ofRightInverseOfCardLE — Mathlib

English

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

Русский

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

LaTeX

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

Lean4

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

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