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[Merged by Bors] - refactor(set_theory/game/pgame): rename and add theorems like -y ≤ -x ↔ x ≤ y
#14653
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src/set_theory/game/pgame.lean
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| by rw [←neg_fuzzy_iff, pgame.neg_zero] | ||
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| theorem neg_congr {x y : pgame} (h : x ≈ y) : -x ≈ -y := | ||
| ⟨neg_le_neg_iff.2 h.2, neg_le_neg_iff.2 h.1⟩ |
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This is now just neg_equiv_neg_iff.2 h, isn't it?
Also, this might be better named equiv.neg for dot notation
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I'll just remove this theorem for now. If we decide in the future that the forward directions of these lemmas deserve names, I'll be sure to give them dot notation.
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…x ↔ x ≤ y` (#14653) For `*` in `le`, `lf`, `lt`, we rename `neg_*_iff : -y * -x ↔ x * y` to `neg_*_neg_iff`, and add the theorems `neg_*_iff : -y * x ↔ x * -y`. We further add many missing corresponding theorems for equivalence and fuzziness.
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-y ≤ -x ↔ x ≤ y-y ≤ -x ↔ x ≤ y
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For
*inle,lf,lt, we renameneg_*_iff : -y * -x ↔ x * ytoneg_*_neg_iff, and add the theoremsneg_*_iff : -y * x ↔ x * -y.We further add many missing corresponding theorems for equivalence and fuzziness.