isLeftRegular_mk — Mathlib

English

For R,S with multiplications, IsLeftRegular (a,b) holds iff IsLeftRegular a and IsLeftRegular b.

Русский

Для пар (a,b) в пределах R × S верно: IsLeftRegular (a,b) ⇔ IsLeftRegular a ∧ IsLeftRegular b.

LaTeX

$$IsLeftRegular( { fst := a, snd := b } ) \iff IsLeftRegular a ∧ IsLeftRegular b$$

Lean4

@[to_additive (attr := simp)]
theorem isLeftRegular_mk {a : R} {b : S} : IsLeftRegular (a, b) ↔ IsLeftRegular a ∧ IsLeftRegular b :=
  have : Nonempty R := ⟨a⟩;
  have : Nonempty S := ⟨b⟩;
  Prod.map_injective

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