The Coq standard library

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 | _ | (3647 entries)
Tactic 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 | _ | (9 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 | _ | (107 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 | _ | (2540 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 | _ | (184 entries)
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 | _ | (118 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 | _ | (523 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 | _ | (166 entries)

## L

law_cosines [lemma, in Coq.Reals.Rgeom]
le [inductive, in Coq.Init.Peano]
Le [module]
LeAxioms [module]
leA_Tree [definition, in Coq.Sorting.Heap]
leA_Tree_Leaf [lemma, in Coq.Sorting.Heap]
leA_Tree_Node [lemma, in Coq.Sorting.Heap]
leb [definition, in Coq.Bool.Bool]
leb_refl [lemma, in Coq.Sets.Uniset]
left [constructor, in Coq.Init.Specif]
leftT [constructor, in Coq.Reals.TypeSyntax]
left_lex [constructor, in Coq.Relations.Relation_Operators]
left_prefix [lemma, in Coq.Wellfounded.Lexicographic_Exponentiation]
left_sym [constructor, in Coq.Relations.Relation_Operators]
lel [definition, in Coq.Lists.PolyList]
lel [definition, in Coq.Lists.List]
lelistA [inductive, in Coq.Sorting.Sorting]
lelistA_inv [lemma, in Coq.Sorting.Sorting]
lel_cons [lemma, in Coq.Lists.List]
lel_cons [lemma, in Coq.Lists.PolyList]
lel_cons_cons [lemma, in Coq.Lists.List]
lel_cons_cons [lemma, in Coq.Lists.PolyList]
lel_nil [lemma, in Coq.Lists.PolyList]
lel_nil [lemma, in Coq.Lists.List]
lel_refl [lemma, in Coq.Lists.PolyList]
lel_refl [lemma, in Coq.Lists.List]
lel_tail [lemma, in Coq.Lists.List]
lel_tail [lemma, in Coq.Lists.PolyList]
lel_trans [lemma, in Coq.Lists.PolyList]
lel_trans [lemma, in Coq.Lists.List]
Lemma1 [lemma, in Coq.Sets.Relations_2_facts]
length [definition, in Coq.Lists.List]
length [definition, in Coq.Lists.PolyList]
Length [lemma, in Coq.Lists.TheoryList]
length_as_fold [lemma, in Coq.IntMap.Mapcard]
length_as_fold_2 [lemma, in Coq.IntMap.Mapcard]
Length_l [definition, in Coq.Lists.TheoryList]
Length_l_pf [lemma, in Coq.Lists.TheoryList]
LeProps [module]
less_than_empty [lemma, in Coq.Sets.Powerset_facts]
less_than_singleton [lemma, in Coq.Sets.Powerset_Classical_facts]
Lexicographic_Exponentiation [module]
Lexicographic_Product [module]
lexprod [inductive, in Coq.Relations.Relation_Operators]
LexProd [definition, in Coq.Wellfounded.Lexicographic_Product]
lex_exp [definition, in Coq.Relations.Relation_Operators]
Lex_Exp [definition, in Coq.Wellfounded.Lexicographic_Exponentiation]
le_aa [constructor, in Coq.Relations.Relation_Operators]
le_ab [constructor, in Coq.Relations.Relation_Operators]
le_add_compat [lemma, in Coq.Num.LeProps]
