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 | _ | other | (22807 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 | _ | other | (926 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 | _ | other | (737 entries)
Variable 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 | _ | other | (2009 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 | _ | other | (494 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 | _ | other | (10305 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 | _ | other | (686 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 | _ | other | (747 entries)
Projection 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 | _ | other | (364 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 | _ | other | (276 entries)
Section 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 | _ | other | (457 entries)
Instance 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 | _ | other | (705 entries)
Abbreviation 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 | _ | other | (1332 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 | _ | other | (3641 entries)
Record 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 | _ | other | (128 entries)

## A (lemma)

AbsList_P2 [in Coq.Reals.RList]
AbsList_P1 [in Coq.Reals.RList]
absorption_orb [in Coq.Bool.Bool]
absorption_andb [in Coq.Bool.Bool]
absurd [in Coq.Init.Logic]
absurd_set [in Coq.Init.Specif]
absurd_PCond_bottom [in Coq.setoid_ring.Field_theory]
absurd_eq_true [in Coq.Bool.Bool]
absurd_eq_bool [in Coq.Bool.Bool]
abs_IZR [in Coq.Reals.Rbasic_fun]
AC [in Coq.Logic.Berardi]
acc_lt_rel [in Coq.Arith.Wf_nat]
Acc_incl [in Coq.Wellfounded.Inclusion]
Acc_union [in Coq.Wellfounded.Union]
acc_B_sum [in Coq.Wellfounded.Disjoint_Union]
acc_A_sum [in Coq.Wellfounded.Disjoint_Union]
Acc_swapprod [in Coq.Wellfounded.Lexicographic_Product]
Acc_symprod [in Coq.Wellfounded.Lexicographic_Product]
acc_A_B_lexprod [in Coq.Wellfounded.Lexicographic_Product]
Acc_inv [in Coq.Init.Wf]
Acc_inverse_rel [in Coq.Wellfounded.Inverse_Image]
Acc_inverse_image [in Coq.Wellfounded.Inverse_Image]
Acc_lemma [in Coq.Wellfounded.Inverse_Image]
acc_implies_P_eventually [in Coq.Logic.ConstructiveEpsilon]
Acc_inv_trans [in Coq.Wellfounded.Transitive_Closure]
Acc_clos_trans [in Coq.Wellfounded.Transitive_Closure]
acc_app [in Coq.Wellfounded.Lexicographic_Exponentiation]
AC_bool_subset_to_bool [in Coq.Logic.Diaconescu]
AC_IF [in Coq.Logic.Berardi]
addmuldiv31_equiv [in Coq.Numbers.Cyclic.Int31.Cyclic31]
add_inj_r [in Coq.setoid_ring.Field_theory]
Add_preserves_Finite [in Coq.Sets.Finite_sets_facts]
Add_inv [in Coq.Sets.Constructive_sets]
Add_not_Empty [in Coq.Sets.Constructive_sets]
Add_intro2 [in Coq.Sets.Constructive_sets]
Add_intro1 [in Coq.Sets.Constructive_sets]
add_term_correct [in Coq.micromega.Tauto]
add_mult_mult_2 [in Coq.Numbers.Cyclic.DoubleCyclic.DoubleSqrt]
add_mult_div_2_plus_1 [in Coq.Numbers.Cyclic.DoubleCyclic.DoubleSqrt]
add_mult_div_2 [in Coq.Numbers.Cyclic.DoubleCyclic.DoubleSqrt]
add_mult_dev_ok [in Coq.setoid_ring.Ring_polynom]
add_pow_list_ok [in Coq.setoid_ring.Ring_polynom]
Add_distributes [in Coq.Sets.Powerset_facts]
Add_commutative' [in Coq.Sets.Powerset_facts]
Add_commutative [in Coq.Sets.Powerset_facts]
Add_covers [in Coq.Sets.Powerset_Classical_facts]
add_soustr_xy [in Coq.Sets.Powerset_Classical_facts]
add_soustr_1 [in Coq.Sets.Powerset_Classical_facts]
add_soustr_2 [in Coq.Sets.Powerset_Classical_facts]
Add_inv [in Coq.Lists.List]
Add_length [in Coq.Lists.List]
Add_in [in Coq.Lists.List]
