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994 | 994 |
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995 | 995 | /-- If the signs of two oriented angles between nonzero vectors are equal, the oriented angles are
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996 | 996 | equal if and only if the unoriented angles are equal. -/
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997 |
| -lemma oangle_eq_iff_angle_eq_of_sign_eq {w x y z : V} (hw : w ≠ 0) (hx : x ≠ 0) (hy : y ≠ 0) |
| 997 | +lemma angle_eq_iff_oangle_eq_of_sign_eq {w x y z : V} (hw : w ≠ 0) (hx : x ≠ 0) (hy : y ≠ 0) |
998 | 998 | (hz : z ≠ 0) (hs : (b.oangle w x).sign = (b.oangle y z).sign) :
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999 | 999 | inner_product_geometry.angle w x = inner_product_geometry.angle y z ↔
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1000 | 1000 | b.oangle w x = b.oangle y z :=
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@@ -1699,11 +1699,11 @@ lemma oangle_eq_of_angle_eq_of_sign_eq {w x y z : V}
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1699 | 1699 |
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1700 | 1700 | /-- If the signs of two oriented angles between nonzero vectors are equal, the oriented angles are
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1701 | 1701 | equal if and only if the unoriented angles are equal. -/
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1702 |
| -lemma oangle_eq_iff_angle_eq_of_sign_eq {w x y z : V} (hw : w ≠ 0) (hx : x ≠ 0) (hy : y ≠ 0) |
| 1702 | +lemma angle_eq_iff_oangle_eq_of_sign_eq {w x y z : V} (hw : w ≠ 0) (hx : x ≠ 0) (hy : y ≠ 0) |
1703 | 1703 | (hz : z ≠ 0) (hs : (o.oangle w x).sign = (o.oangle y z).sign) :
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1704 | 1704 | inner_product_geometry.angle w x = inner_product_geometry.angle y z ↔
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1705 | 1705 | o.oangle w x = o.oangle y z :=
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1706 |
| -(ob).oangle_eq_iff_angle_eq_of_sign_eq hw hx hy hz hs |
| 1706 | +(ob).angle_eq_iff_oangle_eq_of_sign_eq hw hx hy hz hs |
1707 | 1707 |
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1708 | 1708 | /-- The oriented angle between two nonzero vectors is zero if and only if the unoriented angle
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1709 | 1709 | is zero. -/
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@@ -1932,10 +1932,10 @@ lemma oangle_eq_of_angle_eq_of_sign_eq {p₁ p₂ p₃ p₄ p₅ p₆ : P} (h :
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1932 | 1932 |
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1933 | 1933 | /-- If the signs of two nondegenerate oriented angles between points are equal, the oriented
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1934 | 1934 | angles are equal if and only if the unoriented angles are equal. -/
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1935 |
| -lemma oangle_eq_iff_angle_eq_of_sign_eq {p₁ p₂ p₃ p₄ p₅ p₆ : P} (hp₁ : p₁ ≠ p₂) (hp₃ : p₃ ≠ p₂) |
| 1935 | +lemma angle_eq_iff_oangle_eq_of_sign_eq {p₁ p₂ p₃ p₄ p₅ p₆ : P} (hp₁ : p₁ ≠ p₂) (hp₃ : p₃ ≠ p₂) |
1936 | 1936 | (hp₄ : p₄ ≠ p₅) (hp₆ : p₆ ≠ p₅) (hs : (∡ p₁ p₂ p₃).sign = (∡ p₄ p₅ p₆).sign) :
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1937 | 1937 | ∠ p₁ p₂ p₃ = ∠ p₄ p₅ p₆ ↔ ∡ p₁ p₂ p₃ = ∡ p₄ p₅ p₆ :=
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1938 |
| -(o).oangle_eq_iff_angle_eq_of_sign_eq (vsub_ne_zero.2 hp₁) (vsub_ne_zero.2 hp₃) |
| 1938 | +(o).angle_eq_iff_oangle_eq_of_sign_eq (vsub_ne_zero.2 hp₁) (vsub_ne_zero.2 hp₃) |
1939 | 1939 | (vsub_ne_zero.2 hp₄) (vsub_ne_zero.2 hp₆) hs
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1940 | 1940 |
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1941 | 1941 | /-- The unoriented angle at `p` between two points not equal to `p` is zero if and only if the
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