le_add_compat_l [lemma, in Coq.Num.LeProps]
le_add_compat_r [lemma, in Coq.Num.LeProps]
le_antisym [lemma, in Coq.Sets.Integers]
le_antisym [lemma, in Coq.Arith.Le]
Le_AsB [definition, in Coq.Wellfounded.Disjoint_Union]
le_AsB [inductive, in Coq.Relations.Relation_Operators]
le_bb [constructor, in Coq.Relations.Relation_Operators]
le_dec [lemma, in Coq.Arith.Compare]
le_decide [lemma, in Coq.Arith.Compare]
le_elim_rel [lemma, in Coq.Arith.Le]
le_epsilon [lemma, in Coq.Reals.Rbase]
le_eq_compat [lemma, in Coq.Num.LeProps]
le_ge_dec [lemma, in Coq.Arith.Compare_dec]
le_gt_dec [lemma, in Coq.Arith.Compare_dec]
le_gt_S [lemma, in Coq.Arith.Gt]
le_gt_trans [lemma, in Coq.Arith.Gt]
le_INR [lemma, in Coq.Reals.Rbase]
le_IZR [lemma, in Coq.Reals.Rbase]
le_IZR_R1 [lemma, in Coq.Reals.Rbase]
le_le_S_dec [lemma, in Coq.Arith.Compare_dec]
le_le_S_eq [lemma, in Coq.Arith.Compare]
le_le_x_Sy [lemma, in Coq.Num.LeProps]
le_lt_dec [lemma, in Coq.Arith.Compare_dec]
le_lt_eq_dec [lemma, in Coq.Arith.Compare_dec]
le_lt_n_Sm [lemma, in Coq.Arith.Lt]
le_lt_or_eq [lemma, in Coq.Arith.Lt]
le_lt_or_eq [axiom, in Coq.Num.LeAxioms]
le_lt_plus_plus [lemma, in Coq.Arith.Plus]
le_lt_trans [lemma, in Coq.Arith.Lt]
le_lt_trans [lemma, in Coq.Num.LeProps]
le_lt_x_Sy [lemma, in Coq.Num.LeProps]
le_max_l [lemma, in Coq.Arith.Max]
le_max_r [lemma, in Coq.Arith.Max]
le_minus [lemma, in Coq.ZArith.fast_integer]
le_min_l [lemma, in Coq.Arith.Min]
le_min_r [lemma, in Coq.Arith.Min]
le_n [constructor, in Coq.Init.Peano]
le_ni_le [lemma, in Coq.IntMap.Adist]
le_not_gt [lemma, in Coq.Arith.Gt]
le_not_lt [lemma, in Coq.Arith.Lt]
le_n_O_eq [lemma, in Coq.Arith.Le]
le_n_S [lemma, in Coq.Arith.Le]
le_n_Sn [lemma, in Coq.Arith.Le]
le_Order [lemma, in Coq.Sets.Integers]
le_or_le_S [definition, in Coq.Arith.Compare]
le_or_lt [lemma, in Coq.Arith.Lt]
le_O_IZR [lemma, in Coq.Reals.Rbase]
le_O_n [lemma, in Coq.Arith.Le]
le_plus_l [lemma, in Coq.Arith.Plus]
le_plus_minus [lemma, in Coq.Arith.Minus]
le_plus_minus_r [lemma, in Coq.Arith.Minus]
le_plus_plus [lemma, in Coq.Arith.Plus]
le_plus_r [lemma, in Coq.Arith.Plus]
le_plus_trans [lemma, in Coq.Arith.Plus]
le_pred_n [lemma, in Coq.Arith.Le]
le_reflexive [lemma, in Coq.Sets.Integers]
le_reg_l [lemma, in Coq.Arith.Plus]
le_reg_r [lemma, in Coq.Arith.Plus]
le_S [constructor, in Coq.Init.Peano]
le_Sn_n [lemma, in Coq.Arith.Le]
le_Sn_O [lemma, in Coq.Arith.Le]
le_sup [constructor, in Coq.Wellfounded.Well_Ordering]
le_Sx_y_lt [lemma, in Coq.Num.LeProps]
le_S_compat [lemma, in Coq.Num.LeProps]
le_S_gt [lemma, in Coq.Arith.Gt]
le_S_n [lemma, in Coq.Arith.Le]
le_total_order [lemma, in Coq.Sets.Integers]
le_trans [lemma, in Coq.Sets.Integers]
le_trans [lemma, in Coq.Num.LeProps]
le_trans [lemma, in Coq.Arith.Le]
le_trans_S [lemma, in Coq.Arith.Le]
