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)

## I

I [constructor, in Coq.Init.Logic]
IAF [axiom, in Coq.Reals.Ranalysis]
idempot_rev [lemma, in Coq.Lists.PolyList]
identityT [inductive, in Coq.Init.Logic_Type]
identityT_ind_r [definition, in Coq.Init.Logic_Type]
identityT_rect_r [definition, in Coq.Init.Logic_Type]
identityT_rec_r [definition, in Coq.Init.Logic_Type]
IF [definition, in Coq.Init.Logic]
ifb [definition, in Coq.Bool.Bool]
ifdec [definition, in Coq.Bool.DecBool]
ifdec_left [lemma, in Coq.Bool.DecBool]
ifdec_right [lemma, in Coq.Bool.DecBool]
iff [definition, in Coq.Init.Logic]
Iffalse [constructor, in Coq.Bool.IfProp]
Iffalse_inv [lemma, in Coq.Bool.IfProp]
iff_refl [lemma, in Coq.Init.Logic]
iff_sym [lemma, in Coq.Init.Logic]
iff_trans [lemma, in Coq.Init.Logic]
IfProp [inductive, in Coq.Bool.IfProp]
IFProp [definition, in Coq.Logic.Berardi]
IfProp [module]
IfProp_false [lemma, in Coq.Bool.IfProp]
IfProp_or [lemma, in Coq.Bool.IfProp]
IfProp_sum [lemma, in Coq.Bool.IfProp]
IfProp_true [lemma, in Coq.Bool.IfProp]
Iftrue [constructor, in Coq.Bool.IfProp]
Iftrue_inv [lemma, in Coq.Bool.IfProp]
if_negb [lemma, in Coq.Bool.Bool]
Im [inductive, in Coq.Sets.Image]
Image [module]
image_empty [lemma, in Coq.Sets.Image]
Image_set_continuous [lemma, in Coq.Sets.Infinite_sets]
Image_set_continuous' [lemma, in Coq.Sets.Infinite_sets]
implb [definition, in Coq.Bool.Bool]
imply_and_or [lemma, in Coq.Logic.Classical_Prop]
imply_and_or2 [lemma, in Coq.Logic.Classical_Prop]
imply_to_and [lemma, in Coq.Logic.Classical_Prop]
imply_to_or [lemma, in Coq.Logic.Classical_Prop]
imp_not_Req [lemma, in Coq.Reals.Rbase]
imp_simp [lemma, in Coq.Logic.Decidable]
Im_add [lemma, in Coq.Sets.Image]
Im_def [lemma, in Coq.Sets.Image]
Im_intro [constructor, in Coq.Sets.Image]
Im_inv [lemma, in Coq.Sets.Image]
In [definition, in Coq.Sets.Ensembles]
In [definition, in Coq.Lists.List]
In [definition, in Coq.Sets.Uniset]
In [definition, in Coq.Lists.PolyList]
incl [definition, in Coq.Lists.List]
incl [definition, in Coq.Lists.PolyList]
incl [definition, in Coq.Sets.Uniset]
Included [definition, in Coq.Sets.Ensembles]
Included_Add [lemma, in Coq.Sets.Powerset_Classical_facts]
Included_Empty [lemma, in Coq.Sets.Constructive_sets]
Included_Strict_Included [lemma, in Coq.Sets.Classical_sets]
inclusion [definition, in Coq.Relations.Relation_Definitions]
Inclusion [module]
Inclusion_is_an_order [lemma, in Coq.Sets.Powerset]
Inclusion_is_transitive [lemma, in Coq.Sets.Powerset]
incl_add [lemma, in Coq.Sets.Powerset_facts]
incl_add_x [lemma, in Coq.Sets.Powerset_facts]
incl_app [lemma, in Coq.Lists.PolyList]
incl_app [lemma, in Coq.Lists.List]
incl_appl [lemma, in Coq.Lists.PolyList]
incl_appl [lemma, in Coq.Lists.List]
incl_appr [lemma, in Coq.Lists.PolyList]
incl_appr [lemma, in Coq.Lists.List]
incl_card_le [lemma, in Coq.Sets.Finite_sets_facts]
incl_clos_trans [lemma, in Coq.Wellfounded.Transitive_Closure]
