module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.FieldTheory.PurelyInseparable.PerfectClosure | {
"line": 114,
"column": 2
} | {
"line": 114,
"column": 61
} | {
"line": 115,
"column": 2
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝² : Field F\ninst✝¹ : Field E\ninst✝ : Algebra F E\nL : IntermediateField F E\nh : IsPurelyInseparable F ↥L\n⊢ L ≤ perfectClosure F E",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"instSMulOfMul",
"Subring.instSetLike",
"Algebra.alg... | [
"F : Type u\nE : Type v\ninst✝² : Field F\ninst✝¹ : Field E\ninst✝ : Algebra F E\nL : IntermediateField F E\nh : ∀ (x : ↥L), ∃ n, x ^ ringExpChar F ^ n ∈ (algebraMap F ↥L).range\n⊢ L ≤ perfectClosure F E"
] | rw [isPurelyInseparable_iff_pow_mem F (ringExpChar F)] at h | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.FieldTheory.PurelyInseparable.PerfectClosure | {
"line": 222,
"column": 2
} | {
"line": 222,
"column": 41
} | {
"line": 223,
"column": 2
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nK : Type w\ninst✝¹ : Field K\ninst✝ : Algebra F K\nL1 L2 : IntermediateField F E\nh1 : IsPurelyInseparable F ↥L1\nh2 : IsPurelyInseparable F ↥L2\n⊢ IsPurelyInseparable F ↥(L1 ⊔ L2)",
"ppTerm": "?m.25",
"assigned":... | [
"F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nK : Type w\ninst✝¹ : Field K\ninst✝ : Algebra F K\nL1 L2 : IntermediateField F E\nh1 : L1 ≤ perfectClosure F E\nh2 : L2 ≤ perfectClosure F E\n⊢ L1 ⊔ L2 ≤ perfectClosure F E"
] | rw [← le_perfectClosure_iff] at h1 h2 ⊢ | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.FieldTheory.PurelyInseparable.PerfectClosure | {
"line": 314,
"column": 20
} | {
"line": 314,
"column": 42
} | {
"line": 314,
"column": 42
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝³ : Field F\ninst✝² : Field E\ninst✝¹ : Algebra F E\nq n : ℕ\nhF : ExpChar F q\nι : Type u_1\nv : ι → E\ninst✝ : Algebra.IsSeparable F E\nh : Submodule.span F (Set.range v) = ⊤\n⊢ Submodule.span F (Set.range fun x ↦ v x ^ q ^ n) =\n Subalgebra.toSubmodule (Algebra.adjoin... | [
"F : Type u\nE : Type v\ninst✝³ : Field F\ninst✝² : Field E\ninst✝¹ : Algebra F E\nq n : ℕ\nhF : ExpChar F q\nι : Type u_1\nv : ι → E\ninst✝ : Algebra.IsSeparable F E\nh : Submodule.span F (Set.range v) = ⊤\n⊢ Submodule.span F (Set.range fun x ↦ v x ^ q ^ n) = Submodule.span F ↑(Submonoid.closure (Set.range fun x ↦... | Algebra.adjoin_eq_span | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.FieldTheory.PurelyInseparable.Exponent | {
"line": 139,
"column": 2
} | {
"line": 140,
"column": 92
} | {
"line": 142,
"column": 0
} | [
{
"pp": "K : Type u_2\nL : Type u_3\ninst✝³ : Field K\ninst✝² : Field L\ninst✝¹ : Algebra K L\ninst✝ : IsPurelyInseparable K L\na : L\n⊢ minpoly K a = X ^ ringExpChar K ^ elemExponent K a - C (elemReduct K a)",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
"Polynomial.C",
"Comm... | [] | classical
exact Classical.choose_spec <| Nat.find_spec <| minpoly_eq_X_pow_sub_C K (ringExpChar K) a | Lean.Elab.Tactic.evalClassical | Lean.Parser.Tactic.classical |
Mathlib.FieldTheory.PurelyInseparable.Exponent | {
"line": 139,
"column": 2
} | {
"line": 140,
"column": 92
} | {
"line": 142,
"column": 0
} | [
{
"pp": "K : Type u_2\nL : Type u_3\ninst✝³ : Field K\ninst✝² : Field L\ninst✝¹ : Algebra K L\ninst✝ : IsPurelyInseparable K L\na : L\n⊢ minpoly K a = X ^ ringExpChar K ^ elemExponent K a - C (elemReduct K a)",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
"Polynomial.C",
"Comm... | [] | classical
exact Classical.choose_spec <| Nat.find_spec <| minpoly_eq_X_pow_sub_C K (ringExpChar K) a | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.FieldTheory.PurelyInseparable.Exponent | {
"line": 139,
"column": 2
} | {
"line": 140,
"column": 92
} | {
"line": 142,
"column": 0
} | [
{
"pp": "K : Type u_2\nL : Type u_3\ninst✝³ : Field K\ninst✝² : Field L\ninst✝¹ : Algebra K L\ninst✝ : IsPurelyInseparable K L\na : L\n⊢ minpoly K a = X ^ ringExpChar K ^ elemExponent K a - C (elemReduct K a)",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
"Polynomial.C",
"Comm... | [] | classical
exact Classical.choose_spec <| Nat.find_spec <| minpoly_eq_X_pow_sub_C K (ringExpChar K) a | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.FieldTheory.PurelyInseparable.PerfectClosure | {
"line": 389,
"column": 2
} | {
"line": 389,
"column": 6
} | {
"line": 390,
"column": 2
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝³ : Field F\ninst✝² : Field E\ninst✝¹ : Algebra F E\nq : ℕ\nhF : ExpChar F q\ninst✝ : ExpChar E q\nn : ℕ\na : E\nhsep : IsSeparable F a\nhai : IsIntegral F a\nhapi : IsIntegral F ((iterateFrobenius E q n) a)\n⊢ minpoly F ((iterateFrobenius E q n) a) = Polynomial.map (iterat... | [
"F : Type u\nE : Type v\ninst✝³ : Field F\ninst✝² : Field E\ninst✝¹ : Algebra F E\nq : ℕ\nhF : ExpChar F q\ninst✝ : ExpChar E q\nn : ℕ\na : E\nhsep : IsSeparable F a\nhai : IsIntegral F a\nhapi : IsIntegral F ((iterateFrobenius E q n) a)\n⊢ Polynomial.map (iterateFrobenius F q n) (minpoly F a) = minpoly F ((iterate... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.FieldTheory.PurelyInseparable.Exponent | {
"line": 344,
"column": 2
} | {
"line": 346,
"column": 45
} | {
"line": 348,
"column": 0
} | [
{
"pp": "F : Type u_1\nK : Type u_2\nL : Type u_3\ninst✝⁹ : Field K\ninst✝⁸ : Field L\ninst✝⁷ : Algebra K L\ninst✝⁶ : HasExponent K L\np : ℕ\ninst✝⁵ : ExpChar K p\ninst✝⁴ : Field F\ninst✝³ : Algebra F K\ninst✝² : Algebra F L\ninst✝¹ : IsScalarTower F K L\ninst✝ : ExpChar F p\nn : ℕ\nhn : exponent K L ≤ n\na : F... | [] | apply (algebraMap K L).injective
