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)

## S

S [axiom, in Coq.Num.Params]
S [axiom, in Coq.Num.Definitions]
S [constructor, in Coq.Init.Datatypes]
same_relation [definition, in Coq.Relations.Relation_Definitions]
same_relation [definition, in Coq.Sets.Relations_1]
same_relation_is_equivalence [lemma, in Coq.Sets.Relations_1_facts]
Same_set [definition, in Coq.Sets.Ensembles]
scal_continuity [lemma, in Coq.Reals.Ranalysis]
scal_continuous [lemma, in Coq.Reals.Ranalysis]
scal_derivable [lemma, in Coq.Reals.Ranalysis]
scal_derivable_pt [lemma, in Coq.Reals.Ranalysis]
scal_derivable_pt_var [lemma, in Coq.Reals.Ranalysis]
seq [definition, in Coq.Sets.Uniset]
seq_congr [lemma, in Coq.Sets.Uniset]
seq_left [lemma, in Coq.Sets.Uniset]
seq_refl [lemma, in Coq.Sets.Uniset]
seq_right [lemma, in Coq.Sets.Uniset]
seq_sym [lemma, in Coq.Sets.Uniset]
seq_trans [lemma, in Coq.Sets.Uniset]
Set [inductive, in Coq.ZArith.Zpower]
Set [inductive, in Coq.Lists.Streams]
set [definition, in Coq.Lists.ListSet]
setcover_intro [lemma, in Coq.Sets.Powerset_facts]
setcover_inv [lemma, in Coq.Sets.Powerset_Classical_facts]
Setminus [definition, in Coq.Sets.Ensembles]
Setminus_intro [lemma, in Coq.Sets.Constructive_sets]
Setoid [module]
set_add [definition, in Coq.Lists.ListSet]
set_add_elim [lemma, in Coq.Lists.ListSet]
set_add_intro [lemma, in Coq.Lists.ListSet]
set_add_intro1 [lemma, in Coq.Lists.ListSet]
set_add_intro2 [lemma, in Coq.Lists.ListSet]
set_add_not_empty [lemma, in Coq.Lists.ListSet]
set_diff [definition, in Coq.Lists.ListSet]
set_diff_elim1 [lemma, in Coq.Lists.ListSet]
set_diff_intro [lemma, in Coq.Lists.ListSet]
set_fold_left [definition, in Coq.Lists.ListSet]
set_fold_right [definition, in Coq.Lists.ListSet]
set_In [definition, in Coq.Lists.ListSet]
set_inter [definition, in Coq.Lists.ListSet]
set_inter_elim [lemma, in Coq.Lists.ListSet]
set_inter_elim1 [lemma, in Coq.Lists.ListSet]
set_inter_elim2 [lemma, in Coq.Lists.ListSet]
set_inter_intro [lemma, in Coq.Lists.ListSet]
set_In_dec [lemma, in Coq.Lists.ListSet]
set_map [definition, in Coq.Lists.ListSet]
set_mem [definition, in Coq.Lists.ListSet]
set_mem_complete1 [lemma, in Coq.Lists.ListSet]
set_mem_complete2 [lemma, in Coq.Lists.ListSet]
set_mem_correct1 [lemma, in Coq.Lists.ListSet]
set_mem_correct2 [lemma, in Coq.Lists.ListSet]
set_mem_ind [lemma, in Coq.Lists.ListSet]
set_power [definition, in Coq.Lists.ListSet]
set_prod [definition, in Coq.Lists.ListSet]
set_remove [definition, in Coq.Lists.ListSet]
set_union [definition, in Coq.Lists.ListSet]
set_union_elim [lemma, in Coq.Lists.ListSet]
