Documentation Verification Report

Image

📁 Source: Mathlib/Data/Set/Image.lean

Statistics

MetricCount
Definitions0
Theoremspreimage, of_image, of_preimage, preimage, range_comp, set_image, compl_image_eq, existsUnique_of_mem_range, image_injective, image_strictMono, mem_range_iff_existsUnique, mem_set_image, preimage_image, preimage_surjective, subsingleton_image_iff, image_eq_preimage_symm, preimage, image_eq, image_image, mem_preimage_iff, preimage_preimage, set_image, image_preimage, image_surjective, nonempty_preimage, preimage_injective, preimage_subset_preimage_iff, range_comp, range_eq, preimage, mem_range_succ, image_elim_range_some_eq_range, injective_iff, range_elim, range_eq, range_fst, range_snd, image_nontrivial_iff, image, image_const, of_image, preimage, preimage', subset_preimage_const, image, image_of_injOn, preimage, range_mk'', image, preimage, elim_range, canLift, coe_comp_rangeFactorization, compl_compl_image, compl_image, compl_image_set_of, compl_range_inl, compl_range_inr, compl_range_some, disjoint_image_iff, disjoint_image_image, disjoint_image_inl_image_inr, disjoint_image_inl_range_inr, disjoint_image_left, disjoint_image_of_injective, disjoint_image_right, disjoint_powerset_insert, disjoint_preimage_iff, disjoint_range_inl_image_inr, eq_preimage_iff_image_eq, eq_preimage_subtype_val_iff, exists_eq_const_of_preimage_singleton, exists_image_iff, exists_mem_image, exists_range_iff, exists_subset_image_iff, exists_subset_range_and_iff, exists_subtype_range_iff, forall_mem_image, forall_mem_range, forall_subset_image_iff, forall_subset_range_iff, forall_subtype_range_iff, imageFactorization_eq, imageFactorization_surjective, image_comm, image_comp, image_comp_eq, image_compl_eq, image_compl_eq_range_diff_image, image_compl_preimage, image_compl_subset, image_congr, image_congr', image_diff, image_diff_preimage, image_empty, image_eq_empty, image_eq_image, image_eq_preimage_of_inverse, image_eq_range, image_eta, image_id, image_id', image_id_eq, image_image, image_injective, image_insert_eq, image_inter, image_inter_nonempty_iff, image_inter_on, image_inter_preimage, image_inter_subset, image_iterate_eq, image_mono, image_nonempty, image_nontrivial, image_of_range_union_range_eq_univ, image_pair, image_perm, image_preimage_eq, image_preimage_eq_iff, image_preimage_eq_inter_range, image_preimage_eq_of_subset, image_preimage_eq_range_inter, image_preimage_inl_union_image_preimage_inr, image_preimage_inter, image_preimage_subset, image_singleton, image_subset_iff, image_subset_image_iff, image_subset_preimage_of_inverse, image_subset_range, image_sumElim, image_surjective, image_swap_eq_preimage_swap, image_symmDiff, image_union, image_union_image_compl_eq_range, image_univ, image_univ_of_surjective, insert_image_compl_eq_range, insert_none_range_some, instNonemptyElemImage, instNonemptyRange, inter_preimage_subset, isCompl_range_inl_range_inr, isCompl_range_some_none, leftInverse_rangeSplitting, mem_compl_image, mem_image_iff_of_inverse, mem_range_of_mem_image, monotone_image, nonempty_of_nonempty_preimage, nontrivial_of_image, nontrivial_of_preimage, powerset_insert, powerset_insert_injOn, preimage_comp, preimage_comp_eq, preimage_compl, preimage_compl_eq_image_compl, preimage_congr, preimage_const, preimage_const_of_mem, preimage_const_of_notMem, preimage_diff, preimage_empty, preimage_eq_empty, preimage_eq_empty_iff, preimage_eq_iff_eq_image, preimage_eq_preimage, preimage_eq_preimage', preimage_eq_univ_iff, preimage_id, preimage_id', preimage_id_eq, preimage_image_eq, preimage_image_preimage, preimage_image_univ, preimage_injective, preimage_inl_image_inr, preimage_inl_range_inr, preimage_inr_image_inl, preimage_inr_range_inl, preimage_inter, preimage_inter_range, preimage_ite, preimage_iterate_eq, preimage_mono, preimage_preimage, preimage_range, preimage_rangeSplitting, preimage_range_inter, preimage_setOf_eq, preimage_singleton_eq_empty, preimage_singleton_false, preimage_singleton_nonempty, preimage_singleton_true, preimage_subset, preimage_subset_iff, preimage_subset_image_of_inverse, preimage_subset_of_surjOn, preimage_subset_preimage_iff, preimage_subtype_coe_eq_compl, preimage_sumElim, preimage_surjective, preimage_symmDiff, preimage_union, preimage_univ, prod_quotient_preimage_eq_image, rangeFactorization_coe, rangeFactorization_eq, rangeSplitting_injective, range_comp, range_comp', range_comp_subset_range, range_const, range_const_subset, range_diff_image, range_diff_image_subset, range_eq_empty, range_eq_empty_iff, range_eq_iff, range_eq_singleton, range_eq_singleton_iff, range_eq_univ, range_eval, range_id, range_id', range_image, range_inclusion, range_inl, range_inl_inter_range_inr, range_inl_union_range_inr, range_inr, range_inr_inter_range_inl, range_inr_union_range_inl, range_insert, range_inter_ssubset_iff_preimage_ssubset, range_ite_subset, range_ite_subset', range_nonempty, range_nonempty_iff_nonempty, range_quot_lift, range_quot_mk, range_quotient_lift, range_quotient_lift_on', range_quotient_mk, range_quotient_mk', range_singleton, range_some_inter_none, range_some_union_none, range_subset_iff, range_subset_range_iff_exists_comp, range_subset_singleton, range_subtype_map, range_unique, rightInverse_rangeSplitting, subset_image_compl, subset_image_diff, subset_image_iff, subset_image_symmDiff, subset_image_union, subset_preimage_image, subset_preimage_univ, subset_range_iff_exists_image_eq, subset_range_of_surjective, subsingleton_of_image, subsingleton_of_preimage, subsingleton_range, surjective_onto_image, surjective_onto_range, union_preimage_subset, coe_image, coe_image_of_subset, coe_image_subset, coe_image_univ, coe_preimage_self, exists_set_subtype, forall_set_subtype, image_preimage_coe, image_preimage_val, preimage_coe_compl, preimage_coe_compl', preimage_coe_eq_empty, preimage_coe_eq_preimage_coe_iff, preimage_coe_inter_self, preimage_coe_nonempty, preimage_coe_self_inter, preimage_val_eq_preimage_val_iff, preimage_val_subset_preimage_val_iff, range_coe, range_coe_subtype, range_val, range_val_subtype, range_eq, sigma_mk_preimage_image', sigma_mk_preimage_image_eq_self
299
Total299