rw [← map_pow, ← IsScalarTower.algebraMap_apply, map_pow,
algebraMap_iterateFrobeniusₛₗ F K L p hn] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.FieldTheory.PurelyInseparable.Exponent | {
"line": 344,
"column": 2
} | {
"line": 346,
"column": 45
} | {
"line": 348,
"column": 0
} | [
{
"pp": "F : Type u_1\nK : Type u_2\nL : Type u_3\ninst✝⁹ : Field K\ninst✝⁸ : Field L\ninst✝⁷ : Algebra K L\ninst✝⁶ : HasExponent K L\np : ℕ\ninst✝⁵ : ExpChar K p\ninst✝⁴ : Field F\ninst✝³ : Algebra F K\ninst✝² : Algebra F L\ninst✝¹ : IsScalarTower F K L\ninst✝ : ExpChar F p\nn : ℕ\nhn : exponent K L ≤ n\na : F... | [] | apply (algebraMap K L).injective
rw [← map_pow, ← IsScalarTower.algebraMap_apply, map_pow,
algebraMap_iterateFrobeniusₛₗ F K L p hn] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.FieldTheory.RatFunc.Degree | {
"line": 118,
"column": 4
} | {
"line": 118,
"column": 21
} | {
"line": 118,
"column": 22
} | [
{
"pp": "case neg\nK : Type u\ninst✝ : Field K\nx y : K⟮X⟯\nhy : y ≠ 0\nhxy : x + y ≠ 0\nhx : ¬x = 0\n⊢ ↑(x.num * y.denom + x.denom * y.num).natDegree - ↑(x.denom * y.denom).natDegree ≤\n max (↑(x.num * y.denom).natDegree - ↑(y.denom * x.denom).natDegree) y.intDegree",
"ppTerm": "?neg✝",
"assigned": ... | [
"case neg\nK : Type u\ninst✝ : Field K\nx y : K⟮X⟯\nhy : y ≠ 0\nhxy : x + y ≠ 0\nhx : ¬x = 0\n⊢ ↑(x.num * y.denom + x.denom * y.num).natDegree - ↑(x.denom * y.denom).natDegree ≤\n max (↑(x.num * y.denom).natDegree - ↑(x.denom * y.denom).natDegree) y.intDegree"
] | mul_comm y.denom, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.FieldTheory.Relrank | {
"line": 56,
"column": 2
} | {
"line": 56,
"column": 19
} | {
"line": 57,
"column": 2
} | [
{
"pp": "E : Type v\ninst✝ : Field E\nA B C : Subfield E\nh : A ⊓ C = B ⊓ C\n⊢ A.relrank C = B.relrank C",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Subfield.relrank",
"Cardinal",
"id",
"Eq"
],
"usedFVars": [
"E",
"inst✝",
"A",
"... | [
"E : Type v\ninst✝ : Field E\nA B C : Subfield E\nh : A ⊓ C = B ⊓ C\n⊢ Module.rank ↥(A ⊓ C) ↥(extendScalars ⋯) = Module.rank ↥(B ⊓ C) ↥(extendScalars ⋯)"
] | simp_rw [relrank] | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | Mathlib.Tactic.tacticSimp_rw___ |
Mathlib.FieldTheory.Relrank | {
"line": 55,
"column": 80
} | {
"line": 57,
"column": 8
} | {
"line": 59,
"column": 0
} | [
{
"pp": "E : Type v\ninst✝ : Field E\nA B C : Subfield E\nh : A ⊓ C = B ⊓ C\n⊢ A.relrank C = B.relrank C",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"SetLike",
"Subfield.toDivisionRing",
"Subfield.relrank",
"Subfield.toAlgebra",
"Semiring.toModule",
... | [] | by
simp_rw [relrank]
congr! | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.FieldTheory.RatFunc.Luroth | {
"line": 387,
"column": 6
} | {
"line": 389,
"column": 68
} | {
"line": 389,
"column": 68
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nE : IntermediateField K K⟮X⟯\nh : E ≠ ⊥\nthis : (Bivariate.swap (Q₁ h) * Bivariate.swap (Φ E)).natDegree = (Bivariate.swap (θ E)).natDegree\n⊢ (Bivariate.swap (Q₁ h)).natDegree = 0",
"ppTerm": "?m.174",
"assigned": true,
"usedConstants": [
"Iff.mpr",
... | [
"K : Type u_1\ninst✝ : Field K\nE : IntermediateField K K⟮X⟯\nh : E ≠ ⊥\nthis : (Bivariate.swap (Q₁ h)).natDegree + (Bivariate.swap (Φ E)).natDegree = (Bivariate.swap (θ E)).natDegree\n⊢ (Bivariate.swap (Q₁ h)).natDegree = 0"
] | natDegree_mul
((map_ne_zero_iff _ Bivariate.swap.injective).mpr (Q₁_ne_zero h))
((map_ne_zero_iff _ Bivariate.swap.injective).mpr (Φ_ne_zero h)) | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Projection | {
"line": 151,
"column": 4
} | {
"line": 151,
"column": 8
} | {
"line": 152,
"column": 4
} | [
{
"pp": "case mpr\n𝕜 : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁶ : RCLike 𝕜\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace 𝕜 V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\ns : AffineSubspace 𝕜 P\ninst✝¹ : Nonempty ↥s\ninst✝ : s.direction.HasOrthogonalProjection\np : P\nh : p ∈ s\nhp... | [
"case mpr\n𝕜 : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁶ : RCLike 𝕜\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace 𝕜 V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\ns : AffineSubspace 𝕜 P\ninst✝¹ : Nonempty ↥s\ninst✝ : s.direction.HasOrthogonalProjection\np : P\nh : p ∈ s\nhp : p ∈ {↑((o... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Geometry.Euclidean.Altitude | {
"line": 321,
"column": 4
} | {
"line": 358,
"column": 68
} | {
"line": 360,
"column": 0
} | [
{
"pp": "case a\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\nn : ℕ\ns : Simplex ℝ P n\ninst✝ : n.AtLeastTwo\ni j : Fin (n + 1)\nhij : i ≠ j\n⊢ |⟪s.points i -ᵥ s.altitudeFoot i, s.points j -ᵥ s.altitudeFoot j⟫| ≠... | [] | simp_rw [height, dist_eq_norm_vsub]
rw [← Real.norm_eq_abs, ne_eq, norm_inner_eq_norm_iff (by simp) (by simp)]
rintro ⟨r, hr, h⟩
suffices s.points j -ᵥ s.altitudeFoot j = 0 by
simp at this
rw [← Submodule.mem_bot ℝ,
← Submodule.inf_orthogonal_eq_bot (vectorSpan ℝ (Set.range s.points))]
r... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Euclidean.Altitude | {
"line": 321,
"column": 4
} | {
"line": 358,
"column": 68
} | {
"line": 360,
"column": 0
} | [
{
"pp": "case a\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\nn : ℕ\ns : Simplex ℝ P n\ninst✝ : n.AtLeastTwo\ni j : Fin (n + 1)\nhij : i ≠ j\n⊢ |⟪s.points i -ᵥ s.altitudeFoot i, s.points j -ᵥ s.altitudeFoot j⟫| ≠... | [] | simp_rw [height, dist_eq_norm_vsub]
rw [← Real.norm_eq_abs, ne_eq, norm_inner_eq_norm_iff (by simp) (by simp)]