set_union_intro [lemma, in Coq.Lists.ListSet]
set_union_intro1 [lemma, in Coq.Lists.ListSet]
set_union_intro2 [lemma, in Coq.Lists.ListSet]
shift [definition, in Coq.ZArith.Zpower]
shift_nat [definition, in Coq.ZArith.Zpower]
shift_nat_correct [lemma, in Coq.ZArith.Zpower]
shift_nat_plus [lemma, in Coq.ZArith.Zpower]
shift_pos [definition, in Coq.ZArith.Zpower]
shift_pos_correct [lemma, in Coq.ZArith.Zpower]
shift_pos_nat [lemma, in Coq.ZArith.Zpower]
sig [inductive, in Coq.Init.Specif]
sigma [axiom, in Coq.Reals.Rsigma]
sigma_aux [definition, in Coq.Reals.Rsigma]
sigma_aux_inv [lemma, in Coq.Reals.Rsigma]
sigma_diff [lemma, in Coq.Reals.Rsigma]
sigma_diff_neg [lemma, in Coq.Reals.Rsigma]
sigma_eq_arg [lemma, in Coq.Reals.Rsigma]
sigma_first [lemma, in Coq.Reals.Rsigma]
sigma_last [lemma, in Coq.Reals.Rsigma]
sigma_split [lemma, in Coq.Reals.Rsigma]
sigS [inductive, in Coq.Init.Specif]
sigS2 [inductive, in Coq.Init.Specif]
sigT [inductive, in Coq.Reals.TypeSyntax]
sigT [inductive, in Coq.Init.Specif]
sigTT [inductive, in Coq.Reals.TypeSyntax]
sig2 [inductive, in Coq.Init.Specif]
Simplify_add [lemma, in Coq.Sets.Powerset_Classical_facts]
simpl_add_l [lemma, in Coq.ZArith.fast_integer]
simpl_add_r [lemma, in Coq.ZArith.fast_integer]
simpl_fact [lemma, in Coq.Reals.Rfunctions]
simpl_gt_plus_l [lemma, in Coq.Arith.Gt]
simpl_le_plus_l [lemma, in Coq.Arith.Plus]
simpl_lt_plus_l [lemma, in Coq.Arith.Plus]
simpl_plus_l [lemma, in Coq.Arith.Plus]
SIN [lemma, in Coq.Reals.Rtrigo]
sin [axiom, in Coq.Reals.Rtrigo]
sincl_add_x [lemma, in Coq.Sets.Powerset_Classical_facts]
sind [definition, in Coq.Reals.Rtrigo]
Singleton [inductive, in Coq.Sets.Ensembles]
Singleton [definition, in Coq.Sets.Uniset]
SingletonBag [definition, in Coq.Sets.Multiset]
Singleton_atomic [lemma, in Coq.Sets.Powerset_Classical_facts]
Singleton_intro [lemma, in Coq.Sets.Constructive_sets]
Singleton_inv [lemma, in Coq.Sets.Constructive_sets]
Singleton_is_finite [lemma, in Coq.Sets.Finite_sets_facts]
single_limit [lemma, in Coq.Reals.Rlimit]
single_z_r_R1 [lemma, in Coq.Reals.Rbase]
singlx [lemma, in Coq.Sets.Powerset_facts]
sin2 [lemma, in Coq.Reals.Rtrigo]
sin2_cos2 [lemma, in Coq.Reals.Rtrigo]
sin3PI4 [lemma, in Coq.Reals.Rtrigo]
sin_approx [definition, in Coq.Reals.Rtrigo]
SIN_bound [lemma, in Coq.Reals.Rtrigo]
sin_bound [axiom, in Coq.Reals.Rtrigo]
sin_cos [lemma, in Coq.Reals.Rtrigo]
sin_cos5PI4 [lemma, in Coq.Reals.Rtrigo]
sin_cos_PI4 [lemma, in Coq.Reals.Rtrigo]
sin_decreasing_0 [lemma, in Coq.Reals.Rtrigo]
sin_decreasing_1 [lemma, in Coq.Reals.Rtrigo]