Codisjoint

Theorems

NameKindAssumesProvesValidatesDepends On
preimage 📖mathematicalCodisjoint
Set
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
Set.instBooleanAlgebra
CoheytingAlgebra.toOrderTop
Set.preimage

Disjoint

Theorems

NameKindAssumesProvesValidatesDepends On
of_image 📖Disjoint
Set
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
Set.instBooleanAlgebra
HeytingAlgebra.toOrderBot
BiheytingAlgebra.toHeytingAlgebra
Set.image
disjoint_iff_inf_le
Set.disjoint_left
Set.mem_image_of_mem
of_preimage 📖Disjoint
Set
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
Set.instBooleanAlgebra
HeytingAlgebra.toOrderBot
BiheytingAlgebra.toHeytingAlgebra
Set.preimage
Set.disjoint_iff_inter_eq_empty
Set.image_preimage_eq
Set.preimage_inter
inter_eq
Set.image_empty
preimage 📖mathematicalDisjoint
Set
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
Set.instBooleanAlgebra
HeytingAlgebra.toOrderBot
BiheytingAlgebra.toHeytingAlgebra
Set.preimagedisjoint_iff_inf_le
le_bot

EquivLike

Theorems

NameKindAssumesProvesValidatesDepends On
range_comp 📖mathematicalSet.range
DFunLike.coe
toFunLike
Function.Surjective.range_comp
surjective

Function.Commute

Theorems

NameKindAssumesProvesValidatesDepends On
set_image 📖mathematicalFunction.CommuteSet
Set.image
Function.Semiconj.set_image

Function.Injective

Theorems

NameKindAssumesProvesValidatesDepends On
compl_image_eq 📖mathematicalCompl.compl
Set
Set.instCompl
Set.image
Set.instUnion
Set.range
existsUnique_of_mem_range 📖mathematicalSet
Set.instMembership
Set.range
ExistsUniquemem_range_iff_existsUnique
image_injective 📖mathematicalSet
Set.image
Set.preimage_image_eq
image_strictMono 📖mathematicalStrictMono
Set
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
Set.instBooleanAlgebra
Set.image
Monotone.strictMono_of_injective
Set.monotone_image
image_injective
mem_range_iff_existsUnique 📖mathematicalSet
Set.instMembership
Set.range
ExistsUnique
ExistsUnique.exists
mem_set_image 📖mathematicalSet
Set.instMembership
Set.image
preimage_image 📖mathematicalSet.preimage
Set.image
Set.preimage_image_eq
preimage_surjective 📖mathematicalSet
Set.preimage
Set.preimage_surjective
subsingleton_image_iff 📖mathematicalSet.Subsingleton
Set.image
Set.subsingleton_of_image
Set.Subsingleton.image

Function.Involutive

Theorems

NameKindAssumesProvesValidatesDepends On
image_eq_preimage_symm 📖mathematicalFunction.InvolutiveSet.image
Set.preimage
Set.image_eq_preimage_of_inverse
leftInverse
rightInverse
preimage 📖mathematicalFunction.InvolutiveSet
Set.preimage
Function.LeftInverse.preimage_preimage
rightInverse

Function.LeftInverse

Theorems

NameKindAssumesProvesValidatesDepends On
image_eq 📖mathematicalSet.image
Set
Set.instInter
Set.range
Set.preimage
Set.image_preimage_eq_range_inter
preimage_preimage
image_image 📖mathematicalSet.imageSet.image_comp
comp_eq_id
Set.image_id
mem_preimage_iff 📖mathematicalSet
Set.instMembership
Set.preimage
Set.mem_preimage
preimage_preimage 📖mathematicalSet.preimageSet.preimage_comp
comp_eq_id
Set.preimage_id

Function.Semiconj

Theorems

NameKindAssumesProvesValidatesDepends On
set_image 📖mathematicalFunction.SemiconjSet
Set.image
Set.image_comm

