cycleOf — Mathlib

English

cycleOf f x equals if f x = x then 1 else f; i.e., the cycleOf is 1 on fixed points and f otherwise.

Русский

cycleOf f x равно 1 если f x = x, и равно f иначе.

LaTeX

$$cycleOf [DecRel f.SameCycle] (hf : IsCycle f) : cycleOf f x = if f x = x then 1 else f$$

Lean4

protected theorem cycleOf [DecidableRel f.SameCycle] [DecidableEq α] (hf : IsCycle f) :
    cycleOf f x = if f x = x then 1 else f := by
  by_cases hx : f x = x
  · rwa [if_pos hx, cycleOf_eq_one_iff]
  · rwa [if_neg hx, hf.cycleOf_eq]

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