sin_decr_0 [lemma, in Coq.Reals.Rtrigo]
sin_decr_1 [lemma, in Coq.Reals.Rtrigo]
sin_eq_O_2PI_0 [lemma, in Coq.Reals.Rtrigo]
sin_eq_O_2PI_1 [lemma, in Coq.Reals.Rtrigo]
sin_eq_0 [axiom, in Coq.Reals.Rtrigo]
sin_eq_0_0 [lemma, in Coq.Reals.Rtrigo]
sin_eq_0_1 [lemma, in Coq.Reals.Rtrigo]
sin_ge_0 [lemma, in Coq.Reals.Rtrigo]
sin_gt_0 [lemma, in Coq.Reals.Rtrigo]
sin_increasing_0 [lemma, in Coq.Reals.Rtrigo]
sin_increasing_1 [lemma, in Coq.Reals.Rtrigo]
sin_incr_0 [lemma, in Coq.Reals.Rtrigo]
sin_incr_1 [lemma, in Coq.Reals.Rtrigo]
sin_lb [definition, in Coq.Reals.Rtrigo]
sin_lb_ge_0 [lemma, in Coq.Reals.Rtrigo]
sin_lb_gt_0 [axiom, in Coq.Reals.Rtrigo]
sin_le_0 [lemma, in Coq.Reals.Rtrigo]
sin_lt_0 [lemma, in Coq.Reals.Rtrigo]
sin_lt_0_var [lemma, in Coq.Reals.Rtrigo]
sin_minus [axiom, in Coq.Reals.Rtrigo]
sin_neg [lemma, in Coq.Reals.Rtrigo]
sin_period [lemma, in Coq.Reals.Rtrigo]
sin_PI [lemma, in Coq.Reals.Rtrigo]
sin_PI2 [axiom, in Coq.Reals.Rtrigo]
sin_PI3 [lemma, in Coq.Reals.Rtrigo]
sin_PI3_cos_PI6 [lemma, in Coq.Reals.Rtrigo]
sin_PI4 [lemma, in Coq.Reals.Rtrigo]
sin_PI6 [lemma, in Coq.Reals.Rtrigo]
sin_PI6_cos_PI3 [lemma, in Coq.Reals.Rtrigo]
sin_PI_x [lemma, in Coq.Reals.Rtrigo]
sin_plus [axiom, in Coq.Reals.Rtrigo]
sin_shift [lemma, in Coq.Reals.Rtrigo]
sin_term [definition, in Coq.Reals.Rtrigo]
sin_ub [definition, in Coq.Reals.Rtrigo]
sin_0 [lemma, in Coq.Reals.Rtrigo]
sin_2a [lemma, in Coq.Reals.Rtrigo]
sin_2PI [lemma, in Coq.Reals.Rtrigo]
sin_2PI3 [lemma, in Coq.Reals.Rtrigo]
sin_3PI2 [lemma, in Coq.Reals.Rtrigo]
sin_5PI4 [lemma, in Coq.Reals.Rtrigo]
snd [definition, in Coq.Init.Datatypes]
Snd [definition, in Coq.Init.Datatypes]
sndT [definition, in Coq.Init.Logic_Type]
sol_x1 [definition, in Coq.Reals.R_sqr]
sol_x2 [definition, in Coq.Reals.R_sqr]
SOME [constructor, in Coq.IntMap.Map]
Some [constructor, in Coq.Init.Datatypes]
sort [inductive, in Coq.Sorting.Sorting]
Sorting [module]
sort_inv [lemma, in Coq.Sorting.Sorting]
sort_rec [lemma, in Coq.Sorting.Sorting]
Specif [module]
SpecifSyntax [module]
SplitAbs [tactic definition, in Coq.Reals.SplitAbsolu]
SplitAbsolu [tactic definition, in Coq.Reals.SplitAbsolu]
SplitAbsolu [module]
SplitRmult [tactic definition, in Coq.Reals.SplitRmult]
SplitRmult [module]
sp_noswap [constructor, in Coq.Relations.Relation_Operators]
sp_swap [constructor, in Coq.Relations.Relation_Operators]
SqRing [tactic definition, in Coq.Reals.R_sqr]
sqrt [axiom, in Coq.Reals.R_sqr]
sqrt2_neq_0 [lemma, in Coq.Reals.Rtrigo]
sqrt3_2_neq_0 [lemma, in Coq.Reals.Rtrigo]
sqrt_cauchy [lemma, in Coq.Reals.R_sqr]
