Theorems · Theorem · group theory

AddSubgroup.isComplement_range_right

∀ {G : Type u_1} [inst : AddGroup G] {H : AddSubgroup G} {f : Quotient (QuotientAddGroup.rightRel H) → G},
  (∀ (q : Quotient (QuotientAddGroup.rightRel H)), Quotient.mk'' (f q) = q) →
    AddSubgroup.IsComplement (↑H) (Set.range f)

Defined in: Mathlib.GroupTheory.Complement
Cited by: 2 results in Mathlib
Foundations: Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AddGroup

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Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

SetLike.coestatement · cited by 8,199
Set.Elemproof · cited by 7,166
Set.rangestatement and proof · cited by 4,705
AddGroupstatement and proof · cited by 4,410
AddSubgroupstatement and proof · cited by 3,232
Set.domRestrictproof · cited by 383
Quotient.mk''statement and proof · cited by 132
AddSubgroup.IsComplementstatement · cited by 57
QuotientAddGroup.rightRelstatement and proof · cited by 14
AddSubgroup.isComplement_addSubgroup_left_iff_bijectiveproof · cited by 2

Cited by2

Results whose statement or proof uses this declaration.

AddSubgroup.exists_isComplement_rightproof · cited by 3
AddSubgroup.IsComplement.rightQuotientEquiv_applystatement and proof · cited by 0