
test_rev1 [definition, in Top.Poly]
test_rev2 [definition, in Top.Poly]
test_split [definition, in Top.Poly]
thursday [constructor, in Top.Basics]
token [definition, in Top.ImpParser]
tokenize [definition, in Top.ImpParser]
tokenize_ex1 [definition, in Top.ImpParser]
tokenize_helper [definition, in Top.ImpParser]
total_map [definition, in Top.Maps]
transitive [definition, in Top.Rel]
trans_eq [lemma, in Top.Tactics]
trans_eq_example [definition, in Top.Tactics]
trans_eq_example' [definition, in Top.Tactics]
trans_eq_exercise [definition, in Top.Tactics]
tree [inductive, in Top.IndPrinciples]
true [constructor, in Top.Basics]
True_is_true [lemma, in Top.Logic]
tr_rev [definition, in Top.Logic]
tr_rev_correct [lemma, in Top.Logic]
tuesday [constructor, in Top.Basics]
t_apply_empty [lemma, in Top.Maps]
t_empty [definition, in Top.Maps]
t_update [definition, in Top.Maps]
t_update_eq [lemma, in Top.Maps]
t_update_neq [lemma, in Top.Maps]
t_update_permute [lemma, in Top.Maps]
t_update_same [lemma, in Top.Maps]
t_update_shadow [lemma, in Top.Maps]

## U

Union [constructor, in Top.IndProp]
union_disj [lemma, in Top.IndProp]
update [definition, in Top.Maps]
update_eq [lemma, in Top.Maps]
update_example1 [definition, in Top.Maps]
update_example2 [definition, in Top.Maps]
update_example3 [definition, in Top.Maps]
update_example4 [definition, in Top.Maps]
update_neq [lemma, in Top.Maps]
update_permute [lemma, in Top.Maps]
update_same [lemma, in Top.Maps]
update_shadow [lemma, in Top.Maps]

## W

W [definition, in Top.Imp]
wednesday [constructor, in Top.Basics]
white [constructor, in Top.ImpParser]
white [constructor, in Top.Basics]
wrong_ev [inductive, in Top.IndProp]
wrong_ev_SS [constructor, in Top.IndProp]
wrong_ev_0 [constructor, in Top.IndProp]

## X

X [definition, in Top.Imp]
XtimesYinZ [definition, in Top.Imp]

## Y

Y [definition, in Top.Imp]
yes [constructor, in Top.IndPrinciples]
yesno [inductive, in Top.IndPrinciples]

## Z

Z [definition, in Top.Imp]
zero_nbeq_plus_1 [lemma, in Top.Basics]
zero_nbeq_S [lemma, in Top.Induction]
zero_not_one [lemma, in Top.Logic]
zero_not_one' [lemma, in Top.Logic]
zero_or_succ [lemma, in Top.Logic]

## :

:aexp_scope:x_'*'_x [notation, in Top.Imp]
:aexp_scope:x_'+'_x [notation, in Top.Imp]
:aexp_scope:x_'-'_x [notation, in Top.Imp]
:bexp_scope:x_'&&'_x [notation, in Top.Imp]
:bexp_scope:x_'<='_x [notation, in Top.Imp]
:bexp_scope:x_'='_x [notation, in Top.Imp]
:bexp_scope:'!'_x [notation, in Top.Imp]
:com_scope:x_'::='_x [notation, in Top.Imp]
:com_scope:x_';;'_x [notation, in Top.Imp]
:com_scope:'IFB'_x_'THEN'_x_'ELSE'_x_'FI' [notation, in Top.Imp]
:com_scope:'SKIP' [notation, in Top.Imp]
:com_scope:'WHILE'_x_'DO'_x_'END' [notation, in Top.Imp]
:nat_scope:x_'*'_x [notation, in Top.Basics]
:nat_scope:x_'*'_x [notation, in Top.Basics]
:nat_scope:x_'+'_x [notation, in Top.Basics]
:nat_scope:x_'+'_x [notation, in Top.Basics]
:nat_scope:x_'-'_x [notation, in Top.Basics]
:nat_scope:x_'<=?'_x [notation, in Top.ImpParser]
:type_scope:x_'*'_x [notation, in Top.Poly]
::x_'&&'_x [notation, in Top.Basics]
-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}'">::x_'&'_'{'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}' [notation, in Top.Maps]
-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}'">::x_'&'_'{'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}' [notation, in Top.Maps]
-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}'">::x_'&'_'{'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}' [notation, in Top.Maps]
-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}'">::x_'&'_'{'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}' [notation, in Top.Maps]
-->'_x_';'_x_'-->'_x_'}'">::x_'&'_'{'_x_'-->'_x_';'_x_'-->'_x_'}' [notation, in Top.Maps]
-->'_x_'}'">::x_'&'_'{'_x_'-->'_x_'}' [notation, in Top.Maps]
-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}}'">::x_'&'_'{{'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}}' [notation, in Top.Maps]
-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}}'">::x_'&'_'{{'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}}' [notation, in Top.Maps]
-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}}'">::x_'&'_'{{'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}}' [notation, in Top.Maps]
-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}}'">::x_'&'_'{{'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}}' [notation, in Top.Maps]
-->'_x_';'_x_'-->'_x_'}}'">::x_'&'_'{{'_x_'-->'_x_';'_x_'-->'_x_'}}' [notation, in Top.Maps]
-->'_x_'}}'">::x_'&'_'{{'_x_'-->'_x_'}}' [notation, in Top.Maps]
::x_'++'_x [notation, in Top.Poly]
::x_'/'_x_'\\'_x [notation, in Top.Imp]
::x_'::'_x [notation, in Top.Poly]
::x_'<'_x [notation, in Top.IndProp]
::x_'<='_x [notation, in Top.IndPrinciples]
::x_'=~'_x [notation, in Top.IndProp]
::x_'||'_x [notation, in Top.Basics]
::'DO'_'('_x_','_x_')'_'<--'_x_';'_x_'OR'_x [notation, in Top.ImpParser]
::'DO'_'('_x_','_x_')'_'<=='_x_';'_x [notation, in Top.ImpParser]
::'LETOPT'_x_'<=='_x_'IN'_x [notation, in Top.ImpCEvalFun]
::'('_x_','_x_')' [notation, in Top.Poly]
::'['_x_';'_'..'_';'_x_']' [notation, in Top.Poly]
::'['_']' [notation, in Top.Poly]
-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}'">::'{'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}' [notation, in Top.Imp]
-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}'">::'{'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}' [notation, in Top.Imp]
-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}'">::'{'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}' [notation, in Top.Imp]
-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}'">::'{'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}' [notation, in Top.Imp]
-->'_x_';'_x_'-->'_x_'}'">::'{'_x_'-->'_x_';'_x_'-->'_x_'}' [notation, in Top.Imp]
-->'_x_'}'">::'{'_x_'-->'_x_'}' [notation, in Top.Imp]
-->'_x_'}'">::'{'_'-->'_x_'}' [notation, in Top.Maps]

# Notation Index

## A

aevalR_division.:type_scope:x_'\\'_x [in Top.Imp]
aevalR_extended.:type_scope:x_'\\'_x [in Top.Imp]
AExp.aevalR_first_try.:type_scope:x_'\\'_x [in Top.Imp]
AExp.:type_scope:x_'\\'_x [in Top.Imp]