sqrt_def [lemma, in Coq.Reals.R_sqr]
sqrt_div [lemma, in Coq.Reals.R_sqr]
sqrt_eq_0 [lemma, in Coq.Reals.R_sqr]
sqrt_inj [lemma, in Coq.Reals.R_sqr]
sqrt_lem_0 [lemma, in Coq.Reals.R_sqr]
sqrt_less [lemma, in Coq.Reals.R_sqr]
sqrt_le_0 [lemma, in Coq.Reals.R_sqr]
sqrt_le_1 [lemma, in Coq.Reals.R_sqr]
sqrt_lt_R0 [lemma, in Coq.Reals.R_sqr]
sqrt_lt_0 [lemma, in Coq.Reals.R_sqr]
sqrt_lt_1 [lemma, in Coq.Reals.R_sqr]
sqrt_more [lemma, in Coq.Reals.R_sqr]
sqrt_Rsqr [lemma, in Coq.Reals.R_sqr]
sqrt_Rsqr_abs [lemma, in Coq.Reals.R_sqr]
sqrt_square [lemma, in Coq.Reals.R_sqr]
sqrt_times [lemma, in Coq.Reals.R_sqr]
sqrt_0 [lemma, in Coq.Reals.R_sqr]
sqrt_1 [lemma, in Coq.Reals.R_sqr]
sqtr_lem_1 [lemma, in Coq.Reals.R_sqr]
Sstar_contains_Rstar [lemma, in Coq.Sets.Relations_2_facts]
star_monotone [lemma, in Coq.Sets.Relations_2_facts]
Streams [module]
strictincreasing_strictdecreasing_opp [lemma, in Coq.Reals.Ranalysis]
strict_decreasing [definition, in Coq.Reals.Ranalysis]
Strict_Included [definition, in Coq.Sets.Ensembles]
Strict_Included_intro [lemma, in Coq.Sets.Constructive_sets]
Strict_Included_inv [lemma, in Coq.Sets.Classical_sets]
Strict_Included_strict [lemma, in Coq.Sets.Constructive_sets]
Strict_inclusion_is_transitive [lemma, in Coq.Sets.Powerset]
Strict_inclusion_is_transitive_with_inclusion [lemma, in Coq.Sets.Powerset]
Strict_inclusion_is_transitive_with_inclusion_left [lemma, in Coq.Sets.Powerset]
strict_increasing [definition, in Coq.Reals.Ranalysis]
Strict_Rel_is_Strict_Included [lemma, in Coq.Sets.Powerset]
Strict_Rel_of [definition, in Coq.Sets.Partial_Order]
Strict_Rel_Transitive [lemma, in Coq.Sets.Partial_Order]
Strict_Rel_Transitive_with_Rel [lemma, in Coq.Sets.Partial_Order]
Strict_Rel_Transitive_with_Rel_left [lemma, in Coq.Sets.Partial_Order]
Strict_super_set_contains_new_element [lemma, in Coq.Sets.Classical_sets]
Strongly_confluent [definition, in Coq.Sets.Relations_2]
Strong_confluence [lemma, in Coq.Sets.Relations_3_facts]
Strong_confluence_direct [lemma, in Coq.Sets.Relations_3_facts]
Str_nth [definition, in Coq.Lists.Streams]
Str_nth_plus [lemma, in Coq.Lists.Streams]
Str_nth_tl [definition, in Coq.Lists.Streams]
Str_nth_tl_plus [lemma, in Coq.Lists.Streams]
SubProps [module]
Subtract [definition, in Coq.Sets.Ensembles]
Subtract_intro [lemma, in Coq.Sets.Classical_sets]
Subtract_inv [lemma, in Coq.Sets.Classical_sets]
sub_add [lemma, in Coq.ZArith.fast_integer]
Sub_Add_new [lemma, in Coq.Sets.Powerset_Classical_facts]
sub_add_one [lemma, in Coq.ZArith.fast_integer]
sub_neg [definition, in Coq.ZArith.fast_integer]
