module stringlengths 16 90 | startPos dict | endPos dict | nextStartPos dict | goals listlengths 0 96 | goalsAfter listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 375
values | kind stringclasses 379
values |
|---|---|---|---|---|---|---|---|---|
Mathlib.FieldTheory.PurelyInseparable.Tower | {
"line": 173,
"column": 2
} | {
"line": 173,
"column": 37
} | {
"line": 173,
"column": 38
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁷ : Field F\ninst✝⁶ : Field E\ninst✝⁵ : Algebra F E\nK : Type v\ninst✝⁴ : Field K\ninst✝³ : Algebra F K\ninst✝² : Algebra E K\ninst✝¹ : IsScalarTower F E K\ninst✝ : IsPurelyInseparable F E\n⊢ Module.rank F E * insepDegree E K = insepDegree F K",
"ppTerm": "?m.34",
"... | [
"F : Type u\nE : Type v\ninst✝⁷ : Field F\ninst✝⁶ : Field E\ninst✝⁵ : Algebra F E\nK : Type v\ninst✝⁴ : Field K\ninst✝³ : Algebra F K\ninst✝² : Algebra E K\ninst✝¹ : IsScalarTower F E K\ninst✝ : IsPurelyInseparable F E\n⊢ Module.rank F E * insepDegree E K = insepDegree F K"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.RatFunc.IntermediateField | {
"line": 112,
"column": 57
} | {
"line": 112,
"column": 79
} | {
"line": 112,
"column": 80
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nf : K⟮X⟯\nhf : ¬∃ c, f = C c\nthis :\n (f.minpolyX ↥K⟮f⟯).natDegree ≤\n max f.num.natDegree\n (Polynomial.C ((algebraMap ↥K[f] ↥K⟮f⟯) ⟨f, ⋯⟩) * Polynomial.map (algebraMap K ↥K⟮f⟯) f.denom).natDegree\nH : (algebraMap ↥K[f] ↥K⟮f⟯) ⟨f, ⋯⟩ = 0\n⊢ f = C 0",
"ppTer... | [
"K : Type u_1\ninst✝ : Field K\nf : K⟮X⟯\nhf : ¬∃ c, f = C c\nthis :\n (f.minpolyX ↥K⟮f⟯).natDegree ≤\n max f.num.natDegree\n (Polynomial.C ((algebraMap ↥K[f] ↥K⟮f⟯) ⟨f, ⋯⟩) * Polynomial.map (algebraMap K ↥K⟮f⟯) f.denom).natDegree\nH : (algebraMap ↥K[f] ↥K⟮f⟯) ⟨f, ⋯⟩ = 0\n⊢ f = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.PurelyInseparable.Tower | {
"line": 188,
"column": 2
} | {
"line": 188,
"column": 37
} | {
"line": 188,
"column": 38
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁷ : Field F\ninst✝⁶ : Field E\ninst✝⁵ : Algebra F E\nK : Type v\ninst✝⁴ : Field K\ninst✝³ : Algebra F K\ninst✝² : Algebra E K\ninst✝¹ : IsScalarTower F E K\ninst✝ : Algebra.IsAlgebraic F E\n⊢ sepDegree F E * sepDegree E K = sepDegree F K",
"ppTerm": "?m.34",
"assign... | [
"F : Type u\nE : Type v\ninst✝⁷ : Field F\ninst✝⁶ : Field E\ninst✝⁵ : Algebra F E\nK : Type v\ninst✝⁴ : Field K\ninst✝³ : Algebra F K\ninst✝² : Algebra E K\ninst✝¹ : IsScalarTower F E K\ninst✝ : Algebra.IsAlgebraic F E\n⊢ sepDegree F E * sepDegree E K = sepDegree F K"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.PurelyInseparable.Tower | {
"line": 203,
"column": 2
} | {
"line": 203,
"column": 37
} | {
"line": 203,
"column": 38
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁷ : Field F\ninst✝⁶ : Field E\ninst✝⁵ : Algebra F E\nK : Type v\ninst✝⁴ : Field K\ninst✝³ : Algebra F K\ninst✝² : Algebra E K\ninst✝¹ : IsScalarTower F E K\ninst✝ : Algebra.IsAlgebraic F E\n⊢ insepDegree F E * insepDegree E K = insepDegree F K",
"ppTerm": "?m.34",
"... | [
"F : Type u\nE : Type v\ninst✝⁷ : Field F\ninst✝⁶ : Field E\ninst✝⁵ : Algebra F E\nK : Type v\ninst✝⁴ : Field K\ninst✝³ : Algebra F K\ninst✝² : Algebra E K\ninst✝¹ : IsScalarTower F E K\ninst✝ : Algebra.IsAlgebraic F E\n⊢ insepDegree F E * insepDegree E K = insepDegree F K"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.PurelyInseparable.Tower | {
"line": 203,
"column": 2
} | {
"line": 203,
"column": 96
} | {
"line": 205,
"column": 0
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁷ : Field F\ninst✝⁶ : Field E\ninst✝⁵ : Algebra F E\nK : Type v\ninst✝⁴ : Field K\ninst✝³ : Algebra F K\ninst✝² : Algebra E K\ninst✝¹ : IsScalarTower F E K\ninst✝ : Algebra.IsAlgebraic F E\n⊢ insepDegree F E * insepDegree E K = insepDegree F K",
"ppTerm": "?m.34",
"... | [] | simpa only [Cardinal.lift_id] using lift_insepDegree_mul_lift_insepDegree_of_isAlgebraic F E K | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.FieldTheory.PurelyInseparable.Tower | {
"line": 203,
"column": 2
} | {
"line": 203,
"column": 96
} | {
"line": 205,
"column": 0
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁷ : Field F\ninst✝⁶ : Field E\ninst✝⁵ : Algebra F E\nK : Type v\ninst✝⁴ : Field K\ninst✝³ : Algebra F K\ninst✝² : Algebra E K\ninst✝¹ : IsScalarTower F E K\ninst✝ : Algebra.IsAlgebraic F E\n⊢ insepDegree F E * insepDegree E K = insepDegree F K",
"ppTerm": "?m.34",
"... | [] | simpa only [Cardinal.lift_id] using lift_insepDegree_mul_lift_insepDegree_of_isAlgebraic F E K | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.FieldTheory.PurelyInseparable.Tower | {
"line": 203,
"column": 2
} | {
"line": 203,
"column": 96
} | {
"line": 205,
"column": 0
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁷ : Field F\ninst✝⁶ : Field E\ninst✝⁵ : Algebra F E\nK : Type v\ninst✝⁴ : Field K\ninst✝³ : Algebra F K\ninst✝² : Algebra E K\ninst✝¹ : IsScalarTower F E K\ninst✝ : Algebra.IsAlgebraic F E\n⊢ insepDegree F E * insepDegree E K = insepDegree F K",
"ppTerm": "?m.34",
"... | [] | simpa only [Cardinal.lift_id] using lift_insepDegree_mul_lift_insepDegree_of_isAlgebraic F E K | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.FieldTheory.PurelyInseparable.Tower | {
"line": 226,
"column": 2
} | {
"line": 228,
"column": 50
} | {