## B

BreakImp.::x_'/'_x_'\\'_x_'/'_x [in Top.Imp]
BreakImp.::x_'::='_x [in Top.Imp]
BreakImp.::x_';;'_x [in Top.Imp]
BreakImp.::'BREAK' [in Top.Imp]
BreakImp.::'IFB'_x_'THEN'_x_'ELSE'_x_'FI' [in Top.Imp]
BreakImp.::'SKIP' [in Top.Imp]
BreakImp.::'WHILE'_x_'DO'_x_'END' [in Top.Imp]

## M

MyEquality.:type_scope:x_'='_x [in Top.ProofObjects]
MyIff.:type_scope:x_'<->'_x [in Top.Logic]
MyNot.:type_scope:'~'_x [in Top.Logic]

## N

NatList.::x_'++'_x [in Top.Lists]
NatList.::x_'::'_x [in Top.Lists]
NatList.::'('_x_','_x_')' [in Top.Lists]
NatList.::'['_x_';'_'..'_';'_x_']' [in Top.Lists]
NatList.::'['_']' [in Top.Lists]

## P

Playground.::x_'<='_x [in Top.IndProp]

## R

Repeat.::x_'/'_x_'\\'_x [in Top.Auto]
Repeat.::x_'::='_x [in Top.Auto]
Repeat.::x_';'_x [in Top.Auto]
Repeat.::'IFB'_x_'THEN'_x_'ELSE'_x_'FI' [in Top.Auto]
Repeat.::'REPEAT'_x_'UNTIL'_x_'END' [in Top.Auto]
Repeat.::'SKIP' [in Top.Auto]
Repeat.::'WHILE'_x_'DO'_x_'END' [in Top.Auto]

## :

:aexp_scope:x_'*'_x [in Top.Imp]
:aexp_scope:x_'+'_x [in Top.Imp]
:aexp_scope:x_'-'_x [in Top.Imp]
:bexp_scope:x_'&&'_x [in Top.Imp]
:bexp_scope:x_'<='_x [in Top.Imp]
:bexp_scope:x_'='_x [in Top.Imp]
:bexp_scope:'!'_x [in Top.Imp]
:com_scope:x_'::='_x [in Top.Imp]
:com_scope:x_';;'_x [in Top.Imp]
:com_scope:'IFB'_x_'THEN'_x_'ELSE'_x_'FI' [in Top.Imp]
:com_scope:'SKIP' [in Top.Imp]
:com_scope:'WHILE'_x_'DO'_x_'END' [in Top.Imp]
:nat_scope:x_'*'_x [in Top.Basics]
:nat_scope:x_'*'_x [in Top.Basics]
:nat_scope:x_'+'_x [in Top.Basics]
:nat_scope:x_'+'_x [in Top.Basics]
:nat_scope:x_'-'_x [in Top.Basics]
:nat_scope:x_'<=?'_x [in Top.ImpParser]
:type_scope:x_'*'_x [in Top.Poly]
::x_'&&'_x [in Top.Basics]
-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}'">::x_'&'_'{'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}' [in Top.Maps]
-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}'">::x_'&'_'{'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}' [in Top.Maps]
-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}'">::x_'&'_'{'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}' [in Top.Maps]
-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}'">::x_'&'_'{'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}' [in Top.Maps]
-->'_x_';'_x_'-->'_x_'}'">::x_'&'_'{'_x_'-->'_x_';'_x_'-->'_x_'}' [in Top.Maps]
-->'_x_'}'">::x_'&'_'{'_x_'-->'_x_'}' [in Top.Maps]
-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}}'">::x_'&'_'{{'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}}' [in Top.Maps]
-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}}'">::x_'&'_'{{'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}}' [in Top.Maps]
-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}}'">::x_'&'_'{{'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}}' [in Top.Maps]
-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}}'">::x_'&'_'{{'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}}' [in Top.Maps]
-->'_x_';'_x_'-->'_x_'}}'">::x_'&'_'{{'_x_'-->'_x_';'_x_'-->'_x_'}}' [in Top.Maps]
-->'_x_'}}'">::x_'&'_'{{'_x_'-->'_x_'}}' [in Top.Maps]
::x_'++'_x [in Top.Poly]
::x_'/'_x_'\\'_x [in Top.Imp]
::x_'::'_x [in Top.Poly]
::x_'<'_x [in Top.IndProp]
::x_'<='_x [in Top.IndPrinciples]
::x_'=~'_x [in Top.IndProp]
::x_'||'_x [in Top.Basics]
::'DO'_'('_x_','_x_')'_'<--'_x_';'_x_'OR'_x [in Top.ImpParser]
::'DO'_'('_x_','_x_')'_'<=='_x_';'_x [in Top.ImpParser]
::'LETOPT'_x_'<=='_x_'IN'_x [in Top.ImpCEvalFun]
::'('_x_','_x_')' [in Top.Poly]
::'['_x_';'_'..'_';'_x_']' [in Top.Poly]
::'['_']' [in Top.Poly]
-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}'">::'{'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}' [in Top.Imp]
-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}'">::'{'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}' [in Top.Imp]
-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}'">::'{'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}' [in Top.Imp]
-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}'">::'{'_x_'-->'_x_';'_x_'-->'_x_';'_x_'-->'_x_'}' [in Top.Imp]
-->'_x_';'_x_'-->'_x_'}'">::'{'_x_'-->'_x_';'_x_'-->'_x_'}' [in Top.Imp]
-->'_x_'}'">::'{'_x_'-->'_x_'}' [in Top.Imp]
-->'_x_'}'">::'{'_'-->'_x_'}' [in Top.Maps]

# Module Index

## A

aevalR_division [in Top.Imp]
aevalR_extended [in Top.Imp]
AExp [in Top.Imp]
AExp.aevalR_first_try [in Top.Imp]

## B

BreakImp [in Top.Imp]

## E

Exercises [in Top.Poly]
Exercises.Church [in Top.Poly]

## M

MumbleGrumble [in Top.Poly]
MyEquality [in Top.ProofObjects]
MyIff [in Top.Logic]
MyNot [in Top.Logic]

## N

NatList [in Top.Lists]
NatPlayground [in Top.Basics]
NatPlayground2 [in Top.Basics]

## P

PartialMap [in Top.Lists]
Playground [in Top.IndProp]
Props [in Top.ProofObjects]
Props.And [in Top.ProofObjects]
Props.Ex [in Top.ProofObjects]
Props.Or [in Top.ProofObjects]
Pumping [in Top.IndProp]

## R

R [in Top.IndProp]
Repeat [in Top.Auto]

# Library Index

## A

Auto

## B

Basics
Bib

## E

Extraction

## I

Imp
ImpCEvalFun
ImpParser
IndPrinciples
IndProp
Induction

## L

Lists
Logic

## M

Maps

## P

Poly
Postscript
Preface
ProofObjects

## R

Rel

## T

Tactics

# Lemma Index

## A

AExp.aeval_iff_aevalR [in Top.Imp]
AExp.aeval_iff_aevalR' [in Top.Imp]
AExp.beval_iff_bevalR [in Top.Imp]
AExp.foo [in Top.Imp]
AExp.foo' [in Top.Imp]
AExp.In10 [in Top.Imp]
AExp.In10' [in Top.Imp]
AExp.optimize_0plus_b_sound [in Top.Imp]
AExp.optimize_0plus_sound [in Top.Imp]
AExp.optimize_0plus_sound' [in Top.Imp]
AExp.optimize_0plus_sound'' [in Top.Imp]
AExp.silly1 [in Top.Imp]
AExp.silly2 [in Top.Imp]
all3_spec [in Top.Induction]
All_In [in Top.Logic]
andb3_exchange [in Top.Basics]
andb_commutative [in Top.Basics]
andb_commutative' [in Top.Basics]
andb_commutative'' [in Top.Basics]
andb_eq_orb [in Top.Basics]
andb_false_r [in Top.Induction]
andb_true_elim2 [in Top.Basics]
andb_true_iff [in Top.Logic]
and_assoc [in Top.Logic]
and_commut [in Top.Logic]
and_example2 [in Top.Logic]
and_example2' [in Top.Logic]
and_example2'' [in Top.Logic]
and_example3 [in Top.Logic]
and_intro [in Top.Logic]
apply_empty [in Top.Maps]
apply_iff_example [in Top.Logic]
app_assoc [in Top.Poly]
app_exists [in Top.IndProp]
app_length [in Top.Poly]
app_ne [in Top.IndProp]
app_nil_r [in Top.Poly]

