mathlib3
9e039956 - chore(algebra/ordered_field): cleanup (#3723)

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5 years ago
chore(algebra/ordered_field): cleanup (#3723) * drop `mul_zero_lt_mul_inv_of_pos` and `mul_zero_lt_mul_inv_of_neg`; * add `iff` lemmas `one_div_pos/neg/nonneg/nonpos` replacing old implications; * some lemmas now assume `≤` instead of `<`; * rename `mul_lt_of_gt_div_of_neg` to `mul_lt_of_neg_of_div_lt` replacing `>` by `<`. * add `mul_sub_mul_div_mul_neg_iff` and `mul_sub_mul_div_mul_nonpos_iff`, generate implications using `alias`; * drop `div_pos_of_pos_of_pos` (use `div_pos`) and `div_nonneg_of_nonneg_of_pos` (use `div_nonneg`); * replace `div_nonpos_of_nonpos_of_pos` with `div_nonpos_of_nonpos_of_nonneg`; * replace `div_nonpos_of_nonneg_of_neg` with `div_nonpos_of_nonneg_of_nonpos`; * replace `div_mul_le_div_mul_of_div_le_div_pos` and `div_mul_le_div_mul_of_div_le_div_pos'` with `div_mul_le_div_mul_of_div_le_div_nonneg`; I failed to find in the history why we had two equivalent lemmas. * merge `le_mul_of_ge_one_right` and `le_mul_of_one_le_right'` into `le_mul_of_one_le_right`, rename old `le_mul_of_one_le_right` to `le_mul_of_one_le_right'`; * ditto with `le_mul_of_ge_one_left`, `le_mul_of_one_le_left`, and `le_mul_of_one_le_left'`; * ditto with `lt_mul_of_gt_one_right`, `lt_mul_of_one_lt_right`, and `lt_mul_of_one_lt_right'`; * rename `div_lt_of_mul_lt_of_pos` to `div_lt_of_pos_of_lt_mul`; * rename `div_lt_of_mul_gt_of_neg` to `div_lt_of_neg_of_mul_lt`; * rename `mul_le_of_div_le_of_neg` to `mul_le_of_neg_of_div_le`; * rename `div_le_of_mul_le_of_neg` to `div_le_of_neg_of_mul_le`; * rename `div_lt_div_of_lt_of_pos` to `div_lt_div_of_pos_of_lt`, swap arguments; * rename `div_le_div_of_le_of_pos` to `div_le_div_of_pos_of_le`, swap arguments; * rename `div_lt_div_of_lt_of_neg` to `div_lt_div_of_neg_of_lt`, swap arguments; * rename `div_le_div_of_le_of_neg` to `div_le_div_of_neg_of_le`, swap arguments; * rename `one_div_lt_one_div_of_lt_of_neg` to `one_div_lt_one_div_of_neg_of_lt`; * rename `one_div_le_one_div_of_le_of_neg` to `one_div_le_one_div_of_neg_of_le`; * rename `le_of_one_div_le_one_div_of_neg` to `le_of_neg_of_one_div_le_one_div`; * rename `lt_of_one_div_lt_one_div_of_neg` to `lt_of_neg_of_one_div_lt_one_div`; * rename `one_div_le_of_one_div_le_of_pos` to `one_div_le_of_pos_of_one_div_le`; * rename `one_div_le_of_one_div_le_of_neg` to `one_div_le_of_neg_of_one_div_le`.
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