"line": 229,
"column": 2
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁸ : Field F\ninst✝⁷ : Field E\ninst✝⁶ : Algebra F E\nK : Type w\ninst✝⁵ : Field K\ninst✝⁴ : Algebra F K\ninst✝³ : Algebra E K\ninst✝² : IsScalarTower F E K\nS : Set K\ninst✝¹ : IsPurelyInseparable F E\nM : IntermediateField F K := adjoin F S\ninst✝ : Algebra.IsAlgebraic F ↥... | [
"F : Type u\nE : Type v\ninst✝⁸ : Field F\ninst✝⁷ : Field E\ninst✝⁶ : Algebra F E\nK : Type w\ninst✝⁵ : Field K\ninst✝⁴ : Algebra F K\ninst✝³ : Algebra E K\ninst✝² : IsScalarTower F E K\nS : Set K\ninst✝¹ : IsPurelyInseparable F E\nM : IntermediateField F K := adjoin F S\ninst✝ : Algebra.IsAlgebraic F ↥M\nL : Inter... | have hi : M ≤ L.restrictScalars F := by
rw [restrictScalars_adjoin_of_algEquiv (E := K) j rfl, restrictScalars_adjoin]
exact adjoin.mono _ _ _ Set.subset_union_right | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.FieldTheory.PurelyInseparable.Tower | {
"line": 276,
"column": 53
} | {
"line": 276,
"column": 74
} | {
"line": 277,
"column": 4
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁷ : Field F\ninst✝⁶ : Field E\ninst✝⁵ : Algebra F E\nK : Type w\ninst✝⁴ : Field K\ninst✝³ : Algebra F K\ninst✝² : Algebra E K\ninst✝¹ : IsScalarTower F E K\nx : K\nhsep : IsSeparable F x\ninst✝ : IsPurelyInseparable F E\nhi : IsIntegral F x\nhi' : IsIntegral E x\nhsep' : Is... | [
"F : Type u\nE : Type v\ninst✝⁷ : Field F\ninst✝⁶ : Field E\ninst✝⁵ : Algebra F E\nK : Type w\ninst✝⁴ : Field K\ninst✝³ : Algebra F K\ninst✝² : Algebra E K\ninst✝¹ : IsScalarTower F E K\nx : K\nhsep : IsSeparable F x\ninst✝ : IsPurelyInseparable F E\nhi : IsIntegral F x\nhi' : IsIntegral E x\nhsep' : IsSeparable E ... | ← adjoin.finrank hi', | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.FieldTheory.PurelyInseparable.Tower | {
"line": 290,
"column": 4
} | {
"line": 290,
"column": 71
} | {
"line": 291,
"column": 4
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝³ : Field F\ninst✝² : Field E\ninst✝¹ : Algebra F E\nf : F[X]\nhsep : f.Separable\nhirr : Irreducible f\ninst✝ : IsPurelyInseparable F E\nK : Type v := AlgebraicClosure E\nx : K\nhx : (aeval x) f = 0\n⊢ Associated f (minpoly F x)",
"ppTerm": "?m.66",
"assigned": tru... | [
"F : Type u\nE : Type v\ninst✝³ : Field F\ninst✝² : Field E\ninst✝¹ : Algebra F E\nf : F[X]\nhsep : f.Separable\nhirr : Irreducible f\ninst✝ : IsPurelyInseparable F E\nK : Type v := AlgebraicClosure E\nx : K\nhx : (aeval x) f = 0\nthis : IsUnit (C f.leadingCoeff⁻¹)\n⊢ Associated f (minpoly F x)"
] | have := isUnit_C.2 (leadingCoeff_ne_zero.2 hirr.ne_zero).isUnit.inv | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.FieldTheory.Relrank | {
"line": 128,
"column": 4
} | {
"line": 128,
"column": 52
} | {
"line": 128,
"column": 52
} | [
{
"pp": "E : Type v\ninst✝ : Field E\nA : Subfield E\n⊢ Module.rank ↥A ↥⊤ = Module.rank (↥A) E",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"Subfield.toAlgebra",
"Semiring.toModule",
"instSMulOfMul",
"Cardinal",
... | [
"E : Type v\ninst✝ : Field E\nA : Subfield E\n⊢ Module.rank (↥A) E = Module.rank (↥A) E"
] | IntermediateField.topEquiv.toLinearEquiv.rank_eq | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.FieldTheory.Relrank | {
"line": 142,
"column": 2
} | {
"line": 142,
"column": 28
} | {
"line": 142,
"column": 29
} | [
{
"pp": "E : Type v\ninst✝¹ : Field E\nA B : Subfield E\nL : Type v\ninst✝ : Field L\nf : E →+* L\n⊢ (map f A).relrank (map f B) = A.relrank B",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"E : Type v\ninst✝¹ : Field E\nA B : Subfield E\nL : Type v\ninst✝ : Field L\nf : E →+* L\n⊢ (map f A).relrank (map f B) = A.relrank B"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 151,
"column": 2
} | {
"line": 151,
"column": 28
} | {
"line": 151,
"column": 29
} | [
{
"pp": "E : Type v\ninst✝¹ : Field E\nA : Subfield E\nL : Type v\ninst✝ : Field L\nf : L →+* E\nB : Subfield L\n⊢ (comap f A).relrank B = A.relrank (map f B)",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"E : Type v\ninst✝¹ : Field E\nA : Subfield E\nL : Type v\ninst✝ : Field L\nf : L →+* E\nB : Subfield L\n⊢ (comap f A).relrank B = A.relrank (map f B)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 159,
"column": 2
} | {
"line": 159,
"column": 67
} | {
"line": 159,
"column": 68
} | [
{
"pp": "E : Type v\ninst✝¹ : Field E\nL : Type w\ninst✝ : Field L\nA : Subfield E\nf : L →+* E\n⊢ lift.{v, w} (Module.rank (↥(comap f A)) L) = lift.{w, v} (A.relrank f.fieldRange)",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"E : Type v\ninst✝¹ : Field E\nL : Type w\ninst✝ : Field L\nA : Subfield E\nf : L →+* E\n⊢ lift.{v, w} (Module.rank (↥(comap f A)) L) = lift.{w, v} (A.relrank f.fieldRange)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 163,
"column": 2
} | {
"line": 163,
"column": 28
} | {
"line": 163,
"column": 29
} | [
{
"pp": "E : Type v\ninst✝¹ : Field E\nA : Subfield E\nL : Type v\ninst✝ : Field L\nf : L →+* E\n⊢ Module.rank (↥(comap f A)) L = A.relrank f.fieldRange",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"E : Type v\ninst✝¹ : Field E\nA : Subfield E\nL : Type v\ninst✝ : Field L\nf : L →+* E\n⊢ Module.rank (↥(comap f A)) L = A.relrank f.fieldRange"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.RatFunc.Luroth | {
"line": 74,
"column": 4
