opProdIsoCoprod_hom_fst — Mathlib

English

The inverse composed with the lift of f' equals the desc of f'.op in the opposite setting.

Русский

Обратное композицию с подъемом f' даёт desc(f'.op) в противоположной настройке.

LaTeX

$$(opProductIsoCoproduct' hf hc).inv ≫ (hf.lift f').op = hc.desc f'.op$$

Lean4

@[reassoc (attr := simp)]
theorem opProdIsoCoprod_hom_fst : (opProdIsoCoprod A B).hom.unop ≫ prod.fst = coprod.inl.unop := by
  simp [opProdIsoCoprod]

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