Mathlib Map

Theorems · Theorem · group theory

IsAddCommutative.of_setLike_add_comm

∀ {S : Type u_3} {M : Type u_4} [inst : SetLike S M] [inst_1 : Add M] [inst_2 : AddMemClass S M] {s : S},
  (∀ a ∈ s, ∀ b ∈ s, a + b = b + a) → IsAddCommutative ↥s

Alias of the reverse direction of isAddCommutative_iff_of_setLike.

Defined in
Mathlib.Algebra.Group.Subsemigroup.Defs
Cited by
7 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SetLikeAddAddMemClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AddSubsemigroup.isAddCommutative_closure · cited by 0AddSubsemigroup.isAddComm…AddSubsemigroup.isAddCommutative_iSup · cited by 0AddSubsemigroup.isAddComm…AddSubgroup.isAddCommutative_closure · cited by 0AddSubgroup.isAddCommutat…AddSubgroup.isAddCommutative_iSup · cited by 0AddSubgroup.isAddCommutat…AddSubmonoid.isAddCommutative_closure · cited by 0AddSubmonoid.isAddCommuta…AddSubmonoid.isAddCommutative_iSup · cited by 0AddSubmonoid.isAddCommuta…AddSubgroup.comap_injective_isAddCommutative · cited by 0AddSubgroup.comap_injecti…SetLike · cited by 1084SetLikeIsAddCommutative · cited by 40IsAddCommutativeAddMemClass · cited by 17AddMemClassisAddCommutative_iff_of_setLike · cited by 2isAddCommutative_iff_of_s…IsAddCommutative.of_setLike_a…CITED BYCITES

Cites4

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

Cited by7

Results whose statement or proof uses this declaration.