} | {
"line": 74,
"column": 15
} | {
"line": 74,
"column": 16
} | [
{
"pp": "case refine_2\nK : Type u_1\ninst✝ : Field K\nE : IntermediateField K K⟮X⟯\nh : E ≠ ⊥\nf : K[X]\nhf : Polynomial.map (algebraMap K ↥E) f = φ E\n⊢ (aeval X) f = 0",
"ppTerm": "?refine_2",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Algebra.algebraMap",
"AddGroupWithOne.... | [
"case refine_2\nK : Type u_1\ninst✝ : Field K\nE : IntermediateField K K⟮X⟯\nh : E ≠ ⊥\nf : K[X]\nhf : Polynomial.map (algebraMap K ↥E) f = φ E\n⊢ f = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.RatFunc.Luroth | {
"line": 105,
"column": 41
} | {
"line": 105,
"column": 52
} | {
"line": 105,
"column": 53
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nE : IntermediateField K K⟮X⟯\nh : E ≠ ⊥\nx✝ : ∃ c, generator E = C c\nc : K\nhc : generator E = C c\n⊢ (algebraMap K K⟮X⟯) c = generator E",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Algebra.algebraMap",
"CommSemiring.toSemiring",
... | [
"K : Type u_1\ninst✝ : Field K\nE : IntermediateField K K⟮X⟯\nh : E ≠ ⊥\nx✝ : ∃ c, generator E = C c\nc : K\nhc : generator E = C c\n⊢ C c = generator E"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 183,
"column": 2
} | {
"line": 183,
"column": 28
} | {
"line": 183,
"column": 29
} | [
{
"pp": "E : Type v\ninst✝¹ : Field E\nA B : Subfield E\nL : Type v\ninst✝ : Field L\nf : L →+* E\n⊢ (comap f A).relrank (comap f B) = A.relrank (B ⊓ f.fieldRange)",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"E : Type v\ninst✝¹ : Field E\nA B : Subfield E\nL : Type v\ninst✝ : Field L\nf : L →+* E\n⊢ (comap f A).relrank (comap f B) = A.relrank (B ⊓ f.fieldRange)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 192,
"column": 2
} | {
"line": 192,
"column": 37
} | {
"line": 192,
"column": 38
} | [
{
"pp": "E : Type v\ninst✝¹ : Field E\nL : Type w\ninst✝ : Field L\nA B : Subfield E\nf : L →+* E\nh : B ≤ f.fieldRange\n⊢ lift.{v, w} ((comap f A).relrank (comap f B)) = lift.{w, v} (A.relrank B)",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"E : Type v\ninst✝¹ : Field E\nL : Type w\ninst✝ : Field L\nA B : Subfield E\nf : L →+* E\nh : B ≤ f.fieldRange\n⊢ lift.{v, w} ((comap f A).relrank (comap f B)) = lift.{w, v} (A.relrank B)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 197,
"column": 2
} | {
"line": 197,
"column": 28
} | {
"line": 197,
"column": 29
} | [
{
"pp": "E : Type v\ninst✝¹ : Field E\nA B : Subfield E\nL : Type v\ninst✝ : Field L\nf : L →+* E\nh : B ≤ f.fieldRange\n⊢ (comap f A).relrank (comap f B) = A.relrank B",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"E : Type v\ninst✝¹ : Field E\nA B : Subfield E\nL : Type v\ninst✝ : Field L\nf : L →+* E\nh : B ≤ f.fieldRange\n⊢ (comap f A).relrank (comap f B) = A.relrank B"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 212,
"column": 2
} | {
"line": 212,
"column": 13
} | {
"line": 212,
"column": 14
} | [
{
"pp": "E : Type v\ninst✝¹ : Field E\nA B : Subfield E\nL : Type v\ninst✝ : Field L\nf : L →+* E\nh : Function.Surjective ⇑f\n⊢ (comap f A).relrank (comap f B) = A.relrank B",
"ppTerm": "?m.22",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"E : Type v\ninst✝¹ : Field E\nA B : Subfield E\nL : Type v\ninst✝ : Field L\nf : L →+* E\nh : Function.Surjective ⇑f\n⊢ (comap f A).relrank (comap f B) = A.relrank B"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 254,
"column": 2
} | {
"line": 254,
"column": 37
} | {
"line": 254,
"column": 38
} | [
{
"pp": "E : Type v\ninst✝ : Field E\nA B C : Subfield E\nh : B ≤ C\n⊢ A.relrank B * B.relrank C = (A ⊓ B).relrank C",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"E : Type v\ninst✝ : Field E\nA B C : Subfield E\nh : B ≤ C\n⊢ A.relrank B * B.relrank C = (A ⊓ B).relrank C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 264,
"column": 2
} | {
"line": 264,
"column": 37
} | {
"line": 264,
"column": 38
} | [
{
"pp": "E : Type v\ninst✝ : Field E\nA B C : Subfield E\nh : A ≤ B\n⊢ A.relrank (B ⊓ C) * B.relrank C = A.relrank C",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"E : Type v\ninst✝ : Field E\nA B C : Subfield E\nh : A ≤ B\n⊢ A.relrank (B ⊓ C) * B.relrank C = A.relrank C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 356,
"column": 2
} | {
"line": 356,
"column": 28
} | {
"line": 356,
"column": 29
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nA : IntermediateField F E\nL : Type v\ninst✝¹ : Field L\ninst✝ : Algebra F L\nf : L →ₐ[F] E\n⊢ Module.rank (↥(comap f A)) L = A.relrank f.fieldRange",
"ppTerm": "?m.46",
"assigned": false,
"usedConstants": [],... | [
"F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nA : IntermediateField F E\nL : Type v\ninst✝¹ : Field L\ninst✝ : Algebra F L\nf : L →ₐ[F] E\n⊢ Module.rank (↥(comap f A)) L = A.relrank f.fieldRange"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 367,
"column": 2
} | {
"line": 367,
"column": 28
} | {
"line": 367,
"column": 29
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nA : IntermediateField F E\nL : Type v\ninst✝¹ : Field L\ninst✝ : Algebra F L\nf : L →ₐ[F] E\nB : IntermediateField F L\n⊢ (comap f A).relrank B = A.relrank (map f B)",
"ppTerm": "?m.51",
"assigned": false,
"us... | [