rintro ⟨r, hr, h⟩
suffices s.points j -ᵥ s.altitudeFoot j = 0 by
simp at this
rw [← Submodule.mem_bot ℝ,
← Submodule.inf_orthogonal_eq_bot (vectorSpan ℝ (Set.range s.points))]
r... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation | {
"line": 325,
"column": 10
} | {
"line": 325,
"column": 63
} | {
"line": 325,
"column": 63
} | [
{
"pp": "case neg\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\nθ : Real.Angle\nhx : ¬x = 0\nhy : ¬y = 0\n⊢ o.oangle x y = θ ↔ (x ≠ 0 ∧ y ≠ 0 ∧ ∃ r, 0 < r ∧ y = r • (o.rotation θ) x) ∨ θ = 0 ∧ (x = 0 ∨ y = 0)",... | [
"case neg\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\nθ : Real.Angle\nhx : ¬x = 0\nhy : ¬y = 0\n⊢ (∃ r, 0 < r ∧ y = r • (o.rotation θ) x) ↔\n (x ≠ 0 ∧ y ≠ 0 ∧ ∃ r, 0 < r ∧ y = r • (o.rotation θ) x) ∨ θ = 0 ∧ (... | o.oangle_eq_iff_eq_pos_smul_rotation_of_ne_zero hx hy | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation | {
"line": 339,
"column": 2
} | {
"line": 339,
"column": 6
} | {
"line": 340,
"column": 2
} | [
{
"pp": "case h\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)\nf : V ≃ₗᵢ[ℝ] V\nhd : 0 < LinearMap.det ↑f.toLinearEquiv\nthis : Nontrivial V\nx : V\nhx : x ≠ 0\ni : Fin 2\n⊢ ↑f.toLinearEquiv ((o.basisRightAngleRotation x ... | [
"case h\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)\nf : V ≃ₗᵢ[ℝ] V\nhd : 0 < LinearMap.det ↑f.toLinearEquiv\nthis : Nontrivial V\nx : V\nhx : x ≠ 0\ni : Fin 2\n⊢ ↑(o.rotation (o.oangle x (f x))).toLinearEquiv ((o.basisRig... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine | {
"line": 58,
"column": 11
} | {
"line": 58,
"column": 17
} | {
"line": 58,
"column": 18
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝⁷ : NormedAddCommGroup V\ninst✝⁶ : InnerProductSpace ℝ V\ninst✝⁵ : MetricSpace P\ninst✝⁴ : NormedAddTorsor V P\nV₂ : Type u_3\nP₂ : Type u_4\ninst✝³ : NormedAddCommGroup V₂\ninst✝² : InnerProductSpace ℝ V₂\ninst✝¹ : MetricSpace P₂\ninst✝ : NormedAddTorsor V₂ P₂\nf : P →... | [
"V : Type u_1\nP : Type u_2\ninst✝⁷ : NormedAddCommGroup V\ninst✝⁶ : InnerProductSpace ℝ V\ninst✝⁵ : MetricSpace P\ninst✝⁴ : NormedAddTorsor V P\nV₂ : Type u_3\nP₂ : Type u_4\ninst✝³ : NormedAddCommGroup V₂\ninst✝² : InnerProductSpace ℝ V₂\ninst✝¹ : MetricSpace P₂\ninst✝ : NormedAddTorsor V₂ P₂\nf : P →ᵃⁱ[ℝ] P₂\np₁... | angle, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine | {
"line": 71,
"column": 11
} | {
"line": 71,
"column": 17
} | {
"line": 71,
"column": 18
} | [
{
"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\np p₁ p₂ p₃ : P\nr : ℝ\nh : r ≠ 0\n⊢ ∠ ((AffineMap.homothety p r) p₁) ((AffineMap.homothety p r) p₂) ((AffineMap.homothety p r) p₃) = ∠ p₁ p₂ p₃",
"ppTerm":... | [
"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\np p₁ p₂ p₃ : P\nr : ℝ\nh : r ≠ 0\n⊢ InnerProductGeometry.angle ((AffineMap.homothety p r) p₁ -ᵥ (AffineMap.homothety p r) p₂)\n ((AffineMap.homothety p r) p₃ -ᵥ (Affi... | angle, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 138,
"column": 46
} | {
"line": 138,
"column": 52
} | {
"line": 138,
"column": 53
} | [
{
"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 : P\nh : (∡ p₁ p₂ p₃).sign = 1\n⊢ 1 ≠ 0",
"ppTerm": "?m.55",
"assigned": true,
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 138,
"column": 46
} | {
"line": 138,
"column": 52
} | {
"line": 138,
"column": 53
} | [
{
"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 : P\nh : (∡ p₁ p₂ p₃).sign = 1\n⊢ 1 ≠ 0",
"ppTerm": "?m.55",
"assigned": true,
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 138,
"column": 46
} | {
"line": 138,
"column": 52
} | {
"line": 138,
"column": 53
} | [
{
"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 : P\nh : (∡ p₁ p₂ p₃).sign = 1\n⊢ 1 ≠ 0",
"ppTerm": "?m.55",
"assigned": true,
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 143,
"column": 47
} | {
"line": 143,
"column": 53
} | {
"line": 143,
"column": 54
} | [
{
"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 : P\nh : (∡ p₁ p₂ p₃).sign = 1\n⊢ 1 ≠ 0",
"ppTerm": "?m.55",
"assigned": true,
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 143,
"column": 47
} | {
"line": 143,
"column": 53
} | {
"line": 143,
"column": 54
} | [
{
"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 : P\nh : (∡ p₁ p₂ p₃).sign = 1\n⊢ 1 ≠ 0",
"ppTerm": "?m.55",
"assigned": true,
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 143,
"column": 47
} | {
"line": 143,
"column": 53
} | {
"line": 143,
"column": 54
} | [
{
"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 : P\nh : (∡ p₁ p₂ p₃).sign = 1\n⊢ 1 ≠ 0",
"ppTerm": "?m.55",
"assigned": true,
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 148,
"column": 52
} | {
"line": 148,
"column": 58
} | {
"line": 148,
"column": 59
} | [
{
"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 : P\nh : (∡ p₁ p₂ p₃).sign = 1\n⊢ 1 ≠ 0",
"ppTerm": "?m.55",
"assigned": true,
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 148,
"column": 52
} | {
"line": 148,
"column": 58
} | {
"line": 148,
"column": 59
} | [
{
"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 : P\nh : (∡ p₁ p₂ p₃).sign = 1\n⊢ 1 ≠ 0",
"ppTerm": "?m.55",
"assigned": true,
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 148,
"column": 52
} | {
"line": 148,
"column": 58
} | {
"line": 148,
"column": 59
} | [
{
"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 : P\nh : (∡ p₁ p₂ p₃).sign = 1\n⊢ 1 ≠ 0",
"ppTerm": "?m.55",
"assigned": true,
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 153,
"column": 46
} | {
"line": 153,
"column": 52
