module
string
startPos
dict
endPos
dict
nextStartPos
dict
goals
list
goalsAfter
list
ppTac
string
elaborator
string
kind
string
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle
{ "line": 457, "column": 6 }
{ "line": 457, "column": 12 }
{ "line": 457, "column": 13 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\np₁ p₂ p₃ : P\nh : ⟪p₂ -ᵥ p₃, p₁ -ᵥ p₂⟫ = 0\nh0 : p₂ -ᵥ p₃ = 0 ∨ p₁ -ᵥ p₂ ≠ 0\n⊢ dist p₁ p₂ / Real.sin (∠ p₂ p₃ p₁) = dist p₁ p₃", "ppTerm": "?m.143", "...
[ "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\np₁ p₂ p₃ : P\nh : ⟪p₂ -ᵥ p₃, p₁ -ᵥ p₂⟫ = 0\nh0 : p₂ -ᵥ p₃ = 0 ∨ p₁ -ᵥ p₂ ≠ 0\n⊢ dist p₁ p₂ / Real.sin (InnerProductGeometry.angle (p₂ -ᵥ p₃) (p₁ -ᵥ p₃)) = dist p₁ p₃" ]
angle,
Lean.Elab.Tactic.evalRewriteSeq
null
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle
{ "line": 464, "column": 6 }
{ "line": 464, "column": 12 }
{ "line": 464, "column": 13 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\np₁ p₂ p₃ : P\nh : ∠ p₁ p₂ p₃ = π / 2\nh0 : p₁ ≠ p₂ ∨ p₃ = p₂\n⊢ dist p₁ p₂ / Real.tan (∠ p₂ p₃ p₁) = dist p₃ p₂", "ppTerm": "?m.35", "assigned": true, ...
[ "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\np₁ p₂ p₃ : P\nh : InnerProductGeometry.angle (p₁ -ᵥ p₂) (p₃ -ᵥ p₂) = π / 2\nh0 : p₁ ≠ p₂ ∨ p₃ = p₂\n⊢ dist p₁ p₂ / Real.tan (∠ p₂ p₃ p₁) = dist p₃ p₂" ]
angle,
Lean.Elab.Tactic.evalRewriteSeq
null
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle
{ "line": 467, "column": 6 }
{ "line": 467, "column": 12 }
{ "line": 467, "column": 13 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\np₁ p₂ p₃ : P\nh : ⟪p₂ -ᵥ p₃, p₁ -ᵥ p₂⟫ = 0\nh0 : p₂ -ᵥ p₃ = 0 ∨ p₁ -ᵥ p₂ ≠ 0\n⊢ dist p₁ p₂ / Real.tan (∠ p₂ p₃ p₁) = dist p₃ p₂", "ppTerm": "?m.143", "...
[ "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\np₁ p₂ p₃ : P\nh : ⟪p₂ -ᵥ p₃, p₁ -ᵥ p₂⟫ = 0\nh0 : p₂ -ᵥ p₃ = 0 ∨ p₁ -ᵥ p₂ ≠ 0\n⊢ dist p₁ p₂ / Real.tan (InnerProductGeometry.angle (p₂ -ᵥ p₃) (p₁ -ᵥ p₃)) = dist p₃ p₂" ]
angle,
Lean.Elab.Tactic.evalRewriteSeq
null
Mathlib.Geometry.Euclidean.Angle.Unoriented.Projection
{ "line": 33, "column": 6 }
{ "line": 33, "column": 12 }
{ "line": 33, "column": 13 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\np p' : P\ns : AffineSubspace ℝ P\ninst✝ : s.direction.HasOrthogonalProjection\nh : p' ∈ s\nthis : Nonempty ↥s\n⊢ ∠ p (↑((orthogonalProjection s) p)) p' = π / ...
[ "V : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\np p' : P\ns : AffineSubspace ℝ P\ninst✝ : s.direction.HasOrthogonalProjection\nh : p' ∈ s\nthis : Nonempty ↥s\n⊢ InnerProductGeometry.angle (p -ᵥ ↑((orthogonalProjection ...
angle,
Lean.Elab.Tactic.evalRewriteSeq
null
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic
{ "line": 886, "column": 6 }
{ "line": 886, "column": 29 }
{ "line": 886, "column": 30 }
[ { "pp": "V : Type u_1\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace ℝ V\ninst✝ : Fact (finrank ℝ V = 2)\no : Orientation ℝ V (Fin 2)\nx y : V\nr : ℝ\n⊢ (o.oangle (r • y - x) y).sign = -(o.oangle x y).sign", "ppTerm": "?m.43", "assigned": true, "usedConstants": [ "Eq.mpr", "I...
[ "V : Type u_1\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace ℝ V\ninst✝ : Fact (finrank ℝ V = 2)\no : Orientation ℝ V (Fin 2)\nx y : V\nr : ℝ\n⊢ (o.oangle (r • y - x) y).sign = (o.oangle (-x) y).sign" ]
← oangle_sign_neg_left,
Lean.Elab.Tactic.evalRewriteSeq
null
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine
{ "line": 851, "column": 11 }
{ "line": 851, "column": 17 }
{ "line": 851, "column": 18 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\nhd2 : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np₁ p₂ p₃ p₄ : P\nhp₁ : p₁ ≠ p₂\nhp₄ : p₄ ≠ p₂\n⊢ ∠ p₁ p₂ p₃ = ∠ p₃ p₂ p₄ ↔ ∡ p₁ p₂ p₃ = ∡ p₃ p₂ p₄...
[ "V : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\nhd2 : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np₁ p₂ p₃ p₄ : P\nhp₁ : p₁ ≠ p₂\nhp₄ : p₄ ≠ p₂\n⊢ InnerProductGeometry.angle (p₁ -ᵥ p₂) (p₃ -ᵥ p₂) = InnerProdu...
angle,
Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1
null
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic
{ "line": 961, "column": 25 }
{ "line": 961, "column": 61 }
{ "line": 961, "column": 62 }
[ { "pp": "case neg.inl\nV : Type u_1\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace ℝ V\ninst✝ : Fact (finrank ℝ V = 2)\no : Orientation ℝ V (Fin 2)\nx y : V\nhn : ¬x = y\nhy : y ≠ 0\nr : ℝ\nh : r + 1 = 1 ∨ ‖y‖ = 0\nhr0 : 0 ≤ r\nhr : (r + 1) • y = x\n⊢ |(o.oangle (y - x) y).toReal| < π / 2", "ppT...
[ "case neg.inl\nV : Type u_1\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace ℝ V\ninst✝ : Fact (finrank ℝ V = 2)\no : Orientation ℝ V (Fin 2)\nx y : V\nhn : ¬x = y\nhy : y ≠ 0\nr : ℝ\nh : r + 1 = 1\nhr0 : 0 ≤ r\nhr : (r + 1) • y = x\n⊢ |(o.oangle (y - x) y).toReal| < π / 2" ]
or_iff_left (norm_ne_zero_iff.2 hy),
Lean.Elab.Tactic.evalRewriteSeq
null
Mathlib.Geometry.Euclidean.SignedDist
{ "line": 257, "column": 80 }
{ "line": 258, "column": 70 }
{ "line": 260, "column": 0 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\ns : AffineSubspace ℝ P\ninst✝¹ : Nonempty ↥s\ninst✝ : s.direction.HasOrthogonalProjection\np x : P\n⊢ (s.signedInfDist p) x = ((signedDist (p -ᵥ ↑((orthogonal...
[]
by rw [signedInfDist_eq_signedDist_of_mem (orthogonalProjection_mem x)]
[anonymous]
Lean.Parser.Term.byTactic
Mathlib.Geometry.Euclidean.PerpBisector
{ "line": 96, "column": 47 }
{ "line": 96, "column": 70 }
{ "line": 96, "column": 71 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nc p₁ p₂ : P\n⊢ c ∈ perpBisector p₁ p₂ ↔ ⟪c -ᵥ p₁, p₂ -ᵥ p₁⟫ + ⟪c -ᵥ p₂, p₂ -ᵥ p₁⟫ = 0", "ppTerm": "?m.56", "assigned": true, "usedConstants": [ ...