Function.Surjective

Theorems

NameKindAssumesProvesValidatesDepends On
image_preimage 📖mathematicalSet.image
Set.preimage
Set.image_preimage_eq
image_surjective 📖mathematicalSet
Set.image
image_preimage
nonempty_preimage 📖mathematicalSet.Nonempty
Set.preimage
Set.image_nonempty
image_preimage
preimage_injective 📖mathematicalSet
Set.preimage
Set.preimage_eq_preimage
preimage_subset_preimage_iff 📖mathematicalSet
Set.instHasSubset
Set.preimage
Set.preimage_subset_preimage_iff
range_eq
Set.subset_univ
range_comp 📖mathematicalSet.rangeSet.ext
exists
range_eq 📖mathematicalSet.range
Set.univ
Set.range_eq_univ

IsCompl

Theorems

NameKindAssumesProvesValidatesDepends On
preimage 📖mathematicalIsCompl
Set
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
Set.instBooleanAlgebra
Set.instBoundedOrder
Set.preimageDisjoint.preimage
disjoint
Codisjoint.preimage
codisjoint

Nat

Theorems

NameKindAssumesProvesValidatesDepends On
mem_range_succ 📖mathematicalSet
Set.instMembership
Set.range

Option

Theorems

NameKindAssumesProvesValidatesDepends On
image_elim_range_some_eq_range 📖mathematicalSet.image
Set.range
Set.range_comp'
injective_iff 📖mathematicalSet
Set.instMembership
Set.range
some_injective
range_elim 📖mathematicalSet.range
Set
Set.instInsert
range_eq
range_eq 📖mathematicalSet.range
Set
Set.instInsert
Set.ext
Iff.or

Prod

Theorems

NameKindAssumesProvesValidatesDepends On
range_fst 📖mathematicalSet.range
Set.univ
Function.Surjective.range_eq
fst_surjective
range_snd 📖mathematicalSet.range
Set.univ
Function.Surjective.range_eq
snd_surjective