} | {
"line": 153,
"column": 53
} | [
{
"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 : P\nh : (∡ p₁ p₂ p₃).sign = -1\n⊢ -1 ≠ 0",
"ppTerm": "?m.57",
"assigned": true,
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 153,
"column": 46
} | {
"line": 153,
"column": 52
} | {
"line": 153,
"column": 53
} | [
{
"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 : P\nh : (∡ p₁ p₂ p₃).sign = -1\n⊢ -1 ≠ 0",
"ppTerm": "?m.57",
"assigned": true,
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 153,
"column": 46
} | {
"line": 153,
"column": 52
} | {
"line": 153,
"column": 53
} | [
{
"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 : P\nh : (∡ p₁ p₂ p₃).sign = -1\n⊢ -1 ≠ 0",
"ppTerm": "?m.57",
"assigned": true,
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 158,
"column": 47
} | {
"line": 158,
"column": 53
} | {
"line": 158,
"column": 54
} | [
{
"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 : P\nh : (∡ p₁ p₂ p₃).sign = -1\n⊢ -1 ≠ 0",
"ppTerm": "?m.57",
"assigned": true,
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 158,
"column": 47
} | {
"line": 158,
"column": 53
} | {
"line": 158,
"column": 54
} | [
{
"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 : P\nh : (∡ p₁ p₂ p₃).sign = -1\n⊢ -1 ≠ 0",
"ppTerm": "?m.57",
"assigned": true,
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 158,
"column": 47
} | {
"line": 158,
"column": 53
} | {
"line": 158,
"column": 54
} | [
{
"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 : P\nh : (∡ p₁ p₂ p₃).sign = -1\n⊢ -1 ≠ 0",
"ppTerm": "?m.57",
"assigned": true,
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 164,
"column": 52
} | {
"line": 164,
"column": 58
} | {
"line": 164,
"column": 59
} | [
{
"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 : P\nh : (∡ p₁ p₂ p₃).sign = -1\n⊢ -1 ≠ 0",
"ppTerm": "?m.57",
"assigned": true,
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 164,
"column": 52
} | {
"line": 164,
"column": 58
} | {
"line": 164,
"column": 59
} | [
{
"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 : P\nh : (∡ p₁ p₂ p₃).sign = -1\n⊢ -1 ≠ 0",
"ppTerm": "?m.57",
"assigned": true,
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 164,
"column": 52
} | {
"line": 164,
"column": 58
} | {
"line": 164,
"column": 59
} | [
{
"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 : P\nh : (∡ p₁ p₂ p₃).sign = -1\n⊢ -1 ≠ 0",
"ppTerm": "?m.57",
"assigned": true,
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine | {
"line": 268,
"column": 6
} | {
"line": 268,
"column": 12
} | {
"line": 268,
"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 : Sbtw ℝ p₁ p₂ p₃\n⊢ ∠ p₁ p₂ p₃ = π",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"... | [
"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 : Sbtw ℝ p₁ p₂ p₃\n⊢ InnerProductGeometry.angle (p₁ -ᵥ p₂) (p₃ -ᵥ p₂) = π"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 197,
"column": 2
} | {
"line": 202,
"column": 21
} | {
"line": 204,
"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\nhd2 : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np₁ p₂ p₃ : P\n⊢ ∡ p₁ p₂ p₃ ≠ 0 ∧ ∡ p₁ p₂ p₃ ≠ ↑π ↔ AffineIndependent ℝ ![p₁, p₂, p₃]",
"ppTerm... | [] | rw [oangle, o.oangle_ne_zero_and_ne_pi_iff_linearIndependent,
affineIndependent_iff_linearIndependent_vsub ℝ _ (1 : Fin 3), ←
linearIndependent_equiv (finSuccAboveEquiv (1 : Fin 3))]
convert! Iff.rfl
ext i
fin_cases i <;> rfl | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 197,
"column": 2
} | {
"line": 202,
"column": 21
} | {
"line": 204,
"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\nhd2 : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np₁ p₂ p₃ : P\n⊢ ∡ p₁ p₂ p₃ ≠ 0 ∧ ∡ p₁ p₂ p₃ ≠ ↑π ↔ AffineIndependent ℝ ![p₁, p₂, p₃]",
"ppTerm... | [] | rw [oangle, o.oangle_ne_zero_and_ne_pi_iff_linearIndependent,
affineIndependent_iff_linearIndependent_vsub ℝ _ (1 : Fin 3), ←
linearIndependent_equiv (finSuccAboveEquiv (1 : Fin 3))]
convert! Iff.rfl
ext i
fin_cases i <;> rfl | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine | {
"line": 295,
"column": 6
} | {
"line": 295,
"column": 12
} | {
"line": 295,
"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\n⊢ ∠ p₁ p₂ p₃ = π → Sbtw ℝ p₁ p₂ p₃",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"InnerProductSpace... | [
"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\n⊢ InnerProductGeometry.angle (p₁ -ᵥ p₂) (p₃ -ᵥ p₂) = π → Sbtw ℝ p₁ p₂ p₃"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 148,
"column": 53
} | {
"line": 148,
"column": 59
} | {
"line": 148,
"column": 60
} | [
{
"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\nh : (o.oangle x y).sign = 1\n⊢ 1 ≠ 0",
"ppTerm": "?m.50",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_tru... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 148,
"column": 53
} | {
"line": 148,
"column": 59
} | {
"line": 148,
"column": 60
} | [
{
"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\nh : (o.oangle x y).sign = 1\n⊢ 1 ≠ 0",
"ppTerm": "?m.50",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_tru... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 148,
"column": 53
} | {
"line": 148,
"column": 59
} | {
"line": 148,
"column": 60
} | [
{
"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\nh : (o.oangle x y).sign = 1\n⊢ 1 ≠ 0",
"ppTerm": "?m.50",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_tru... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 152,
"column": 54
} | {
"line": 152,
"column": 60
} | {
"line": 152,
"column": 61
} | [
{