[ "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nc p₁ p₂ : P\n⊢ c ∈ perpBisector p₁ p₂ ↔ ⟪c -ᵥ p₁, p₂ -ᵥ p₁⟫ = -⟪c -ᵥ p₂, p₂ -ᵥ p₁⟫" ]
add_eq_zero_iff_eq_neg,
Lean.Elab.Tactic.evalRewriteSeq
null
Mathlib.Geometry.Euclidean.Sphere.Basic
{ "line": 369, "column": 4 }
{ "line": 375, "column": 87 }
{ "line": 377, "column": 0 }
[ { "pp": "case inr\nV : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\nS : AffineSubspace ℝ P\ninst✝¹ : Nonempty ↥S\ninst✝ : S.direction.HasOrthogonalProjection\nps : Set ↥S\nh : Cospherical (Subtype.val '' ps)\np₀ : ↥S...
[]
rcases h with ⟨c, r, hr⟩ let c' : S := orthogonalProjection S c refine ⟨c', dist p₀ c', fun p hp => ?_⟩ have hp_dist : dist (p : P) c = r := by grind have hp₀_dist : dist (p₀ : P) c = r := by grind have hpp₀ : dist (p : P) (c : P) = dist (p₀ : P) (c : P) := hp_dist.trans hp₀_dist.symm exact (dis...
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Geometry.Euclidean.Sphere.Basic
{ "line": 369, "column": 4 }
{ "line": 375, "column": 87 }
{ "line": 377, "column": 0 }
[ { "pp": "case inr\nV : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\nS : AffineSubspace ℝ P\ninst✝¹ : Nonempty ↥S\ninst✝ : S.direction.HasOrthogonalProjection\nps : Set ↥S\nh : Cospherical (Subtype.val '' ps)\np₀ : ↥S...
[]
rcases h with ⟨c, r, hr⟩ let c' : S := orthogonalProjection S c refine ⟨c', dist p₀ c', fun p hp => ?_⟩ have hp_dist : dist (p : P) c = r := by grind have hp₀_dist : dist (p₀ : P) c = r := by grind have hpp₀ : dist (p : P) (c : P) = dist (p₀ : P) (c : P) := hp_dist.trans hp₀_dist.symm exact (dis...
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Geometry.Euclidean.Sphere.Basic
{ "line": 397, "column": 14 }
{ "line": 397, "column": 20 }
{ "line": 397, "column": 21 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Set P\nhs : Cospherical s\np : Fin 3 → P\nhps : Set.range p ⊆ s\nhpi : Function.Injective p\nv : V\nhv : ∀ (i : Fin 3), ∃ r, p i = r • v +ᵥ p 0\nh : v = 0\...
[]
decide
Lean.Elab.Tactic.evalDecide
Lean.Parser.Tactic.decide
Mathlib.Geometry.Euclidean.Sphere.Basic
{ "line": 397, "column": 14 }
{ "line": 397, "column": 20 }
{ "line": 397, "column": 21 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Set P\nhs : Cospherical s\np : Fin 3 → P\nhps : Set.range p ⊆ s\nhpi : Function.Injective p\nv : V\nhv : ∀ (i : Fin 3), ∃ r, p i = r • v +ᵥ p 0\nh : v = 0\...
[]
decide
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Geometry.Euclidean.Sphere.Basic
{ "line": 397, "column": 14 }
{ "line": 397, "column": 20 }
{ "line": 397, "column": 21 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Set P\nhs : Cospherical s\np : Fin 3 → P\nhps : Set.range p ⊆ s\nhpi : Function.Injective p\nv : V\nhv : ∀ (i : Fin 3), ∃ r, p i = r • v +ᵥ p 0\nh : v = 0\...
[]
decide
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Geometry.Euclidean.Sphere.Basic
{ "line": 420, "column": 46 }
{ "line": 420, "column": 52 }
{ "line": 420, "column": 52 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Set P\np : Fin 3 → P\nhps : Set.range p ⊆ s\nhpi : Function.Injective p\nv : V\nhv0 : v ≠ 0\nc : P\nr : ℝ\nhs : ∀ p ∈ s, dist p c = r\nhs' : ∀ (i : Fin 3),...
[]
decide
Lean.Elab.Tactic.evalDecide
Lean.Parser.Tactic.decide
Mathlib.Geometry.Euclidean.Sphere.Basic
{ "line": 420, "column": 46 }
{ "line": 420, "column": 52 }
{ "line": 420, "column": 52 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Set P\np : Fin 3 → P\nhps : Set.range p ⊆ s\nhpi : Function.Injective p\nv : V\nhv0 : v ≠ 0\nc : P\nr : ℝ\nhs : ∀ p ∈ s, dist p c = r\nhs' : ∀ (i : Fin 3),...
[]
decide
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Geometry.Euclidean.Sphere.Basic
{ "line": 420, "column": 46 }
{ "line": 420, "column": 52 }
{ "line": 420, "column": 52 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Set P\np : Fin 3 → P\nhps : Set.range p ⊆ s\nhpi : Function.Injective p\nv : V\nhv0 : v ≠ 0\nc : P\nr : ℝ\nhs : ∀ p ∈ s, dist p c = r\nhs' : ∀ (i : Fin 3),...
[]
decide
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Geometry.Euclidean.Sphere.Basic
{ "line": 420, "column": 67 }
{ "line": 420, "column": 73 }
{ "line": 420, "column": 73 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Set P\np : Fin 3 → P\nhps : Set.range p ⊆ s\nhpi : Function.Injective p\nv : V\nhv0 : v ≠ 0\nc : P\nr : ℝ\nhs : ∀ p ∈ s, dist p c = r\nhs' : ∀ (i : Fin 3),...
[]
decide
Lean.Elab.Tactic.evalDecide
Lean.Parser.Tactic.decide
Mathlib.Geometry.Euclidean.Sphere.Basic
{ "line": 420, "column": 67 }
{ "line": 420, "column": 73 }
{ "line": 420, "column": 73 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Set P\np : Fin 3 → P\nhps : Set.range p ⊆ s\nhpi : Function.Injective p\nv : V\nhv0 : v ≠ 0\nc : P\nr : ℝ\nhs : ∀ p ∈ s, dist p c = r\nhs' : ∀ (i : Fin 3),...
[]
decide
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Geometry.Euclidean.Sphere.Basic
{ "line": 420, "column": 67 }
{ "line": 420, "column": 73 }
{ "line": 420, "column": 73 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Set P\np : Fin 3 → P\nhps : Set.range p ⊆ s\nhpi : Function.Injective p\nv : V\nhv0 : v ≠ 0\nc : P\nr : ℝ\nhs : ∀ p ∈ s, dist p c = r\nhs' : ∀ (i : Fin 3),...
[]
decide
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Geometry.Euclidean.Sphere.Basic
{ "line": 421, "column": 12 }
{ "line": 421, "column": 18 }
{ "line": 421, "column": 19 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Set P\np : Fin 3 → P\nhps : Set.range p ⊆ s\nhpi : Function.Injective p\nv : V\nhv0 : v ≠ 0\nc : P\nr : ℝ\nhs : ∀ p ∈ s, dist p c = r\nhs' : ∀ (i : Fin 3),...
[]
decide
Lean.Elab.Tactic.evalDecide
Lean.Parser.Tactic.decide
Mathlib.Geometry.Euclidean.Sphere.Basic
{ "line": 421, "column": 12 }
{ "line": 421, "column": 18 }
{ "line": 421, "column": 19 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Set P\np : Fin 3 → P\nhps : Set.range p ⊆ s\nhpi : Function.Injective p\nv : V\nhv0 : v ≠ 0\nc : P\nr : ℝ\nhs : ∀ p ∈ s, dist p c = r\nhs' : ∀ (i : Fin 3),...
