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chore(algebra/field_power): slightly simplify proof of min_le_of_zpow…
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…_le_max (#13023)
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Ruben-VandeVelde committed Mar 29, 2022
1 parent 541c80d commit d5fee32
Showing 1 changed file with 2 additions and 3 deletions.
5 changes: 2 additions & 3 deletions src/algebra/field_power.lean
Expand Up @@ -169,9 +169,8 @@ lemma min_le_of_zpow_le_max {x : K} (hx : 1 < x) {a b c : ℤ}
(h_max : x ^ (-c) ≤ max (x ^ (-a)) (x ^ (-b)) ) : min a b ≤ c :=
begin
rw min_le_iff,
cases le_max_iff.mp h_max with h; [left, right];
rw [zpow_le_iff_le hx, neg_le_neg_iff] at h;
exact h
refine or.imp (λ h, _) (λ h, _) (le_max_iff.mp h_max);
rwa [zpow_le_iff_le hx, neg_le_neg_iff] at h
end

@[simp] lemma pos_div_pow_pos {a b : K} (ha : 0 < a) (hb : 0 < b) (k : ℕ) : 0 < a/b^k :=
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