pprodCongr — Mathlib

English

If e is a PartialEquiv and e' is an Equiv, then transEquiv equals trans with toPartialEquiv.

Русский

Если e — PartialEquiv, а e' — Equiv, то transEquiv равен трансформации trans через toPartialEquiv.

LaTeX

$$$e.transEquiv e' = e.trans e'.toPartialEquiv$$$

Lean4

/-- Product of two equivalences, in terms of `PProd`. If `α ≃ β` and `γ ≃ δ`, then
`PProd α γ ≃ PProd β δ`. -/
@[simps (attr := grind =) apply symm_apply]
def pprodCongr (e₁ : α ≃ β) (e₂ : γ ≃ δ) : PProd α γ ≃ PProd β δ
    where
  toFun x := ⟨e₁ x.1, e₂ x.2⟩
  invFun x := ⟨e₁.symm x.1, e₂.symm x.2⟩
  left_inv := by grind
  right_inv := by grind

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