## B

beq_id_refl [in Top.Lists]
beq_id_true [in Top.Tactics]
beq_list_true_iff [in Top.Logic]
beq_natP [in Top.IndProp]
beq_natP_practice [in Top.IndProp]
beq_nat_false_iff [in Top.Logic]
beq_nat_refl [in Top.Induction]
beq_nat_sym [in Top.Tactics]
beq_nat_trans [in Top.Tactics]
beq_nat_true [in Top.Tactics]
beq_nat_true_iff [in Top.Logic]
beq_nat_0_l [in Top.Tactics]
beq_stringP [in Top.Maps]
beq_string_false_iff [in Top.Maps]
beq_string_refl [in Top.Maps]
beq_string_true_iff [in Top.Maps]
bool_fn_applied_thrice [in Top.Tactics]
BreakImp.break_ignore [in Top.Imp]
BreakImp.ceval_deterministic [in Top.Imp]
BreakImp.while_break_true [in Top.Imp]
BreakImp.while_continue [in Top.Imp]
BreakImp.while_stops_on_break [in Top.Imp]

## C

ceval_and_ceval_step_coincide [in Top.ImpCEvalFun]
ceval_deterministic [in Top.Imp]
ceval_deterministic [in Top.Auto]
ceval_deterministic' [in Top.Auto]
ceval_deterministic' [in Top.ImpCEvalFun]
ceval_deterministic'' [in Top.Auto]
ceval_deterministic''' [in Top.Auto]
ceval_deterministic'''' [in Top.Auto]
ceval_deterministic''''' [in Top.Auto]
ceval_deterministic'_alt [in Top.Auto]
ceval_step_more [in Top.ImpCEvalFun]
ceval_step__ceval [in Top.ImpCEvalFun]
ceval__ceval_step [in Top.ImpCEvalFun]
char_eps_suffix [in Top.IndProp]
char_nomatch_char [in Top.IndProp]
combine_odd_even_elim_even [in Top.Logic]
combine_odd_even_elim_odd [in Top.Logic]
combine_odd_even_intro [in Top.Logic]
combine_split [in Top.Tactics]
contradiction_implies_anything [in Top.Logic]
contrapositive [in Top.Logic]

## D

derive_corr [in Top.IndProp]
dist_exists_or [in Top.Logic]
dist_not_exists [in Top.Logic]
double_injective [in Top.Tactics]
double_injective_FAILED [in Top.Tactics]
double_injective_take2 [in Top.Tactics]
double_injective_take2_FAILED [in Top.Tactics]
double_neg [in Top.Logic]
double_plus [in Top.Induction]

## E

empty_is_empty [in Top.IndProp]
empty_matches_eps [in Top.IndProp]
empty_nomatch_ne [in Top.IndProp]
equality__leibniz_equality [in Top.ProofObjects]
evenb_double [in Top.Logic]
evenb_double_conv [in Top.Logic]
evenb_S [in Top.Induction]
even5_nonsense [in Top.IndProp]
even_bool_prop [in Top.Logic]
evSS_ev [in Top.IndProp]
evSS_ev [in Top.IndProp]
ev'_ev [in Top.IndProp]
ev_double [in Top.IndProp]
ev_even [in Top.IndProp]
ev_even_firsttry [in Top.IndProp]
ev_even_iff [in Top.IndProp]
ev_ev' [in Top.IndPrinciples]
ev_ev__ev [in Top.IndProp]
ev_minus2 [in Top.IndProp]
ev_minus2' [in Top.IndProp]
ev_plus4 [in Top.ProofObjects]
ev_plus4 [in Top.IndProp]
ev_plus_plus [in Top.IndProp]
ev_sum [in Top.IndProp]
ev_4 [in Top.ProofObjects]
ev_4 [in Top.IndProp]
ev_4' [in Top.ProofObjects]
ev_4' [in Top.IndProp]
ev_4'' [in Top.ProofObjects]
ev_8 [in Top.ProofObjects]
excluded_middle_irrefutable [in Top.Logic]
Exercises.curry_uncurry [in Top.Poly]
Exercises.fold_length_correct [in Top.Poly]
Exercises.uncurry_curry [in Top.Poly]
exists_example_2 [in Top.Logic]
ex_falso_quodlibet [in Top.Logic]

## F

false_beq_string [in Top.Maps]
filter_exercise [in Top.Tactics]
filter_not_empty_In [in Top.IndProp]
filter_not_empty_In' [in Top.IndProp]
forallb_true_iff [in Top.Logic]
four_is_even [in Top.Logic]
f_equal [in Top.Tactics]

## I

identity_fn_applied_twice [in Top.Basics]
iff_refl [in Top.Logic]
iff_reflect [in Top.IndProp]
iff_sym [in Top.Logic]
iff_trans [in Top.Logic]
inversion_ex1 [in Top.Tactics]
inversion_ex2 [in Top.Tactics]
inversion_ex4 [in Top.Tactics]
inversion_ex5 [in Top.Tactics]
In_app_iff [in Top.Logic]
In_map [in Top.Logic]
In_map_iff [in Top.Logic]
in_re_match [in Top.IndProp]
in_split [in Top.IndProp]

## L

leb_complete [in Top.IndProp]
leb_correct [in Top.IndProp]
leb_iff [in Top.IndProp]
leb_refl [in Top.Induction]
leb_true_trans [in Top.IndProp]
leibniz_equality__equality [in Top.ProofObjects]
le_antisym [in Top.Auto]
le_antisymmetric [in Top.Rel]
le_not_a_partial_function [in Top.Rel]
le_not_symmetric [in Top.Rel]
le_order [in Top.Rel]
le_plus_l [in Top.IndProp]
le_reflexive [in Top.Rel]
le_Sn_le [in Top.Rel]
le_Sn_n [in Top.Rel]
le_step [in Top.Rel]
le_S_n [in Top.Rel]
le_trans [in Top.Rel]
le_trans [in Top.IndProp]
loop_never_stops [in Top.Imp]
lt_S [in Top.IndProp]
lt_trans [in Top.Rel]
lt_trans' [in Top.Rel]
lt_trans'' [in Top.Rel]

## M

map_rev [in Top.Poly]
match_eps_refl [in Top.IndProp]
minus_diag [in Top.Induction]
MStar' [in Top.IndProp]
MStar'' [in Top.IndProp]
MStar1 [in Top.IndProp]
mult_assoc [in Top.Induction]
mult_comm [in Top.Induction]
mult_eq_0 [in Top.Logic]
mult_plus_distr_r [in Top.Induction]
mult_S_1 [in Top.Basics]
mult_0 [in Top.Logic]
mult_0_l [in Top.Basics]
mult_0_plus [in Top.Basics]
mult_0_plus' [in Top.Induction]
mult_0_r [in Top.Induction]
mult_0_r' [in Top.IndPrinciples]
mult_0_r'' [in Top.IndPrinciples]
mult_0_3 [in Top.Logic]
mult_1_l [in Top.Induction]
MUnion' [in Top.IndProp]
MyEquality.four [in Top.ProofObjects]

