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chore(algebra/ordered_group): deduplicate (#5403)
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I deleted many `a_of_b` lemmas for which `a_iff_b` existed, then restored (most? all?) of them using `alias` command.
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urkud committed Dec 19, 2020
1 parent 63e7fc9 commit 5de6757
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2 changes: 1 addition & 1 deletion src/algebra/group_power/lemmas.lean
Expand Up @@ -365,7 +365,7 @@ calc 1 + (n + 2) •ℕ a ≤ 1 + (n + 2) •ℕ a + (n •ℕ (a * a * (2 + a))
/-- Bernoulli's inequality reformulated to estimate `a^n`. -/
theorem one_add_sub_mul_le_pow [linear_ordered_ring R]
{a : R} (H : -1 ≤ a) (n : ℕ) : 1 + n •ℕ (a - 1) ≤ a ^ n :=
have -2 ≤ a - 1, by { rw [bit0, neg_add, ← sub_eq_add_neg], exact sub_le_sub_right H 1 },
have -2 ≤ a - 1, by rwa [bit0, neg_add, ← sub_eq_add_neg, sub_le_sub_iff_right],
by simpa only [add_sub_cancel'_right] using one_add_mul_le_pow this n

namespace int
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