Mathlib Map

Theorems · Theorem · group theory

ZeroMemClass.coe_nonempty

∀ {S : Type u_3} {M : Type u_4} [inst : Zero M] [inst_1 : SetLike S M] [ZeroMemClass S M] (s : S), (↑s).Nonempty

The underlying set of a term of a ZeroMemClass is nonempty.

Defined in
Mathlib.Algebra.Group.Submonoid.Defs
Cited by
2 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
ZeroSetLikeZeroMemClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

finite_zmultiples · cited by 3finite_zmultiplesAddSubgroup.addOrderOf_le_card · cited by 1AddSubgroup.addOrderOf_le…SetLike.coe · cited by 8199SetLike.coeSet.Nonempty · cited by 2627Set.NonemptySetLike · cited by 1084SetLikeZeroMemClass.zero_mem · cited by 162ZeroMemClass.zero_memZeroMemClass · cited by 25ZeroMemClassZeroMemClass.coe_nonemptyCITED BYCITES

Cites5

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Cited by2

Results whose statement or proof uses this declaration.