incl_cons [lemma, in Coq.Lists.PolyList]
incl_cons [lemma, in Coq.Lists.List]
incl_left [lemma, in Coq.Sets.Uniset]
incl_refl [lemma, in Coq.Lists.PolyList]
incl_refl [lemma, in Coq.Lists.List]
incl_right [lemma, in Coq.Sets.Uniset]
incl_soustr [lemma, in Coq.Sets.Powerset_Classical_facts]
incl_soustr_add_l [lemma, in Coq.Sets.Powerset_Classical_facts]
incl_soustr_add_r [lemma, in Coq.Sets.Powerset_Classical_facts]
incl_soustr_in [lemma, in Coq.Sets.Powerset_Classical_facts]
incl_st_add_soustr [lemma, in Coq.Sets.Powerset_Classical_facts]
incl_st_card_lt [lemma, in Coq.Sets.Finite_sets_facts]
incl_tl [lemma, in Coq.Lists.PolyList]
incl_tl [lemma, in Coq.Lists.List]
incl_tran [lemma, in Coq.Lists.PolyList]
incl_tran [lemma, in Coq.Lists.List]
increasing [definition, in Coq.Reals.Ranalysis]
increasing_decreasing [lemma, in Coq.Reals.Ranalysis]
increasing_decreasing_opp [lemma, in Coq.Reals.Ranalysis]
Index [lemma, in Coq.Lists.TheoryList]
index_p [definition, in Coq.Lists.TheoryList]
Index_p [lemma, in Coq.Lists.TheoryList]
induction_gtof1 [lemma, in Coq.Arith.Wf_nat]
induction_gtof2 [lemma, in Coq.Arith.Wf_nat]
induction_ltof1 [lemma, in Coq.Arith.Wf_nat]
induction_ltof2 [lemma, in Coq.Arith.Wf_nat]
Ind_proof [lemma, in Coq.Relations.Newman]
ind_0_1_SS [lemma, in Coq.Arith.Div2]
INFERIEUR [constructor, in Coq.ZArith.fast_integer]
Infinite_sets [module]
infinit_sum [definition, in Coq.Reals.Rfunctions]
infty [constructor, in Coq.IntMap.Adist]
inf_dec [definition, in Coq.Arith.Div]
Inhabited [inductive, in Coq.Sets.Ensembles]
Inhabited_add [lemma, in Coq.Sets.Constructive_sets]
Inhabited_intro [constructor, in Coq.Sets.Ensembles]
Inhabited_not_empty [lemma, in Coq.Sets.Constructive_sets]
Inhabited_Setminus [lemma, in Coq.Sets.Classical_sets]
inh_card_gt_O [lemma, in Coq.Sets.Finite_sets_facts]
injective [definition, in Coq.Sets.Image]
injective_preserves_cardinal [lemma, in Coq.Sets.Image]
inject_nat [definition, in Coq.ZArith.zarith_aux]
inject_nat_complete [lemma, in Coq.ZArith.Wf_Z]
inject_nat_complete_inf [lemma, in Coq.ZArith.Wf_Z]
inject_nat_prop [lemma, in Coq.ZArith.Wf_Z]
inject_nat_set [lemma, in Coq.ZArith.Wf_Z]
inj_eq [lemma, in Coq.ZArith.auxiliary]
inj_ge [lemma, in Coq.ZArith.auxiliary]
inj_gt [lemma, in Coq.ZArith.auxiliary]
inj_le [lemma, in Coq.ZArith.auxiliary]
inj_lt [lemma, in Coq.ZArith.auxiliary]
inj_minus1 [lemma, in Coq.ZArith.auxiliary]
inj_minus2 [lemma, in Coq.ZArith.auxiliary]
inj_minus_aux [lemma, in Coq.Arith.Minus]
inj_mult [lemma, in Coq.ZArith.auxiliary]
inj_neq [lemma, in Coq.ZArith.auxiliary]
inj_pair2 [lemma, in Coq.Logic.Eqdep]
inj_plus [lemma, in Coq.ZArith.auxiliary]
inj_right_pair [lemma, in Coq.Logic.Eqdep_dec]
inj_S [lemma, in Coq.ZArith.auxiliary]
inl [constructor, in Coq.Init.Datatypes]
inleft [constructor, in Coq.Init.Specif]
inleftT [constructor, in Coq.Reals.TypeSyntax]
INR [definition, in Coq.Reals.Raxioms]
InR [inductive, in Coq.Lists.TheoryList]
inr [constructor, in Coq.Init.Datatypes]
