Documentation Verification Report

Basic

πŸ“ Source: Mathlib/Logic/Basic.lean

Statistics

MetricCount
DefinitionsbyContradiction', choice_of_byContradiction', dec, decEq, decPred, decRel, existsCases, classicalRecOn, Fact, swapβ‚‚, eq, decidable_arguments, decidable_namespace, Β«fact_non-instancesΒ», Xor', decidableEq_of_subsingleton, hidden, instDecidableFact, instDecidableXor'
19
Theoremsexists, rotate, imp_left, imp_right, elim, imp_left, imp_right, intro, axiom_of_choice, by_cases, by_contradiction, choose_eq, choose_eq', prop_complete, some_specβ‚‚, and_forall_ne, eq_or_ne, forall_or_left, forall_or_right, ne_or_eq, not_forallβ‚‚, or_not_of_imp, rec_eq_cast, trans_ne, fst, snd, imp, imp, elim, out, mt, mtr, and, iff, imp, ne, ne_left, ne_right, not, not_left, not_right, or, swap, ne_of_notMem, ne_of_notMem', dite_eq_left_iff, dite_eq_right_iff, dite_ne_left_iff, dite_ne_right_iff, ite_eq_left_iff, ite_eq_right_iff, ite_ne_left_iff, ite_ne_right_iff, ne_or_ne, trans_eq, decidable_imp_symm, imp_symm, elim3, imp3, rotate, exists_iff, forall_iff, or, and_forall_ne, and_iff_not_or_not, and_or_imp, and_symm_left, and_symm_right, apply_diteβ‚‚, apply_ite_left, apply_iteβ‚‚, beq_eq_beq, beq_eq_decide, beq_ext, beq_ext_iff, bex_def, by_cases, by_contra, by_contradiction, cast_heq_iff_heq, congr_arg_heq, congr_arg_refl, congr_fun_congr_arg, congr_fun_rfl, congr_heq, congr_refl_left, congr_refl_right, dcongr_heq, dec_em, dec_em', dite_apply, dite_dite_comm, dite_eq_iff, dite_eq_iff', dite_eq_or_eq, dite_mem, dite_ne_left_iff, dite_ne_right_iff, dite_prop_iff_and, dite_prop_iff_or, em, em', eqRec_heq', eq_cast_iff_heq, eq_equivalence, eq_false_intro, eq_iff_eq_cancel_left, eq_iff_eq_cancel_right, eq_ite_iff, eq_or_ne, eq_true_intro, exists_and_exists_comm, exists_apply_eq, exists_apply_eq_apply', exists_apply_eq_apply2, exists_apply_eq_apply2', exists_apply_eq_apply3, exists_apply_eq_apply3', exists_exists_and_eq_and, exists_exists_and_exists_and_eq_and, exists_exists_eq_and, exists_exists_exists_and_eq, exists_iff_of_forall, exists_mem_of_exists, exists_mem_or, exists_mem_or_left, exists_of_exists_mem, exists_or_forall_not, exists_prop_of_false, exists_swap, existsβ‚‚_comm, fact_iff, forall_and_index, forall_and_index', forall_and_left, forall_and_right, forall_apply_eq_imp_iff', forall_cond_comm, forall_eq_apply_imp_iff', forall_imp_iff_exists_imp, forall_mem_comm, forall_or_exists_not, forall_or_left, forall_or_of_or_forall, forall_or_right, forall_prop_congr, forall_prop_congr', forall_swap, forall_true_iff, forall_true_iff', forall_true_left, forallβ‚‚_and, forallβ‚‚_imp, forallβ‚‚_or_left, forallβ‚‚_swap, forallβ‚‚_true_iff, forall₃_imp, forall₃_true_iff, heq_cast_iff_heq, heq_iff_exists_cast_eq, heq_iff_exists_eq_cast, heq_of_eq_cast, heq_rec_iff_heq, if_congr, if_ctx_congr, iff_eq_eq, iff_iff_and_or_not_and_not, iff_iff_not_or_and_or_not, iff_mpr_iff_true_intro, iff_not_comm, imp_and_neg_imp_iff, imp_congr_ctx_eq, imp_congr_eq, imp_forall_iff, imp_forall_iff_forall, imp_iff_not_or, imp_iff_or_not, imp_iff_right_iff, imp_or, imp_or', instCommutativeXor', instSubsingletonSubtype_mathlib, ite_and, ite_apply, ite_eq_iff, ite_eq_iff', ite_eq_or_eq, ite_ite_comm, ite_mem, ite_ne_left_iff, ite_ne_right_iff, ite_or, ite_prop_iff_and, ite_prop_iff_or, lawful_beq_subsingleton, mem_dite, mem_ite, ne_and_eq_iff_right, ne_of_eq_of_ne, ne_of_ne_of_eq, ne_or_eq, not_and_not_right, not_and_or, not_beq_of_ne, not_exists_mem, not_forall_not, not_forallβ‚‚, not_forallβ‚‚_of_existsβ‚‚_not, not_iff, not_iff_comm, not_iff_not, not_imp, not_imp_comm, not_imp_not, not_imp_self, not_ne_iff, not_or_of_imp, not_xor, of_not_imp, of_not_not, or_congr_left', or_congr_right', or_iff_not_and_not, or_not, or_not_of_imp, peirce, rec_heq_iff_heq, rec_heq_of_heq, xor_comm, xor_def, xor_false, xor_iff_iff_not, xor_iff_not_iff, xor_iff_not_iff', xor_iff_or_and_not_and, xor_not_left, xor_not_not, xor_not_right, xor_self, xor_true
240
Total259

