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 |
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