Theorems · Definition · group theory
Subsemigroup.prodEquiv
{M : Type u_1} →
{N : Type u_2} →
[inst : Mul M] → [inst_1 : Mul N] → (s : Subsemigroup M) → (t : Subsemigroup N) → ↥(s.prod t) ≃* ↥s × ↥tThe product of subsemigroups is isomorphic to their product as semigroups.
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- Depth 13 from the axioms · uses no axioms
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivproof · cited by 8,337
- SetLike.coeproof · cited by 8,199
- Set.Elemproof · cited by 7,166
- SProd.sprodproof · cited by 1,750
- MulEquivstatement · cited by 1,142
- Subsemigroupstatement and proof · cited by 323
- Subsemigroup.prodstatement · cited by 11
- Equiv.Set.prodproof · cited by 9
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