And

Theorems

NameKindAssumesProvesValidatesDepends On
exists πŸ“–β€”β€”β€”β€”β€”
rotate πŸ“–β€”β€”β€”β€”β€”

BAll

Theorems

NameKindAssumesProvesValidatesDepends On
imp_left πŸ“–β€”β€”β€”β€”β€”
imp_right πŸ“–β€”β€”β€”β€”β€”

BEx

Theorems

NameKindAssumesProvesValidatesDepends On
elim πŸ“–β€”β€”β€”β€”β€”
imp_left πŸ“–β€”β€”β€”β€”β€”
imp_right πŸ“–β€”β€”β€”β€”β€”
intro πŸ“–β€”β€”β€”β€”β€”

Classical

Definitions

NameCategoryTheorems
byContradiction' πŸ“–CompOpβ€”
choice_of_byContradiction' πŸ“–CompOpβ€”
dec πŸ“–CompOpβ€”
decEq πŸ“–CompOpβ€”
decPred πŸ“–CompOp
2 mathmath: Finsupp.supportedEquivFinsupp_apply_support_val, Finsupp.supportedEquivFinsupp_symm_apply_coe_apply
decRel πŸ“–CompOpβ€”
existsCases πŸ“–CompOpβ€”

Theorems

NameKindAssumesProvesValidatesDepends On
axiom_of_choice πŸ“–β€”β€”β€”β€”β€”
by_cases πŸ“–β€”β€”β€”β€”β€”
by_contradiction πŸ“–β€”β€”β€”β€”β€”
choose_eq πŸ“–β€”β€”β€”β€”β€”
choose_eq' πŸ“–β€”β€”β€”β€”β€”
prop_complete πŸ“–β€”β€”β€”β€”β€”
some_specβ‚‚ πŸ“–β€”β€”β€”β€”β€”

Decidable

Theorems

NameKindAssumesProvesValidatesDepends On
and_forall_ne πŸ“–β€”β€”β€”β€”β€”
eq_or_ne πŸ“–β€”β€”β€”β€”dec_em
forall_or_left πŸ“–β€”β€”β€”β€”forall_or_of_or_forall
forall_or_right πŸ“–β€”β€”β€”β€”β€”
ne_or_eq πŸ“–β€”β€”β€”β€”dec_em'
not_forallβ‚‚ πŸ“–β€”β€”β€”β€”Not.decidable_imp_symm
not_forallβ‚‚_of_existsβ‚‚_not
or_not_of_imp πŸ“–β€”β€”β€”β€”β€”

Eq

Theorems

NameKindAssumesProvesValidatesDepends On
rec_eq_cast πŸ“–β€”β€”β€”β€”β€”
trans_ne πŸ“–β€”β€”β€”β€”ne_of_eq_of_ne

Exists

Definitions

NameCategoryTheorems
classicalRecOn πŸ“–CompOpβ€”

Theorems

NameKindAssumesProvesValidatesDepends On
fst πŸ“–β€”β€”β€”β€”β€”
snd πŸ“–mathematicalβ€”fstβ€”fst