inright [constructor, in Coq.Init.Specif]
inrightT [constructor, in Coq.Reals.TypeSyntax]
INR2 [definition, in Coq.Reals.Rbase]
InR_app_or [lemma, in Coq.Lists.TheoryList]
InR_cons_inv [lemma, in Coq.Lists.TheoryList]
INR_eq [lemma, in Coq.Reals.Rbase]
INR_eq_INR2 [lemma, in Coq.Reals.Rbase]
INR_fact_neq_0 [lemma, in Coq.Reals.Rfunctions]
inR_hd [constructor, in Coq.Lists.TheoryList]
InR_INV [lemma, in Coq.Lists.TheoryList]
InR_inv [definition, in Coq.Lists.TheoryList]
INR_IZR_INZ [lemma, in Coq.Reals.Rbase]
INR_le [lemma, in Coq.Reals.Rbase]
INR_lt [lemma, in Coq.Reals.Rbase]
INR_lt_1 [lemma, in Coq.Reals.Rbase]
InR_or_app [lemma, in Coq.Lists.TheoryList]
INR_pos [lemma, in Coq.Reals.Rbase]
inR_tl [constructor, in Coq.Lists.TheoryList]
insert [lemma, in Coq.Sorting.Heap]
insert_exist [constructor, in Coq.Sorting.Heap]
insert_spec [inductive, in Coq.Sorting.Heap]
inser_trans_R [lemma, in Coq.Reals.Rbase]
inst [lemma, in Coq.Init.Logic_Type]
Integers [inductive, in Coq.Sets.Integers]
Integers [module]
Integers_defn [constructor, in Coq.Sets.Integers]
Integers_has_no_ub [lemma, in Coq.Sets.Integers]
Integers_infinite [lemma, in Coq.Sets.Integers]
Intersection [inductive, in Coq.Sets.Ensembles]
Intersection_commutative [lemma, in Coq.Sets.Powerset_facts]
Intersection_decreases_l [lemma, in Coq.Sets.Powerset]
Intersection_decreases_r [lemma, in Coq.Sets.Powerset]
Intersection_intro [constructor, in Coq.Sets.Ensembles]
Intersection_inv [lemma, in Coq.Sets.Constructive_sets]
Intersection_is_Glb [lemma, in Coq.Sets.Powerset]
Intersection_maximal [lemma, in Coq.Sets.Powerset]
Intersection_preserves_finite [lemma, in Coq.Sets.Finite_sets_facts]
interval_split [lemma, in Coq.IntMap.Lsort]
intro_Z [lemma, in Coq.ZArith.auxiliary]
Int_part [definition, in Coq.Reals.R_Ifp]
Int_part_INR [lemma, in Coq.Reals.R_Ifp]
Inverse_Image [module]
inverse_image_of_eq [lemma, in Coq.Relations.Relations]
inverse_image_of_equivalence [lemma, in Coq.Relations.Relations]
invert_heap [lemma, in Coq.Sorting.Heap]
inv_continuity [lemma, in Coq.Reals.Ranalysis]
inv_continuous [lemma, in Coq.Reals.Ranalysis]
INZ [definition, in Coq.Reals.Rbase]
in_app_or [lemma, in Coq.Lists.List]
in_app_or [lemma, in Coq.Lists.PolyList]
in_cons [lemma, in Coq.Lists.PolyList]
in_cons [lemma, in Coq.Lists.List]
In_dec [lemma, in Coq.Lists.PolyList]
in_dom [definition, in Coq.IntMap.Fset]
in_dom_delta [lemma, in Coq.IntMap.Fset]
in_dom_DMerge_1 [lemma, in Coq.IntMap.Mapfold]
in_dom_DMerge_2 [lemma, in Coq.IntMap.Mapfold]
in_dom_DMerge_3 [lemma, in Coq.IntMap.Mapfold]
in_dom_merge [lemma, in Coq.IntMap.Fset]
in_dom_M0 [lemma, in Coq.IntMap.Fset]
in_dom_M1 [lemma, in Coq.IntMap.Fset]
in_dom_M1_1 [lemma, in Coq.IntMap.Fset]
in_dom_M1_2 [lemma, in Coq.IntMap.Fset]
in_dom_none [lemma, in Coq.IntMap.Fset]
in_dom_put [lemma, in Coq.IntMap.Fset]
in_dom_put_behind [lemma, in Coq.IntMap.Fset]
in_dom_remove [lemma, in Coq.IntMap.Fset]
in_dom_restrby [lemma, in Coq.IntMap.Fset]
