[Merged by Bors] - feat(analysis/convex/between): more transitivity variants #17527
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Add more variants of transitivity lemmas, giving that one endpoint is not equal to the middle point in cases where the hypotheses imply weak betweenness (and we already have the corresponding transitivity lemmas for that), and that one endpoint is not equal to the middle point, but don't imply strict betweenness.
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YaelDillies
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| lemma wbtw.trans_left_ne [no_zero_smul_divisors R V] {w x y z : P} (h₁ : wbtw R w y z) | ||
| (h₂ : wbtw R w x y) (h : y ≠ z) : x ≠ z := |
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This to me reads like you're doing transitivity on the rightmost two elements, so it should rather be
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| lemma wbtw.trans_left_ne [no_zero_smul_divisors R V] {w x y z : P} (h₁ : wbtw R w y z) | |
| (h₂ : wbtw R w x y) (h : y ≠ z) : x ≠ z := | |
| lemma wbtw.trans_right_ne [no_zero_smul_divisors R V] {w x y z : P} (h₁ : wbtw R w x y) | |
| (h₂ : wbtw R w y z) (h : y ≠ z) : x ≠ z := |
but I see you already have been using another in the rest of the file.
jcommelin
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Dec 6, 2022
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Add more variants of transitivity lemmas, giving that one endpoint is not equal to the middle point in cases where the hypotheses imply weak betweenness (and we already have the corresponding transitivity lemmas for that), and that one endpoint is not equal to the middle point, but don't imply strict betweenness.
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Add more variants of transitivity lemmas, giving that one endpoint is not equal to the middle point in cases where the hypotheses imply weak betweenness (and we already have the corresponding transitivity lemmas for that), and that one endpoint is not equal to the middle point, but don't imply strict betweenness.