Existsβ‚‚

Theorems

NameKindAssumesProvesValidatesDepends On
imp πŸ“–β€”β€”β€”β€”β€”

Exists₃

Theorems

NameKindAssumesProvesValidatesDepends On
imp πŸ“–β€”β€”β€”β€”Existsβ‚‚.imp

Fact

Theorems

NameKindAssumesProvesValidatesDepends On
elim πŸ“–β€”β€”β€”β€”out
out πŸ“–β€”β€”β€”β€”β€”

Function

Definitions

NameCategoryTheorems
swapβ‚‚ πŸ“–CompOpβ€”

Theorems

NameKindAssumesProvesValidatesDepends On
mt πŸ“–β€”β€”β€”β€”β€”
mtr πŸ“–β€”β€”β€”β€”not_imp_not

Iff

Definitions

NameCategoryTheorems
eq πŸ“–CompOpβ€”

Theorems

NameKindAssumesProvesValidatesDepends On
and πŸ“–β€”β€”β€”β€”β€”
iff πŸ“–β€”β€”β€”β€”β€”
imp πŸ“–β€”β€”β€”β€”β€”
ne πŸ“–β€”β€”β€”β€”not
ne_left πŸ“–β€”β€”β€”β€”not_left
ne_right πŸ“–β€”β€”β€”β€”not_right
not πŸ“–β€”β€”β€”β€”β€”
not_left πŸ“–β€”β€”β€”β€”not
not_right πŸ“–β€”β€”β€”β€”not
or πŸ“–β€”β€”β€”β€”β€”

Imp

Theorems

NameKindAssumesProvesValidatesDepends On
swap πŸ“–β€”β€”β€”β€”β€”

LibraryNote

Definitions

NameCategoryTheorems
decidable_arguments πŸ“–CompOpβ€”
decidable_namespace πŸ“–CompOpβ€”
Β«fact_non-instancesΒ» πŸ“–CompOpβ€”

Membership.mem

Theorems

NameKindAssumesProvesValidatesDepends On
ne_of_notMem πŸ“–β€”β€”β€”β€”β€”
ne_of_notMem' πŸ“–β€”β€”β€”β€”β€”

Ne

Theorems

NameKindAssumesProvesValidatesDepends On
dite_eq_left_iff πŸ“–β€”β€”β€”β€”of_not_not
dite_eq_right_iff πŸ“–β€”β€”β€”β€”β€”
dite_ne_left_iff πŸ“–β€”β€”β€”β€”dite_ne_left_iff
exists_iff_of_forall
dite_ne_right_iff πŸ“–β€”β€”β€”β€”dite_ne_right_iff
exists_iff_of_forall
ite_eq_left_iff πŸ“–β€”β€”β€”β€”dite_eq_left_iff
ite_eq_right_iff πŸ“–β€”β€”β€”β€”dite_eq_right_iff
ite_ne_left_iff πŸ“–β€”β€”β€”β€”dite_ne_left_iff
ite_ne_right_iff πŸ“–β€”β€”β€”β€”dite_ne_right_iff
ne_or_ne πŸ“–β€”β€”β€”β€”not_and_or
trans_eq πŸ“–β€”β€”β€”β€”ne_of_ne_of_eq

Not

Theorems

NameKindAssumesProvesValidatesDepends On
decidable_imp_symm πŸ“–β€”β€”β€”β€”β€”
imp_symm πŸ“–β€”β€”β€”β€”decidable_imp_symm

Or

Theorems

NameKindAssumesProvesValidatesDepends On
elim3 πŸ“–β€”β€”β€”β€”β€”
imp3 πŸ“–β€”β€”β€”β€”β€”
rotate πŸ“–β€”β€”β€”β€”β€”

Prop

Theorems

NameKindAssumesProvesValidatesDepends On
exists_iff πŸ“–β€”β€”β€”β€”by_cases
forall_iff πŸ“–β€”β€”β€”β€”β€”

Xor'

Theorems

NameKindAssumesProvesValidatesDepends On
or πŸ“–β€”Xor'β€”β€”β€”

(root)