"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\nh : (o.oangle x y).sign = 1\n⊢ 1 ≠ 0",
"ppTerm": "?m.50",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_tru... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 152,
"column": 54
} | {
"line": 152,
"column": 60
} | {
"line": 152,
"column": 61
} | [
{
"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\nh : (o.oangle x y).sign = 1\n⊢ 1 ≠ 0",
"ppTerm": "?m.50",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_tru... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 152,
"column": 54
} | {
"line": 152,
"column": 60
} | {
"line": 152,
"column": 61
} | [
{
"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\nh : (o.oangle x y).sign = 1\n⊢ 1 ≠ 0",
"ppTerm": "?m.50",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_tru... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 156,
"column": 43
} | {
"line": 156,
"column": 49
} | {
"line": 156,
"column": 50
} | [
{
"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\nh : (o.oangle x y).sign = 1\n⊢ 1 ≠ 0",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_tru... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 156,
"column": 43
} | {
"line": 156,
"column": 49
} | {
"line": 156,
"column": 50
} | [
{
"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\nh : (o.oangle x y).sign = 1\n⊢ 1 ≠ 0",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_tru... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 156,
"column": 43
} | {
"line": 156,
"column": 49
} | {
"line": 156,
"column": 50
} | [
{
"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\nh : (o.oangle x y).sign = 1\n⊢ 1 ≠ 0",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_tru... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 160,
"column": 53
} | {
"line": 160,
"column": 59
} | {
"line": 160,
"column": 60
} | [
{
"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\nh : (o.oangle x y).sign = -1\n⊢ -1 ≠ 0",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_t... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 160,
"column": 53
} | {
"line": 160,
"column": 59
} | {
"line": 160,
"column": 60
} | [
{
"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\nh : (o.oangle x y).sign = -1\n⊢ -1 ≠ 0",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_t... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 160,
"column": 53
} | {
"line": 160,
"column": 59
} | {
"line": 160,
"column": 60
} | [
{
"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\nh : (o.oangle x y).sign = -1\n⊢ -1 ≠ 0",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_t... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 164,
"column": 54
} | {
"line": 164,
"column": 60
} | {
"line": 164,
"column": 61
} | [
{
"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\nh : (o.oangle x y).sign = -1\n⊢ -1 ≠ 0",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_t... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 164,
"column": 54
} | {
"line": 164,
"column": 60
} | {
"line": 164,
"column": 61
} | [
{
"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\nh : (o.oangle x y).sign = -1\n⊢ -1 ≠ 0",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_t... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 164,
"column": 54
} | {
"line": 164,
"column": 60
} | {
"line": 164,
"column": 61
} | [
{
"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\nh : (o.oangle x y).sign = -1\n⊢ -1 ≠ 0",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_t... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 168,
"column": 43
} | {
"line": 168,
"column": 49
} | {
"line": 168,
"column": 50
} | [
{
"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\nh : (o.oangle x y).sign = -1\n⊢ -1 ≠ 0",
"ppTerm": "?m.50",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_t... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 168,
"column": 43
} | {
"line": 168,
"column": 49
} | {
"line": 168,
"column": 50
} | [
{
"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\nh : (o.oangle x y).sign = -1\n⊢ -1 ≠ 0",
"ppTerm": "?m.50",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_t... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 168,
"column": 43
} | {
"line": 168,
"column": 49
} | {
"line": 168,
"column": 50
} | [
{
"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\nh : (o.oangle x y).sign = -1\n⊢ -1 ≠ 0",
"ppTerm": "?m.50",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_t... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Euclidean.Projection | {
"line": 538,
"column": 6
} | {
"line": 538,
"column": 39
} | {
"line": 538,
"column": 40
} | [
{
"pp": "𝕜 : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝¹¹ : RCLike 𝕜\ninst✝¹⁰ : NormedAddCommGroup V\ninst✝⁹ : InnerProductSpace 𝕜 V\nV₂ : Type u_4\nP₂ : Type u_5\ninst✝⁸ : NormedAddCommGroup V₂\ninst✝⁷ : InnerProductSpace 𝕜 V₂\ninst✝⁶ : MetricSpace P\ninst✝⁵ : NormedAddTorsor V P\ninst✝⁴ : MetricSpace P₂\... | [
"𝕜 : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝¹¹ : RCLike 𝕜\ninst✝¹⁰ : NormedAddCommGroup V\ninst✝⁹ : InnerProductSpace 𝕜 V\nV₂ : Type u_4\nP₂ : Type u_5\ninst✝⁸ : NormedAddCommGroup V₂\ninst✝⁷ : InnerProductSpace 𝕜 V₂\ninst✝⁶ : MetricSpace P\ninst✝⁵ : NormedAddTorsor V P\ninst✝⁴ : MetricSpace P₂\ninst✝³ : No... | ← AffineIsometry.coe_toAffineMap, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine | {
"line": 312,
"column": 6
} | {
"line": 312,
"column": 12
} | {
"line": 312,