[]
decide
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Geometry.Euclidean.Sphere.Basic
{ "line": 421, "column": 12 }
{ "line": 421, "column": 18 }
{ "line": 421, "column": 19 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Set P\np : Fin 3 → P\nhps : Set.range p ⊆ s\nhpi : Function.Injective p\nv : V\nhv0 : v ≠ 0\nc : P\nr : ℝ\nhs : ∀ p ∈ s, dist p c = r\nhs' : ∀ (i : Fin 3),...
[]
decide
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Geometry.Euclidean.Basic
{ "line": 152, "column": 62 }
{ "line": 152, "column": 68 }
{ "line": 153, "column": 6 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\ns : AffineSubspace ℝ P\ninst✝ : FiniteDimensional ℝ ↥s.direction\nhd : finrank ℝ ↥s.direction = 2\nc₁ c₂ p₁ p₂ p : P\nhc₁s : c₁ ∈ s\nhc₂s : c₂ ∈ s\nhp₁s : p₁ ...
[]
decide
Lean.Elab.Tactic.evalDecide
Lean.Parser.Tactic.decide
Mathlib.Geometry.Euclidean.Sphere.Basic
{ "line": 473, "column": 4 }
{ "line": 473, "column": 81 }
{ "line": 474, "column": 2 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\np₁ p₂ p : P\ns : Sphere P\nhp₁ : p₁ ∈ s\nhp₂ : p₂ ∈ s\no : P := s.center\nt : ℝ\nhpt : (AffineMap.lineMap p₁ p₂) t = p\nht₀ : 0 ≤ t\nht₁ : t ≤ 1\nhne₁ : p ≠ p₁...
[]
rw [← hpt, vsub_left_cancel h, AffineMap.lineMap_same, AffineMap.const_apply]
Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1
Lean.Parser.Tactic.rwSeq
Mathlib.Geometry.Euclidean.Sphere.Basic
{ "line": 473, "column": 4 }
{ "line": 473, "column": 81 }
{ "line": 474, "column": 2 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\np₁ p₂ p : P\ns : Sphere P\nhp₁ : p₁ ∈ s\nhp₂ : p₂ ∈ s\no : P := s.center\nt : ℝ\nhpt : (AffineMap.lineMap p₁ p₂) t = p\nht₀ : 0 ≤ t\nht₁ : t ≤ 1\nhne₁ : p ≠ p₁...
[]
rw [← hpt, vsub_left_cancel h, AffineMap.lineMap_same, AffineMap.const_apply]
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Geometry.Euclidean.Sphere.Basic
{ "line": 473, "column": 4 }
{ "line": 473, "column": 81 }
{ "line": 474, "column": 2 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\np₁ p₂ p : P\ns : Sphere P\nhp₁ : p₁ ∈ s\nhp₂ : p₂ ∈ s\no : P := s.center\nt : ℝ\nhpt : (AffineMap.lineMap p₁ p₂) t = p\nht₀ : 0 ≤ t\nht₁ : t ≤ 1\nhne₁ : p ≠ p₁...
[]
rw [← hpt, vsub_left_cancel h, AffineMap.lineMap_same, AffineMap.const_apply]
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Geometry.Euclidean.Sphere.OrthRadius
{ "line": 251, "column": 8 }
{ "line": 251, "column": 57 }
{ "line": 252, "column": 8 }
[ { "pp": "case inl.inl.inl\nV : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Sphere P\nh : dist s.center s.center < s.radius\nhs : Subsingleton V\n⊢ Metric.sphere s.center s.radius ∩ ↑(s.orthRadius s.center) = ∅ ↔\...
[ "case inl.inl.inl\nV : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Sphere P\nh : dist s.center s.center < s.radius\nhs : Subsingleton V\nhs' : Subsingleton P\n⊢ Metric.sphere s.center s.radius ∩ ↑(s.orthRadius s.cent...
have hs' := (AddTorsor.subsingleton_iff V P).1 hs
Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1
Lean.Parser.Tactic.tacticHave__
Mathlib.Geometry.Euclidean.Angle.Bisector
{ "line": 319, "column": 46 }
{ "line": 319, "column": 52 }
{ "line": 319, "column": 53 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\ninst✝¹ : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np p₁ p₂ p₃ : P\nha : AffineIndependent ℝ ![p₁, p₂, p₃]\nh : dist p ↑((orthogonalProjection line...
[]
decide
Lean.Elab.Tactic.evalDecide
Lean.Parser.Tactic.decide
Mathlib.Geometry.Euclidean.Angle.Bisector
{ "line": 319, "column": 46 }
{ "line": 319, "column": 52 }
{ "line": 319, "column": 53 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\ninst✝¹ : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np p₁ p₂ p₃ : P\nha : AffineIndependent ℝ ![p₁, p₂, p₃]\nh : dist p ↑((orthogonalProjection line...
[]
decide
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Geometry.Euclidean.Angle.Bisector
{ "line": 319, "column": 46 }
{ "line": 319, "column": 52 }
{ "line": 319, "column": 53 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\ninst✝¹ : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np p₁ p₂ p₃ : P\nha : AffineIndependent ℝ ![p₁, p₂, p₃]\nh : dist p ↑((orthogonalProjection line...
[]
decide
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Geometry.Euclidean.Angle.Bisector
{ "line": 320, "column": 46 }
{ "line": 320, "column": 52 }
{ "line": 320, "column": 53 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\ninst✝¹ : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np p₁ p₂ p₃ : P\nha : AffineIndependent ℝ ![p₁, p₂, p₃]\nh : dist p ↑((orthogonalProjection line...
[]
decide
Lean.Elab.Tactic.evalDecide
Lean.Parser.Tactic.decide
Mathlib.Geometry.Euclidean.Angle.Bisector
{ "line": 320, "column": 46 }
{ "line": 320, "column": 52 }
{ "line": 320, "column": 53 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\ninst✝¹ : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np p₁ p₂ p₃ : P\nha : AffineIndependent ℝ ![p₁, p₂, p₃]\nh : dist p ↑((orthogonalProjection line...
[]
decide
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Geometry.Euclidean.Angle.Bisector
{ "line": 320, "column": 46 }
{ "line": 320, "column": 52 }
{ "line": 320, "column": 53 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\ninst✝¹ : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np p₁ p₂ p₃ : P\nha : AffineIndependent ℝ ![p₁, p₂, p₃]\nh : dist p ↑((orthogonalProjection line...
[]
decide
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Geometry.Euclidean.Angle.Bisector
{ "line": 345, "column": 27 }
{ "line": 345, "column": 33 }
{ "line": 345, "column": 34 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\ninst✝¹ : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np p₁ p₂ p₃ : P\nha : AffineIndependent ℝ ![p₁, p₂, p₃]\n⊢ 0 ≠ 1", "ppTerm": "?m.160", "...
[]
decide
Lean.Elab.Tactic.evalDecide
Lean.Parser.Tactic.decide
Mathlib.Geometry.Euclidean.Angle.Bisector
{ "line": 345, "column": 27 }
{ "line": 345, "column": 33 }
{ "line": 345, "column": 34 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\ninst✝¹ : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np p₁ p₂ p₃ : P\nha : AffineIndependent ℝ ![p₁, p₂, p₃]\n⊢ 0 ≠ 1", "ppTerm": "?m.160", "...
[]
decide
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Geometry.Euclidean.Angle.Bisector
{ "line": 345, "column": 27 }
{ "line": 345, "column": 33 }
{ "line": 345, "column": 34 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\ninst✝¹ : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np p₁ p₂ p₃ : P\nha : AffineIndependent ℝ ![p₁, p₂, p₃]\n⊢ 0 ≠ 1", "ppTerm": "?m.160", "...
[]
decide
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Geometry.Euclidean.Angle.Bisector
{ "line": 346, "column": 27 }
{ "line": 346, "column": 33 }
{ "line": 346, "column": 34 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\ninst✝¹ : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np p₁ p₂ p₃ : P\nha : AffineIndependent ℝ ![p₁, p₂, p₃]\n⊢ 0 ≠ 2", "ppTerm": "?m.183", "...