Set

Theorems

NameKindAssumesProvesValidatesDepends On
canLift 📖mathematicalCanLift
Set
image
subset_range_iff_exists_image_eq
CanLift.prf
coe_comp_rangeFactorization 📖mathematicalElem
range
Set
instMembership
rangeFactorization
compl_compl_image 📖mathematicalimage
Compl.compl
BooleanAlgebra.toCompl
image_comp
compl_comp_compl
image_id
compl_image 📖mathematicalimage
Set
Compl.compl
instCompl
preimage
image_eq_preimage_of_inverse
compl_compl
compl_image_set_of 📖mathematicalimage
Set
Compl.compl
instCompl
setOf
compl_image
compl_range_inl 📖mathematicalCompl.compl
Set
instCompl
range
IsCompl.compl_eq
isCompl_range_inl_range_inr
compl_range_inr 📖mathematicalCompl.compl
Set
instCompl
range
IsCompl.compl_eq
IsCompl.symm
isCompl_range_inl_range_inr
compl_range_some 📖mathematicalCompl.compl
Set
instCompl
range
instSingletonSet
IsCompl.compl_eq
isCompl_range_some_none
disjoint_image_iff 📖mathematicalDisjoint
Set
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
instBooleanAlgebra
HeytingAlgebra.toOrderBot
BiheytingAlgebra.toHeytingAlgebra
image
Disjoint.of_image
disjoint_image_of_injective
disjoint_image_image 📖mathematicalDisjoint
Set
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
instBooleanAlgebra
HeytingAlgebra.toOrderBot
BiheytingAlgebra.toHeytingAlgebra
image
disjoint_iff_inf_le
disjoint_image_inl_image_inr 📖mathematicalDisjoint
Set
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
instBooleanAlgebra
HeytingAlgebra.toOrderBot
BiheytingAlgebra.toHeytingAlgebra
image
disjoint_image_image
disjoint_image_inl_range_inr 📖mathematicalDisjoint
Set
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
instBooleanAlgebra
HeytingAlgebra.toOrderBot
BiheytingAlgebra.toHeytingAlgebra
image
range
disjoint_image_left 📖mathematicalDisjoint
Set
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
instBooleanAlgebra
HeytingAlgebra.toOrderBot
BiheytingAlgebra.toHeytingAlgebra
image
preimage
disjoint_image_of_injective 📖mathematicalDisjoint
Set
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
instBooleanAlgebra
HeytingAlgebra.toOrderBot
BiheytingAlgebra.toHeytingAlgebra
imagedisjoint_image_image
disjoint_iff
disjoint_image_right 📖mathematicalDisjoint
Set
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
instBooleanAlgebra
HeytingAlgebra.toOrderBot
BiheytingAlgebra.toHeytingAlgebra
image
preimage
disjoint_comm
disjoint_image_left
disjoint_powerset_insert 📖mathematicalSet
instMembership
Disjoint
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
instBooleanAlgebra
HeytingAlgebra.toOrderBot
BiheytingAlgebra.toHeytingAlgebra
powerset
image
instInsert
disjoint_preimage_iff 📖mathematicalDisjoint
Set
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
instBooleanAlgebra
HeytingAlgebra.toOrderBot
BiheytingAlgebra.toHeytingAlgebra
preimage
Disjoint.of_preimage
Disjoint.preimage
disjoint_range_inl_image_inr 📖mathematicalDisjoint
Set
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
instBooleanAlgebra
HeytingAlgebra.toOrderBot
BiheytingAlgebra.toHeytingAlgebra
range
image
eq_preimage_iff_image_eq 📖mathematicalFunction.Bijectivepreimage
image
image_eq_image
Function.Surjective.image_preimage
eq_preimage_subtype_val_iff 📖mathematicalpreimage
Set
instMembership
exists_eq_const_of_preimage_singleton 📖preimage
Set
instSingletonSet
instEmptyCollection
univ
em
eq_univ_iff_forall
eq_empty_iff_forall_notMem
exists_image_iff 📖mathematicalSet
instMembership
image
Subtype.prop
exists_mem_image 📖mathematicalSet
instMembership
image
exists_range_iff 📖mathematicalSet
instMembership
range
exists_subset_image_iff 📖mathematicalSet
instHasSubset
image
exists_subset_range_and_iff 📖mathematicalSet
instHasSubset
range
image
exists_range_iff
range_image
exists_subtype_range_iff 📖mathematicalSet
instMembership
range
mem_range_self
forall_mem_image 📖
forall_mem_range 📖
forall_subset_image_iff 📖mathematicalimage
forall_subset_range_iff 📖mathematicalimageforall_mem_range
range_image
forall_subtype_range_iff 📖mathematicalSet
instMembership
range
mem_range_self
imageFactorization_eq 📖mathematicalElem
Set
instMembership
image
imageFactorization
imageFactorization_surjective 📖mathematicalElem
image
imageFactorization
image_comm 📖mathematicalimage
image_comp 📖mathematicalimageimage_congr
ext
image_comp_eq 📖mathematicalimage
Set
image_compl_eq 📖mathematicalFunction.Bijectiveimage
Compl.compl
Set
instCompl
Subset.antisymm
image_compl_subset
subset_image_compl
image_compl_eq_range_diff_image 📖mathematicalimage
Compl.compl
Set
instCompl
instSDiff
range
image_univ
image_diff
compl_eq_univ_diff
image_compl_preimage 📖mathematicalimage
Compl.compl
Set
instCompl
preimage
instSDiff
range
compl_eq_univ_diff
image_diff_preimage
image_univ
image_compl_subset 📖mathematicalSet
instHasSubset
image
Compl.compl
instCompl
Disjoint.subset_compl_left
image_inter
inter_compl_self
image_empty
image_congr 📖mathematicalimageext
image_congr' 📖mathematicalimage
image_diff 📖mathematicalimage
Set
instSDiff
Subset.antisymm
Subset.trans
image_inter_subset
inter_subset_inter_right
image_compl_subset
subset_image_diff
image_diff_preimage 📖mathematicalimage
Set
instSDiff
preimage
image_inter_preimage
image_empty 📖mathematicalimage
Set
instEmptyCollection
image_eq_empty 📖mathematicalimage
Set
instEmptyCollection
image_eq_image 📖mathematicalimagepreimage_image_eq