"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 : Wbtw ℝ p₁ p₂ p₃\nhp₂p₁ : p₂ ≠ p₁\n⊢ ∠ p₂ p₁ p₃ = 0",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"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 : Wbtw ℝ p₁ p₂ p₃\nhp₂p₁ : p₂ ≠ p₁\n⊢ InnerProductGeometry.angle (p₂ -ᵥ p₁) (p₃ -ᵥ p₁) = 0"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine | {
"line": 320,
"column": 4
} | {
"line": 320,
"column": 25
} | {
"line": 320,
"column": 26
} | [
{
"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 p₃ : P\nr : ℝ\nhr1 : r ≤ 1\nhp₂p₁ : (AffineMap.lineMap p₁ p₃) r ≠ p₁\nhr0' : r ≠ 0\nhr0 : 0 < r\n⊢ p₃ -ᵥ p₁ = (r⁻¹ * r) • (p₃ -ᵥ p₁)",
"ppTerm": "?m.156... | [
"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 p₃ : P\nr : ℝ\nhr1 : r ≤ 1\nhp₂p₁ : (AffineMap.lineMap p₁ p₃) r ≠ p₁\nhr0' : r ≠ 0\nhr0 : 0 < r\n⊢ p₃ -ᵥ p₁ = 1 • (p₃ -ᵥ p₁)"
] | inv_mul_cancel₀ hr0', | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine | {
"line": 364,
"column": 8
} | {
"line": 364,
"column": 14
} | {
"line": 364,
"column": 15
} | [
{
"pp": "case mp\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\np₁ p₂ p₃ : P\n⊢ ∠ p₁ p₂ p₃ = 0 → p₁ ≠ p₂ ∧ Wbtw ℝ p₂ p₁ p₃ ∨ p₃ ≠ p₂ ∧ Wbtw ℝ p₂ p₃ p₁",
"ppTerm": "?mp",
"assigned": true,
"usedConstants... | [
"case mp\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\np₁ p₂ p₃ : P\n⊢ InnerProductGeometry.angle (p₁ -ᵥ p₂) (p₃ -ᵥ p₂) = 0 → p₁ ≠ p₂ ∧ Wbtw ℝ p₂ p₁ p₃ ∨ p₃ ≠ p₂ ∧ Wbtw ℝ p₂ p₃ p₁"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 69,
"column": 6
} | {
"line": 69,
"column": 12
} | {
"line": 69,
"column": 13
} | [
{
"pp": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : ⟪x, y⟫ = 0\n⊢ angle x (x + y) = Real.arccos (‖x‖ / ‖x + y‖)",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"Real",
"instHDiv",
"HMul.hMul"... | [
"V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : ⟪x, y⟫ = 0\n⊢ Real.arccos (⟪x, x + y⟫ / (‖x‖ * ‖x + y‖)) = Real.arccos (‖x‖ / ‖x + y‖)"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 310,
"column": 11
} | {
"line": 310,
"column": 30
} | {
"line": 310,
"column": 30
} | [
{
"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 : P\nh : dist p₁ p₂ = dist p₁ p₃\n⊢ ∡ p₁ p₂ p₃ = ∡ p₂ p₃ p₁",
"ppTerm": "?m.40",
... | [
"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 : P\nh : ‖p₁ -ᵥ p₂‖ = ‖p₁ -ᵥ p₃‖\n⊢ ∡ p₁ p₂ p₃ = ∡ p₂ p₃ p₁"
] | dist_eq_norm_vsub V | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 318,
"column": 11
} | {
"line": 318,
"column": 30
} | {
"line": 318,
"column": 30
} | [
{
"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 : P\nhn : p₂ ≠ p₃\nh : dist p₁ p₂ = dist p₁ p₃\n⊢ ∡ p₃ p₁ p₂ = ↑π - 2 • ∡ p₁ p₂ p₃",
... | [
"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 : P\nhn : p₂ ≠ p₃\nh : ‖p₁ -ᵥ p₂‖ = ‖p₁ -ᵥ p₃‖\n⊢ ∡ p₃ p₁ p₂ = ↑π - 2 • ∡ p₁ p₂ p₃"
] | dist_eq_norm_vsub V | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 328,
"column": 11
} | {
"line": 328,
"column": 30
} | {
"line": 328,
"column": 30
} | [
{
"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 : P\nh : dist p₁ p₂ = dist p₁ p₃\n⊢ |(∡ p₁ p₂ p₃).toReal| < π / 2",
"ppTerm": "?m.42"... | [
"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 : P\nh : ‖p₁ -ᵥ p₂‖ = ‖p₁ -ᵥ p₃‖\n⊢ |(∡ p₁ p₂ p₃).toReal| < π / 2"
] | dist_eq_norm_vsub V | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 432,
"column": 6
} | {
"line": 432,
"column": 12
} | {
"line": 432,
"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\nhd2 : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np₁ p₂ p₃ : P\nh : ∡ p₁ p₂ p₃ = ↑(π / 2)\n⊢ ∠ p₁ p₂ p₃ = π / 2",
"ppTerm": "?m.48",
"assign... | [
"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 : P\nh : ∡ p₁ p₂ p₃ = ↑(π / 2)\n⊢ InnerProductGeometry.angle (p₁ -ᵥ p₂) (p₃ -ᵥ p₂) = π / 2"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 445,
"column": 6
} | {
"line": 445,
"column": 12
} | {
"line": 445,
"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\nhd2 : Fact (finrank ℝ V = 2)\ninst✝ : Oriented ℝ V (Fin 2)\np₁ p₂ p₃ : P\nh : ∡ p₁ p₂ p₃ = ↑(-π / 2)\n⊢ ∠ p₁ p₂ p₃ = π / 2",
"ppTerm": "?m.50",
"assig... | [
"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 : P\nh : ∡ p₁ p₂ p₃ = ↑(-π / 2)\n⊢ InnerProductGeometry.angle (p₁ -ᵥ p₂) (p₃ -ᵥ p₂) = π / 2"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 458,
"column": 40
} | {
"line": 458,
"column": 69
} | {
"line": 458,
"column": 70
} | [
{
"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 : P\n⊢ (o.oangle (p₁ -ᵥ p₂) (p₂ -ᵥ p₃ - (p₂ -ᵥ p₁))).sign = -(o.oangle (p₁ -ᵥ p₂) (p₃ -ᵥ ... | [
"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 : P\n⊢ (o.oangle (p₁ -ᵥ p₂) (-(p₃ -ᵥ p₂) - (p₂ -ᵥ p₁))).sign = -(o.oangle (p₁ -ᵥ p₂) (p₃ -ᵥ p₂)).sign... | ← neg_vsub_eq_vsub_rev p₃ p₂, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 332,
"column": 31
} | {
"line": 332,
"column": 37
} | {
"line": 332,
"column": 38
} | [
{
"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\n⊢ ‖p₁ -ᵥ p₃‖ * ‖p₁ -ᵥ p₃‖ = ‖p₁ -ᵥ p₂‖ * ‖p₁ -ᵥ p₂‖ + ‖p₂ -ᵥ p₃‖ * ‖p₂ -ᵥ p₃‖ ↔ ∠ p₁ p₂ p₃ = π / 2",
"ppTerm": "?m.65",
"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\n⊢ ‖p₁ -ᵥ p₃‖ * ‖p₁ -ᵥ p₃‖ = ‖p₁ -ᵥ p₂‖ * ‖p₁ -ᵥ p₂‖ + ‖p₂ -ᵥ p₃‖ * ‖p₂ -ᵥ p₃‖ ↔\n InnerProductGeometry.angle (p₁ -ᵥ p₂) (p₃ -ᵥ p₂) = π / 2"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
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} | {
"line": 338,
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{
"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\n⊢ ∠ p₂ p₃ p₁ = Real.arccos (dist p₃ p₂ / dist p₁ p₃)",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": ... | [