sub_pos [definition, in Coq.ZArith.fast_integer]
sub_pos_SUPERIEUR [lemma, in Coq.ZArith.fast_integer]
sub_pos_x_x [lemma, in Coq.ZArith.fast_integer]
sub_un [definition, in Coq.ZArith.fast_integer]
sum [inductive, in Coq.Init.Datatypes]
sumbool [inductive, in Coq.Init.Specif]
Sumbool [module]
sumboolT [inductive, in Coq.Reals.TypeSyntax]
sumbool_and [lemma, in Coq.Bool.Sumbool]
sumbool_not [lemma, in Coq.Bool.Sumbool]
sumbool_of_bool [lemma, in Coq.Bool.Sumbool]
sumbool_or [lemma, in Coq.Bool.Sumbool]
sumor [inductive, in Coq.Init.Specif]
sumorT [inductive, in Coq.Reals.TypeSyntax]
sum_continuity [lemma, in Coq.Reals.Ranalysis]
sum_continuous [lemma, in Coq.Reals.Ranalysis]
sum_derivable [lemma, in Coq.Reals.Ranalysis]
sum_derivable_pt [lemma, in Coq.Reals.Ranalysis]
sum_derivable_pt_var [lemma, in Coq.Reals.Ranalysis]
sum_f [definition, in Coq.Reals.Rfunctions]
sum_fct_cte_derivable [lemma, in Coq.Reals.Ranalysis]
sum_fct_cte_derivable_pt [lemma, in Coq.Reals.Ranalysis]
sum_fct_cte_derive_pt [lemma, in Coq.Reals.Ranalysis]
sum_f_R0 [definition, in Coq.Reals.Rfunctions]
sum_f_R0_triangle [lemma, in Coq.Reals.Rfunctions]
sum_inequa_Rle_lt [lemma, in Coq.Reals.Rbase]
sum_nat [definition, in Coq.Reals.Rfunctions]
sum_nat_f [definition, in Coq.Reals.Rfunctions]
sum_nat_f_O [definition, in Coq.Reals.Rfunctions]
sum_nat_O [definition, in Coq.Reals.Rfunctions]
sup [constructor, in Coq.Wellfounded.Well_Ordering]
SUPERIEUR [constructor, in Coq.ZArith.fast_integer]
SUPERIEUR_POS [lemma, in Coq.ZArith.fast_integer]
Sup0 [tactic definition, in Coq.Reals.DiscrR]
swapprod [inductive, in Coq.Relations.Relation_Operators]
SwapProd [definition, in Coq.Wellfounded.Lexicographic_Product]
swap_Acc [lemma, in Coq.Wellfounded.Lexicographic_Product]
Symmetric [definition, in Coq.Sets.Relations_1]
symmetric [definition, in Coq.Relations.Relation_Definitions]
Symprod [definition, in Coq.Wellfounded.Lexicographic_Product]
symprod [inductive, in Coq.Relations.Relation_Operators]
sym_eq [lemma, in Coq.Init.Logic]
sym_EqSt [lemma, in Coq.Lists.Streams]
sym_eqT [lemma, in Coq.Init.Logic_Type]
sym_equal [definition, in Coq.Init.Logic]
sym_idT [lemma, in Coq.Init.Logic_Type]
sym_not_eq [lemma, in Coq.Init.Logic]
sym_not_eqT [lemma, in Coq.Init.Logic_Type]
sym_not_equal [definition, in Coq.Init.Logic]
sym_not_idT [lemma, in Coq.Init.Logic_Type]
S_eq_compat [axiom, in Coq.Num.EqAxioms]
S_INR [lemma, in Coq.Reals.Rbase]
S_O_plus_INR [lemma, in Coq.Reals.Rbase]
S_pred [lemma, in Coq.Arith.Lt]
S_0_1 [axiom, in Coq.Num.Axioms]

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)