nthHomSeq_one — Mathlib

English

nthHomSeq f_compat 1 ≈ 1 in ZMod(p).

Русский

nthHomSeq f_compat 1 эквивалентно 1 в ZMod(p).

LaTeX

$$nthHomSeq f_compat 1 ≈ 1$$

Lean4

theorem nthHomSeq_one : nthHomSeq f_compat 1 ≈ 1 := by
  intro ε hε
  change _ < _ at hε
  use 1
  intro j hj
  haveI : Fact (1 < p ^ j) := ⟨Nat.one_lt_pow (by cutsat) hp_prime.1.one_lt⟩
  suffices (ZMod.cast (1 : ZMod (p ^ j)) : ℚ) = 1 by simp [nthHomSeq, nthHom, this, hε]
  rw [ZMod.cast_eq_val, ZMod.val_one, Nat.cast_one]

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