[Merged by Bors] - refactor(algebra/order/ring): turn sq_le_sq into an iff
#14511
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| @@ -341,57 +341,46 @@ by simpa only [sq] using abs_mul_abs_self x | |||
| theorem abs_sq (x : R) : |x ^ 2| = x ^ 2 := | |||
| by simpa only [sq] using abs_mul_self x | |||
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| theorem sq_lt_sq (h : |x| < |y|) : x ^ 2 < y ^ 2 := | |||
| by simpa only [sq_abs] using pow_lt_pow_of_lt_left h (abs_nonneg x) (1:ℕ).succ_pos | |||
| theorem sq_lt_sq : x ^ 2 < y ^ 2 ↔ |x| < |y| := | |||
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Shouldn't this be called sq_lt_sq_iff or something like that?
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We're not very consistent about iffs. E.g., we have sub_pos. Formally, this should be something like sq_lt_sq_iff_abs_lt_abs but this is to long.
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Thanks! bors merge |
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sq_le_sq into an iffsq_le_sq into an iff
tomaz1502
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Jun 3, 2022
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sq_le_sqandsq_lt_sqare nowifflemmas;abs_le_abs_of_sq_le_sqandabs_lt_abs_of_sq_lt_sq.