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] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
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"column": 6
} | {
"line": 340,
"column": 12
} | {
"line": 340,
"column": 13
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{
"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\n⊢ ∠ p₂ p₃ p₁ = Real.arccos (dist p₃ p₂ / dist p₁ p₃)",
"ppTerm": "?m.92",
"assigned": true,
"usedConsta... | [
"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\n⊢ InnerProductGeometry.angle (p₂ -ᵥ p₃) (p₁ -ᵥ p₃) = Real.arccos (dist p₃ p₂ / dist p₁ p₃)"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
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"column": 6
} | {
"line": 346,
"column": 12
} | {
"line": 346,
"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⊢ ∠ p₂ p₃ p₁ = Real.arcsin (dist p₁ p₂ / dist p₁ p₃)",
"ppTerm": "?m.35",
"assigned": tru... | [
"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⊢ ∠ p₂ p₃ p₁ = Real.arcsin (dist p₁ p₂ / dist p₁ p₃)"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 349,
"column": 6
} | {
"line": 349,
"column": 12
} | {
"line": 349,
"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⊢ ∠ p₂ p₃ p₁ = Real.arcsin (dist p₁ p₂ / dist p₁ p₃)",
"ppTerm": "?m.141",
... | [
"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⊢ InnerProductGeometry.angle (p₂ -ᵥ p₃) (p₁ -ᵥ p₃) = Real.arcsin (dist p₁ p₂ / dist p₁ p₃)"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 355,
"column": 6
} | {
"line": 355,
"column": 12
} | {
"line": 355,
"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 : p₃ ≠ p₂\n⊢ ∠ p₂ p₃ p₁ = Real.arctan (dist p₁ p₂ / dist p₃ p₂)",
"ppTerm": "?m.34",
"assigned": true,
"us... | [
"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 : p₃ ≠ p₂\n⊢ ∠ p₂ p₃ p₁ = Real.arctan (dist p₁ p₂ / dist p₃ p₂)"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 358,
"column": 6
} | {
"line": 358,
"column": 12
} | {
"line": 358,
"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\n⊢ ∠ p₂ p₃ p₁ = Real.arctan (dist p₁ p₂ / dist p₃ p₂)",
"ppTerm": "?m.127",
"assigned": t... | [
"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\n⊢ InnerProductGeometry.angle (p₂ -ᵥ p₃) (p₁ -ᵥ p₃) = Real.arctan (dist p₁ p₂ / dist p₃ p₂)"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 364,
"column": 6
} | {
"line": 364,
"column": 12
} | {
"line": 364,
"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⊢ 0 < ∠ p₂ p₃ p₁",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Rea... | [
"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⊢ 0 < ∠ p₂ p₃ p₁"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 367,
"column": 6
} | {
"line": 367,
"column": 12
} | {
"line": 367,
"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⊢ 0 < ∠ p₂ p₃ p₁",
"ppTerm": "?m.138",
"assigned": true,
"usedConstan... | [
"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⊢ 0 < InnerProductGeometry.angle (p₂ -ᵥ p₃) (p₁ -ᵥ p₃)"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 373,
"column": 6
} | {
"line": 373,
"column": 12
} | {
"line": 373,
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} | [
{
"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\n⊢ ∠ p₂ p₃ p₁ ≤ π / 2",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"Real",
"instHDiv"... | [
"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\n⊢ ∠ p₂ p₃ p₁ ≤ π / 2"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
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"column": 6
} | {
"line": 375,
"column": 12
} | {
"line": 375,
"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\n⊢ ∠ p₂ p₃ p₁ ≤ π / 2",
"ppTerm": "?m.91",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"R... | [
"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\n⊢ InnerProductGeometry.angle (p₂ -ᵥ p₃) (p₁ -ᵥ p₃) ≤ π / 2"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 381,
"column": 6
} | {
"line": 381,
"column": 12
} | {
"line": 381,
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} | [
{
"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 : p₃ ≠ p₂\n⊢ ∠ p₂ p₃ p₁ < π / 2",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Real",
... | [
"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 : p₃ ≠ p₂\n⊢ ∠ p₂ p₃ p₁ < π / 2"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 384,
"column": 6
} | {
"line": 384,
"column": 12
} | {
"line": 384,
"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\n⊢ ∠ p₂ p₃ p₁ < π / 2",
"ppTerm": "?m.126",
"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\np₁ p₂ p₃ : P\nh : ⟪p₂ -ᵥ p₃, p₁ -ᵥ p₂⟫ = 0\nh0 : p₂ -ᵥ p₃ ≠ 0\n⊢ InnerProductGeometry.angle (p₂ -ᵥ p₃) (p₁ -ᵥ p₃) < π / 2"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 390,
"column": 6
} | {
"line": 390,
"column": 12
} | {
"line": 390,
"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\n⊢ Real.cos (∠ p₂ p₃ p₁) = dist p₃ p₂ / dist p₁ p₃",
"ppTerm": "?m.33",
"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\np₁ p₂ p₃ : P\nh : InnerProductGeometry.angle (p₁ -ᵥ p₂) (p₃ -ᵥ p₂) = π / 2\n⊢ Real.cos (∠ p₂ p₃ p₁) = dist p₃ p₂ / dist p₁ p₃"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 392,
"column": 6
} | {
"line": 392,
"column": 12
} | {
"line": 392,
"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\n⊢ Real.cos (∠ p₂ p₃ p₁) = dist p₃ p₂ / dist p₁ p₃",
"ppTerm": "?m.92",
"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\np₁ p₂ p₃ : P\nh : ⟪p₂ -ᵥ p₃, p₁ -ᵥ p₂⟫ = 0\n⊢ Real.cos (InnerProductGeometry.angle (p₂ -ᵥ p₃) (p₁ -ᵥ p₃)) = dist p₃ p₂ / dist p₁ p₃"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 398,
