ofLeftInverseOfCardLE — Mathlib

English

From a left inverse and a card inequality, construct an equivalence α ≃ β.

Русский

Из левой обратной и неравенства кардиналов строится эквив α ≃ β.

LaTeX

$$$\\text{There exists } f: α \\to β, g: β \\to α \\text{ with left inverse and card bound } \\Rightarrow α \\simeq β$$$

Lean4

/-- Construct an equivalence from functions that are inverse to each other. -/
@[simps]
def ofLeftInverseOfCardLE (hβα : card β ≤ card α) (f : α → β) (g : β → α) (h : LeftInverse g f) : α ≃ β
    where
  toFun := f
  invFun := g
  left_inv := h
  right_inv := h.rightInverse_of_card_le hβα

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