Theorems · Theorem · group theory
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}
[IsAddCommutative ↥s] ⦃a b : M⦄, a ∈ s → b ∈ s → a + b = b + aCommutativity of addition in commutative subobjects.
- Defined in
- Mathlib.Algebra.Group.Subsemigroup.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLikestatement and proof · cited by 1,084
- IsAddCommutativestatement and proof · cited by 40
- AddMemClassstatement and proof · cited by 17
- isAddCommutative_iff_of_setLikeproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- AddSubsemigroup.isAddCommutative_iSupproof · cited by 0
- AddSubgroup.add_comm_of_mem_isAddCommutativeproof · cited by 0
- AddSubgroup.isAddCommutative_iSupproof · cited by 0
- AddSubmonoid.isAddCommutative_iSupproof · cited by 0
- AddSubgroup.comap_injective_isAddCommutativeproof · cited by 0