Theorems · Theorem · group theory
Subsemigroup.isMulCommutative_closure
∀ (M : Type u_1) [inst : Semigroup M] {s : Set M},
(∀ a ∈ s, ∀ b ∈ s, a * b = b * a) → IsMulCommutative ↥(Subsemigroup.closure s)If all the elements of a set s commute, then closure s is commutative.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semigroup
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- Setstatement and proof · cited by 53,352
- SetLike.coeproof · cited by 8,199
- Subsemigroupstatement · cited by 323
- Semigroupstatement and proof · cited by 202
- IsMulCommutativestatement · cited by 95
- Subsemigroup.closurestatement and proof · cited by 43
- IsMulCommutative.of_setLike_mul_commproof · cited by 16
- Set.centralizer_centralizer_comm_of_commproof · cited by 11
- Subsemigroup.centralizerproof · cited by 10
- Subsemigroup.closure_le_centralizer_centralizerproof · cited by 1
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