"F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nA : IntermediateField F E\nL : Type v\ninst✝¹ : Field L\ninst✝ : Algebra F L\nf : L →ₐ[F] E\nB : IntermediateField F L\n⊢ (comap f A).relrank B = A.relrank (map f B)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Convex.Cone.Face.Basic | {
"line": 107,
"column": 4
} | {
"line": 107,
"column": 20
} | {
"line": 107,
"column": 21
} | [
{
"pp": "R : Type u_1\nM : Type u_2\ninst✝⁴ : Semiring R\ninst✝³ : PartialOrder R\ninst✝² : IsOrderedRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nC : PointedCone R M\nF : Set (PointedCone R M)\nh : ∀ f ∈ F, f.IsFaceOf C\nx✝ y✝ : M\na : R\nxc : x✝ ∈ C\nyc : y✝ ∈ C\na0 : 0 < a\na✝ : a • x✝ + y✝ ∈ C\nh' : ... | [
"R : Type u_1\nM : Type u_2\ninst✝⁴ : Semiring R\ninst✝³ : PartialOrder R\ninst✝² : IsOrderedRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nC : PointedCone R M\nF : Set (PointedCone R M)\nh : ∀ f ∈ F, f.IsFaceOf C\nx✝ y✝ : M\na : R\nxc : x✝ ∈ C\nyc : y✝ ∈ C\na0 : 0 < a\na✝ : a • x✝ + y✝ ∈ C\nh' : ∀ p ∈ F, a •... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 379,
"column": 2
} | {
"line": 379,
"column": 28
} | {
"line": 379,
"column": 29
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nA B : IntermediateField F E\nL : Type v\ninst✝¹ : Field L\ninst✝ : Algebra F L\nf : E →ₐ[F] L\n⊢ (map f A).relrank (map f B) = A.relrank B",
"ppTerm": "?m.48",
"assigned": false,
"usedConstants": [],
"used... | [
"F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nA B : IntermediateField F E\nL : Type v\ninst✝¹ : Field L\ninst✝ : Algebra F L\nf : E →ₐ[F] L\n⊢ (map f A).relrank (map f B) = A.relrank B"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Convex.Cone.Face.Basic | {
"line": 112,
"column": 2
} | {
"line": 112,
"column": 19
} | {
"line": 112,
"column": 20
} | [
{
"pp": "R : Type u_1\nM : Type u_2\ninst✝⁴ : Semiring R\ninst✝³ : PartialOrder R\ninst✝² : IsOrderedRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nC F : PointedCone R M\nhF : F.IsFaceOf C\nx y : M\nhx : x ∈ C\nhy : y ∈ C\nhxy : x + y ∈ F\na✝ : Nontrivial R\n⊢ x ∈ F",
"ppTerm": "?m.63",
"assigned"... | [
"R : Type u_1\nM : Type u_2\ninst✝⁴ : Semiring R\ninst✝³ : PartialOrder R\ninst✝² : IsOrderedRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nC F : PointedCone R M\nhF : F.IsFaceOf C\nx y : M\nhx : x ∈ C\nhy : y ∈ C\nhxy : x + y ∈ F\na✝ : Nontrivial R\n⊢ x ∈ F"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 393,
"column": 2
} | {
"line": 393,
"column": 28
} | {
"line": 393,
"column": 29
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nA B : IntermediateField F E\nL : Type v\ninst✝¹ : Field L\ninst✝ : Algebra F L\nf : L →ₐ[F] E\n⊢ (comap f A).relrank (comap f B) = A.relrank (B ⊓ f.fieldRange)",
"ppTerm": "?m.58",
"assigned": false,
"usedCons... | [
"F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nA B : IntermediateField F E\nL : Type v\ninst✝¹ : Field L\ninst✝ : Algebra F L\nf : L →ₐ[F] E\n⊢ (comap f A).relrank (comap f B) = A.relrank (B ⊓ f.fieldRange)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 401,
"column": 2
} | {
"line": 401,
"column": 37
} | {
"line": 401,
"column": 38
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nL : Type w\ninst✝¹ : Field L\ninst✝ : Algebra F L\nA B : IntermediateField F E\nf : L →ₐ[F] E\nh : B ≤ f.fieldRange\n⊢ Cardinal.lift.{v, w} ((comap f A).relrank (comap f B)) = Cardinal.lift.{w, v} (A.relrank B)",
"ppT... | [
"F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nL : Type w\ninst✝¹ : Field L\ninst✝ : Algebra F L\nA B : IntermediateField F E\nf : L →ₐ[F] E\nh : B ≤ f.fieldRange\n⊢ Cardinal.lift.{v, w} ((comap f A).relrank (comap f B)) = Cardinal.lift.{w, v} (A.relrank B)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 406,
"column": 2
} | {
"line": 406,
"column": 28
} | {
"line": 406,
"column": 29
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nA B : IntermediateField F E\nL : Type v\ninst✝¹ : Field L\ninst✝ : Algebra F L\nf : L →ₐ[F] E\nh : B ≤ f.fieldRange\n⊢ (comap f A).relrank (comap f B) = A.relrank B",
"ppTerm": "?m.58",
"assigned": false,
"use... | [
"F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nA B : IntermediateField F E\nL : Type v\ninst✝¹ : Field L\ninst✝ : Algebra F L\nf : L →ₐ[F] E\nh : B ≤ f.fieldRange\n⊢ (comap f A).relrank (comap f B) = A.relrank B"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 420,
"column": 2
} | {
"line": 420,
"column": 13
} | {
"line": 420,
"column": 14
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nA B : IntermediateField F E\nL : Type v\ninst✝¹ : Field L\ninst✝ : Algebra F L\nf : L →ₐ[F] E\nh : Function.Surjective ⇑f\n⊢ (comap f A).relrank (comap f B) = A.relrank B",
"ppTerm": "?m.51",
"assigned": false,
... | [
"F : Type u\nE : Type v\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\nA B : IntermediateField F E\nL : Type v\ninst✝¹ : Field L\ninst✝ : Algebra F L\nf : L →ₐ[F] E\nh : Function.Surjective ⇑f\n⊢ (comap f A).relrank (comap f B) = A.relrank B"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.RatFunc.Luroth | {
"line": 348,
"column": 4
} | {
"line": 348,
"column": 76
} | {
"line": 348,
"column": 77
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nE : IntermediateField K K⟮X⟯\nh : E ≠ ⊥\nthis :\n Polynomial.C ((algebraMap K[X] K⟮X⟯) (g E)) * Polynomial.map (algebraMap (↥E) K⟮X⟯) (q E) *\n Polynomial.map (algebraMap (↥E) K⟮X⟯) (φ E) =\n Polynomial.map (algebraMap K[X] K⟮X⟯) (θ E)\n⊢ Polynomial.C ((algebraMa... | [