image_eq_preimage_of_inverse 📖mathematicalimage
preimage
Subset.antisymm
image_subset_preimage_of_inverse
preimage_subset_image_of_inverse
image_eq_range 📖mathematicalimage
range
Elem
Set
instMembership
ext
image_eta 📖mathematicalimage
image_id 📖mathematicalimageimage_congr
image_id'
image_id' 📖mathematicalimageext
image_id_eq 📖mathematicalimage
Set
ext
image_congr
image_image 📖mathematicalimageimage_comp
image_injective 📖mathematicalSet
image
singleton_eq_singleton_iff
image_singleton
Function.Injective.image_injective
image_insert_eq 📖mathematicalimage
Set
instInsert
image_inter 📖mathematicalimage
Set
instInter
image_inter_on
image_inter_nonempty_iff 📖mathematicalNonempty
Set
instInter
image
preimage
image_inter_preimage
image_nonempty
image_inter_on 📖mathematicalimage
Set
instInter
HasSubset.Subset.antisymm
instAntisymmSubset
image_inter_subset
image_inter_preimage 📖mathematicalimage
Set
instInter
preimage
image_inter_subset 📖mathematicalSet
instHasSubset
image
instInter
subset_inter
image_mono
inter_subset_left
inter_subset_right
image_iterate_eq 📖mathematicalimage
Nat.iterate
Set
image_id_eq
Function.iterate_succ'
image_comp_eq
image_mono 📖mathematicalSet
instHasSubset
image
image_nonempty 📖mathematicalNonempty
image
Nonempty.of_image
Nonempty.image
image_nontrivial 📖mathematicalNontrivial
image
nontrivial_of_image
Nontrivial.image
image_of_range_union_range_eq_univ 📖mathematicalSet
instUnion
range
univ
image
preimage
image_comp
image_preimage_eq_inter_range
image_union
inter_union_distrib_left
inter_univ
image_pair 📖mathematicalimage
Set
instInsert
instSingletonSet
image_perm 📖mathematicalSet
instHasSubset
setOf
DFunLike.coe
Equiv.Perm
EquivLike.toFunLike
Equiv.instEquivLike
imageext
eq_or_ne
Equiv.injective
Equiv.apply_symm_apply
image_preimage_eq 📖mathematicalimage
preimage
Subset.antisymm
image_preimage_subset
image_preimage_eq_iff 📖mathematicalimage
preimage
Set
instHasSubset
range
image_preimage_eq_inter_range 📖mathematicalimage
preimage
Set
instInter
range
image_preimage_eq_of_subset 📖mathematicalSet
instHasSubset
range
image
preimage
image_preimage_eq_range_inter 📖mathematicalimage
preimage
Set
instInter
range
image_preimage_inl_union_image_preimage_inr 📖mathematicalSet
instUnion
image
preimage
preimage_sumElim
preimage_id
image_preimage_inter 📖mathematicalimage
Set
instInter
preimage
inter_comm
image_inter_preimage
image_preimage_subset 📖mathematicalSet
instHasSubset
image
preimage
image_subset_iff
Subset.rfl
image_singleton 📖mathematicalimage
Set
instSingletonSet
image_subset_iff 📖mathematicalSet
instHasSubset
image
preimage
forall_mem_image
image_subset_image_iff 📖mathematicalSet
instHasSubset
image
image_subset_preimage_of_inverse 📖mathematicalSet
instHasSubset
image
preimage
Function.LeftInverse.mem_preimage_iff
image_subset_range 📖mathematicalSet
instHasSubset
image
range
image_univ
image_mono
subset_univ
image_sumElim 📖mathematicalimage
Set
instUnion
preimage
image_surjective 📖mathematicalSet
image
mem_singleton
Function.Surjective.image_surjective
image_swap_eq_preimage_swap 📖mathematicalimage
preimage
image_eq_preimage_of_inverse
Prod.swap_leftInverse
Prod.swap_rightInverse
image_symmDiff 📖mathematicalimage
symmDiff
Set
SemilatticeSup.toMax
Lattice.toSemilatticeSup
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
instBooleanAlgebra
instSDiff
image_union
image_diff
image_union 📖mathematicalimage
Set
instUnion
image_union_image_compl_eq_range 📖mathematicalSet
instUnion
image
Compl.compl
instCompl
range
image_univ 📖mathematicalimage
univ
range
image_univ_of_surjective 📖mathematicalimage
univ
eq_univ_of_forall
insert_image_compl_eq_range 📖mathematicalSet
instInsert
image
Compl.compl
instCompl
instSingletonSet
range
insert_none_range_some 📖mathematicalSet
instInsert
range
univ
IsCompl.sup_eq_top
IsCompl.symm
isCompl_range_some_none
instNonemptyElemImage 📖mathematicalElem
image
Nonempty.to_subtype
Nonempty.image
Nonempty.of_subtype
instNonemptyRange 📖mathematicalElem
range
Nonempty.to_subtype
range_nonempty
inter_preimage_subset 📖mathematicalSet
instHasSubset
instInter
preimage
image
mem_image_of_mem
isCompl_range_inl_range_inr 📖mathematicalIsCompl
Set
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
instBooleanAlgebra
instBoundedOrder
range
IsCompl.of_le
mem_range_self
isCompl_range_some_none 📖mathematicalIsCompl
Set
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
instBooleanAlgebra
instBoundedOrder
range
instSingletonSet
IsCompl.of_le
mem_range_self
leftInverse_rangeSplitting 📖mathematicalElem
range
rangeFactorization
rangeSplitting
apply_rangeSplitting
mem_compl_image 📖mathematicalSet
instMembership
image
Compl.compl
BooleanAlgebra.toCompl
mem_image_iff_of_inverse 📖mathematicalSet
instMembership
image
image_eq_preimage_of_inverse
mem_preimage
mem_range_of_mem_image 📖mathematicalSet
instMembership
image
rangeimage_subset_range
monotone_image 📖mathematicalMonotone
Set
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
instBooleanAlgebra
image
image_mono
nonempty_of_nonempty_preimage 📖Nonempty
preimage
nontrivial_of_image 📖Nontrivial
image
nontrivial_of_preimage 📖Nontrivial
preimage
Nontrivial.mono
Nontrivial.image
image_preimage_subset
powerset_insert 📖mathematicalpowerset
Set
instInsert
instUnion
image
ext
powerset_insert_injOn 📖mathematicalSet
instMembership
