[Merged by Bors] - feat(Geometry/Euclidean/Angle/Oriented/RightAngle): angles less than π / 2#30600
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[Merged by Bors] - feat(Geometry/Euclidean/Angle/Oriented/RightAngle): angles less than π / 2#30600jsm28 wants to merge 3 commits intoleanprover-community:masterfrom
π / 2#30600jsm28 wants to merge 3 commits intoleanprover-community:masterfrom
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…ality of twice angles
Add lemmas that two angles less than `π / 2` are equal if and only if
twice those angles are equal, along with a separate lemma
```lean
lemma toReal_neg_eq_neg_toReal_iff {θ : Angle} : (-θ).toReal = -(θ.toReal) ↔ θ ≠ π := by
```
which isn't directly connected but turns out to be useful in the same
application (dealing with angles in right-angled triangles that are
less then `π / 2`, when you have two such triangles that are
oppositely-oriented).
…`π / 2` Add a lemma that an oriented angle in a right-angled triangle is less than `π / 2`, even in degenerate cases (there's already a corresponding lemma for unoriented angles, but that one needs to exclude some degenerate cases because of the different default values for oriented and unoriented angles involving zero vectors). Deduce lemmas that, for such angles involved in right-angled triangles, equality of the angles (i.e. equality mod 2π) follows from equality of twice the angles (i.e. equality of the angles mod π).
PR summary 4086670d5aImport changes for modified filesNo significant changes to the import graph Import changes for all files
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…`π / 2` (#30600) Add a lemma that an oriented angle in a right-angled triangle is less than `π / 2`, even in degenerate cases (there's already a corresponding lemma for unoriented angles, but that one needs to exclude some degenerate cases because of the different default values for oriented and unoriented angles involving zero vectors). Deduce lemmas that, for such angles involved in right-angled triangles, equality of the angles (i.e. equality mod 2π) follows from equality of twice the angles (i.e. equality of the angles mod π).
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…`π / 2` (leanprover-community#30600) Add a lemma that an oriented angle in a right-angled triangle is less than `π / 2`, even in degenerate cases (there's already a corresponding lemma for unoriented angles, but that one needs to exclude some degenerate cases because of the different default values for oriented and unoriented angles involving zero vectors). Deduce lemmas that, for such angles involved in right-angled triangles, equality of the angles (i.e. equality mod 2π) follows from equality of twice the angles (i.e. equality of the angles mod π).
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…`π / 2` (leanprover-community#30600) Add a lemma that an oriented angle in a right-angled triangle is less than `π / 2`, even in degenerate cases (there's already a corresponding lemma for unoriented angles, but that one needs to exclude some degenerate cases because of the different default values for oriented and unoriented angles involving zero vectors). Deduce lemmas that, for such angles involved in right-angled triangles, equality of the angles (i.e. equality mod 2π) follows from equality of twice the angles (i.e. equality of the angles mod π).
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Add a lemma that an oriented angle in a right-angled triangle is less than
π / 2, even in degenerate cases (there's already a corresponding lemma for unoriented angles, but that one needs to exclude some degenerate cases because of the different default values for oriented and unoriented angles involving zero vectors). Deduce lemmas that, for such angles involved in right-angled triangles, equality of the angles (i.e. equality mod 2π) follows from equality of twice the angles (i.e. equality of the angles mod π).