Definitions

NameCategoryTheorems
Fact πŸ“–CompData
30 mathmath: finrank_real_complex_fact', PNat.instFactPrimeValOfPrime, instFactPrimeValNat, Fintype.card_fin_two, fact_one_le_two_ennreal, EuclideanSpace.instFactEqNatFinrankFin, fact_iff, CharP.exists', CharP.char_is_prime_of_pos, Rat.AbsoluteValue.equiv_real_or_padic, fact_one_le_top_ennreal, Polynomial.fact_irreducible_factor, CategoryTheory.MorphismProperty.smallObjectΞΊ_isRegular, PNat.fact_prime_two, instFactIsCuspInftyRealOfIsArithmetic, Nat.Prime.one_lt', ZeroLEOneClass.factZeroLtOne, fact_one_le_one_ennreal, PNat.fact_prime_five, Nat.fact_prime_two, Nat.fact_prime_three, Complex.finrank_real_complex_fact, Rat.AbsoluteValue.equiv_padic_of_bounded, PNat.fact_prime_three, Fact.Manifold.instLeReal, Polynomial.instTwoPiPos, instFactMemSetQuasispectrumOfNat, Polynomial.Gal.splits_β„š_β„‚, Cardinal.fact_isRegular_aleph0, ZeroLEOneClass.factZeroLeOne
Xor' πŸ“–MathDef
38 mathmath: Finset.prod_filter_xor, xor_not_right, Int.even_xor'_odd, xor_not_not, Bool.coe_xor_iff, IsMIntegralCurve.periodic_xor_injective, xor_iff_not_iff, xor_not_left, not_inseparable_iff_exists_open, xor_comm, xor_self, xor_def, xor_true, Int.even_xor'_odd', instCommutativeXor', Subgroup.relIndex_eq_two_iff, Finset.sum_filter_xor, Subgroup.index_eq_two_iff, xor_iff_iff_not, AddSubgroup.index_eq_two_iff', Finset.mem_union_of_disjoint, xor_iff_or_and_not_and, exists_isOpen_xor'_mem, t0Space_iff_exists_isOpen_xor'_mem, Subgroup.relIindex_eq_two_iff', not_xor, Nat.even_xor_odd, AddSubgroup.relIindex_eq_two_iff', symmDiff_eq_Xor', Subgroup.index_eq_two_iff', AddSubgroup.index_eq_two_iff, xor_iff_not_iff', Subgroup.dense_xor'_cyclic, Nat.even_xor_odd', xor_false, AddSubgroup.dense_xor'_cyclic, Set.mem_union_of_disjoint, AddSubgroup.relIndex_eq_two_iff
decidableEq_of_subsingleton πŸ“–CompOp
7 mathmath: Matrix.det_add_replicateCol_mul_replicateRow, PiTensorProduct.subsingletonEquiv_symm_apply, Matrix.uniqueAlgEquiv_apply, Matrix.uniqueAlgEquiv_symm_apply, LinearMap.toMatrix_singleton, Matrix.updateCol_subsingleton, Matrix.updateRow_subsingleton
hidden πŸ“–CompOpβ€”
instDecidableFact πŸ“–CompOpβ€”
instDecidableXor' πŸ“–CompOp
2 mathmath: Finset.prod_filter_xor, Finset.sum_filter_xor