[]
decide
Lean.Elab.Tactic.evalDecide
Lean.Parser.Tactic.decide
Mathlib.Geometry.Euclidean.Angle.Bisector
{ "line": 346, "column": 27 }
{ "line": 346, "column": 33 }
{ "line": 346, "column": 34 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\ninst✝¹ : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np p₁ p₂ p₃ : P\nha : AffineIndependent ℝ ![p₁, p₂, p₃]\n⊢ 0 ≠ 2", "ppTerm": "?m.183", "...
[]
decide
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Geometry.Euclidean.Angle.Bisector
{ "line": 346, "column": 27 }
{ "line": 346, "column": 33 }
{ "line": 346, "column": 34 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\ninst✝¹ : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np p₁ p₂ p₃ : P\nha : AffineIndependent ℝ ![p₁, p₂, p₃]\n⊢ 0 ≠ 2", "ppTerm": "?m.183", "...
[]
decide
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Geometry.Euclidean.Angle.Sphere
{ "line": 136, "column": 6 }
{ "line": 136, "column": 12 }
{ "line": 136, "column": 13 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Sphere P\np q : P\nas : AffineSubspace ℝ P\nh : s.IsTangentAt p as\nhq_mem : q ∈ as\nh1 : InnerProductGeometry.angle (q -ᵥ p) (p -ᵥ s.center) = π / 2\n⊢ ∠ ...
[ "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Sphere P\np q : P\nas : AffineSubspace ℝ P\nh : s.IsTangentAt p as\nhq_mem : q ∈ as\nh1 : InnerProductGeometry.angle (q -ᵥ p) (p -ᵥ s.center) = π / 2\n⊢ InnerProductGe...
angle,
Lean.Elab.Tactic.evalRewriteSeq
null
Mathlib.Geometry.Euclidean.Angle.Sphere
{ "line": 147, "column": 9 }
{ "line": 147, "column": 15 }
{ "line": 147, "column": 16 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Sphere P\np q : P\nh : ∠ q p s.center = π / 2\nhp : p ∈ s\nhp_mem : p ∈ line[ℝ, p, q]\n⊢ ⟪q -ᵥ p, p -ᵥ s.center⟫_ℝ = 0", "ppTerm": "?m.75", "assign...
[ "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Sphere P\np q : P\nh : InnerProductGeometry.angle (q -ᵥ p) (s.center -ᵥ p) = π / 2\nhp : p ∈ s\nhp_mem : p ∈ line[ℝ, p, q]\n⊢ ⟪q -ᵥ p, p -ᵥ s.center⟫_ℝ = 0" ]
angle,
Lean.Elab.Tactic.evalRewriteSeq
null
Mathlib.Geometry.Euclidean.Angle.Incenter
{ "line": 192, "column": 2 }
{ "line": 193, "column": 37 }
{ "line": 194, "column": 2 }
[ { "pp": "case inr.inr.inl\nV : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\nhd2 : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\nt : Triangle ℝ P\ni₁ i₂ i₃ : Fin 3\nh₁₂ : i₁ ≠ i₂\nh₁₃ : i₁ ≠ i₃\nh₂₃ : i₂ ≠ i₃\...
[ "case inr.inr.inr\nV : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\nhd2 : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\nt : Triangle ℝ P\ni₁ i₂ i₃ : Fin 3\nh₁₂ : i₁ ≠ i₂\nh₁₃ : i₁ ≠ i₃\nh₂₃ : i₂ ≠ i₃\nsigns : Fin...
· rw [hs, t.oangle_excenter_singleton_eq_add_pi h₁₂.symm h₂₃ h₁₃] at h simp [Real.Angle.pi_ne_zero] at h
Lean.Elab.Tactic.evalTacticCDot
Lean.cdot
Mathlib.Geometry.Euclidean.Angle.Sphere
{ "line": 482, "column": 8 }
{ "line": 482, "column": 14 }
{ "line": 482, "column": 15 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\nhd2 : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np₁ p₂ p₃ p₄ : P\nh : 2 • ∡ p₁ p₂ p₄ = 2 • ∡ p₁ p₃ p₄\nhn : ¬Collinear ℝ {p₁, p₂, p₄}\nhn' : ¬Colli...
[]
decide
Lean.Elab.Tactic.evalDecide
Lean.Parser.Tactic.decide
Mathlib.Geometry.Euclidean.Angle.Sphere
{ "line": 482, "column": 8 }
{ "line": 482, "column": 14 }
{ "line": 482, "column": 15 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\nhd2 : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np₁ p₂ p₃ p₄ : P\nh : 2 • ∡ p₁ p₂ p₄ = 2 • ∡ p₁ p₃ p₄\nhn : ¬Collinear ℝ {p₁, p₂, p₄}\nhn' : ¬Colli...
[]
decide
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Geometry.Euclidean.Angle.Sphere
{ "line": 482, "column": 8 }
{ "line": 482, "column": 14 }
{ "line": 482, "column": 15 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\nhd2 : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np₁ p₂ p₃ p₄ : P\nh : 2 • ∡ p₁ p₂ p₄ = 2 • ∡ p₁ p₃ p₄\nhn : ¬Collinear ℝ {p₁, p₂, p₄}\nhn' : ¬Colli...
[]
decide
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Geometry.Euclidean.Angle.Sphere
{ "line": 482, "column": 38 }
{ "line": 482, "column": 44 }
{ "line": 482, "column": 45 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\nhd2 : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np₁ p₂ p₃ p₄ : P\nh : 2 • ∡ p₁ p₂ p₄ = 2 • ∡ p₁ p₃ p₄\nhn : ¬Collinear ℝ {p₁, p₂, p₄}\nhn' : ¬Colli...
[]
decide
Lean.Elab.Tactic.evalDecide
Lean.Parser.Tactic.decide
Mathlib.Geometry.Euclidean.Angle.Sphere
{ "line": 482, "column": 38 }
{ "line": 482, "column": 44 }
{ "line": 482, "column": 45 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\nhd2 : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np₁ p₂ p₃ p₄ : P\nh : 2 • ∡ p₁ p₂ p₄ = 2 • ∡ p₁ p₃ p₄\nhn : ¬Collinear ℝ {p₁, p₂, p₄}\nhn' : ¬Colli...
[]
decide
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Geometry.Euclidean.Angle.Sphere
{ "line": 482, "column": 38 }
{ "line": 482, "column": 44 }
{ "line": 482, "column": 45 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\nhd2 : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np₁ p₂ p₃ p₄ : P\nh : 2 • ∡ p₁ p₂ p₄ = 2 • ∡ p₁ p₃ p₄\nhn : ¬Collinear ℝ {p₁, p₂, p₄}\nhn' : ¬Colli...
[]
decide
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Geometry.Euclidean.Angle.Sphere
{ "line": 482, "column": 68 }
{ "line": 482, "column": 74 }
{ "line": 482, "column": 74 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\nhd2 : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np₁ p₂ p₃ p₄ : P\nh : 2 • ∡ p₁ p₂ p₄ = 2 • ∡ p₁ p₃ p₄\nhn : ¬Collinear ℝ {p₁, p₂, p₄}\nhn' : ¬Colli...
[]
decide
Lean.Elab.Tactic.evalDecide
Lean.Parser.Tactic.decide
Mathlib.Geometry.Euclidean.Angle.Sphere
{ "line": 482, "column": 68 }
{ "line": 482, "column": 74 }
{ "line": 482, "column": 74 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\nhd2 : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np₁ p₂ p₃ p₄ : P\nh : 2 • ∡ p₁ p₂ p₄ = 2 • ∡ p₁ p₃ p₄\nhn : ¬Collinear ℝ {p₁, p₂, p₄}\nhn' : ¬Colli...
