card_eq_card_units_add_one — Mathlib

English

For finite α and β, Infinite (α ⊕ β) holds iff Infinite α or Infinite β.

Русский

Для конечных α и β условие Infinite(α ⊕ β) эквивалентно Infinite(α) или Infinite(β).

LaTeX

$$$$\\text{Infinite}(\\alpha \\oplus \\beta) \\iff \\text{Infinite}(\\alpha) \\lor \\text{Infinite}(\\beta).$$$$

Lean4

theorem card_eq_card_units_add_one [GroupWithZero α] [Fintype α] [DecidableEq α] :
    Fintype.card α = Fintype.card αˣ + 1 := by rw [Fintype.card_units, tsub_add_cancel_of_le Fintype.card_pos]

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