## N

NatList.app_assoc [in Top.Lists]
NatList.app_assoc4 [in Top.Lists]
NatList.app_length [in Top.Lists]
NatList.app_nil_r [in Top.Lists]
NatList.beq_natlist_refl [in Top.Lists]
NatList.ble_n_Sn [in Top.Lists]
NatList.count_member_nonzero [in Top.Lists]
NatList.fst_swap_is_snd [in Top.Lists]
NatList.nil_app [in Top.Lists]
NatList.nonzeros_app [in Top.Lists]
NatList.option_elim_hd [in Top.Lists]
NatList.remove_decreases_count [in Top.Lists]
NatList.rev_app_distr [in Top.Lists]
NatList.rev_involutive [in Top.Lists]
NatList.rev_length [in Top.Lists]
NatList.rev_length_firsttry [in Top.Lists]
NatList.snd_fst_is_swap [in Top.Lists]
NatList.surjective_pairing [in Top.Lists]
NatList.surjective_pairing' [in Top.Lists]
NatList.surjective_pairing_stuck [in Top.Lists]
NatList.tl_length_pred [in Top.Lists]
negb_involutive [in Top.Basics]
next_nat_closure_is_le [in Top.Rel]
next_nat_partial_function [in Top.Rel]
not_both_true_and_false [in Top.Logic]
not_equiv_false [in Top.IndProp]
not_exists_dist [in Top.Logic]
not_False [in Top.Logic]
not_implies_our_not [in Top.Logic]
not_true_iff_false [in Top.Logic]
not_true_is_false [in Top.Logic]
not_true_is_false' [in Top.Logic]
no_whiles_eqv [in Top.Imp]
nth_error_after_last [in Top.Tactics]
null_matches_none [in Top.IndProp]
n_le_m__Sn_le_Sm [in Top.IndProp]

## O

one_not_even [in Top.IndProp]
orb_true_iff [in Top.Logic]
or_assoc [in Top.Logic]
or_commut [in Top.Logic]
or_distributes_over_and [in Top.Logic]
or_example [in Top.Logic]
or_intro [in Top.Logic]
O_le_n [in Top.IndProp]

## P

PartialMap.update_eq [in Top.Lists]
PartialMap.update_neq [in Top.Lists]
pigeonhole_principle [in Top.IndProp]
Playground.test_le1 [in Top.IndProp]
Playground.test_le2 [in Top.IndProp]
Playground.test_le3 [in Top.IndProp]
plus2_spec [in Top.Imp]
plus_assoc [in Top.Induction]
plus_assoc' [in Top.IndPrinciples]
plus_assoc' [in Top.Induction]
plus_assoc'' [in Top.Induction]
plus_ble_compat_l [in Top.Induction]
plus_comm [in Top.Induction]
plus_comm' [in Top.IndPrinciples]
plus_comm'' [in Top.IndPrinciples]
plus_comm3 [in Top.Logic]
plus_comm3_take2 [in Top.Logic]
plus_comm3_take3 [in Top.Logic]
plus_fact_is_true [in Top.Logic]
plus_id_example [in Top.Basics]
plus_id_exercise [in Top.Basics]
plus_lt [in Top.IndProp]
plus_n_n_injective [in Top.Tactics]
plus_n_O [in Top.Induction]
plus_n_O_firsttry [in Top.Induction]
plus_n_O_secondtry [in Top.Induction]
plus_n_Sm [in Top.Induction]
plus_one_r' [in Top.IndPrinciples]
plus_O_n [in Top.Basics]
plus_O_n' [in Top.Basics]
plus_rearrange [in Top.Induction]
plus_rearrange_firsttry [in Top.Induction]
plus_swap [in Top.Induction]
plus_swap' [in Top.Induction]
plus_1_l [in Top.Basics]
plus_1_neq_0 [in Top.Basics]
plus_1_neq_0' [in Top.Basics]
plus_1_neq_0_firsttry [in Top.Basics]
plus_2_2_is_4 [in Top.Logic]
proj1 [in Top.Logic]
proj2 [in Top.Logic]
Props.and_comm [in Top.ProofObjects]
provable_equiv_true [in Top.IndProp]
Pumping.napp_plus [in Top.IndProp]
Pumping.pumping [in Top.IndProp]
pup_to_2_ceval [in Top.Imp]

## R

reflect_iff [in Top.IndProp]
regex_refl [in Top.IndProp]
reg_exp_of_list_spec [in Top.IndProp]
Repeat.ceval_deterministic [in Top.Auto]
Repeat.ceval_deterministic' [in Top.Auto]
restricted_excluded_middle [in Top.Logic]
restricted_excluded_middle_eq [in Top.Logic]
rev_app_distr [in Top.Poly]
rev_exercise1 [in Top.Tactics]
rev_involutive [in Top.Poly]
re_not_empty_correct [in Top.IndProp]
rsc_R [in Top.Rel]
rsc_trans [in Top.Rel]
rtc_rsc_coincide [in Top.Rel]
R.R_equiv_fR [in Top.IndProp]

## S

sillyfun1_odd [in Top.Tactics]
sillyfun1_odd_FAILED [in Top.Tactics]
sillyfun_false [in Top.Tactics]
silly1 [in Top.Tactics]
silly2 [in Top.Tactics]
silly2a [in Top.Tactics]
silly3' [in Top.Tactics]
silly3_firsttry [in Top.Tactics]
silly_ex [in Top.Tactics]
silly_fact_1 [in Top.Tactics]
silly_fact_2 [in Top.Tactics]
silly_fact_2' [in Top.Tactics]
silly_fact_2_FAILED [in Top.Tactics]
Sn_le_Sm__n_le_m [in Top.IndProp]
split_combine [in Top.Tactics]
square_mult [in Top.Tactics]
SSSSev__even [in Top.IndProp]
star_app [in Top.IndProp]
star_app [in Top.IndProp]
star_app [in Top.IndProp]
star_ne [in Top.IndProp]
succ_inj [in Top.Logic]
s_compile_correct [in Top.Imp]
S_inj [in Top.Tactics]
S_injective [in Top.Tactics]
S_nbeq_0 [in Top.Induction]

## T

trans_eq [in Top.Tactics]
True_is_true [in Top.Logic]
tr_rev_correct [in Top.Logic]
t_apply_empty [in Top.Maps]
t_update_eq [in Top.Maps]
t_update_neq [in Top.Maps]
t_update_permute [in Top.Maps]
t_update_same [in Top.Maps]
t_update_shadow [in Top.Maps]

## U

union_disj [in Top.IndProp]
update_eq [in Top.Maps]
update_neq [in Top.Maps]
update_permute [in Top.Maps]
update_same [in Top.Maps]
update_shadow [in Top.Maps]

## Z

zero_nbeq_plus_1 [in Top.Basics]
zero_nbeq_S [in Top.Induction]
zero_not_one [in Top.Logic]
zero_not_one' [in Top.Logic]
zero_or_succ [in Top.Logic]