"K : Type u_1\ninst✝ : Field K\nE : IntermediateField K K⟮X⟯\nh : E ≠ ⊥\nthis :\n Polynomial.C ((algebraMap K[X] K⟮X⟯) (g E)) * Polynomial.map (algebraMap (↥E) K⟮X⟯) (q E) *\n Polynomial.map (algebraMap (↥E) K⟮X⟯) (φ E) =\n Polynomial.map (algebraMap K[X] K⟮X⟯) (θ E)\n⊢ Polynomial.C ((algebraMap K[X] K⟮X⟯)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 479,
"column": 2
} | {
"line": 479,
"column": 37
} | {
"line": 479,
"column": 38
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝² : Field F\ninst✝¹ : Field E\ninst✝ : Algebra F E\nA B C : IntermediateField F E\nh : B ≤ C\n⊢ A.relrank B * B.relrank C = (A ⊓ B).relrank C",
"ppTerm": "?m.38",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"F : Type u\nE : Type v\ninst✝² : Field F\ninst✝¹ : Field E\ninst✝ : Algebra F E\nA B C : IntermediateField F E\nh : B ≤ C\n⊢ A.relrank B * B.relrank C = (A ⊓ B).relrank C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 489,
"column": 2
} | {
"line": 489,
"column": 37
} | {
"line": 489,
"column": 38
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝² : Field F\ninst✝¹ : Field E\ninst✝ : Algebra F E\nA B C : IntermediateField F E\nh : A ≤ B\n⊢ A.relrank (B ⊓ C) * B.relrank C = A.relrank C",
"ppTerm": "?m.38",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"F : Type u\nE : Type v\ninst✝² : Field F\ninst✝¹ : Field E\ninst✝ : Algebra F E\nA B C : IntermediateField F E\nh : A ≤ B\n⊢ A.relrank (B ⊓ C) * B.relrank C = A.relrank C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Convex.Cone.Face.Basic | {
"line": 223,
"column": 2
} | {
"line": 223,
"column": 59
} | {
"line": 223,
"column": 60
} | [
{
"pp": "R : Type u_1\nM : Type u_2\ninst✝⁴ : DivisionRing R\ninst✝³ : LinearOrder R\ninst✝² : IsOrderedRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nC F : PointedCone R M\nh₁ : F ≤ C\nh₂ : ∀ {x y : M}, x ∈ C → y ∈ C → x + y ∈ F → x ∈ F\nx✝ y✝ : M\na✝ : R\nhx : x✝ ∈ C\nhy : y✝ ∈ C\nha : 0 < a✝\nhaxy : a✝... | [
"R : Type u_1\nM : Type u_2\ninst✝⁴ : DivisionRing R\ninst✝³ : LinearOrder R\ninst✝² : IsOrderedRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nC F : PointedCone R M\nh₁ : F ≤ C\nh₂ : ∀ {x y : M}, x ∈ C → y ∈ C → x + y ∈ F → x ∈ F\nx✝ y✝ : M\na✝ : R\nhx : x✝ ∈ C\nhy : y✝ ∈ C\nha : 0 < a✝\nhaxy : a✝ • x✝ + y✝ ∈... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Convex.Cone.Face.Basic | {
"line": 231,
"column": 2
} | {
"line": 231,
"column": 35
} | {
"line": 231,
"column": 36
} | [
{
"pp": "R : Type u_1\nM : Type u_2\ninst✝⁴ : DivisionRing R\ninst✝³ : LinearOrder R\ninst✝² : IsOrderedRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nC : PointedCone R M\nx✝ y✝ : M\nxc : x✝ ∈ C\nyc : y✝ ∈ C\nxyf : x✝ + y✝ ∈ C ∧ -y✝ + -x✝ ∈ C\n⊢ -x✝ ∈ C",
"ppTerm": "?m.77",
"assigned": false,
... | [
"R : Type u_1\nM : Type u_2\ninst✝⁴ : DivisionRing R\ninst✝³ : LinearOrder R\ninst✝² : IsOrderedRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nC : PointedCone R M\nx✝ y✝ : M\nxc : x✝ ∈ C\nyc : y✝ ∈ C\nxyf : x✝ + y✝ ∈ C ∧ -y✝ + -x✝ ∈ C\n⊢ -x✝ ∈ C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Convex.Cone.Face.Basic | {
"line": 251,
"column": 24
} | {
"line": 251,
"column": 46
} | {
"line": 251,
"column": 47
} | [
{
"pp": "R : Type u_1\nM : Type u_2\nN : Type u_3\ninst✝⁶ : DivisionRing R\ninst✝⁵ : LinearOrder R\ninst✝⁴ : IsOrderedRing R\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : AddCommGroup N\ninst✝ : Module R N\nC₁ F₁ : PointedCone R M\nC₂ F₂ : PointedCone R N\nhF₁ : F₁.IsFaceOf C₁\nhF₂ : F₂.IsFaceOf C₂\nx... | [
"R : Type u_1\nM : Type u_2\nN : Type u_3\ninst✝⁶ : DivisionRing R\ninst✝⁵ : LinearOrder R\ninst✝⁴ : IsOrderedRing R\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : AddCommGroup N\ninst✝ : Module R N\nC₁ F₁ : PointedCone R M\nC₂ F₂ : PointedCone R N\nhF₁ : F₁.IsFaceOf C₁\nhF₂ : F₂.IsFaceOf C₂\nx : M × N\nhx... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Diffeology.Basic | {
"line": 326,
"column": 4
} | {
"line": 326,
"column": 53
} | {
"line": 327,
"column": 4
} | [
{
"pp": "X : Type u_1\nd : CorePlotsOn X\nn : ℕ\np : EuclideanSpace ℝ (Fin n) → X\nh :\n ∀ (x : EuclideanSpace ℝ (Fin n)),\n ∃ u,\n IsOpen u ∧\n x ∈ u ∧\n ∀ {m : ℕ} {f : EuclideanSpace ℝ (Fin m) → EuclideanSpace ℝ (Fin n)},\n (∀ (x : EuclideanSpace ℝ (Fin m)), f x ∈ u) → Cont... | [
"X : Type u_1\nd : CorePlotsOn X\nn : ℕ\np : EuclideanSpace ℝ (Fin n) → X\nh :\n ∀ (x : EuclideanSpace ℝ (Fin n)),\n ∃ u,\n IsOpen u ∧\n x ∈ u ∧\n ∀ {m : ℕ} {f : EuclideanSpace ℝ (Fin m) → EuclideanSpace ℝ (Fin n)},\n (∀ (x : EuclideanSpace ℝ (Fin m)), f x ∈ u) → ContDiff ℝ ∞ f →... | let ⟨ε, hε, hε'⟩ := Metric.isOpen_iff.mp hu x hxu | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLet___1 | Lean.Parser.Tactic.tacticLet__ |
Mathlib.FieldTheory.RatFunc.Luroth | {
"line": 452,
"column": 12
} | {
"line": 452,
"column": 23
} | {
"line": 452,
"column": 24
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nE : IntermediateField K K⟮X⟯\nh : E ≠ ⊥\nF : Type u_1 := AlgebraicClosure K\nH : ¬(Polynomial.map (algebraMap K F) (Q₂ h)).degree ≤ 0\nα : F\nhα : (aeval α) (Q₂ h) = 0\neq :\n (Polynomial.mapRingHom (algebraMap K F)) (g E) * Polynomial.C ((aeval α) (f E)) =\n (Polynom... | [