le_WO [inductive, in Coq.Wellfounded.Well_Ordering]
limit1_in [definition, in Coq.Reals.Rlimit]
limit_comp [lemma, in Coq.Reals.Rlimit]
limit_free [lemma, in Coq.Reals.Rlimit]
limit_in [definition, in Coq.Reals.Rlimit]
limit_inv [lemma, in Coq.Reals.Rlimit]
limit_minus [lemma, in Coq.Reals.Rlimit]
limit_mul [lemma, in Coq.Reals.Rlimit]
limit_plus [lemma, in Coq.Reals.Rlimit]
limit_Ropp [lemma, in Coq.Reals.Rlimit]
lim_x [lemma, in Coq.Reals.Rlimit]
list [inductive, in Coq.Lists.PolyList]
List [definition, in Coq.Wellfounded.Lexicographic_Exponentiation]
list [inductive, in Coq.Lists.List]
List [module]
ListSet [module]
list_contents [definition, in Coq.Sorting.Permutation]
list_contents_app [lemma, in Coq.Sorting.Permutation]
List_Dom [axiom, in Coq.Lists.List]
list_eq_dec [lemma, in Coq.Lists.PolyList]
list_power [definition, in Coq.Lists.PolyList]
list_prod [definition, in Coq.Lists.PolyList]
list_to_heap [lemma, in Coq.Sorting.Heap]
Locally_confluent [definition, in Coq.Sets.Relations_3]
locally_confluent [definition, in Coq.Sets.Relations_3]
local_confluence [definition, in Coq.Relations.Newman]
Logic [module]
LogicSyntax [module]
Logic_Type [module]
Logic_TypeSyntax [module]
log_inf [definition, in Coq.ZArith.Zlogarithm]
log_inf_correct [lemma, in Coq.ZArith.Zlogarithm]
log_inf_correct1 [definition, in Coq.ZArith.Zlogarithm]
log_inf_correct2 [definition, in Coq.ZArith.Zlogarithm]
log_inf_le_log_sup [lemma, in Coq.ZArith.Zlogarithm]
log_inf_shift_nat [lemma, in Coq.ZArith.Zlogarithm]
log_near [definition, in Coq.ZArith.Zlogarithm]
log_near_correct1 [lemma, in Coq.ZArith.Zlogarithm]
log_near_correct2 [lemma, in Coq.ZArith.Zlogarithm]
log_sup [definition, in Coq.ZArith.Zlogarithm]
log_sup_correct1 [lemma, in Coq.ZArith.Zlogarithm]
log_sup_correct2 [lemma, in Coq.ZArith.Zlogarithm]
log_sup_le_Slog_inf [lemma, in Coq.ZArith.Zlogarithm]
log_sup_log_inf [lemma, in Coq.ZArith.Zlogarithm]
log_sup_shift_nat [lemma, in Coq.ZArith.Zlogarithm]
Lower_Bound [inductive, in Coq.Sets.Cpo]
Lower_Bound_definition [constructor, in Coq.Sets.Cpo]
low_trans [lemma, in Coq.Sorting.Heap]
Lsort [module]
lt [axiom, in Coq.Num.Params]
lt [definition, in Coq.Init.Peano]
Lt [module]
ltl [definition, in Coq.Wellfounded.Lexicographic_Exponentiation]
Ltl [inductive, in Coq.Relations.Relation_Operators]
ltl_unit [lemma, in Coq.Wellfounded.Lexicographic_Exponentiation]
ltof [definition, in Coq.Arith.Wf_nat]
LtProps [module]
lt_add_compat [lemma, in Coq.Num.LtProps]
lt_add_compat_l [axiom, in Coq.Num.Axioms]
lt_add_compat_r [lemma, in Coq.Num.LtProps]
lt_add_compat_weak_l [lemma, in Coq.Num.LeProps]
lt_add_compat_weak_r [lemma, in Coq.Num.LeProps]
lt_anti_refl [axiom, in Coq.Num.Axioms]
lt_anti_sym [lemma, in Coq.Num.LtProps]
lt_div2 [lemma, in Coq.Arith.Div2]