Theorems

NameKindAssumesProvesValidatesDepends On
and_forall_ne πŸ“–β€”β€”β€”β€”Decidable.and_forall_ne
and_iff_not_or_not πŸ“–β€”β€”β€”β€”β€”
and_or_imp πŸ“–β€”β€”β€”β€”β€”
and_symm_left πŸ“–β€”β€”β€”β€”β€”
and_symm_right πŸ“–β€”β€”β€”β€”β€”
apply_diteβ‚‚ πŸ“–β€”β€”β€”β€”β€”
apply_ite_left πŸ“–β€”β€”β€”β€”β€”
apply_iteβ‚‚ πŸ“–β€”β€”β€”β€”apply_diteβ‚‚
beq_eq_beq πŸ“–β€”β€”β€”β€”β€”
beq_eq_decide πŸ“–β€”β€”β€”β€”β€”
beq_ext πŸ“–β€”β€”β€”β€”β€”
beq_ext_iff πŸ“–β€”β€”β€”β€”beq_ext
bex_def πŸ“–β€”β€”β€”β€”β€”
by_cases πŸ“–β€”β€”β€”β€”β€”
by_contra πŸ“–β€”β€”β€”β€”by_contradiction
by_contradiction πŸ“–β€”β€”β€”β€”β€”
cast_heq_iff_heq πŸ“–β€”β€”β€”β€”β€”
congr_arg_heq πŸ“–β€”β€”β€”β€”β€”
congr_arg_refl πŸ“–β€”β€”β€”β€”β€”
congr_fun_congr_arg πŸ“–β€”β€”β€”β€”β€”
congr_fun_rfl πŸ“–β€”β€”β€”β€”β€”
congr_heq πŸ“–β€”β€”β€”β€”β€”
congr_refl_left πŸ“–β€”β€”β€”β€”β€”
congr_refl_right πŸ“–β€”β€”β€”β€”β€”
dcongr_heq πŸ“–β€”β€”β€”β€”β€”
dec_em πŸ“–β€”β€”β€”β€”β€”
dec_em' πŸ“–β€”β€”β€”β€”dec_em
dite_apply πŸ“–β€”β€”β€”β€”β€”
dite_dite_comm πŸ“–β€”β€”β€”β€”β€”
dite_eq_iff πŸ“–β€”β€”β€”β€”β€”
dite_eq_iff' πŸ“–β€”β€”β€”β€”em
dite_eq_or_eq πŸ“–β€”β€”β€”β€”β€”
dite_mem πŸ“–β€”β€”β€”β€”β€”
dite_ne_left_iff πŸ“–β€”β€”β€”β€”β€”
dite_ne_right_iff πŸ“–β€”β€”β€”β€”β€”
dite_prop_iff_and πŸ“–β€”β€”β€”β€”β€”
dite_prop_iff_or πŸ“–β€”β€”β€”β€”β€”
em πŸ“–β€”β€”β€”β€”β€”
em' πŸ“–β€”β€”β€”β€”em
eqRec_heq' πŸ“–β€”β€”β€”β€”β€”
eq_cast_iff_heq πŸ“–β€”β€”β€”β€”heq_of_eq_cast
eq_equivalence πŸ“–β€”β€”β€”β€”β€”
eq_false_intro πŸ“–β€”β€”β€”β€”β€”
eq_iff_eq_cancel_left πŸ“–β€”β€”β€”β€”β€”
eq_iff_eq_cancel_right πŸ“–β€”β€”β€”β€”β€”
eq_ite_iff πŸ“–β€”β€”β€”β€”ite_eq_iff
Iff.or
Iff.and
eq_or_ne πŸ“–β€”β€”β€”β€”em
eq_true_intro πŸ“–β€”β€”β€”β€”β€”
exists_and_exists_comm πŸ“–β€”β€”β€”β€”β€”
exists_apply_eq πŸ“–β€”β€”β€”β€”β€”
exists_apply_eq_apply' πŸ“–β€”β€”β€”β€”β€”
exists_apply_eq_apply2 πŸ“–β€”β€”β€”β€”β€”
exists_apply_eq_apply2' πŸ“–β€”β€”β€”β€”β€”
exists_apply_eq_apply3 πŸ“–β€”β€”β€”β€”β€”
exists_apply_eq_apply3' πŸ“–β€”β€”β€”β€”β€”
exists_exists_and_eq_and πŸ“–β€”β€”β€”β€”β€”
exists_exists_and_exists_and_eq_and πŸ“–β€”β€”β€”β€”β€”
exists_exists_eq_and πŸ“–β€”β€”β€”β€”β€”
exists_exists_exists_and_eq πŸ“–β€”β€”β€”β€”β€”
exists_iff_of_forall πŸ“–β€”β€”β€”β€”Exists.fst
exists_mem_of_exists πŸ“–β€”β€”β€”β€”β€”
