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[Merged by Bors] - chore(algebra/ordered_field): cleanup #3723
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* 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_ot_of_div_lt_of_neg` 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.
sgouezel
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Aug 9, 2020
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Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr>
* 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 `mul_lt_of_div_lt_of_neg` to `mul_lt_of_neg_of_div_lt`; * 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`;
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* 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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* 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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chore(algebra/ordered_field): cleanup
[Merged by Bors] - chore(algebra/ordered_field): cleanup
Aug 10, 2020
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mul_zero_lt_mul_inv_of_pos
andmul_zero_lt_mul_inv_of_neg
;iff
lemmasone_div_pos/neg/nonneg/nonpos
replacing oldimplications;
≤
instead of<
;mul_lt_of_gt_div_of_neg
tomul_lt_of_neg_of_div_lt
replacing
>
by<
.mul_sub_mul_div_mul_neg_iff
andmul_sub_mul_div_mul_nonpos_iff
,generate implications using
alias
;div_pos_of_pos_of_pos
(usediv_pos
) anddiv_nonneg_of_nonneg_of_pos
(usediv_nonneg
);div_nonpos_of_nonpos_of_pos
withdiv_nonpos_of_nonpos_of_nonneg
;div_nonpos_of_nonneg_of_neg
withdiv_nonpos_of_nonneg_of_nonpos
;div_mul_le_div_mul_of_div_le_div_pos
anddiv_mul_le_div_mul_of_div_le_div_pos'
withdiv_mul_le_div_mul_of_div_le_div_nonneg
; I failed to findin the history why we had two equivalent lemmas.
le_mul_of_ge_one_right
andle_mul_of_one_le_right'
intole_mul_of_one_le_right
, rename oldle_mul_of_one_le_right
tole_mul_of_one_le_right'
;le_mul_of_ge_one_left
,le_mul_of_one_le_left
, andle_mul_of_one_le_left'
;lt_mul_of_gt_one_right
,lt_mul_of_one_lt_right
, andlt_mul_of_one_lt_right'
;div_lt_of_mul_lt_of_pos
todiv_lt_of_pos_of_lt_mul
;div_lt_of_mul_gt_of_neg
todiv_lt_of_neg_of_mul_lt
;mul_le_of_div_le_of_neg
tomul_le_of_neg_of_div_le
;div_le_of_mul_le_of_neg
todiv_le_of_neg_of_mul_le
;div_lt_div_of_lt_of_pos
todiv_lt_div_of_pos_of_lt
, swaparguments;
div_le_div_of_le_of_pos
todiv_le_div_of_pos_of_le
, swaparguments;
div_lt_div_of_lt_of_neg
todiv_lt_div_of_neg_of_lt
, swaparguments;
div_le_div_of_le_of_neg
todiv_le_div_of_neg_of_le
, swaparguments;
one_div_lt_one_div_of_lt_of_neg
toone_div_lt_one_div_of_neg_of_lt
;one_div_le_one_div_of_le_of_neg
toone_div_le_one_div_of_neg_of_le
;le_of_one_div_le_one_div_of_neg
tole_of_neg_of_one_div_le_one_div
;lt_of_one_div_lt_one_div_of_neg
tolt_of_neg_of_one_div_lt_one_div
;one_div_le_of_one_div_le_of_pos
toone_div_le_of_pos_of_one_div_le
;one_div_le_of_one_div_le_of_neg
toone_div_le_of_neg_of_one_div_le
.