Theorems · Theorem · group theory
setLike_mul_comm
∀ {S : Type u_3} {M : Type u_4} [inst : SetLike S M] [inst_1 : Mul M] [inst_2 : MulMemClass S M] {s : S}
[IsMulCommutative ↥s] ⦃a b : M⦄, a ∈ s → b ∈ s → a * b = b * aCommutativity of multiplication in commutative subobjects.
- Defined in
- Mathlib.Algebra.Group.Subsemigroup.Defs
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 19 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
- IsMulCommutativestatement and proof · cited by 95
- MulMemClassstatement and proof · cited by 25
- isMulCommutative_iff_of_setLikeproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- NonUnitalSubsemiring.isMulCommutative_iSupproof · cited by 3
- Subsemigroup.isMulCommutative_iSupproof · cited by 2
- Subgroup.mul_comm_of_mem_isMulCommutativeproof · cited by 0
- Subgroup.comap_injective_isMulCommutativeproof · cited by 0
- Subgroup.isMulCommutative_iSupproof · cited by 0
- Submonoid.isMulCommutative_iSupproof · cited by 0