[]
decide
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Geometry.Euclidean.Angle.Sphere
{ "line": 482, "column": 68 }
{ "line": 482, "column": 74 }
{ "line": 482, "column": 74 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\nhd2 : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np₁ p₂ p₃ p₄ : P\nh : 2 • ∡ p₁ p₂ p₄ = 2 • ∡ p₁ p₃ p₄\nhn : ¬Collinear ℝ {p₁, p₂, p₄}\nhn' : ¬Colli...
[]
decide
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Geometry.Euclidean.Incenter
{ "line": 390, "column": 2 }
{ "line": 390, "column": 41 }
{ "line": 392, "column": 0 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\nn : ℕ\ninst✝ : NeZero n\ns : Simplex ℝ P n\nsigns : Finset (Fin (n + 1))\nS : AffineSubspace ℝ P\nhS : affineSpan ℝ (Set.range s.points) ≤ S\nh : (s.restrict ...
[]
exact (h.excenter_map S.subtypeₐᵢ).symm
Lean.Elab.Tactic.evalExact
Lean.Parser.Tactic.exact
Mathlib.Geometry.Euclidean.Circumcenter
{ "line": 286, "column": 35 }
{ "line": 286, "column": 41 }
{ "line": 286, "column": 41 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Simplex ℝ P 0\ni : Fin 1\nh : s.circumcenter ∈ affineSpan ℝ (Set.range s.points)\n⊢ 0 < 1", "ppTerm": "?m.48", "assigned": true, "usedConstants...
[]
decide
Lean.Elab.Tactic.evalDecide
Lean.Parser.Tactic.decide
Mathlib.Geometry.Euclidean.Circumcenter
{ "line": 286, "column": 35 }
{ "line": 286, "column": 41 }
{ "line": 286, "column": 41 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Simplex ℝ P 0\ni : Fin 1\nh : s.circumcenter ∈ affineSpan ℝ (Set.range s.points)\n⊢ 0 < 1", "ppTerm": "?m.48", "assigned": true, "usedConstants...
[]
decide
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Geometry.Euclidean.Circumcenter
{ "line": 286, "column": 35 }
{ "line": 286, "column": 41 }
{ "line": 286, "column": 41 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Simplex ℝ P 0\ni : Fin 1\nh : s.circumcenter ∈ affineSpan ℝ (Set.range s.points)\n⊢ 0 < 1", "ppTerm": "?m.48", "assigned": true, "usedConstants...
[]
decide
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Geometry.Euclidean.Triangle
{ "line": 119, "column": 8 }
{ "line": 119, "column": 12 }
{ "line": 120, "column": 8 }
[ { "pp": "case neg\nV : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nhpi : angle x y ≠ π\nhxy : ¬x = y\nh : (‖y‖ - ‖x‖) * -1 = (‖y‖ - ‖x‖) * (⟪x, y⟫ / (‖x‖ * ‖y‖))\nhx0 : ¬x = 0\nhy0 : ¬y = 0\n⊢ ‖x‖ = ‖y‖", "ppTerm": "?neg✝", "assigned": true, "usedConstants": [ ...
[ "case neg\nV : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nhpi : angle x y ≠ π\nhxy : ¬x = y\nh : (‖y‖ - ‖x‖) * -1 = (‖y‖ - ‖x‖) * (⟪x, y⟫ / (‖x‖ * ‖y‖))\nhx0 : ¬x = 0\nhy0 : ¬y = 0\n⊢ ‖y‖ = ‖x‖" ]
symm
Lean.Elab.Tactic.evalSymm
Lean.Parser.Tactic.symm
Mathlib.Geometry.Euclidean.Circumcenter
{ "line": 502, "column": 2 }
{ "line": 502, "column": 6 }
{ "line": 503, "column": 2 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nn : ℕ\ns : Simplex ℝ P n\ni : Fin (n + 1)\n⊢ s.pointsWithCircumcenter (pointIndex i) =\n (affineCombination ℝ univ s.pointsWithCircumcenter) (pointWeightsWi...
[ "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nn : ℕ\ns : Simplex ℝ P n\ni : Fin (n + 1)\n⊢ (affineCombination ℝ univ s.pointsWithCircumcenter) (pointWeightsWithCircumcenter i) =\n s.pointsWithCircumcenter (pointInd...
symm
Lean.Elab.Tactic.evalSymm
Lean.Parser.Tactic.symm
Mathlib.Geometry.Euclidean.Circumcenter
{ "line": 562, "column": 2 }
{ "line": 562, "column": 6 }
{ "line": 563, "column": 2 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nn : ℕ\ns : Simplex ℝ P n\n⊢ s.pointsWithCircumcenter circumcenterIndex =\n (affineCombination ℝ univ s.pointsWithCircumcenter) (circumcenterWeightsWithCircu...
[ "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nn : ℕ\ns : Simplex ℝ P n\n⊢ (affineCombination ℝ univ s.pointsWithCircumcenter) (circumcenterWeightsWithCircumcenter n) =\n s.pointsWithCircumcenter circumcenterIndex" ...
symm
Lean.Elab.Tactic.evalSymm
Lean.Parser.Tactic.symm
Mathlib.Geometry.Euclidean.Circumcenter
{ "line": 602, "column": 28 }
{ "line": 602, "column": 64 }
{ "line": 602, "column": 65 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nn : ℕ\ns : Simplex ℝ P n\ni₁ i₂ : Fin (n + 1)\nh : i₁ ≠ i₂\nhc : #{i₁, i₂} = 2\nW : AffineSubspace ℝ P := affineSpan ℝ (s.points '' {i₁, i₂})\nh_faces : ↑((ort...
[ "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nn : ℕ\ns : Simplex ℝ P n\ni₁ i₂ : Fin (n + 1)\nh : i₁ ≠ i₂\nhc : #{i₁, i₂} = 2\nW : AffineSubspace ℝ P := affineSpan ℝ (s.points '' {i₁, i₂})\nh_faces : ↑((orthogonalProje...
weightedVSub_vadd_affineCombination,
Lean.Elab.Tactic.evalRewriteSeq
null
Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality
{ "line": 253, "column": 6 }
{ "line": 253, "column": 21 }
{ "line": 254, "column": 6 }
[ { "pp": "case pos.hr\nV : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\ny : V\nhy left✝ : y ≠ 0\nr : ℝ≥0\nhr : 0 < ↑r\nhxz₁ : ¬angle 0 (↑r • y) = π\nhxz₂ : ¬angle 0 (↑r • y) = 0\nh_sin_xz : Real.sin (angle 0 (↑r • y)) ≠ 0\n⊢ IsUnit r", "ppTerm": "?pos.hr✝", "assigned": true, ...
[ "case pos.hr\nV : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\ny : V\nhy left✝ : y ≠ 0\nr : ℝ≥0\nhxz₁ : ¬angle 0 (↑r • y) = π\nhxz₂ : ¬angle 0 (↑r • y) = 0\nh_sin_xz : Real.sin (angle 0 (↑r • y)) ≠ 0\nhr : 0 < r\n⊢ IsUnit r" ]
norm_cast at hr
Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticNorm_cast___1
Lean.Parser.Tactic.tacticNorm_cast__
Mathlib.Topology.MetricSpace.Congruence
{ "line": 119, "column": 22 }
{ "line": 119, "column": 39 }
{ "line": 119, "column": 40 }
[ { "pp": "ι : Type u_1\nP₁ : Type u_3\nP₂ : Type u_4\nP₃ : Type u_5\nv₁ : ι → P₁\nv₂ : ι → P₂\ninst✝² : PseudoEMetricSpace P₁\ninst✝¹ : PseudoEMetricSpace P₂\ninst✝ : PseudoEMetricSpace P₃\nf : P₂ → P₃\nhf : Isometry f\n⊢ f ∘ v₂ ≅ v₁ ↔ v₁ ≅ v₂", "ppTerm": "?m.26", "assigned": true, "usedConstants": [...