InjOn
instInsert
powerset
preimage_comp 📖mathematicalpreimage
preimage_comp_eq 📖mathematicalpreimage
Set
preimage_compl 📖mathematicalpreimage
Compl.compl
Set
instCompl
preimage_compl_eq_image_compl 📖mathematicalpreimage
Compl.compl
BooleanAlgebra.toCompl
image
ext
compl_compl
compl_eq_comm
preimage_congr 📖mathematicalpreimage
preimage_const 📖mathematicalpreimage
Set
instMembership
univ
instEmptyCollection
preimage_const_of_mem 📖mathematicalSet
instMembership
preimage
univ
eq_univ_of_forall
preimage_const_of_notMem 📖mathematicalSet
instMembership
preimage
instEmptyCollection
eq_empty_of_subset_empty
preimage_diff 📖mathematicalpreimage
Set
instSDiff
preimage_empty 📖mathematicalpreimage
Set
instEmptyCollection
preimage_eq_empty 📖mathematicalDisjoint
Set
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
instBooleanAlgebra
HeytingAlgebra.toOrderBot
BiheytingAlgebra.toHeytingAlgebra
range
preimage
instEmptyCollection
preimage_range
Disjoint.preimage
preimage_eq_empty_iff 📖mathematicalpreimage
Set
instEmptyCollection
Disjoint
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
instBooleanAlgebra
HeytingAlgebra.toOrderBot
BiheytingAlgebra.toHeytingAlgebra
range
preimage_eq_empty
preimage_eq_iff_eq_image 📖mathematicalFunction.Bijectivepreimage
image
image_eq_image
Function.Surjective.image_preimage
preimage_eq_preimage 📖mathematicalpreimagepreimage_injective
preimage_eq_preimage' 📖mathematicalSet
instHasSubset
range
preimageSubset.antisymm
preimage_subset_preimage_iff
subset_refl
instReflSubset
preimage_eq_univ_iff 📖mathematicalpreimage
univ
Set
instHasSubset
range
univ_subset_iff
image_subset_iff
image_univ
preimage_id 📖mathematicalpreimage
preimage_id' 📖mathematicalpreimage
preimage_id_eq 📖mathematicalpreimage
Set
preimage_image_eq 📖mathematicalpreimage
image
Subset.antisymm
subset_preimage_image
preimage_image_preimage 📖mathematicalpreimage
image
image_preimage_eq_range_inter
preimage_range_inter
preimage_image_univ 📖mathematicalpreimage
image
univ
Subset.antisymm
subset_preimage_image
preimage_injective 📖mathematicalSet
preimage
Function.injective_comp_right_iff_surjective
instNontrivialProp
preimage_inl_image_inr 📖mathematicalpreimage
image
Set
instEmptyCollection
ext
preimage_inl_range_inr 📖mathematicalpreimage
range
Set
instEmptyCollection
image_univ
preimage_inl_image_inr
preimage_inr_image_inl 📖mathematicalpreimage
image
Set
instEmptyCollection
ext
preimage_inr_range_inl 📖mathematicalpreimage
range
Set
instEmptyCollection
image_univ
preimage_inr_image_inl
preimage_inter 📖mathematicalpreimage
Set
instInter
preimage_inter_range 📖mathematicalpreimage
Set
instInter
range
ext
preimage_ite 📖mathematicalpreimage
ite
preimage_iterate_eq 📖mathematicalpreimage
Nat.iterate
Set
Function.iterate_succ
Function.iterate_succ'
preimage_comp_eq
preimage_mono 📖mathematicalSet
instHasSubset
preimage
preimage_preimage 📖mathematicalpreimagepreimage_comp
preimage_range 📖mathematicalpreimage
range
univ
eq_univ_of_forall
mem_range_self
preimage_rangeSplitting 📖mathematicalpreimage
Elem
range
rangeSplitting
image
rangeFactorization
image_eq_preimage_of_inverse
rightInverse_rangeSplitting
leftInverse_rangeSplitting
preimage_range_inter 📖mathematicalpreimage
Set
instInter
range
inter_comm
preimage_inter_range
preimage_setOf_eq 📖mathematicalpreimage
setOf
preimage_singleton_eq_empty 📖mathematicalpreimage
Set
instSingletonSet
instEmptyCollection
instMembership
range
not_nonempty_iff_eq_empty
Iff.not
preimage_singleton_nonempty
preimage_singleton_false 📖mathematicalpreimage
Set
instSingletonSet
setOf
ext
preimage_singleton_nonempty 📖mathematicalNonempty
preimage
Set
instSingletonSet
instMembership
range
preimage_singleton_true 📖mathematicalpreimage
Set
instSingletonSet
setOf
ext
preimage_subset 📖Set
instHasSubset
image
InjOn
preimage
preimage_subset_iff 📖mathematicalSet
instHasSubset
preimage
instMembership
preimage_subset_image_of_inverse 📖mathematicalSet
instHasSubset
preimage
image
preimage_subset_of_surjOn 📖mathematicalSurjOnSet
instHasSubset
preimage
Function.Injective.mem_set_image
preimage_subset_preimage_iff 📖mathematicalSet
instHasSubset
range
preimage
preimage_subtype_coe_eq_compl 📖mathematicalSet
instHasSubset
instUnion
instInter
instEmptyCollection
preimage
instMembership
Compl.compl
instCompl
ext
eq_empty_iff_forall_notMem
preimage_sumElim 📖mathematicalpreimage
Set
instUnion
image
ext
preimage_surjective 📖mathematicalSet
preimage
Function.surjective_comp_right_iff_injective
instNontrivialProp
preimage_symmDiff 📖mathematicalpreimage
symmDiff
Set
SemilatticeSup.toMax
Lattice.toSemilatticeSup
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
instBooleanAlgebra
instSDiff
preimage_union 📖mathematicalpreimage
Set
instUnion
preimage_univ 📖mathematicalpreimage
univ
prod_quotient_preimage_eq_image 📖mathematicalQuotient.mk''setOf
Set
instMembership
image
preimage
ext
Quot.induction_on₂
rangeFactorization_coe 📖mathematicalSet
instMembership
range
rangeFactorization
rangeFactorization_eq 📖mathematicalSet
instMembership
range
rangeFactorization
rangeSplitting_injective 📖mathematicalElem
range
rangeSplitting
leftInverse_rangeSplitting
range_comp 📖mathematicalrange
image
ext
range_comp' 📖mathematicalrange
image
range_comp
range_comp_subset_range 📖mathematicalSet
instHasSubset
range
range_const 📖mathematicalrange
Set