"K : Type u_1\ninst✝ : Field K\nE : IntermediateField K K⟮X⟯\nh : E ≠ ⊥\nF : Type u_1 := AlgebraicClosure K\nH : ¬(Polynomial.map (algebraMap K F) (Q₂ h)).degree ≤ 0\nα : F\nhα : (aeval α) (Q₂ h) = 0\neq :\n (Polynomial.mapRingHom (algebraMap K F)) (g E) * Polynomial.C ((aeval α) (f E)) =\n (Polynomial.mapRingH... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.RatFunc.Luroth | {
"line": 453,
"column": 7
} | {
"line": 453,
"column": 18
} | {
"line": 453,
"column": 19
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nE : IntermediateField K K⟮X⟯\nh : E ≠ ⊥\nF : Type u_1 := AlgebraicClosure K\nH : ¬(Polynomial.map (algebraMap K F) (Q₂ h)).degree ≤ 0\nα : F\nhα : (aeval α) (Q₂ h) = 0\neq :\n (Polynomial.mapRingHom (algebraMap K F)) (g E) * Polynomial.C ((aeval α) (f E)) =\n (Polynom... | [
"K : Type u_1\ninst✝ : Field K\nE : IntermediateField K K⟮X⟯\nh : E ≠ ⊥\nF : Type u_1 := AlgebraicClosure K\nH : ¬(Polynomial.map (algebraMap K F) (Q₂ h)).degree ≤ 0\nα : F\nhα : (aeval α) (Q₂ h) = 0\neq :\n (Polynomial.mapRingHom (algebraMap K F)) (g E) * Polynomial.C ((aeval α) (f E)) =\n (Polynomial.mapRingH... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Projection | {
"line": 211,
"column": 2
} | {
"line": 211,
"column": 13
} | {
"line": 211,
"column": 14
} | [
{
"pp": "𝕜 : 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\n⊢ s.direction.orthogona... | [
"𝕜 : 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\n⊢ p -ᵥ ↑((orthogonalProjection s) p... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Projection | {
"line": 210,
"column": 80
} | {
"line": 211,
"column": 68
} | {
"line": 213,
"column": 0
} | [
{
"pp": "𝕜 : 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\n⊢ s.direction.orthogona... | [] | by
simpa using vsub_orthogonalProjection_mem_direction_orthogonal _ _ | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Geometry.Euclidean.Projection | {
"line": 226,
"column": 6
} | {
"line": 226,
"column": 27
} | {
"line": 226,
"column": 28
} | [
{
"pp": "𝕜 : 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 q : P\nhqs : q ∈ s\nhpq : p ... | [
"𝕜 : 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 q : P\nhqs : q ∈ s\nhpq : p -ᵥ q ∈ s.dir... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Projection | {
"line": 237,
"column": 2
} | {
"line": 237,
"column": 13
} | {
"line": 237,
"column": 14
} | [
{
"pp": "𝕜 : 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\nq : ↥s\n⊢ (orthogonalPr... | [
"𝕜 : 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\nq : ↥s\n⊢ (orthogonalProjection s) ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation | {
"line": 49,
"column": 6
} | {
"line": 53,
"column": 42
} | {
"line": 54,
"column": 6
} | [
{
"pp": "V : Type u_1\nV' : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : NormedAddCommGroup V'\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : InnerProductSpace ℝ V'\ninst✝¹ : Fact (finrank ℝ V = 2)\ninst✝ : Fact (finrank ℝ V' = 2)\no : Orientation ℝ V (Fin 2)\nθ : Real.Angle\nx y : V\n⊢ ⟪(θ.cos • LinearMap.id +... | [
"V : Type u_1\nV' : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : NormedAddCommGroup V'\ninst✝³ : InnerProductSpace ℝ V\ninst✝² : InnerProductSpace ℝ V'\ninst✝¹ : Fact (finrank ℝ V = 2)\ninst✝ : Fact (finrank ℝ V' = 2)\no : Orientation ℝ V (Fin 2)\nθ : Real.Angle\nx y : V\n⊢ θ.cos * (θ.cos * ⟪x, y⟫ + θ.sin * (o... | simp only [RCLike.conj_to_real, id, LinearMap.smul_apply, LinearMap.add_apply,
LinearMap.id_coe, LinearEquiv.coe_coe, LinearIsometryEquiv.coe_toLinearEquiv,
Orientation.areaForm_rightAngleRotation_left, Orientation.inner_rightAngleRotation_left,
Orientation.inner_rightAngleRotation_right, inner_... | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation | {
"line": 111,
"column": 2
} | {
"line": 111,
"column": 18
} | {
"line": 111,
"column": 19
} | [
{
"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)\nθ : Real.Angle\nthis : Nontrivial V\nx : V\nhx : x ≠ 0\n⊢ LinearMap.det\n ((Matrix.toLin (o.basisRightAngleRotation x hx) (o.basisRightAngleRotation x hx))\n ... | [
"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)\nθ : Real.Angle\nthis : Nontrivial V\nx : V\nhx : x ≠ 0\n⊢ θ.cos * θ.cos + θ.sin * θ.sin = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation | {
"line": 118,
"column": 4
} | {
"line": 118,
"column": 57
} | {
"line": 118,
"column": 58
} | [
{
"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)\nθ : Real.Angle\n⊢ ↑(LinearEquiv.det (o.rotation θ).toLinearEquiv) = ↑1",
"ppTerm": "?m.55",
"assigned": true,
"usedConstants": [
"LinearEquiv.det",... | [
"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)\nθ : Real.Angle\n⊢ LinearMap.det ↑(o.rotation θ).toLinearEquiv = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Projection | {
"line": 362,
"column": 6
} | {
"line": 362,
"column": 44
} | {
"line": 363,
"column": 6
} | [
{
"pp": "𝕜 : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : RCLike 𝕜\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace 𝕜 V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : AffineSubspace 𝕜 P\np₁ p₂ : P\nhp₁ : p₁ ∈ s\nhp₂ : p₂ ∈ s\nr₁ r₂ : 𝕜\nv : V\nhv : v ∈ s.directionᗮ\n⊢ ‖p₁ -ᵥ p₂‖ * ‖p... | [