exists_mem_or πŸ“–β€”β€”β€”β€”β€”
exists_mem_or_left πŸ“–β€”β€”β€”β€”β€”
exists_of_exists_mem πŸ“–β€”β€”β€”β€”β€”
exists_or_forall_not πŸ“–β€”β€”β€”β€”em
exists_prop_of_false πŸ“–β€”β€”β€”β€”Exists.fst
exists_swap πŸ“–β€”β€”β€”β€”β€”
existsβ‚‚_comm πŸ“–β€”β€”β€”β€”β€”
fact_iff πŸ“–mathematicalβ€”Factβ€”Fact.out
forall_and_index πŸ“–β€”β€”β€”β€”β€”
forall_and_index' πŸ“–β€”β€”β€”β€”forall_and_index
forall_and_left πŸ“–β€”β€”β€”β€”β€”
forall_and_right πŸ“–β€”β€”β€”β€”β€”
forall_apply_eq_imp_iff' πŸ“–β€”β€”β€”β€”β€”
forall_cond_comm πŸ“–β€”β€”β€”β€”β€”
forall_eq_apply_imp_iff' πŸ“–β€”β€”β€”β€”β€”
forall_imp_iff_exists_imp πŸ“–β€”β€”β€”β€”not_forall_not
forall_mem_comm πŸ“–β€”β€”β€”β€”forall_cond_comm
forall_or_exists_not πŸ“–β€”β€”β€”β€”em
forall_or_left πŸ“–β€”β€”β€”β€”Decidable.forall_or_left
forall_or_of_or_forall πŸ“–β€”β€”β€”β€”β€”
forall_or_right πŸ“–β€”β€”β€”β€”Decidable.forall_or_right
forall_prop_congr πŸ“–β€”β€”β€”β€”β€”
forall_prop_congr' πŸ“–β€”β€”β€”β€”forall_prop_congr
forall_swap πŸ“–β€”β€”β€”β€”β€”
forall_true_iff πŸ“–β€”β€”β€”β€”β€”
forall_true_iff' πŸ“–β€”β€”β€”β€”β€”
forall_true_left πŸ“–β€”β€”β€”β€”β€”
forallβ‚‚_and πŸ“–β€”β€”β€”β€”β€”
forallβ‚‚_imp πŸ“–β€”β€”β€”β€”β€”
forallβ‚‚_or_left πŸ“–β€”β€”β€”β€”β€”
forallβ‚‚_swap πŸ“–β€”β€”β€”β€”β€”
forallβ‚‚_true_iff πŸ“–β€”β€”β€”β€”β€”
forall₃_imp πŸ“–β€”β€”β€”β€”forallβ‚‚_imp
forall₃_true_iff πŸ“–β€”β€”β€”β€”β€”
heq_cast_iff_heq πŸ“–β€”β€”β€”β€”β€”
heq_iff_exists_cast_eq πŸ“–β€”β€”β€”β€”β€”
heq_iff_exists_eq_cast πŸ“–β€”β€”β€”β€”eq_cast_iff_heq
heq_of_eq_cast πŸ“–β€”β€”β€”β€”β€”
heq_rec_iff_heq πŸ“–β€”β€”β€”β€”β€”
if_congr πŸ“–β€”β€”β€”β€”if_ctx_congr
if_ctx_congr πŸ“–β€”β€”β€”β€”β€”
iff_eq_eq πŸ“–β€”β€”β€”β€”β€”
iff_iff_and_or_not_and_not πŸ“–β€”β€”β€”β€”β€”
iff_iff_not_or_and_or_not πŸ“–β€”β€”β€”β€”β€”
iff_mpr_iff_true_intro πŸ“–β€”β€”β€”β€”β€”
iff_not_comm πŸ“–β€”β€”β€”β€”β€”
imp_and_neg_imp_iff πŸ“–β€”β€”β€”β€”β€”
imp_congr_ctx_eq πŸ“–β€”β€”β€”β€”β€”
imp_congr_eq πŸ“–β€”β€”β€”β€”β€”
imp_forall_iff πŸ“–β€”β€”β€”β€”forall_swap
imp_forall_iff_forall πŸ“–β€”β€”β€”β€”β€”
imp_iff_not_or πŸ“–β€”β€”β€”β€”β€”
imp_iff_or_not πŸ“–β€”β€”β€”β€”β€”
imp_iff_right_iff πŸ“–β€”β€”β€”β€”β€”
imp_or πŸ“–β€”β€”β€”β€”β€”
imp_or' πŸ“–β€”β€”β€”β€”β€”
instCommutativeXor' πŸ“–mathematicalβ€”Xor'β€”xor_comm
instSubsingletonSubtype_mathlib πŸ“–β€”β€”β€”β€”β€”