"column": 6
} | {
"line": 398,
"column": 12
} | {
"line": 398,
"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⊢ Real.sin (∠ p₂ p₃ p₁) = dist p₁ p₂ / dist p₁ p₃",
"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⊢ Real.sin (∠ p₂ p₃ p₁) = dist p₁ p₂ / dist p₁ p₃"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 401,
"column": 6
} | {
"line": 401,
"column": 12
} | {
"line": 401,
"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⊢ Real.sin (∠ p₂ p₃ p₁) = dist p₁ p₂ / dist p₁ p₃",
"ppTerm": "?m.141",
"... | [
"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⊢ Real.sin (InnerProductGeometry.angle (p₂ -ᵥ p₃) (p₁ -ᵥ p₃)) = dist p₁ p₂ / dist p₁ p₃"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 407,
"column": 6
} | {
"line": 407,
"column": 12
} | {
"line": 407,
"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\n⊢ Real.tan (∠ p₂ p₃ p₁) = dist p₁ p₂ / dist p₃ p₂",
"ppTerm": "?m.33",
"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\np₁ p₂ p₃ : P\nh : InnerProductGeometry.angle (p₁ -ᵥ p₂) (p₃ -ᵥ p₂) = π / 2\n⊢ Real.tan (∠ p₂ p₃ p₁) = dist p₁ p₂ / dist p₃ p₂"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 409,
"column": 6
} | {
"line": 409,
"column": 12
} | {
"line": 409,
"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\n⊢ Real.tan (∠ p₂ p₃ p₁) = dist p₁ p₂ / dist p₃ p₂",
"ppTerm": "?m.92",
"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\np₁ p₂ p₃ : P\nh : ⟪p₂ -ᵥ p₃, p₁ -ᵥ p₂⟫ = 0\n⊢ Real.tan (InnerProductGeometry.angle (p₂ -ᵥ p₃) (p₁ -ᵥ p₃)) = dist p₁ p₂ / dist p₃ p₂"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 416,
"column": 6
} | {
"line": 416,
"column": 12
} | {
"line": 416,
"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\n⊢ Real.cos (∠ p₂ p₃ p₁) * dist p₁ p₃ = dist p₃ p₂",
"ppTerm": "?m.33",
"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\np₁ p₂ p₃ : P\nh : InnerProductGeometry.angle (p₁ -ᵥ p₂) (p₃ -ᵥ p₂) = π / 2\n⊢ Real.cos (∠ p₂ p₃ p₁) * dist p₁ p₃ = dist p₃ p₂"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 418,
"column": 6
} | {
"line": 418,
"column": 12
} | {
"line": 418,
"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\n⊢ Real.cos (∠ p₂ p₃ p₁) * dist p₁ p₃ = dist p₃ p₂",
"ppTerm": "?m.92",
"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\np₁ p₂ p₃ : P\nh : ⟪p₂ -ᵥ p₃, p₁ -ᵥ p₂⟫ = 0\n⊢ Real.cos (InnerProductGeometry.angle (p₂ -ᵥ p₃) (p₁ -ᵥ p₃)) * dist p₁ p₃ = dist p₃ p₂"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 425,
"column": 6
} | {
"line": 425,
"column": 12
} | {
"line": 425,
"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\n⊢ Real.sin (∠ p₂ p₃ p₁) * dist p₁ p₃ = dist p₁ p₂",
"ppTerm": "?m.33",
"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\np₁ p₂ p₃ : P\nh : InnerProductGeometry.angle (p₁ -ᵥ p₂) (p₃ -ᵥ p₂) = π / 2\n⊢ Real.sin (∠ p₂ p₃ p₁) * dist p₁ p₃ = dist p₁ p₂"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 427,
"column": 6
} | {
"line": 427,
"column": 12
} | {
"line": 427,
"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\n⊢ Real.sin (∠ p₂ p₃ p₁) * dist p₁ p₃ = dist p₁ p₂",
"ppTerm": "?m.92",
"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\np₁ p₂ p₃ : P\nh : ⟪p₂ -ᵥ p₃, p₁ -ᵥ p₂⟫ = 0\n⊢ Real.sin (InnerProductGeometry.angle (p₂ -ᵥ p₃) (p₁ -ᵥ p₃)) * dist p₁ p₃ = dist p₁ p₂"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 427,
"column": 2
} | {
"line": 428,
"column": 56
} | {
"line": 430,
"column": 0
} | [
{
"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\n⊢ Real.sin (∠ p₂ p₃ p₁) * dist p₁ p₃ = dist p₁ p₂",
"ppTerm": "?m.92",
"assigned": true,
"usedConstants... | [] | rw [angle, dist_eq_norm_vsub V p₁ p₂, dist_eq_norm_vsub V p₁ p₃, ← vsub_add_vsub_cancel p₁ p₂ p₃,
add_comm, sin_angle_add_mul_norm_of_inner_eq_zero h] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 434,
"column": 6
} | {
"line": 434,
"column": 12
} | {
"line": 434,
"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⊢ Real.tan (∠ p₂ p₃ p₁) * dist p₃ p₂ = dist p₁ 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⊢ Real.tan (∠ p₂ p₃ p₁) * dist p₃ p₂ = dist p₁ p₂"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 437,
"column": 6
} | {
"line": 437,
"column": 12
} | {
"line": 437,
"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⊢ Real.tan (∠ p₂ p₃ p₁) * dist p₃ p₂ = dist p₁ 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⊢ Real.tan (InnerProductGeometry.angle (p₂ -ᵥ p₃) (p₁ -ᵥ p₃)) * dist p₃ p₂ = dist p₁ p₂"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 444,
"column": 6
} | {
"line": 444,
"column": 12
} | {
"line": 444,
"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 p₃ p₂ / Real.cos (∠ p₂ p₃ p₁) = dist p₁ p₃",
"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 p₃ p₂ / Real.cos (∠ p₂ p₃ p₁) = dist p₁ p₃"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 447,
"column": 6
} | {
"line": 447,
"column": 12
} | {
"line": 447,
"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 p₃ p₂ / Real.cos (∠ 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 p₃ p₂ / Real.cos (InnerProductGeometry.angle (p₂ -ᵥ p₃) (p₁ -ᵥ p₃)) = dist p₁ p₃"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 454,
"column": 6
} | {
"line": 454,
"column": 12
} | {
"line": 454,
"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.sin (∠ p₂ p₃ p₁) = dist p₁ p₃",
"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.sin (∠ p₂ p₃ p₁) = dist p₁ p₃"
] | angle, | Lean.Elab.Tactic.evalRewriteSeq | null |
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