"𝕜 : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : RCLike 𝕜\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace 𝕜 V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : AffineSubspace 𝕜 P\np₁ p₂ : P\nhp₁ : p₁ ∈ s\nhp₂ : p₂ ∈ s\nr₁ r₂ : 𝕜\nv : V\nhv : v ∈ s.directionᗮ\n⊢ ‖p₁ -ᵥ p₂‖ * ‖p₁ -ᵥ p₂‖ + ‖... | rw [norm_smul, dist_eq_norm_vsub V p₁] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Geometry.Euclidean.Projection | {
"line": 463,
"column": 63
} | {
"line": 463,
"column": 98
} | {
"line": 464,
"column": 4
} | [
{
"pp": "𝕜 : 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\n⊢ s.direction.reflectio... | [
"𝕜 : 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\n⊢ p -ᵥ ↑(Classical.arbitrary ↥s) ∈ ... | s.direction.reflection_eq_self_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Altitude | {
"line": 168,
"column": 6
} | {
"line": 168,
"column": 17
} | {
"line": 168,
"column": 18
} | [
{
"pp": "case mpr.refine_1\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\ninst✝ : NeZero n\ns : Simplex ℝ P n\ni : Fin (n + 1)\np : P\nhne : p ≠ s.points i\nh : p -ᵥ s.points i ∈ (s.altitude i).direction\n⊢... | [
"case mpr.refine_1\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\ninst✝ : NeZero n\ns : Simplex ℝ P n\ni : Fin (n + 1)\np : P\nhne : p ≠ s.points i\nh : p -ᵥ s.points i ∈ (s.altitude i).direction\n⊢ p -ᵥ s.poin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Altitude | {
"line": 171,
"column": 31
} | {
"line": 171,
"column": 42
} | {
"line": 171,
"column": 43
} | [
{
"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\ni : Fin (n + 1)\np : P\nhne : p ≠ s.points i\nh : p -ᵥ s.points i ∈ (s.altitude i).direction\n⊢ id (p -ᵥ s.points ... | [
"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\ni : Fin (n + 1)\np : P\nhne : p ≠ s.points i\nh : p -ᵥ s.points i ∈ (s.altitude i).direction\n⊢ ¬p = s.points i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Projection | {
"line": 481,
"column": 4
} | {
"line": 481,
"column": 15
} | {
"line": 481,
"column": 16
} | [
{
"pp": "case mp\n𝕜 : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁸ : RCLike 𝕜\ninst✝⁷ : NormedAddCommGroup V\ninst✝⁶ : InnerProductSpace 𝕜 V\ninst✝⁵ : MetricSpace P\ninst✝⁴ : NormedAddTorsor V P\ns₁ s₂ : AffineSubspace 𝕜 P\ninst✝³ : Nonempty ↥s₁\ninst✝² : Nonempty ↥s₂\ninst✝¹ : s₁.direction.HasOrthogonalPro... | [
"case mp\n𝕜 : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁸ : RCLike 𝕜\ninst✝⁷ : NormedAddCommGroup V\ninst✝⁶ : InnerProductSpace 𝕜 V\ninst✝⁵ : MetricSpace P\ninst✝⁴ : NormedAddTorsor V P\ns₁ s₂ : AffineSubspace 𝕜 P\ninst✝³ : Nonempty ↥s₁\ninst✝² : Nonempty ↥s₂\ninst✝¹ : s₁.direction.HasOrthogonalProjection\nins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Altitude | {
"line": 206,
"column": 2
} | {
"line": 206,
"column": 34
} | {
"line": 208,
"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\ni : Fin (n + 1)\n⊢ s.altitudeFoot i ∈ affineSpan ℝ (Set.range (s.faceOpposite i).points)",
"ppTerm": "?m.66",
... | [] | exact orthogonalProjection_mem _ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 243,
"column": 2
} | {
"line": 243,
"column": 63
} | {
"line": 245,
"column": 0
} | [
{
"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\n⊢ o.oangle (-x) y + o.oangle (-y) x = 0",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
... | [] | rw [oangle_neg_left_eq_neg_right, oangle_rev, neg_add_cancel] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 243,
"column": 2
} | {
"line": 243,
"column": 63
} | {
"line": 245,
"column": 0
} | [
{
"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\n⊢ o.oangle (-x) y + o.oangle (-y) x = 0",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
... | [] | rw [oangle_neg_left_eq_neg_right, oangle_rev, neg_add_cancel] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 243,
"column": 2
} | {
"line": 243,
"column": 63
} | {
"line": 245,
"column": 0
} | [
{
"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\n⊢ o.oangle (-x) y + o.oangle (-y) x = 0",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
... | [] | rw [oangle_neg_left_eq_neg_right, oangle_rev, neg_add_cancel] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation | {
"line": 251,
"column": 4
} | {
"line": 251,
"column": 23
} | {
"line": 251,
"column": 24
} | [
{
"pp": "case mp\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 : V\nhx : x ≠ 0\nθ : Real.Angle\nh : (o.rotation θ) x = x\n⊢ 0 = θ",
"ppTerm": "?mp",
"assigned": false,
"usedConstants": [],
"usedFVars":... | [
"case mp\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 : V\nhx : x ≠ 0\nθ : Real.Angle\nh : (o.rotation θ) x = x\n⊢ 0 = θ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation | {
"line": 249,
"column": 2
} | {
"line": 251,
"column": 55
} | {
"line": 252,
"column": 2
} | [
{
"pp": "case mp\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 : V\nhx : x ≠ 0\nθ : Real.Angle\n⊢ (o.rotation θ) x = x → θ = 0",
"ppTerm": "?mp",
"assigned": true,
"usedConstants": [
"LinearIsometryE... | [
"case mpr\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 : V\nhx : x ≠ 0\nθ : Real.Angle\n⊢ θ = 0 → (o.rotation θ) x = x"
] | · intro h
rw [eq_comm]
simpa [hx, h] using o.oangle_rotation_right hx hx θ | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 359,
"column": 2
} | {
"line": 359,
"column": 13
} | {
"line": 359,
"column": 14
} | [
{
