Theorems · Definition · group theory

Submonoid.prodEquiv

{N : Type u_2} →
  [inst : MulOneClass N] →
    {M : Type u_5} → [inst_1 : MulOneClass M] → (s : Submonoid M) → (t : Submonoid N) → ↥(s.prod t) ≃* ↥s × ↥t

The product of Submonoids is isomorphic to their product as Monoids.

Defined in: Mathlib.Algebra.Group.Submonoid.Operations
Cited by: 0 results in Mathlib
Foundations: Depth 16 from the axioms · uses no axioms
Assumes: MulOneClass MulOneClass

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Equivproof · cited by 8,337
SetLike.coeproof · cited by 8,199
Set.Elemproof · cited by 7,166
Submonoidstatement and proof · cited by 3,086
SProd.sprodproof · cited by 1,750
MulEquivstatement · cited by 1,142
MulOneClassstatement and proof · cited by 1,018
Submonoid.prodstatement · cited by 27
Equiv.Set.prodproof · cited by 9

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