flip — Mathlib

English

Each basis vector of adjustToOrientation is either the corresponding vector or its negation.

Русский

Каждый вектор базиса adjustToOrientation равен соответствующему вектору или его отрицанию.

LaTeX

$$$$ \\text{For all } i,\\; e.{\\rm adjustToOrientation} x\\,i = e\\,i \\quad\\lor\\quad e.{\\rm adjustToOrientation} x\\,i = -e\\,i $$$$

Lean4

/-- Given a perfect pairing between `M`and `N`, we may interchange the roles of `M` and `N`. -/
protected theorem flip (hp : p.IsPerfPair) : p.flip.IsPerfPair
    where
  bijective_left := IsPerfPair.bijective_right p
  bijective_right := IsPerfPair.bijective_left p

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