Add_split [in Coq.Lists.List]
Add_app [in Coq.Lists.List]
adherence_P4 [in Coq.Reals.Rtopology]
adherence_P3 [in Coq.Reals.Rtopology]
adherence_P2 [in Coq.Reals.Rtopology]
adherence_P1 [in Coq.Reals.Rtopology]
AlembertC3_step2 [in Coq.Reals.Alembert]
AlembertC3_step1 [in Coq.Reals.Alembert]
Alembert_sin [in Coq.Reals.Rtrigo_def]
Alembert_cos [in Coq.Reals.Rtrigo_def]
Alembert_C6 [in Coq.Reals.Alembert]
Alembert_C5 [in Coq.Reals.Alembert]
Alembert_C4 [in Coq.Reals.Alembert]
Alembert_C3 [in Coq.Reals.Alembert]
Alembert_C2 [in Coq.Reals.Alembert]
Alembert_C1 [in Coq.Reals.Alembert]
Alembert_exp [in Coq.Reals.Rtrigo_fun]
all_not_not_ex [in Coq.Logic.Classical_Pred_Type]
alternated_series_ineq [in Coq.Reals.AltSeries]
alternated_series [in Coq.Reals.AltSeries]
Alt_PI_RGT_0 [in Coq.Reals.AltSeries]
Alt_PI_ineq [in Coq.Reals.AltSeries]
Alt_PI_eq [in Coq.Reals.Ratan]
Alt_PI_tg [in Coq.Reals.Ratan]
Alt_CVU [in Coq.Reals.Ratan]
Alt_first_term_bound [in Coq.Reals.Ratan]
andb_true_intro [in Coq.Init.Datatypes]
andb_prop [in Coq.Init.Datatypes]
andb_lazy_alt [in Coq.Bool.Bool]
andb_if [in Coq.Bool.Bool]
andb_prop_elim [in Coq.Bool.Bool]
andb_prop_intro [in Coq.Bool.Bool]
andb_orb_distrib_l [in Coq.Bool.Bool]
andb_orb_distrib_r [in Coq.Bool.Bool]
andb_assoc [in Coq.Bool.Bool]
andb_comm [in Coq.Bool.Bool]
andb_negb_r [in Coq.Bool.Bool]
andb_false_elim [in Coq.Bool.Bool]
andb_true_l [in Coq.Bool.Bool]
andb_true_r [in Coq.Bool.Bool]
andb_diag [in Coq.Bool.Bool]
andb_false_l [in Coq.Bool.Bool]
andb_false_r [in Coq.Bool.Bool]
andb_false_intro2 [in Coq.Bool.Bool]
andb_false_intro1 [in Coq.Bool.Bool]
andb_true_eq [in Coq.Bool.Bool]
andb_false_iff [in Coq.Bool.Bool]
andb_true_iff [in Coq.Bool.Bool]
and_not_or [in Coq.Logic.Classical_Prop]
and_assoc [in Coq.Init.Logic]
and_comm [in Coq.Init.Logic]
and_cancel_r [in Coq.Init.Logic]
and_cancel_l [in Coq.Init.Logic]
and_iff_compat_r [in Coq.Init.Logic]
and_iff_compat_l [in Coq.Init.Logic]
antiderivative_P4 [in Coq.Reals.NewtonInt]
antiderivative_P3 [in Coq.Reals.NewtonInt]
antiderivative_P2 [in Coq.Reals.NewtonInt]
antiderivative_P1 [in Coq.Reals.NewtonInt]
antiderivative_Ucte [in Coq.Reals.MVT]
append_neutral_l [in Coq.FSets.FMapPositive]
append_neutral_r [in Coq.FSets.FMapPositive]
append_assoc_1 [in Coq.FSets.FMapPositive]
append_assoc_0 [in Coq.FSets.FMapPositive]
append_correct2 [in Coq.Strings.String]
append_correct1 [in Coq.Strings.String]
approximants_grow' [in Coq.Sets.Infinite_sets]
approximants_grow [in Coq.Sets.Infinite_sets]
approximant_can_be_any_size [in Coq.Sets.Infinite_sets]
approx_min [in Coq.Reals.SeqProp]
approx_maj [in Coq.Reals.SeqProp]
app_removelast_last [in Coq.Lists.List]
app_nth2 [in Coq.Lists.List]
app_nth1 [in Coq.Lists.List]
app_inv_tail [in Coq.Lists.List]
app_inv_head [in Coq.Lists.List]
app_length [in Coq.Lists.List]
app_inj_tail [in Coq.Lists.List]
app_eq_unit [in Coq.Lists.List]
app_eq_nil [in Coq.Lists.List]
app_comm_cons [in Coq.Lists.List]
app_assoc_reverse [in Coq.Lists.List]
app_assoc [in Coq.Lists.List]
app_nil_end [in Coq.Lists.List]
app_nil_r [in Coq.Lists.List]
app_nil_l [in Coq.Lists.List]
app_cons_not_nil [in Coq.Lists.List]
ARadd_assoc2 [in Coq.setoid_ring.Ring_theory]
ARadd_assoc1 [in Coq.setoid_ring.Ring_theory]
ARadd_0_r [in Coq.setoid_ring.Ring_theory]
archimed_cor1 [in Coq.Reals.Rtrigo_def]
arcsinh_0 [in Coq.Reals.Rpower]
arcsinh_le [in Coq.Reals.Rpower]
arcsinh_lt [in Coq.Reals.Rpower]
arcsinh_sinh [in Coq.Reals.Rpower]
ARdistr_r [in Coq.setoid_ring.Ring_theory]
ARgen_phiPOS_mult [in Coq.setoid_ring.Ncring_initial]