[ "ι : Type u_1\nP₁ : Type u_3\nP₂ : Type u_4\nP₃ : Type u_5\nv₁ : ι → P₁\nv₂ : ι → P₂\ninst✝² : PseudoEMetricSpace P₁\ninst✝¹ : PseudoEMetricSpace P₂\ninst✝ : PseudoEMetricSpace P₃\nf : P₂ → P₃\nhf : Isometry f\n⊢ v₂ ≅ v₁ ↔ v₁ ≅ v₂" ]
comp_left_iff hf,
Lean.Elab.Tactic.evalRewriteSeq
null
Mathlib.Topology.MetricSpace.Similarity
{ "line": 238, "column": 2 }
{ "line": 239, "column": 24 }
{ "line": 241, "column": 0 }
[ { "pp": "ι : Type u_1\nP₁ : Type u_3\nP₂ : Type u_4\nv₁ : ι → P₁\nv₂ : ι → P₂\ninst✝¹ : PseudoMetricSpace P₁\ninst✝ : PseudoMetricSpace P₂\n⊢ Similar v₁ v₂ ↔ ∃ r, r ≠ 0 ∧ Pairwise fun i₁ i₂ ↦ dist (v₁ i₁) (v₁ i₂) = ↑r * dist (v₂ i₁) (v₂ i₂)", "ppTerm": "?m.22", "assigned": true, "usedConstants": [ ...
[]
simp_rw [similar_iff_exists_pairwise_nndist_eq, dist_nndist] exact_mod_cast Iff.rfl
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Topology.MetricSpace.Similarity
{ "line": 238, "column": 2 }
{ "line": 239, "column": 24 }
{ "line": 241, "column": 0 }
[ { "pp": "ι : Type u_1\nP₁ : Type u_3\nP₂ : Type u_4\nv₁ : ι → P₁\nv₂ : ι → P₂\ninst✝¹ : PseudoMetricSpace P₁\ninst✝ : PseudoMetricSpace P₂\n⊢ Similar v₁ v₂ ↔ ∃ r, r ≠ 0 ∧ Pairwise fun i₁ i₂ ↦ dist (v₁ i₁) (v₁ i₂) = ↑r * dist (v₂ i₁) (v₂ i₂)", "ppTerm": "?m.22", "assigned": true, "usedConstants": [ ...
[]
simp_rw [similar_iff_exists_pairwise_nndist_eq, dist_nndist] exact_mod_cast Iff.rfl
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Geometry.Euclidean.Simplex
{ "line": 42, "column": 6 }
{ "line": 42, "column": 12 }
{ "line": 42, "column": 13 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nn : ℕ\ns : Simplex ℝ P n\ni₁ i₂ i₃ : Fin (n + 1)\nh₁₂ : i₁ ≠ i₂\nh₁₃ : i₁ ≠ i₃\nh₂₃ : i₂ ≠ i₃\nr : ℝ\nhr : ∀ (i j : Fin (n + 1)), i ≠ j → dist (s.points i) (s....
[ "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nn : ℕ\ns : Simplex ℝ P n\ni₁ i₂ i₃ : Fin (n + 1)\nh₁₂ : i₁ ≠ i₂\nh₁₃ : i₁ ≠ i₃\nh₂₃ : i₂ ≠ i₃\nr : ℝ\nhr : ∀ (i j : Fin (n + 1)), i ≠ j → dist (s.points i) (s.points j) = ...
angle,
Lean.Elab.Tactic.evalRewriteSeq
null
Mathlib.Topology.MetricSpace.Similarity
{ "line": 323, "column": 39 }
{ "line": 323, "column": 74 }
{ "line": 323, "column": 74 }
[ { "pp": "case h.«0».«0»\nP₁ : Type u_3\nP₂ : Type u_4\ninst✝¹ : PseudoMetricSpace P₁\ninst✝ : PseudoMetricSpace P₂\na b c : P₁\na' b' c' : P₂\nh_ne : dist a b ≠ 0\nh_ne' : dist a' b' ≠ 0\nheq1 : dist a b * dist b' c' = dist b c * dist a' b'\nheq2 : dist a b * dist c' a' = dist c a * dist a' b'\nr : ℝ := dist a ...
[]
rw [dist_self, dist_self, mul_zero]
Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1
Lean.Parser.Tactic.rwSeq
Mathlib.Topology.MetricSpace.Similarity
{ "line": 323, "column": 39 }
{ "line": 323, "column": 74 }
{ "line": 323, "column": 74 }
[ { "pp": "case h.«0».«1»\nP₁ : Type u_3\nP₂ : Type u_4\ninst✝¹ : PseudoMetricSpace P₁\ninst✝ : PseudoMetricSpace P₂\na b c : P₁\na' b' c' : P₂\nh_ne : dist a b ≠ 0\nh_ne' : dist a' b' ≠ 0\nheq1 : dist a b * dist b' c' = dist b c * dist a' b'\nheq2 : dist a b * dist c' a' = dist c a * dist a' b'\nr : ℝ := dist a ...
[ "case h.«0».«1»\nP₁ : Type u_3\nP₂ : Type u_4\ninst✝¹ : PseudoMetricSpace P₁\ninst✝ : PseudoMetricSpace P₂\na b c : P₁\na' b' c' : P₂\nh_ne : dist a b ≠ 0\nh_ne' : dist a' b' ≠ 0\nheq1 : dist a b * dist b' c' = dist b c * dist a' b'\nheq2 : dist a b * dist c' a' = dist c a * dist a' b'\nr : ℝ := dist a b / dist a' ...
rw [dist_self, dist_self, mul_zero]
Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1
Lean.Parser.Tactic.rwSeq
Mathlib.Geometry.Euclidean.MongePoint
{ "line": 172, "column": 33 }
{ "line": 172, "column": 39 }
{ "line": 172, "column": 40 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nn : ℕ\ns : Simplex ℝ P (n + 2)\na✝ : Fin (n + 2 + 1)\n⊢ 1 ≤ 2", "ppTerm": "?m.247", "assigned": true, "usedConstants": [ "of_decide_eq_true",...
[]
decide
Lean.Elab.Tactic.evalDecide
Lean.Parser.Tactic.decide
Mathlib.Geometry.Euclidean.MongePoint
{ "line": 172, "column": 33 }
{ "line": 172, "column": 39 }
{ "line": 172, "column": 40 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nn : ℕ\ns : Simplex ℝ P (n + 2)\na✝ : Fin (n + 2 + 1)\n⊢ 1 ≤ 2", "ppTerm": "?m.247", "assigned": true, "usedConstants": [ "of_decide_eq_true",...
[]
decide
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Geometry.Euclidean.MongePoint
{ "line": 172, "column": 33 }
{ "line": 172, "column": 39 }
{ "line": 172, "column": 40 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nn : ℕ\ns : Simplex ℝ P (n + 2)\na✝ : Fin (n + 2 + 1)\n⊢ 1 ≤ 2", "ppTerm": "?m.247", "assigned": true, "usedConstants": [ "of_decide_eq_true",...
[]
decide
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Geometry.Euclidean.MongePoint
{ "line": 172, "column": 54 }
{ "line": 172, "column": 60 }
{ "line": 172, "column": 61 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nn : ℕ\ns : Simplex ℝ P (n + 2)\na✝ : Fin (n + 2 + 1)\n⊢ 2 - 1 = 1", "ppTerm": "?m.264", "assigned": true, "usedConstants": [ "of_decide_eq_tr...
[]
decide
Lean.Elab.Tactic.evalDecide
Lean.Parser.Tactic.decide
Mathlib.Geometry.Euclidean.MongePoint
{ "line": 172, "column": 54 }
{ "line": 172, "column": 60 }
{ "line": 172, "column": 61 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nn : ℕ\ns : Simplex ℝ P (n + 2)\na✝ : Fin (n + 2 + 1)\n⊢ 2 - 1 = 1", "ppTerm": "?m.264", "assigned": true, "usedConstants": [ "of_decide_eq_tr...