# Constructor Index

## A

aevalR_division.ADiv [in Top.Imp]
aevalR_division.AMinus [in Top.Imp]
aevalR_division.AMult [in Top.Imp]
aevalR_division.ANum [in Top.Imp]
aevalR_division.APlus [in Top.Imp]
aevalR_division.E_ADiv [in Top.Imp]
aevalR_division.E_AMinus [in Top.Imp]
aevalR_division.E_AMult [in Top.Imp]
aevalR_division.E_ANum [in Top.Imp]
aevalR_division.E_APlus [in Top.Imp]
aevalR_extended.AAny [in Top.Imp]
aevalR_extended.AMinus [in Top.Imp]
aevalR_extended.AMult [in Top.Imp]
aevalR_extended.ANum [in Top.Imp]
aevalR_extended.APlus [in Top.Imp]
aevalR_extended.E_AMinus [in Top.Imp]
aevalR_extended.E_AMult [in Top.Imp]
aevalR_extended.E_ANum [in Top.Imp]
aevalR_extended.E_Any [in Top.Imp]
aevalR_extended.E_APlus [in Top.Imp]
AExp.aevalR_first_try.E_AMinus [in Top.Imp]
AExp.aevalR_first_try.E_AMult [in Top.Imp]
AExp.aevalR_first_try.E_ANum [in Top.Imp]
AExp.aevalR_first_try.E_APlus [in Top.Imp]
AExp.AMinus [in Top.Imp]
AExp.AMult [in Top.Imp]
AExp.ANum [in Top.Imp]
AExp.APlus [in Top.Imp]
AExp.BAnd [in Top.Imp]
AExp.BEq [in Top.Imp]
AExp.BFalse [in Top.Imp]
AExp.BLe [in Top.Imp]
AExp.BNot [in Top.Imp]
AExp.BTrue [in Top.Imp]
AExp.E_AMinus [in Top.Imp]
AExp.E_AMult [in Top.Imp]
AExp.E_ANum [in Top.Imp]
AExp.E_APlus [in Top.Imp]
AId [in Top.Imp]
alpha [in Top.ImpParser]
AMinus [in Top.Imp]
AMult [in Top.Imp]
ANum [in Top.Imp]
APlus [in Top.Imp]
App [in Top.IndProp]

## B

BAnd [in Top.Imp]
Baz1 [in Top.Lists]
Baz2 [in Top.Lists]
bempty [in Top.IndPrinciples]
BEq [in Top.Imp]
BFalse [in Top.Imp]
black [in Top.Basics]
BLe [in Top.Imp]
bleaf [in Top.IndPrinciples]
blue [in Top.IndPrinciples]
blue [in Top.Basics]
BNot [in Top.Imp]
bool_cons [in Top.Poly]
bool_nil [in Top.Poly]
BreakImp.CAss [in Top.Imp]
BreakImp.CBreak [in Top.Imp]
BreakImp.CIf [in Top.Imp]
BreakImp.CSeq [in Top.Imp]
BreakImp.CSkip [in Top.Imp]
BreakImp.CWhile [in Top.Imp]
BreakImp.E_Skip [in Top.Imp]
BreakImp.SBreak [in Top.Imp]
BreakImp.SContinue [in Top.Imp]
BTrue [in Top.Imp]

## C

CAss [in Top.Imp]
Char [in Top.IndProp]
CIf [in Top.Imp]
cons [in Top.Poly]
cons' [in Top.Poly]
CSeq [in Top.Imp]
CSkip [in Top.Imp]
CWhile [in Top.Imp]
C1 [in Top.IndPrinciples]
C2 [in Top.IndPrinciples]

## D

digit [in Top.ImpParser]

## E

EmptySet [in Top.IndProp]
EmptyStr [in Top.IndProp]
ev'_sum [in Top.IndProp]
ev'_0 [in Top.IndProp]
ev'_2 [in Top.IndProp]
ev_SS [in Top.IndProp]
ev_0 [in Top.IndProp]
E_Ass [in Top.Imp]
E_IfFalse [in Top.Imp]
E_IfTrue [in Top.Imp]
E_Seq [in Top.Imp]
E_Skip [in Top.Imp]
E_WhileFalse [in Top.Imp]
E_WhileTrue [in Top.Imp]

## F

false [in Top.Basics]
friday [in Top.Basics]

## G

green [in Top.Basics]
green [in Top.IndPrinciples]

## I

Id [in Top.Lists]

## L

leaf [in Top.IndPrinciples]
le_n [in Top.IndPrinciples]
le_S [in Top.IndPrinciples]

## M

MApp [in Top.IndProp]
MChar [in Top.IndProp]
MEmpty [in Top.IndProp]
monday [in Top.Basics]
MStarApp [in Top.IndProp]
MStar0 [in Top.IndProp]
MumbleGrumble.a [in Top.Poly]
MumbleGrumble.b [in Top.Poly]
MumbleGrumble.c [in Top.Poly]
MumbleGrumble.d [in Top.Poly]
MumbleGrumble.e [in Top.Poly]
MUnionL [in Top.IndProp]
MUnionR [in Top.IndProp]
MyEquality.eq_refl [in Top.ProofObjects]

## N

NatList.cons [in Top.Lists]
NatList.nil [in Top.Lists]
NatList.None [in Top.Lists]
NatList.pair [in Top.Lists]
NatList.Some [in Top.Lists]
NatPlayground.O [in Top.Basics]
NatPlayground.S [in Top.Basics]
NatPlayground.stop [in Top.Basics]
NatPlayground.tick [in Top.Basics]
nbranch [in Top.IndPrinciples]
ncons [in Top.IndPrinciples]
ne_1 [in Top.IndProp]
ne_2 [in Top.IndProp]
nil [in Top.Poly]
nil' [in Top.Poly]
nn [in Top.IndProp]
nnil [in Top.IndPrinciples]
nnil1 [in Top.IndPrinciples]
no [in Top.IndPrinciples]
node [in Top.IndPrinciples]
None [in Top.Poly]
NoneE [in Top.ImpParser]
nsnoc1 [in Top.IndPrinciples]

## O

other [in Top.ImpParser]

## P

pair [in Top.Poly]
PartialMap.empty [in Top.Lists]
PartialMap.record [in Top.Lists]
Playground.le_n [in Top.IndProp]
Playground.le_S [in Top.IndProp]
primary [in Top.Basics]
Props.And.conj [in Top.ProofObjects]
Props.Ex.ex_intro [in Top.ProofObjects]
Props.I [in Top.ProofObjects]
Props.Or.or_introl [in Top.ProofObjects]
Props.Or.or_intror [in Top.ProofObjects]

## R

red [in Top.Basics]
red [in Top.IndPrinciples]
ReflectF [in Top.IndProp]
ReflectT [in Top.IndProp]
Repeat.CAsgn [in Top.Auto]
Repeat.CIf [in Top.Auto]
Repeat.CRepeat [in Top.Auto]
Repeat.CSeq [in Top.Auto]
Repeat.CSkip [in Top.Auto]
Repeat.CWhile [in Top.Auto]
Repeat.E_Ass [in Top.Auto]
Repeat.E_IfFalse [in Top.Auto]
Repeat.E_IfTrue [in Top.Auto]
Repeat.E_RepeatEnd [in Top.Auto]
Repeat.E_RepeatLoop [in Top.Auto]
Repeat.E_Seq [in Top.Auto]
Repeat.E_Skip [in Top.Auto]
Repeat.E_WhileFalse [in Top.Auto]
Repeat.E_WhileTrue [in Top.Auto]
rt1n_refl [in Top.Rel]
rt1n_trans [in Top.Rel]
rt_refl [in Top.Rel]
rt_step [in Top.Rel]
rt_trans [in Top.Rel]
R.c1 [in Top.IndProp]
R.c2 [in Top.IndProp]
R.c3 [in Top.IndProp]
R.c4 [in Top.IndProp]
R.c5 [in Top.IndProp]