ARgen_phiPOS_add [in Coq.setoid_ring.Ncring_initial]
ARgen_phiPOS_Psucc [in Coq.setoid_ring.Ncring_initial]
ARgen_phiPOS_mult [in Coq.setoid_ring.InitialRing]
ARgen_phiPOS_add [in Coq.setoid_ring.InitialRing]
ARgen_phiPOS_Psucc [in Coq.setoid_ring.InitialRing]
ARmul_assoc2 [in Coq.setoid_ring.Ring_theory]
ARmul_assoc1 [in Coq.setoid_ring.Ring_theory]
ARmul_0_r [in Coq.setoid_ring.Ring_theory]
ARmul_1_r [in Coq.setoid_ring.Ring_theory]
ARopp_zero [in Coq.setoid_ring.Ring_theory]
ARopp_mul_r [in Coq.setoid_ring.Ring_theory]
ARth_SRth [in Coq.setoid_ring.Ring_theory]
ascii_nat_embedding [in Coq.Strings.Ascii]
ascii_N_embedding [in Coq.Strings.Ascii]
atan_sub_correct [in Coq.Reals.Machin]
atan_eq_ps_atan [in Coq.Reals.Ratan]
atan_1 [in Coq.Reals.Ratan]
atan_0 [in Coq.Reals.Ratan]
atan_increasing [in Coq.Reals.Ratan]
atan_opp [in Coq.Reals.Ratan]
atan_right_inv [in Coq.Reals.Ratan]
atan_bound [in Coq.Reals.Ratan]
aux [in Coq.Logic.ClassicalFacts]
AvlProofs.add_avl [in Coq.FSets.FMapFullAVL]
AvlProofs.add_avl_1 [in Coq.FSets.FMapFullAVL]
AvlProofs.avl_node [in Coq.FSets.FMapFullAVL]
AvlProofs.bal_height_2 [in Coq.FSets.FMapFullAVL]
AvlProofs.bal_height_1 [in Coq.FSets.FMapFullAVL]
AvlProofs.bal_avl [in Coq.FSets.FMapFullAVL]
AvlProofs.concat_avl [in Coq.FSets.FMapFullAVL]
AvlProofs.create_height [in Coq.FSets.FMapFullAVL]
AvlProofs.create_avl [in Coq.FSets.FMapFullAVL]
AvlProofs.empty_avl [in Coq.FSets.FMapFullAVL]
AvlProofs.height_0 [in Coq.FSets.FMapFullAVL]
AvlProofs.height_non_negative [in Coq.FSets.FMapFullAVL]
AvlProofs.join_avl [in Coq.FSets.FMapFullAVL]
AvlProofs.join_avl_1 [in Coq.FSets.FMapFullAVL]
AvlProofs.mapi_avl [in Coq.FSets.FMapFullAVL]
AvlProofs.mapi_height [in Coq.FSets.FMapFullAVL]
AvlProofs.map_option_avl [in Coq.FSets.FMapFullAVL]
AvlProofs.map_avl [in Coq.FSets.FMapFullAVL]
AvlProofs.map_height [in Coq.FSets.FMapFullAVL]
AvlProofs.map2_avl [in Coq.FSets.FMapFullAVL]
AvlProofs.map2_opt_avl [in Coq.FSets.FMapFullAVL]
AvlProofs.merge_avl [in Coq.FSets.FMapFullAVL]
AvlProofs.merge_avl_1 [in Coq.FSets.FMapFullAVL]
AvlProofs.remove_avl [in Coq.FSets.FMapFullAVL]
AvlProofs.remove_avl_1 [in Coq.FSets.FMapFullAVL]
AvlProofs.remove_min_avl [in Coq.FSets.FMapFullAVL]
AvlProofs.remove_min_avl_1 [in Coq.FSets.FMapFullAVL]
AvlProofs.split_avl [in Coq.FSets.FMapFullAVL]
A1_cvg [in Coq.Reals.Cos_rel]

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 | _ | other | (22807 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 | _ | other | (926 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 | _ | other | (737 entries)
Variable 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 | _ | other | (2009 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 | _ | other | (494 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 | _ | other | (10305 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 | _ | other | (686 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 | _ | other | (747 entries)
Projection 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 | _ | other | (364 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 | _ | other | (276 entries)
Section 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 | _ | other | (457 entries)
Instance 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 | _ | other | (705 entries)
Abbreviation 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 | _ | other | (1332 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 | _ | other | (3641 entries)
Record 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 | _ | other | (128 entries)