instSingletonSet
range_eq_singleton
range_const_subset 📖mathematicalSet
instHasSubset
range
instSingletonSet
range_subset_iff
range_diff_image 📖mathematicalSet
instSDiff
range
image
Compl.compl
instCompl
image_compl_eq_range_diff_image
range_diff_image_subset 📖mathematicalSet
instHasSubset
instSDiff
range
image
Compl.compl
instCompl
range_eq_empty 📖mathematicalrange
Set
instEmptyCollection
range_eq_empty_iff
range_eq_empty_iff 📖mathematicalrange
Set
instEmptyCollection
IsEmpty
not_nonempty_iff
range_nonempty_iff_nonempty
not_nonempty_iff_eq_empty
range_eq_iff 📖mathematicalrange
Set
instMembership
range_eq_singleton 📖mathematicalrange
Set
instSingletonSet
range_eq_singleton_iff
range_eq_singleton_iff 📖mathematicalrange
Set
instSingletonSet
range_eq_univ 📖mathematicalrange
univ
eq_univ_iff_forall
range_eval 📖mathematicalrange
Function.eval
univ
Function.Surjective.range_eq
Function.surjective_eval
range_id 📖mathematicalrange
univ
range_eq_univ
range_id' 📖mathematicalrange
univ
range_id
range_image 📖mathematicalrange
Set
image
powerset
ext
subset_range_iff_exists_image_eq
range_inclusion 📖mathematicalSet
instHasSubset
range
Elem
inclusion
setOf
instMembership
ext
range_inl 📖mathematicalrange
setOf
ext
range_inl_inter_range_inr 📖mathematicalSet
instInter
range
instEmptyCollection
IsCompl.inf_eq_bot
isCompl_range_inl_range_inr
range_inl_union_range_inr 📖mathematicalSet
instUnion
range
univ
IsCompl.sup_eq_top
isCompl_range_inl_range_inr
range_inr 📖mathematicalrange
setOf
ext
range_inr_inter_range_inl 📖mathematicalSet
instInter
range
instEmptyCollection
IsCompl.inf_eq_bot
IsCompl.symm
isCompl_range_inl_range_inr
range_inr_union_range_inl 📖mathematicalSet
instUnion
range
univ
IsCompl.sup_eq_top
IsCompl.symm
isCompl_range_inl_range_inr
range_insert 📖mathematicalrange
Elem
Set
instInsert
instMembership
mem_insert
mem_insert_of_mem
ext
mem_insert
mem_insert_of_mem
range_inter_ssubset_iff_preimage_ssubset 📖mathematicalSet
instHasSSubset
instInter
range
preimage
range_ite_subset 📖mathematicalSet
instHasSubset
range
instUnion
range_ite_subset' 📖mathematicalSet
instHasSubset
range
instUnion
range_nonempty 📖mathematicalNonempty
range
range_nonempty_iff_nonempty
range_nonempty_iff_nonempty 📖mathematicalNonempty
range
mem_range_self
range_quot_lift 📖mathematicalrangeext
Function.Surjective.exists
Quot.mk_surjective
range_quot_mk 📖mathematicalrange
univ
Function.Surjective.range_eq
Quot.mk_surjective
range_quotient_lift 📖mathematicalrangerange_quot_lift
range_quotient_lift_on' 📖mathematicalrange
Quotient.liftOn'
range_quot_lift
range_quotient_mk 📖mathematicalrange
univ
range_quotient_mk' 📖mathematicalrange
univ
range_singleton 📖mathematicalrange
Elem
Set
instSingletonSet
instMembership
mem_singleton
range_unique
range_some_inter_none 📖mathematicalSet
instInter
range
instSingletonSet
instEmptyCollection
IsCompl.inf_eq_bot
isCompl_range_some_none
range_some_union_none 📖mathematicalSet
instUnion
range
instSingletonSet
univ
IsCompl.sup_eq_top
isCompl_range_some_none
range_subset_iff 📖mathematicalSet
instHasSubset
range
instMembership
forall_mem_range
range_subset_range_iff_exists_comp 📖mathematicalSet
instHasSubset
range
range_subset_singleton 📖mathematicalSet
instHasSubset
range
instSingletonSet
range_subtype_map 📖mathematicalrange
Subtype.map
preimage
image
setOf
ext
range_unique 📖mathematicalrange
Set
instSingletonSet
Unique.instInhabited
Unique.eq_default
rightInverse_rangeSplitting 📖mathematicalElem
range
rangeFactorization
rangeSplitting
Function.LeftInverse.rightInverse_of_injective
leftInverse_rangeSplitting
subset_image_compl 📖mathematicalSet
instHasSubset
Compl.compl
instCompl
image
compl_subset_iff_union
image_union
union_compl_self
image_univ_of_surjective
subset_image_diff 📖mathematicalSet
instHasSubset
instSDiff
image
diff_subset_iff
image_union
union_diff_self
image_mono
subset_union_right
subset_image_iff 📖mathematicalSet
instHasSubset
image
inter_subset_right
image_preimage_inter
inter_eq_left
image_mono
subset_image_symmDiff 📖mathematicalSet
instHasSubset
symmDiff
SemilatticeSup.toMax
Lattice.toSemilatticeSup
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
instBooleanAlgebra
instSDiff
image
HasSubset.Subset.trans
instIsTransSubset
union_subset_union
subset_image_diff
superset_of_eq
instReflSubset
image_union
subset_image_union 📖mathematicalSet
instHasSubset
image
instUnion
preimage
image_subset_iff
union_preimage_subset
subset_preimage_image 📖mathematicalSet
instHasSubset
preimage
image
mem_image_of_mem
subset_preimage_univ 📖mathematicalSet
instHasSubset
preimage
univ
subset_univ
subset_range_iff_exists_image_eq 📖mathematicalSet
instHasSubset
range
image
image_preimage_eq_iff
image_subset_range
subset_range_of_surjective 📖mathematicalSet
instHasSubset
range
subset_univ
Function.Surjective.range_eq
subsingleton_of_image 📖Subsingleton
image
Subsingleton.anti
Subsingleton.preimage
subset_preimage_image
subsingleton_of_preimage 📖Subsingleton
preimage
subsingleton_range 📖mathematicalSubsingleton
range
forall_mem_range
surjective_onto_image 📖mathematicalElem
image
imageFactorization
imageFactorization_surjective
surjective_onto_range 📖mathematicalElem
range
rangeFactorization
rangeFactorization_surjective
union_preimage_subset 📖mathematicalSet
instHasSubset
instUnion
preimage
image
mem_image_of_mem

