Theorems · Theorem · group theory

sub_mem

∀ {M : Type u_3} {S : Type u_4} [inst : SubNegMonoid M] [inst_1 : SetLike S M] [hSM : AddSubgroupClass S M] {H : S}
  {x y : M}, x ∈ H → y ∈ H → x - y ∈ H

An additive subgroup is closed under subtraction.

Defined in

Mathlib.Algebra.Group.Subgroup.Defs

Cited by

40 results in Mathlib

Foundations

Depth 7 from the axioms · uses no axioms

Assumes

SubNegMonoidSetLikeAddSubgroupClass