prodEquiv — Mathlib

English

The product of nonunital subsemirings is isomorphic to their product as semigroups.

Русский

Произведение неупорядоченных подполусемирингов изоморфно их произведению как полупервыми.

LaTeX

$$$\\operatorname{prodEquiv}(s,t) : s.prod t \\cong+* s \\times t$$$

Lean4

/-- Product of non-unital subsemirings is isomorphic to their product as semigroups. -/
def prodEquiv (s : NonUnitalSubsemiring R) (t : NonUnitalSubsemiring S) : s.prod t ≃+* s × t :=
  { Equiv.Set.prod (s : Set R) (t : Set S) with
    map_mul' := fun _ _ => rfl
    map_add' := fun _ _ => rfl }

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