pow_smul_ne_of_lt_period — Mathlib

English

If hmt: IsMultiplyPretransitive G α (|α|−2), then alternatingGroup α ≤ G.

Русский

Если hmt: IsMultiplyPretransitive G α (|α|−2), то alternatingGroup α ≤ G.

LaTeX

$$alternatingGroup α ≤ G$$

Lean4

/-- For any non-zero `n` less than the period of `m` on `a`, `a` is moved by `m ^ n`. -/
@[to_additive /-- For any non-zero `n` less than the period of `m` on `a`, `a` is moved by `n • m`. -/
    ]
theorem pow_smul_ne_of_lt_period {m : M} {a : α} {n : ℕ} (n_pos : 0 < n) (n_lt_period : n < period m a) :
    m ^ n • a ≠ a := fun a_fixed => not_le_of_gt n_lt_period <| period_le_of_fixed n_pos a_fixed

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