[]
decide
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Geometry.Euclidean.MongePoint
{ "line": 172, "column": 54 }
{ "line": 172, "column": 60 }
{ "line": 172, "column": 61 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nn : ℕ\ns : Simplex ℝ P (n + 2)\na✝ : Fin (n + 2 + 1)\n⊢ 2 - 1 = 1", "ppTerm": "?m.264", "assigned": true, "usedConstants": [ "of_decide_eq_tr...
[]
decide
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Topology.MetricSpace.Similarity
{ "line": 323, "column": 39 }
{ "line": 323, "column": 74 }
{ "line": 323, "column": 74 }
[ { "pp": "case h.«0».«2»\nP₁ : Type u_3\nP₂ : Type u_4\ninst✝¹ : PseudoMetricSpace P₁\ninst✝ : PseudoMetricSpace P₂\na b c : P₁\na' b' c' : P₂\nh_ne : dist a b ≠ 0\nh_ne' : dist a' b' ≠ 0\nheq1 : dist a b * dist b' c' = dist b c * dist a' b'\nheq2 : dist a b * dist c' a' = dist c a * dist a' b'\nr : ℝ := dist a ...
[ "case h.«0».«2»\nP₁ : Type u_3\nP₂ : Type u_4\ninst✝¹ : PseudoMetricSpace P₁\ninst✝ : PseudoMetricSpace P₂\na b c : P₁\na' b' c' : P₂\nh_ne : dist a b ≠ 0\nh_ne' : dist a' b' ≠ 0\nheq1 : dist a b * dist b' c' = dist b c * dist a' b'\nheq2 : dist a b * dist c' a' = dist c a * dist a' b'\nr : ℝ := dist a b / dist a' ...
rw [dist_self, dist_self, mul_zero]
Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1
Lean.Parser.Tactic.rwSeq
Mathlib.Geometry.Euclidean.MongePoint
{ "line": 172, "column": 33 }
{ "line": 172, "column": 39 }
{ "line": 172, "column": 40 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nn : ℕ\ns : Simplex ℝ P (n + 2)\n⊢ 1 ≤ 2", "ppTerm": "?m.283", "assigned": true, "usedConstants": [ "of_decide_eq_true", "id", "in...
[]
decide
Lean.Elab.Tactic.evalDecide
Lean.Parser.Tactic.decide
Mathlib.Topology.MetricSpace.Similarity
{ "line": 323, "column": 39 }
{ "line": 323, "column": 74 }
{ "line": 323, "column": 74 }
[ { "pp": "case h.«1».«0»\nP₁ : Type u_3\nP₂ : Type u_4\ninst✝¹ : PseudoMetricSpace P₁\ninst✝ : PseudoMetricSpace P₂\na b c : P₁\na' b' c' : P₂\nh_ne : dist a b ≠ 0\nh_ne' : dist a' b' ≠ 0\nheq1 : dist a b * dist b' c' = dist b c * dist a' b'\nheq2 : dist a b * dist c' a' = dist c a * dist a' b'\nr : ℝ := dist a ...
[ "case h.«1».«0»\nP₁ : Type u_3\nP₂ : Type u_4\ninst✝¹ : PseudoMetricSpace P₁\ninst✝ : PseudoMetricSpace P₂\na b c : P₁\na' b' c' : P₂\nh_ne : dist a b ≠ 0\nh_ne' : dist a' b' ≠ 0\nheq1 : dist a b * dist b' c' = dist b c * dist a' b'\nheq2 : dist a b * dist c' a' = dist c a * dist a' b'\nr : ℝ := dist a b / dist a' ...
rw [dist_self, dist_self, mul_zero]
Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1
Lean.Parser.Tactic.rwSeq
Mathlib.Geometry.Euclidean.MongePoint
{ "line": 172, "column": 33 }
{ "line": 172, "column": 39 }
{ "line": 172, "column": 40 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nn : ℕ\ns : Simplex ℝ P (n + 2)\n⊢ 1 ≤ 2", "ppTerm": "?m.283", "assigned": true, "usedConstants": [ "of_decide_eq_true", "id", "in...
[]
decide
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Geometry.Euclidean.MongePoint
{ "line": 172, "column": 33 }
{ "line": 172, "column": 39 }
{ "line": 172, "column": 40 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nn : ℕ\ns : Simplex ℝ P (n + 2)\n⊢ 1 ≤ 2", "ppTerm": "?m.283", "assigned": true, "usedConstants": [ "of_decide_eq_true", "id", "in...
[]
decide
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Geometry.Euclidean.MongePoint
{ "line": 172, "column": 54 }
{ "line": 172, "column": 60 }
{ "line": 172, "column": 61 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nn : ℕ\ns : Simplex ℝ P (n + 2)\n⊢ 2 - 1 = 1", "ppTerm": "?m.300", "assigned": true, "usedConstants": [ "of_decide_eq_true", "HSub.hSub"...
[]
decide
Lean.Elab.Tactic.evalDecide
Lean.Parser.Tactic.decide
Mathlib.Geometry.Euclidean.MongePoint
{ "line": 172, "column": 54 }
{ "line": 172, "column": 60 }
{ "line": 172, "column": 61 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nn : ℕ\ns : Simplex ℝ P (n + 2)\n⊢ 2 - 1 = 1", "ppTerm": "?m.300", "assigned": true, "usedConstants": [ "of_decide_eq_true", "HSub.hSub"...
[]
decide
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Geometry.Euclidean.MongePoint
{ "line": 172, "column": 54 }
{ "line": 172, "column": 60 }
{ "line": 172, "column": 61 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nn : ℕ\ns : Simplex ℝ P (n + 2)\n⊢ 2 - 1 = 1", "ppTerm": "?m.300", "assigned": true, "usedConstants": [ "of_decide_eq_true", "HSub.hSub"...
[]
decide
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Topology.MetricSpace.Similarity
{ "line": 323, "column": 39 }
{ "line": 323, "column": 74 }
{ "line": 323, "column": 74 }
[ { "pp": "case h.«1».«1»\nP₁ : Type u_3\nP₂ : Type u_4\ninst✝¹ : PseudoMetricSpace P₁\ninst✝ : PseudoMetricSpace P₂\na b c : P₁\na' b' c' : P₂\nh_ne : dist a b ≠ 0\nh_ne' : dist a' b' ≠ 0\nheq1 : dist a b * dist b' c' = dist b c * dist a' b'\nheq2 : dist a b * dist c' a' = dist c a * dist a' b'\nr : ℝ := dist a ...
[]
rw [dist_self, dist_self, mul_zero]
Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1
Lean.Parser.Tactic.rwSeq
Mathlib.Topology.MetricSpace.Similarity
{ "line": 323, "column": 39 }
{ "line": 323, "column": 74 }
{ "line": 323, "column": 74 }
[ { "pp": "case h.«1».«2»\nP₁ : Type u_3\nP₂ : Type u_4\ninst✝¹ : PseudoMetricSpace P₁\ninst✝ : PseudoMetricSpace P₂\na b c : P₁\na' b' c' : P₂\nh_ne : dist a b ≠ 0\nh_ne' : dist a' b' ≠ 0\nheq1 : dist a b * dist b' c' = dist b c * dist a' b'\nheq2 : dist a b * dist c' a' = dist c a * dist a' b'\nr : ℝ := dist a ...
[ "case h.«1».«2»\nP₁ : Type u_3\nP₂ : Type u_4\ninst✝¹ : PseudoMetricSpace P₁\ninst✝ : PseudoMetricSpace P₂\na b c : P₁\na' b' c' : P₂\nh_ne : dist a b ≠ 0\nh_ne' : dist a' b' ≠ 0\nheq1 : dist a b * dist b' c' = dist b c * dist a' b'\nheq2 : dist a b * dist c' a' = dist c a * dist a' b'\nr : ℝ := dist a b / dist a' ...
rw [dist_self, dist_self, mul_zero]
Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1
Lean.Parser.Tactic.rwSeq
Mathlib.Topology.MetricSpace.Similarity
{ "line": 323, "column": 39 }
{ "line": 323, "column": 74 }
{ "line": 323, "column": 74 }
[ { "pp": "case h.«2».«0»\nP₁ : Type u_3\nP₂ : Type u_4\ninst✝¹ : PseudoMetricSpace P₁\ninst✝ : PseudoMetricSpace P₂\na b c : P₁\na' b' c' : P₂\nh_ne : dist a b ≠ 0\nh_ne' : dist a' b' ≠ 0\nheq1 : dist a b * dist b' c' = dist b c * dist a' b'\nheq2 : dist a b * dist c' a' = dist c a * dist a' b'\nr : ℝ := dist a ...