## S

saturday [in Top.Basics]
SLoad [in Top.Imp]
SMinus [in Top.Imp]
SMult [in Top.Imp]
Some [in Top.Poly]
SomeE [in Top.ImpParser]
SPlus [in Top.Imp]
SPush [in Top.Imp]
sq [in Top.IndProp]
Star [in Top.IndProp]
sunday [in Top.Basics]

## T

thursday [in Top.Basics]
true [in Top.Basics]
tuesday [in Top.Basics]

## U

Union [in Top.IndProp]

## W

wednesday [in Top.Basics]
white [in Top.ImpParser]
white [in Top.Basics]
wrong_ev_SS [in Top.IndProp]
wrong_ev_0 [in Top.IndProp]

## Y

yes [in Top.IndPrinciples]

# Axiom Index

## F

functional_extensionality [in Top.Logic]

# Inductive Index

## A

aevalR_division.aevalR [in Top.Imp]
aevalR_division.aexp [in Top.Imp]
aevalR_extended.aevalR [in Top.Imp]
aevalR_extended.aexp [in Top.Imp]
aexp [in Top.Imp]
AExp.aevalR [in Top.Imp]
AExp.aevalR_first_try.aevalR [in Top.Imp]
AExp.aexp [in Top.Imp]
AExp.bevalR [in Top.Imp]
AExp.bexp [in Top.Imp]

## B

baz [in Top.Lists]
bexp [in Top.Imp]
bool [in Top.Basics]
boollist [in Top.Poly]
BreakImp.ceval [in Top.Imp]
BreakImp.com [in Top.Imp]
BreakImp.result [in Top.Imp]
byntree [in Top.IndPrinciples]

## C

ceval [in Top.Imp]
chartype [in Top.ImpParser]
clos_refl_trans [in Top.Rel]
clos_refl_trans_1n [in Top.Rel]
color [in Top.Basics]
com [in Top.Imp]

## D

day [in Top.Basics]

## E

ev [in Top.IndProp]
ev' [in Top.IndProp]
exp_match [in Top.IndProp]
ExSet [in Top.IndPrinciples]

## F

foo' [in Top.IndPrinciples]

## I

id [in Top.Lists]

## L

le [in Top.IndPrinciples]
list [in Top.Poly]
list' [in Top.Poly]

## M

MumbleGrumble.grumble [in Top.Poly]
MumbleGrumble.mumble [in Top.Poly]
MyEquality.eq [in Top.ProofObjects]

## N

natlist [in Top.IndPrinciples]
NatList.natlist [in Top.Lists]
NatList.natoption [in Top.Lists]
NatList.natprod [in Top.Lists]
natlist1 [in Top.IndPrinciples]
NatPlayground.nat [in Top.Basics]
NatPlayground.nat' [in Top.Basics]
next_even [in Top.IndProp]
next_nat [in Top.IndProp]
nostutter [in Top.IndProp]
no_whilesR [in Top.Imp]

## O

option [in Top.Poly]
optionE [in Top.ImpParser]

## P

PartialMap.partial_map [in Top.Lists]
Playground.le [in Top.IndProp]
prod [in Top.Poly]
Props.And.and [in Top.ProofObjects]
Props.Ex.ex [in Top.ProofObjects]
Props.False [in Top.ProofObjects]
Props.Or.or [in Top.ProofObjects]
Props.True [in Top.ProofObjects]

## R

reflect [in Top.IndProp]
reg_exp [in Top.IndProp]
repeats [in Top.IndProp]
Repeat.ceval [in Top.Auto]
Repeat.com [in Top.Auto]
rgb [in Top.Basics]
rgb [in Top.IndPrinciples]
R.R [in Top.IndProp]

## S

sinstr [in Top.Imp]
square_of [in Top.IndProp]

## T

tree [in Top.IndPrinciples]

## W

wrong_ev [in Top.IndProp]

## Y

yesno [in Top.IndPrinciples]

# Definition Index

## A

add1 [in Top.ProofObjects]
aeval [in Top.Imp]
AExp.aeval [in Top.Imp]
AExp.beval [in Top.Imp]
AExp.optimize_0plus [in Top.Imp]
AExp.optimize_0plus_b [in Top.Imp]
AExp.silly_presburger_example [in Top.Imp]
AExp.test_aeval1 [in Top.Imp]
AExp.test_optimize_0plus [in Top.Imp]
aexp1 [in Top.Imp]
All [in Top.Logic]
andb [in Top.Basics]
andb3 [in Top.Basics]
and_example [in Top.Logic]
and_example' [in Top.Logic]
and_exercise [in Top.Logic]
antisymmetric [in Top.Rel]
app [in Top.Poly]
auto_example_1 [in Top.Auto]
auto_example_1' [in Top.Auto]
auto_example_2 [in Top.Auto]
auto_example_3 [in Top.Auto]
auto_example_4 [in Top.Auto]
auto_example_6 [in Top.Auto]
auto_example_6' [in Top.Auto]
auto_example_7 [in Top.Auto]
auto_example_7' [in Top.Auto]

## B

bar [in Top.Tactics]
beq_id [in Top.Lists]
beq_list [in Top.Logic]
beq_nat [in Top.Basics]
beq_string [in Top.Maps]
beval [in Top.Imp]
bexp1 [in Top.Imp]
bignumber [in Top.ImpParser]
blt_nat [in Top.Basics]
bool_to_bexp [in Top.Imp]

## C

c [in Top.IndProp]
ceval'_example1 [in Top.Auto]
ceval_example1 [in Top.Auto]
ceval_example1 [in Top.Imp]
ceval_example2 [in Top.Imp]
ceval_fun_no_while [in Top.Imp]
ceval_step [in Top.ImpCEvalFun]
ceval_step1 [in Top.ImpCEvalFun]
ceval_step2 [in Top.ImpCEvalFun]
ceval_step3 [in Top.ImpCEvalFun]
classifyChar [in Top.ImpParser]
combine [in Top.Poly]
combine_odd_even [in Top.Logic]
constfun [in Top.Poly]
constfun_example1 [in Top.Poly]
constfun_example2 [in Top.Poly]
count [in Top.IndProp]
countoddmembers' [in Top.Poly]

## D

d [in Top.IndProp]
derive [in Top.IndProp]
derives [in Top.IndProp]
de_morgan_not_and_not [in Top.Logic]
doit3times [in Top.Poly]
double [in Top.Induction]
double_negation_elimination [in Top.Logic]