ite_and πŸ“–β€”β€”β€”β€”β€”
ite_apply πŸ“–β€”β€”β€”β€”dite_apply
ite_eq_iff πŸ“–β€”β€”β€”β€”dite_eq_iff
ite_eq_iff' πŸ“–β€”β€”β€”β€”dite_eq_iff'
ite_eq_or_eq πŸ“–β€”β€”β€”β€”β€”
ite_ite_comm πŸ“–β€”β€”β€”β€”dite_dite_comm
ite_mem πŸ“–β€”β€”β€”β€”dite_mem
ite_ne_left_iff πŸ“–β€”β€”β€”β€”dite_ne_left_iff
ite_ne_right_iff πŸ“–β€”β€”β€”β€”dite_ne_right_iff
ite_or πŸ“–β€”β€”β€”β€”β€”
ite_prop_iff_and πŸ“–β€”β€”β€”β€”β€”
ite_prop_iff_or πŸ“–β€”β€”β€”β€”β€”
lawful_beq_subsingleton πŸ“–β€”β€”β€”β€”beq_ext
mem_dite πŸ“–β€”β€”β€”β€”β€”
mem_ite πŸ“–β€”β€”β€”β€”mem_dite
ne_and_eq_iff_right πŸ“–β€”β€”β€”β€”β€”
ne_of_eq_of_ne πŸ“–β€”β€”β€”β€”β€”
ne_of_ne_of_eq πŸ“–β€”β€”β€”β€”β€”
ne_or_eq πŸ“–β€”β€”β€”β€”em'
not_and_not_right πŸ“–β€”β€”β€”β€”β€”
not_and_or πŸ“–β€”β€”β€”β€”β€”
not_beq_of_ne πŸ“–β€”β€”β€”β€”β€”
not_exists_mem πŸ“–β€”β€”β€”β€”β€”
not_forall_not πŸ“–β€”β€”β€”β€”β€”
not_forallβ‚‚ πŸ“–β€”β€”β€”β€”Decidable.not_forallβ‚‚
not_forallβ‚‚_of_existsβ‚‚_not πŸ“–β€”β€”β€”β€”β€”
not_iff πŸ“–β€”β€”β€”β€”β€”
not_iff_comm πŸ“–β€”β€”β€”β€”β€”
not_iff_not πŸ“–β€”β€”β€”β€”β€”
not_imp πŸ“–β€”β€”β€”β€”β€”
not_imp_comm πŸ“–β€”β€”β€”β€”β€”
not_imp_not πŸ“–β€”β€”β€”β€”β€”
not_imp_self πŸ“–β€”β€”β€”β€”β€”
not_ne_iff πŸ“–β€”β€”β€”β€”β€”
not_or_of_imp πŸ“–β€”β€”β€”β€”β€”
not_xor πŸ“–mathematicalβ€”Xor'β€”β€”
of_not_imp πŸ“–β€”β€”β€”β€”β€”
of_not_not πŸ“–β€”β€”β€”β€”by_contra
or_congr_left' πŸ“–β€”β€”β€”β€”β€”
or_congr_right' πŸ“–β€”β€”β€”β€”β€”
or_iff_not_and_not πŸ“–β€”β€”β€”β€”β€”
or_not πŸ“–β€”β€”β€”β€”em
or_not_of_imp πŸ“–β€”β€”β€”β€”Decidable.or_not_of_imp
peirce πŸ“–β€”β€”β€”β€”β€”
rec_heq_iff_heq πŸ“–β€”β€”β€”β€”β€”
rec_heq_of_heq πŸ“–β€”β€”β€”β€”β€”
xor_comm πŸ“–mathematicalβ€”Xor'β€”β€”
xor_def πŸ“–mathematicalβ€”Xor'β€”β€”
xor_false πŸ“–mathematicalβ€”Xor'β€”β€”
xor_iff_iff_not πŸ“–mathematicalβ€”Xor'β€”xor_not_right
xor_iff_not_iff πŸ“–mathematicalβ€”Xor'β€”Iff.not_right
not_xor
xor_iff_not_iff' πŸ“–mathematicalβ€”Xor'β€”xor_not_left
xor_iff_or_and_not_and πŸ“–mathematicalβ€”Xor'β€”Xor'.eq_1
not_and_or
xor_not_left πŸ“–mathematicalβ€”Xor'β€”β€”
xor_not_not πŸ“–mathematicalβ€”Xor'β€”β€”
xor_not_right πŸ“–mathematicalβ€”Xor'β€”β€”
xor_self πŸ“–mathematicalβ€”Xor'β€”β€”
xor_true πŸ“–mathematicalβ€”Xor'β€”β€”

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