Theorems · Theorem · group theory
Submonoid.isMulCommutative_iSup
∀ {M : Type u_1} [inst : MulOneClass M] {ι : Sort u_4} [Nonempty ι] {S : ι → Submonoid M}
[hS : ∀ (i : ι), IsMulCommutative ↥(S i)], Directed (fun x1 x2 => x1 ≤ x2) S → IsMulCommutative ↥(⨆ i, S i)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Submonoidstatement and proof · cited by 3,086
- iSupstatement · cited by 2,415
- MulOneClassstatement and proof · cited by 1,018
- Directedstatement and proof · cited by 213
- IsMulCommutativestatement and proof · cited by 95
- IsMulCommutative.of_setLike_mul_commproof · cited by 16
- setLike_mul_commproof · cited by 6
- Submonoid.coe_iSup_of_directedproof · cited by 3
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