## E

eauto_example [in Top.Auto]
eg1 [in Top.ImpParser]
empty [in Top.Maps]
empty_state [in Top.Extraction]
equivalence [in Top.Rel]
evenb [in Top.Basics]
even_1000 [in Top.Logic]
even_1000' [in Top.Logic]
even_1000'' [in Top.Logic]
ev_plus2 [in Top.ProofObjects]
ev_plus2' [in Top.ProofObjects]
ev_plus2'' [in Top.ProofObjects]
ev_plus4' [in Top.ProofObjects]
ev_plus4'' [in Top.ProofObjects]
ev_4''' [in Top.ProofObjects]
ev_8' [in Top.ProofObjects]
examplemap [in Top.Maps]
examplemap' [in Top.Maps]
excluded_middle [in Top.Logic]
Exercises.Church.exp [in Top.Poly]
Exercises.Church.exp_1 [in Top.Poly]
Exercises.Church.exp_2 [in Top.Poly]
Exercises.Church.exp_3 [in Top.Poly]
Exercises.Church.mult [in Top.Poly]
Exercises.Church.mult_1 [in Top.Poly]
Exercises.Church.mult_2 [in Top.Poly]
Exercises.Church.mult_3 [in Top.Poly]
Exercises.Church.nat [in Top.Poly]
Exercises.Church.one [in Top.Poly]
Exercises.Church.plus [in Top.Poly]
Exercises.Church.plus_1 [in Top.Poly]
Exercises.Church.plus_2 [in Top.Poly]
Exercises.Church.plus_3 [in Top.Poly]
Exercises.Church.succ [in Top.Poly]
Exercises.Church.succ_1 [in Top.Poly]
Exercises.Church.succ_2 [in Top.Poly]
Exercises.Church.succ_3 [in Top.Poly]
Exercises.Church.three [in Top.Poly]
Exercises.Church.two [in Top.Poly]
Exercises.Church.zero [in Top.Poly]
Exercises.fold_length [in Top.Poly]
Exercises.fold_map [in Top.Poly]
Exercises.prod_curry [in Top.Poly]
Exercises.prod_uncurry [in Top.Poly]
Exercises.test_fold_length1 [in Top.Poly]
Exercises.test_map1' [in Top.Poly]
exp [in Top.Basics]
expect [in Top.ImpParser]

## F

factorial [in Top.Basics]
fact_in_coq [in Top.Imp]
filter [in Top.Poly]
filter_even_gt7 [in Top.Poly]
firstExpect [in Top.ImpParser]
flat_map [in Top.Poly]
fold [in Top.Poly]
fold_example1 [in Top.Poly]
fold_example2 [in Top.Poly]
fold_example3 [in Top.Poly]
foo [in Top.Tactics]
forallb [in Top.Logic]
fst [in Top.Poly]
ftrue [in Top.Poly]
function_equality_ex1 [in Top.Logic]
function_equality_ex2 [in Top.Logic]
function_equality_ex2 [in Top.Logic]

## H

hd_error [in Top.Poly]

## I

implies_to_or [in Top.Logic]
In [in Top.Logic]
informal_not_PNP_TODO [in Top.Logic]
injective [in Top.Logic]
inversion_ex3 [in Top.Tactics]
inversion_ex6 [in Top.Tactics]
In_example_1 [in Top.Logic]
In_example_2 [in Top.Logic]
isAlpha [in Top.ImpParser]
isDigit [in Top.ImpParser]
isLowerAlpha [in Top.ImpParser]
isred [in Top.Basics]
isWhite [in Top.ImpParser]
is_der [in Top.IndProp]
is_even_prime [in Top.Logic]
is_fortytwo [in Top.Auto]
is_three [in Top.Logic]

## L

leb [in Top.Basics]
lemma_application_ex [in Top.Logic]
length [in Top.Poly]
length_is_1 [in Top.Poly]
list123 [in Top.Poly]
list123' [in Top.Poly]
list123'' [in Top.Poly]
list123''' [in Top.Poly]
list_of_string [in Top.ImpParser]
loop [in Top.Imp]
lt [in Top.IndProp]

## M

many [in Top.ImpParser]
many_helper [in Top.ImpParser]
map [in Top.Poly]
matches_regex [in Top.IndProp]
match_eps [in Top.IndProp]
minustwo [in Top.Basics]
monochrome [in Top.Basics]
MyEquality.four' [in Top.ProofObjects]
MyEquality.singleton [in Top.ProofObjects]
MyIff.iff [in Top.Logic]
mynil [in Top.Poly]
mynil [in Top.Poly]
mynil' [in Top.Poly]
MyNot.not [in Top.Logic]

## N

nandb [in Top.Basics]
NatList.add [in Top.Lists]
NatList.alternate [in Top.Lists]
NatList.app [in Top.Lists]
NatList.bag [in Top.Lists]
NatList.beq_natlist [in Top.Lists]
NatList.count [in Top.Lists]
NatList.countoddmembers [in Top.Lists]
NatList.fst [in Top.Lists]
NatList.fst' [in Top.Lists]
NatList.hd [in Top.Lists]
NatList.hd_error [in Top.Lists]
NatList.length [in Top.Lists]
NatList.member [in Top.Lists]
NatList.mylist [in Top.Lists]
NatList.mylist1 [in Top.Lists]
NatList.mylist2 [in Top.Lists]
NatList.mylist3 [in Top.Lists]
NatList.nonzeros [in Top.Lists]
NatList.nth_bad [in Top.Lists]
NatList.nth_error [in Top.Lists]
NatList.nth_error' [in Top.Lists]
NatList.oddmembers [in Top.Lists]
NatList.option_elim [in Top.Lists]
NatList.remove_all [in Top.Lists]
NatList.remove_one [in Top.Lists]
NatList.repeat [in Top.Lists]
NatList.rev [in Top.Lists]
NatList.snd [in Top.Lists]
NatList.snd' [in Top.Lists]
NatList.subset [in Top.Lists]
NatList.sum [in Top.Lists]
NatList.swap_pair [in Top.Lists]
NatList.test_add1 [in Top.Lists]
NatList.test_add2 [in Top.Lists]
NatList.test_alternate1 [in Top.Lists]
NatList.test_alternate2 [in Top.Lists]
NatList.test_alternate3 [in Top.Lists]
NatList.test_alternate4 [in Top.Lists]
NatList.test_app1 [in Top.Lists]
NatList.test_app2 [in Top.Lists]
NatList.test_app3 [in Top.Lists]
NatList.test_beq_natlist1 [in Top.Lists]
NatList.test_beq_natlist2 [in Top.Lists]
NatList.test_beq_natlist3 [in Top.Lists]
NatList.test_countoddmembers1 [in Top.Lists]
NatList.test_countoddmembers2 [in Top.Lists]
NatList.test_countoddmembers3 [in Top.Lists]
NatList.test_count1 [in Top.Lists]
NatList.test_count2 [in Top.Lists]
NatList.test_hd1 [in Top.Lists]
NatList.test_hd2 [in Top.Lists]
NatList.test_hd_error1 [in Top.Lists]
NatList.test_hd_error2 [in Top.Lists]
NatList.test_hd_error3 [in Top.Lists]
NatList.test_member1 [in Top.Lists]
NatList.test_member2 [in Top.Lists]
NatList.test_nonzeros [in Top.Lists]
NatList.test_nth_error1 [in Top.Lists]
NatList.test_nth_error2 [in Top.Lists]
NatList.test_nth_error3 [in Top.Lists]
NatList.test_oddmembers [in Top.Lists]
NatList.test_remove_all1 [in Top.Lists]
NatList.test_remove_all2 [in Top.Lists]
NatList.test_remove_all3 [in Top.Lists]
NatList.test_remove_all4 [in Top.Lists]
NatList.test_remove_one1 [in Top.Lists]
NatList.test_remove_one2 [in Top.Lists]
NatList.test_remove_one3 [in Top.Lists]
NatList.test_remove_one4 [in Top.Lists]
NatList.test_rev1 [in Top.Lists]
NatList.test_rev2 [in Top.Lists]
NatList.test_subset1 [in Top.Lists]
NatList.test_subset2 [in Top.Lists]
NatList.test_sum1 [in Top.Lists]
NatList.test_tl [in Top.Lists]
NatList.tl [in Top.Lists]
NatPlayground.pred [in Top.Basics]
NatPlayground2.minus [in Top.Basics]
NatPlayground2.mult [in Top.Basics]
NatPlayground2.plus [in Top.Basics]
NatPlayground2.test_mult1 [in Top.Basics]
negb [in Top.Basics]
next_weekday [in Top.Basics]
no_whiles [in Top.Imp]
nth_error [in Top.Poly]

