truncate_liftFun — Mathlib

English

For hm : n ≤ m, (TruncatedWittVector.truncate hm).comp (WittVector.truncate m) = WittVector.truncate n.

Русский

Для hm: n ≤ m, (TruncatedWittVector.truncate hm).comp (WittVector.truncate m) = WittVector.truncate n.

LaTeX

$$$$ ((\\mathrm{TruncatedWittVector.truncate} hm).comp (\\mathrm{WittVector.truncate} m)) = \\mathrm{WittVector.truncate} n. $$$$

Lean4

@[simp]
theorem truncate_liftFun (s : S) : WittVector.truncate n (liftFun f s) = f n s :=
  by
  ext i
  simp only [liftFun, TruncatedWittVector.coeff_mk, WittVector.truncate_mk']
  rw [← f_compat (i + 1) n i.is_lt, RingHom.comp_apply, TruncatedWittVector.coeff_truncate]
  congr 1 with _

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