fst — Mathlib

English

The application lemma holds: sumArrowEquivProdArrow_apply (x) = Equiv.sumArrowEquivProdArrow α β S x.

Русский

Лемма применения: sumArrowEquivProdArrow_apply( x ) = Equiv.sumArrowEquivProdArrow α β S x.

LaTeX

$$$$ \mathrm{sumArrowEquivProdArrow}(α, β, R, S)\;x = \mathrm{Equiv}.\mathrm{sumArrowEquivProdArrow}(α, β, S)\;x. $$$$

Lean4

/-- First projection as `AlgHom`. -/
def fst : A × B →ₐ[R] A :=
  { RingHom.fst A B with commutes' := fun _r => rfl }

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