Set.InjOn

Theorems

NameKindAssumesProvesValidatesDepends On
image_nontrivial_iff 📖mathematicalSet.InjOnSet.Nontrivial
Set.image
Set.nontrivial_of_image
Set.Nontrivial.image_of_injOn

Set.Nonempty

Theorems

NameKindAssumesProvesValidatesDepends On
image 📖mathematicalSet.NonemptySet.imageSet.mem_image_of_mem
image_const 📖mathematicalSet.NonemptySet.image
Set
Set.instSingletonSet
Set.ext
Set.mem_singleton
Set.eq_of_mem_singleton
of_image 📖Set.Nonempty
Set.image
preimage 📖mathematicalSet.NonemptySet.preimage
preimage' 📖mathematicalSet.Nonempty
Set
Set.instHasSubset
Set.range
Set.preimage
subset_preimage_const 📖mathematicalSet.NonemptySet
Set.instHasSubset
Set.preimage
Set.instMembership
Set.image_subset_iff
image_const
Set.singleton_subset_iff

Set.Nontrivial

Theorems

NameKindAssumesProvesValidatesDepends On
image 📖mathematicalSet.NontrivialSet.imageSet.mem_image_of_mem
image_of_injOn 📖mathematicalSet.Nontrivial
Set.InjOn
Set.imageSet.mem_image_of_mem
preimage 📖mathematicalSet.NontrivialSet.preimage

Set.Quotient

Theorems

NameKindAssumesProvesValidatesDepends On
range_mk'' 📖mathematicalSet.range
Quotient.mk''
Set.univ

Set.Subsingleton

Theorems

NameKindAssumesProvesValidatesDepends On
image 📖mathematicalSet.SubsingletonSet.image
preimage 📖mathematicalSet.SubsingletonSet.preimage

Set.Sum

Theorems

NameKindAssumesProvesValidatesDepends On
elim_range 📖mathematicalSet.range
Set
Set.instUnion
Sum.range_eq

Subtype

Theorems

NameKindAssumesProvesValidatesDepends On
coe_image 📖mathematicalSet.image
setOf
Set
Set.instMembership
Set.ext
coe_image_of_subset 📖mathematicalSet
Set.instHasSubset
Set.image
Set.Elem
Set.instMembership
setOf
Set.ext
Set.mem_image
coe_image_subset 📖mathematicalSet
Set.instHasSubset
Set.image
Set.instMembership
coe_image_univ 📖mathematicalSet.image
Set
Set.instMembership
Set.univ
Set.image_univ
range_coe
coe_preimage_self 📖mathematicalSet.preimage
Set
Set.instMembership
Set.univ
Set.preimage_range
range_coe
exists_set_subtype 📖mathematicalSet.image
Set
Set.instMembership
Set.instHasSubset
Set.exists_subset_range_and_iff
range_coe
forall_set_subtype 📖mathematicalSet.image
Set
Set.instMembership
Set.forall_subset_range_iff
range_coe
image_preimage_coe 📖mathematicalSet.image
Set
Set.instMembership
Set.preimage
Set.instInter
Set.image_preimage_eq_range_inter
range_coe
image_preimage_val 📖mathematicalSet.image
Set
Set.instMembership
Set.preimage
Set.instInter
image_preimage_coe
preimage_coe_compl 📖mathematicalSet.preimage
Set
Set.instMembership
Compl.compl
Set.instCompl
Set.instEmptyCollection
preimage_coe_eq_empty
Set.inter_compl_self
preimage_coe_compl' 📖mathematicalSet.preimage
Set.Elem
Compl.compl
Set
Set.instCompl
Set.instMembership
Set.instEmptyCollection
preimage_coe_eq_empty
Set.compl_inter_self
preimage_coe_eq_empty 📖mathematicalSet.preimage
Set
Set.instMembership
Set.instEmptyCollection
Set.instInter
preimage_coe_eq_preimage_coe_iff 📖mathematicalSet.preimage
Set
Set.instMembership
Set.instInter
image_preimage_coe
Function.Injective.image_injective
coe_injective
preimage_coe_inter_self 📖mathematicalSet.preimage
Set
Set.instMembership
Set.instInter
Set.inter_comm
preimage_coe_self_inter
preimage_coe_nonempty 📖mathematicalSet.Nonempty
Set
Set.instMembership
Set.preimage
Set.instInter
image_preimage_coe
Set.image_nonempty
preimage_coe_self_inter 📖mathematicalSet.preimage
Set
Set.instMembership
Set.instInter
preimage_coe_eq_preimage_coe_iff
Set.inter_assoc
Set.inter_self
preimage_val_eq_preimage_val_iff 📖mathematicalSet.preimage
Set
Set.instMembership
Set.instInter
preimage_coe_eq_preimage_coe_iff
preimage_val_subset_preimage_val_iff 📖mathematicalSet
Set.Elem
Set.instHasSubset
Set.preimage
Set.instMembership
Set.instInter
image_preimage_coe
Set.image_mono
range_coe 📖mathematicalSet.range
Set
Set.instMembership
Set.image_univ
coe_image
range_coe_subtype 📖mathematicalSet.range
setOf
range_coe
range_val 📖mathematicalSet.range
Set
Set.instMembership
range_coe
range_val_subtype 📖mathematicalSet.range
setOf
range_coe

Sum

Theorems

NameKindAssumesProvesValidatesDepends On
range_eq 📖mathematicalSet.range
Set
Set.instUnion
Set.ext

(root)

Theorems

NameKindAssumesProvesValidatesDepends On
sigma_mk_preimage_image' 📖mathematicalSet.preimage
Set.image
Set
Set.instEmptyCollection
sigma_mk_preimage_image_eq_self 📖mathematicalSet.preimage
Set.image

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