## O

oddb [in Top.Basics]
option_map [in Top.Poly]
orb [in Top.Basics]
order [in Top.Rel]

## P

parse [in Top.ImpParser]
parseAExp [in Top.ImpParser]
parseAtomicExp [in Top.ImpParser]
parseBExp [in Top.ImpParser]
parseConjunctionExp [in Top.ImpParser]
parseIdentifier [in Top.ImpParser]
parseNumber [in Top.ImpParser]
parsePrimaryExp [in Top.ImpParser]
parseProductExp [in Top.ImpParser]
parser [in Top.ImpParser]
parseSequencedCommand [in Top.ImpParser]
parseSimpleCommand [in Top.ImpParser]
parseSumExp [in Top.ImpParser]
PartialMap.find [in Top.Lists]
PartialMap.update [in Top.Lists]
partial_function [in Top.Rel]
partial_map [in Top.Maps]
partition [in Top.Poly]
peirce [in Top.Logic]
plus' [in Top.Basics]
plus2 [in Top.Imp]
plus3 [in Top.Poly]
plus_fact [in Top.Logic]
preorder [in Top.Rel]
Props.and_comm' [in Top.ProofObjects]
Props.and_comm'_aux [in Top.ProofObjects]
Props.conj_fact [in Top.ProofObjects]
Props.ex_ev_Sn [in Top.ProofObjects]
Props.or_comm [in Top.ProofObjects]
Props.some_nat_is_even [in Top.ProofObjects]
Pumping.napp [in Top.IndProp]
Pumping.pumping_constant [in Top.IndProp]
pup_to_n [in Top.ImpCEvalFun]
pup_to_n [in Top.Imp]
P_m0r [in Top.IndPrinciples]
P_m0r' [in Top.IndPrinciples]

## R

reflexive [in Top.Rel]
refl_matches_eps [in Top.IndProp]
regex_match [in Top.IndProp]
reg_exp_ex1 [in Top.IndProp]
reg_exp_ex2 [in Top.IndProp]
reg_exp_ex3 [in Top.IndProp]
reg_exp_ex4 [in Top.IndProp]
reg_exp_of_list [in Top.IndProp]
relation [in Top.Rel]
repeat [in Top.Poly]
repeat' [in Top.Poly]
repeat'' [in Top.Poly]
repeat''' [in Top.Poly]
rev [in Top.Poly]
rev_append [in Top.Logic]
re_chars [in Top.IndProp]
re_not_empty [in Top.IndProp]
R.fR [in Top.IndProp]

## S

sillyfun [in Top.Tactics]
sillyfun1 [in Top.Tactics]
snd [in Top.Poly]
split [in Top.Poly]
split [in Top.Tactics]
split_combine_statement [in Top.Tactics]
square [in Top.Tactics]
state [in Top.Imp]
string [in Top.IndProp]
string_of_list [in Top.ImpParser]
st12 [in Top.Auto]
st21 [in Top.Auto]
subtract_slowly [in Top.Imp]
subtract_slowly_body [in Top.Imp]
subtract_3_from_5_slowly [in Top.Imp]
symmetric [in Top.Rel]
s_compile [in Top.Imp]
s_compile1 [in Top.Imp]
s_execute [in Top.Imp]
s_execute1 [in Top.Imp]
s_execute2 [in Top.Imp]

## T

testParsing [in Top.ImpParser]
test_andb31 [in Top.Basics]
test_andb32 [in Top.Basics]
test_andb33 [in Top.Basics]
test_andb34 [in Top.Basics]
test_anon_fun' [in Top.Poly]
test_blt_nat1 [in Top.Basics]
test_blt_nat2 [in Top.Basics]
test_blt_nat3 [in Top.Basics]
test_ceval [in Top.ImpCEvalFun]
test_countoddmembers'1 [in Top.Poly]
test_countoddmembers'2 [in Top.Poly]
test_countoddmembers'3 [in Top.Poly]
test_der0 [in Top.IndProp]
test_der1 [in Top.IndProp]
test_der2 [in Top.IndProp]
test_der3 [in Top.IndProp]
test_der4 [in Top.IndProp]
test_der5 [in Top.IndProp]
test_der6 [in Top.IndProp]
test_der7 [in Top.IndProp]
test_doit3times [in Top.Poly]
test_doit3times' [in Top.Poly]
test_factorial1 [in Top.Basics]
test_factorial2 [in Top.Basics]
test_filter1 [in Top.Poly]
test_filter2 [in Top.Poly]
test_filter2' [in Top.Poly]
test_filter_even_gt7_1 [in Top.Poly]
test_filter_even_gt7_2 [in Top.Poly]
test_flat_map1 [in Top.Poly]
test_hd_error1 [in Top.Poly]
test_hd_error2 [in Top.Poly]
test_leb1 [in Top.Basics]
test_leb2 [in Top.Basics]
test_leb3 [in Top.Basics]
test_length1 [in Top.Poly]
test_map1 [in Top.Poly]
test_map2 [in Top.Poly]
test_map3 [in Top.Poly]
test_nandb1 [in Top.Basics]
test_nandb2 [in Top.Basics]
test_nandb3 [in Top.Basics]
test_nandb4 [in Top.Basics]
test_next_weekday [in Top.Basics]
test_nostutter_1 [in Top.IndProp]
test_nostutter_2 [in Top.IndProp]
test_nostutter_3 [in Top.IndProp]
test_nostutter_4 [in Top.IndProp]
test_nth_error1 [in Top.Poly]
test_nth_error2 [in Top.Poly]
test_nth_error3 [in Top.Poly]
test_oddb1 [in Top.Basics]
test_oddb2 [in Top.Basics]
test_orb1 [in Top.Basics]
test_orb2 [in Top.Basics]
test_orb3 [in Top.Basics]
test_orb4 [in Top.Basics]
test_orb5 [in Top.Basics]
test_partition1 [in Top.Poly]
test_partition2 [in Top.Poly]
test_plus3 [in Top.Poly]
test_plus3' [in Top.Poly]
test_plus3'' [in Top.Poly]
test_repeat1 [in Top.Poly]
test_repeat2 [in Top.Poly]
test_rev1 [in Top.Poly]
test_rev2 [in Top.Poly]
test_split [in Top.Poly]
token [in Top.ImpParser]
tokenize [in Top.ImpParser]
tokenize_ex1 [in Top.ImpParser]
tokenize_helper [in Top.ImpParser]
total_map [in Top.Maps]
transitive [in Top.Rel]
trans_eq_example [in Top.Tactics]
trans_eq_example' [in Top.Tactics]
trans_eq_exercise [in Top.Tactics]
tr_rev [in Top.Logic]
t_empty [in Top.Maps]
t_update [in Top.Maps]

## U

update [in Top.Maps]
update_example1 [in Top.Maps]
update_example2 [in Top.Maps]
update_example3 [in Top.Maps]
update_example4 [in Top.Maps]

## W

W [in Top.Imp]

## X

X [in Top.Imp]
XtimesYinZ [in Top.Imp]

## Y

Y [in Top.Imp]

## Z

Z [in Top.Imp]

Global Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | : | _ | (1163 entries)
Notation Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | : | _ | (79 entries)
Module Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (23 entries)
Library Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (19 entries)
Lemma Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (343 entries)
Constructor Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (201 entries)
Axiom Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (1 entry)
Inductive Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (71 entries)
Definition Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (426 entries)