in_dom_restrto [lemma, in Coq.IntMap.Fset]
in_dom_some [lemma, in Coq.IntMap.Fset]
in_eq [lemma, in Coq.Lists.List]
in_eq [lemma, in Coq.Lists.PolyList]
in_FSet [definition, in Coq.IntMap.Fset]
in_FSet_delta [lemma, in Coq.IntMap.Fset]
in_FSet_diff [lemma, in Coq.IntMap.Fset]
in_FSet_inter [lemma, in Coq.IntMap.Fset]
in_FSet_union [lemma, in Coq.IntMap.Fset]
in_hd [constructor, in Coq.Lists.TheoryList]
In_Image_elim [lemma, in Coq.Sets.Image]
in_int [definition, in Coq.Arith.Between]
in_int_between [lemma, in Coq.Arith.Between]
in_int_exists [lemma, in Coq.Arith.Between]
in_int_intro [lemma, in Coq.Arith.Between]
in_int_lt [lemma, in Coq.Arith.Between]
in_int_p_Sq [lemma, in Coq.Arith.Between]
in_int_S [lemma, in Coq.Arith.Between]
in_int_Sp_q [lemma, in Coq.Arith.Between]
in_inv [lemma, in Coq.Lists.PolyList]
In_In_spec [lemma, in Coq.Lists.TheoryList]
in_map [lemma, in Coq.Lists.PolyList]
in_nil [lemma, in Coq.Lists.PolyList]
in_or_app [lemma, in Coq.Lists.List]
in_or_app [lemma, in Coq.Lists.PolyList]
in_prod [lemma, in Coq.Lists.PolyList]
in_prod_aux [lemma, in Coq.Lists.PolyList]
In_singleton [constructor, in Coq.Sets.Ensembles]
In_spec [inductive, in Coq.Lists.TheoryList]
in_tl [constructor, in Coq.Lists.TheoryList]
Isnil [definition, in Coq.Lists.TheoryList]
Isnil_dec [lemma, in Coq.Lists.TheoryList]
Isnil_nil [lemma, in Coq.Lists.TheoryList]
isometric_rotation [lemma, in Coq.Reals.Rgeom]
isometric_rotation_0 [lemma, in Coq.Reals.Rgeom]
isometric_rot_trans [lemma, in Coq.Reals.Rgeom]
isometric_translation [lemma, in Coq.Reals.Rgeom]
isometric_trans_rot [lemma, in Coq.Reals.Rgeom]
Isrealint [tactic definition, in Coq.Reals.DiscrR]
IsSucc [definition, in Coq.Init.Peano]
is_double_moins_un [lemma, in Coq.ZArith.fast_integer]
is_heap [inductive, in Coq.Sorting.Heap]
is_heap_rec [lemma, in Coq.Sorting.Heap]
is_lub [definition, in Coq.Reals.Raxioms]
Is_power [definition, in Coq.ZArith.Zlogarithm]
Is_power_correct [lemma, in Coq.ZArith.Zlogarithm]
Is_power_or [lemma, in Coq.ZArith.Zlogarithm]
Is_true [definition, in Coq.Bool.Bool]
Is_true_eq_left [lemma, in Coq.Bool.Bool]
Is_true_eq_right [lemma, in Coq.Bool.Bool]
Is_true_eq_true [lemma, in Coq.Bool.Bool]
Is_true_eq_true2 [lemma, in Coq.Bool.Bool]
is_upper_bound [definition, in Coq.Reals.Raxioms]
IT [constructor, in Coq.Init.Logic_Type]
Item [lemma, in Coq.Lists.TheoryList]
iter [definition, in Coq.ZArith.Zmisc]
iter_convert [lemma, in Coq.ZArith.Zmisc]
iter_nat [definition, in Coq.ZArith.Zmisc]
iter_nat_invariant [lemma, in Coq.ZArith.Zmisc]
iter_nat_plus [lemma, in Coq.ZArith.Zmisc]
iter_pos [definition, in Coq.ZArith.Zmisc]
iter_pos_add [lemma, in Coq.ZArith.Zmisc]
iter_pos_invariant [lemma, in Coq.ZArith.Zmisc]
IZN [lemma, in Coq.Reals.Rbase]
IZR [definition, in Coq.Reals.Raxioms]
IZR_ge [lemma, in Coq.Reals.Rbase]
IZR_le [lemma, in Coq.Reals.Rbase]
IZR_lt [lemma, in Coq.Reals.Rbase]

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)