lt_eq_compat [axiom, in Coq.Num.EqAxioms]
lt_eq_lt_dec [lemma, in Coq.Arith.Compare_dec]
Lt_hd [constructor, in Coq.Relations.Relation_Operators]
lt_INR [lemma, in Coq.Reals.Rbase]
lt_INR_0 [lemma, in Coq.Reals.Rbase]
lt_IZR [lemma, in Coq.Reals.Rbase]
lt_le [lemma, in Coq.Num.LeProps]
lt_le_plus_plus [lemma, in Coq.Arith.Plus]
lt_le_S [lemma, in Coq.Arith.Lt]
lt_le_Sx_y [lemma, in Coq.Num.DiscrProps]
lt_le_trans [lemma, in Coq.Num.LeProps]
lt_le_trans [lemma, in Coq.Arith.Lt]
lt_le_weak [lemma, in Coq.Arith.Lt]
lt_lt_x_Sy [lemma, in Coq.Num.LtProps]
lt_minus [lemma, in Coq.Arith.Minus]
lt_mult_left [lemma, in Coq.ZArith.fast_integer]
lt_neq [lemma, in Coq.Num.LtProps]
lt_neq_sym [lemma, in Coq.Num.LtProps]
Lt_nil [constructor, in Coq.Relations.Relation_Operators]
lt_not_le [lemma, in Coq.Arith.Lt]
lt_not_sym [lemma, in Coq.Arith.Lt]
lt_n_n [lemma, in Coq.Arith.Lt]
lt_n_O [lemma, in Coq.Arith.Lt]
lt_n_S [lemma, in Coq.Arith.Lt]
lt_n_Sm_le [lemma, in Coq.Arith.Lt]
lt_n_Sn [lemma, in Coq.Arith.Lt]
lt_or_eq [definition, in Coq.Arith.Compare]
lt_or_eq_le [axiom, in Coq.Num.LeAxioms]
lt_O_IZR [lemma, in Coq.Reals.Rbase]
lt_O_minus_lt [lemma, in Coq.Arith.Minus]
lt_O_neq [lemma, in Coq.Arith.Lt]
lt_O_Sn [lemma, in Coq.Arith.Lt]
lt_plus_plus [lemma, in Coq.Arith.Plus]
lt_plus_trans [lemma, in Coq.Arith.Plus]
lt_pred [lemma, in Coq.Arith.Lt]
lt_pred_n_n [lemma, in Coq.Arith.Lt]
lt_reg_l [lemma, in Coq.Arith.Plus]
lt_reg_r [lemma, in Coq.Arith.Plus]
lt_S [lemma, in Coq.Arith.Lt]
lt_Sx_y_lt [lemma, in Coq.Num.LtProps]
lt_S_compat [axiom, in Coq.Num.Axioms]
lt_S_n [lemma, in Coq.Arith.Lt]
Lt_tl [constructor, in Coq.Relations.Relation_Operators]
lt_trans [axiom, in Coq.Num.Axioms]
lt_trans [lemma, in Coq.Arith.Lt]
lt_wf [lemma, in Coq.Arith.Wf_nat]
lt_wf_double_ind [lemma, in Coq.Arith.Wf_nat]
lt_wf_double_rec [lemma, in Coq.Arith.Wf_nat]
lt_wf_ind [lemma, in Coq.Arith.Wf_nat]
lt_wf_rec [lemma, in Coq.Arith.Wf_nat]
lt_wf_rec1 [lemma, in Coq.Arith.Wf_nat]
lt_x_Sx [axiom, in Coq.Num.Axioms]
lt_x_Sy_le [axiom, in Coq.Num.DiscrAxioms]
lt_0_1 [lemma, in Coq.Num.LtProps]
Lub [inductive, in Coq.Sets.Cpo]
Lub_definition [constructor, in Coq.Sets.Cpo]
L1 [lemma, in Coq.Logic.Berardi]

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 | _ | (3647 entries)
Tactic 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 | _ | (9 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 | _ | (107 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 | _ | (2540 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 | _ | (184 entries)
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 | _ | (118 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 | _ | (523 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 | _ | (166 entries)