[ "case h.«2».«0»\nP₁ : Type u_3\nP₂ : Type u_4\ninst✝¹ : PseudoMetricSpace P₁\ninst✝ : PseudoMetricSpace P₂\na b c : P₁\na' b' c' : P₂\nh_ne : dist a b ≠ 0\nh_ne' : dist a' b' ≠ 0\nheq1 : dist a b * dist b' c' = dist b c * dist a' b'\nheq2 : dist a b * dist c' a' = dist c a * dist a' b'\nr : ℝ := dist a b / dist a' ...
rw [dist_self, dist_self, mul_zero]
Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1
Lean.Parser.Tactic.rwSeq
Mathlib.Geometry.Euclidean.Simplex
{ "line": 93, "column": 31 }
{ "line": 93, "column": 37 }
{ "line": 93, "column": 37 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle ℝ P\nh : Simplex.AcuteAngled t\n⊢ 0 ≠ 1", "ppTerm": "?m.158", "assigned": true, "usedConstants": [ "instDecidableNot", "in...
[]
decide
Lean.Elab.Tactic.evalDecide
Lean.Parser.Tactic.decide
Mathlib.Geometry.Euclidean.Simplex
{ "line": 93, "column": 31 }
{ "line": 93, "column": 37 }
{ "line": 93, "column": 37 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle ℝ P\nh : Simplex.AcuteAngled t\n⊢ 0 ≠ 1", "ppTerm": "?m.158", "assigned": true, "usedConstants": [ "instDecidableNot", "in...
[]
decide
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Geometry.Euclidean.Simplex
{ "line": 93, "column": 31 }
{ "line": 93, "column": 37 }
{ "line": 93, "column": 37 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle ℝ P\nh : Simplex.AcuteAngled t\n⊢ 0 ≠ 1", "ppTerm": "?m.158", "assigned": true, "usedConstants": [ "instDecidableNot", "in...
[]
decide
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Geometry.Euclidean.Simplex
{ "line": 93, "column": 43 }
{ "line": 93, "column": 49 }
{ "line": 93, "column": 49 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle ℝ P\nh : Simplex.AcuteAngled t\n⊢ 0 ≠ 2", "ppTerm": "?m.159", "assigned": true, "usedConstants": [ "instDecidableNot", "in...
[]
decide
Lean.Elab.Tactic.evalDecide
Lean.Parser.Tactic.decide
Mathlib.Geometry.Euclidean.Simplex
{ "line": 93, "column": 43 }
{ "line": 93, "column": 49 }
{ "line": 93, "column": 49 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle ℝ P\nh : Simplex.AcuteAngled t\n⊢ 0 ≠ 2", "ppTerm": "?m.159", "assigned": true, "usedConstants": [ "instDecidableNot", "in...
[]
decide
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Geometry.Euclidean.Simplex
{ "line": 93, "column": 43 }
{ "line": 93, "column": 49 }
{ "line": 93, "column": 49 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle ℝ P\nh : Simplex.AcuteAngled t\n⊢ 0 ≠ 2", "ppTerm": "?m.159", "assigned": true, "usedConstants": [ "instDecidableNot", "in...
[]
decide
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Geometry.Euclidean.Simplex
{ "line": 93, "column": 55 }
{ "line": 93, "column": 61 }
{ "line": 93, "column": 61 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle ℝ P\nh : Simplex.AcuteAngled t\n⊢ 1 ≠ 2", "ppTerm": "?m.160", "assigned": true, "usedConstants": [ "instDecidableNot", "in...
[]
decide
Lean.Elab.Tactic.evalDecide
Lean.Parser.Tactic.decide
Mathlib.Geometry.Euclidean.Simplex
{ "line": 93, "column": 55 }
{ "line": 93, "column": 61 }
{ "line": 93, "column": 61 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle ℝ P\nh : Simplex.AcuteAngled t\n⊢ 1 ≠ 2", "ppTerm": "?m.160", "assigned": true, "usedConstants": [ "instDecidableNot", "in...
[]
decide
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Geometry.Euclidean.Simplex
{ "line": 93, "column": 55 }
{ "line": 93, "column": 61 }
{ "line": 93, "column": 61 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle ℝ P\nh : Simplex.AcuteAngled t\n⊢ 1 ≠ 2", "ppTerm": "?m.160", "assigned": true, "usedConstants": [ "instDecidableNot", "in...
[]
decide
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Geometry.Euclidean.Simplex
{ "line": 94, "column": 31 }
{ "line": 94, "column": 37 }
{ "line": 94, "column": 37 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle ℝ P\nh : Simplex.AcuteAngled t\n⊢ 1 ≠ 2", "ppTerm": "?m.166", "assigned": true, "usedConstants": [ "instDecidableNot", "in...
[]
decide
Lean.Elab.Tactic.evalDecide
Lean.Parser.Tactic.decide
Mathlib.Geometry.Euclidean.Simplex
{ "line": 94, "column": 31 }
{ "line": 94, "column": 37 }
{ "line": 94, "column": 37 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle ℝ P\nh : Simplex.AcuteAngled t\n⊢ 1 ≠ 2", "ppTerm": "?m.166", "assigned": true, "usedConstants": [ "instDecidableNot", "in...
[]
decide
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Geometry.Euclidean.Simplex
{ "line": 94, "column": 31 }
{ "line": 94, "column": 37 }
{ "line": 94, "column": 37 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle ℝ P\nh : Simplex.AcuteAngled t\n⊢ 1 ≠ 2", "ppTerm": "?m.166", "assigned": true, "usedConstants": [ "instDecidableNot", "in...
[]
decide
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Geometry.Euclidean.Simplex
{ "line": 94, "column": 43 }
{ "line": 94, "column": 49 }
{ "line": 94, "column": 49 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle ℝ P\nh : Simplex.AcuteAngled t\n⊢ 1 ≠ 0", "ppTerm": "?m.167", "assigned": true, "usedConstants": [ "instDecidableNot", "in...
[]
decide
Lean.Elab.Tactic.evalDecide
Lean.Parser.Tactic.decide
Mathlib.Geometry.Euclidean.Simplex
{ "line": 94, "column": 43 }
{ "line": 94, "column": 49 }
{ "line": 94, "column": 49 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle ℝ P\nh : Simplex.AcuteAngled t\n⊢ 1 ≠ 0", "ppTerm": "?m.167", "assigned": true, "usedConstants": [ "instDecidableNot", "in...
[]
decide
Lean.Elab.Tactic.evalTacticSeq1Indented
Lean.Parser.Tactic.tacticSeq1Indented
Mathlib.Geometry.Euclidean.Simplex
{ "line": 94, "column": 43 }
{ "line": 94, "column": 49 }
{ "line": 94, "column": 49 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle ℝ P\nh : Simplex.AcuteAngled t\n⊢ 1 ≠ 0", "ppTerm": "?m.167", "assigned": true, "usedConstants": [ "instDecidableNot", "in...
[]
decide
Lean.Elab.Tactic.evalTacticSeq
Lean.Parser.Tactic.tacticSeq
Mathlib.Geometry.Euclidean.Simplex
{ "line": 94, "column": 55 }
{ "line": 94, "column": 61 }
{ "line": 94, "column": 61 }
[ { "pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle ℝ P\nh : Simplex.AcuteAngled t\n⊢ 2 ≠ 0", "ppTerm": "?m.168", "assigned": true, "usedConstants": [ "instDecidableNot", "in...
[]
decide
Lean.Elab.Tactic.evalDecide
Lean.Parser.Tactic.decide