"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\n⊢ 0 ≤ (↑⟪x, y⟫ + (o.areaForm x) y • I).re ∧ (↑⟪x, y⟫ + (o.areaForm x) y • I).im = 0 ↔ SameRay ℝ x y",
"ppTerm": "?m.59",
"assigned": true,
"used... | [
"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\n⊢ 0 ≤ ⟪x, y⟫ ∧ (o.areaForm x) y = 0 ↔ SameRay ℝ x y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Altitude | {
"line": 352,
"column": 10
} | {
"line": 352,
"column": 21
} | {
"line": 352,
"column": 22
} | [
{
"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\ns : Simplex ℝ P n\ninst✝ : n.AtLeastTwo\ni j : Fin (n + 1)\nhij : i ≠ j\nr : ℝ\nhr : r ≠ 0\nh : s.points j -ᵥ s.altitudeFoot j = r • (s.points i -ᵥ s.a... | [
"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\ns : Simplex ℝ P n\ninst✝ : n.AtLeastTwo\ni j : Fin (n + 1)\nhij : i ≠ j\nr : ℝ\nhr : r ≠ 0\nh : s.points j -ᵥ s.altitudeFoot j = r • (s.points i -ᵥ s.altitudeFoot ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine | {
"line": 108,
"column": 2
} | {
"line": 108,
"column": 32
} | {
"line": 108,
"column": 33
} | [
{
"pp": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nv₁ v₂ v₃ v : V\n⊢ ∠ (v₁ - v) (v₂ - v) (v₃ - v) = ∠ v₁ v₂ v₃",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nv₁ v₂ v₃ v : V\n⊢ ∠ (v₁ - v) (v₂ - v) (v₃ - v) = ∠ v₁ v₂ v₃"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine | {
"line": 113,
"column": 2
} | {
"line": 113,
"column": 32
} | {
"line": 113,
"column": 33
} | [
{
"pp": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nv v₁ v₂ v₃ : V\n⊢ ∠ (v - v₁) (v - v₂) (v - v₃) = ∠ v₁ v₂ v₃",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nv v₁ v₂ v₃ : V\n⊢ ∠ (v - v₁) (v - v₂) (v - v₃) = ∠ v₁ v₂ v₃"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine | {
"line": 118,
"column": 2
} | {
"line": 118,
"column": 29
} | {
"line": 118,
"column": 30
} | [
{
"pp": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nv₁ v₂ v₃ : V\n⊢ ∠ (-v₁) (-v₂) (-v₃) = ∠ v₁ v₂ v₃",
"ppTerm": "?m.24",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nv₁ v₂ v₃ : V\n⊢ ∠ (-v₁) (-v₂) (-v₃) = ∠ v₁ v₂ v₃"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation | {
"line": 361,
"column": 45
} | {
"line": 362,
"column": 85
} | {
"line": 364,
"column": 0
} | [
{
"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)\nθ : Real.Angle\nf : V ≃ₗᵢ[ℝ] ℂ\nhf : (map (Fin 2) f.toLinearEquiv) o = Complex.orientation\nx : V\n⊢ f ((o.rotation θ) x) = ↑θ.toCircle * f x",
"ppTerm": "?m.76"... | [] | by
rw [← Complex.rotation, ← hf, o.rotation_map, LinearIsometryEquiv.symm_apply_apply] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 426,
"column": 25
} | {
"line": 426,
"column": 36
} | {
"line": 426,
"column": 37
} | [
{
"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)\ny : V\nhy : y ≠ 0\nr : ℝ\nhr : 0 ≤ r\nh₁ : ‖r • y‖ = ‖y‖\nh₂ : SameRay ℝ (r • y) y\n⊢ ‖y‖ ≠ 0",
"ppTerm": "?m.138",
"assigned": true,
"usedConstants": [
... | [
"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)\ny : V\nhy : y ≠ 0\nr : ℝ\nhr : 0 ≤ r\nh₁ : ‖r • y‖ = ‖y‖\nh₂ : SameRay ℝ (r • y) y\n⊢ ¬y = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 429,
"column": 6
} | {
"line": 429,
"column": 47
} | {
"line": 429,
"column": 48
} | [
{
"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)\ny : V\nhy : y ≠ 0\nr : ℝ\nhr : 0 ≤ r\nh₁ : ‖r • y‖ = ‖y‖\nh₂ : SameRay ℝ (r • y) y\nthis : ‖y‖ ≠ 0\n⊢ r * ‖y‖ = 1 * ‖y‖",
"ppTerm": "?m.163",
"assigned": tru... | [
"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)\ny : V\nhy : y ≠ 0\nr : ℝ\nhr : 0 ≤ r\nh₁ : ‖r • y‖ = ‖y‖\nh₂ : SameRay ℝ (r • y) y\nthis : ‖y‖ ≠ 0\n⊢ r * ‖y‖ = ‖y‖"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 107,
"column": 2
} | {
"line": 107,
"column": 18
} | {
"line": 107,
"column": 19
} | [
{
"pp": "case neg\nV : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : ⟪x, y⟫ = 0\nh0 : x = 0 ∨ y ≠ 0\nhx : ¬x = 0\n⊢ ‖x‖ * ‖x‖ < ‖x‖ * ‖x‖ + ‖y‖ * ‖y‖",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Norm.nor... | [
"case neg\nV : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : ⟪x, y⟫ = 0\nh0 : x = 0 ∨ y ≠ 0\nhx : ¬x = 0\n⊢ ¬y = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine | {
"line": 398,
"column": 2
} | {
"line": 398,
"column": 31
} | {
"line": 398,
"column": 32
} | [
{
"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 p p₂ p₃ : P\nh : Sbtw ℝ p₂ p₁ p\n⊢ ∠ p₁ p₂ p₃ = ∠ p p₂ p₃",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"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 p p₂ p₃ : P\nh : Sbtw ℝ p₂ p₁ p\n⊢ ∠ p₁ p₂ p₃ = ∠ p p₂ p₃"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine | {
"line": 411,
"column": 2
} | {
"line": 411,
"column": 31
} | {
"line": 411,
"column": 32
} | [
{
"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 p p₂ p₃ : P\nh : Wbtw ℝ p₂ p₁ p\nhp₁p₂ : p₁ ≠ p₂\n⊢ ∠ p₁ p₂ p₃ = ∠ p p₂ p₃",
"ppTerm": "?m.26",
"assigned": false,
"usedConstants": [],
"use... | [
"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 p p₂ p₃ : P\nh : Wbtw ℝ p₂ p₁ p\nhp₁p₂ : p₁ ≠ p₂\n⊢ ∠ p₁ p₂ p₃ = ∠ p p₂ p₃"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 601,
"column": 8
} | {
"line": 601,
"column": 19
} | {
"line": 601,
"column": 20
} | [
{
"pp": "case inl.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 z : V\nh : InnerProductGeometry.angle 0 x = InnerProductGeometry.angle y z\nhs : (o.oangle 0 x).sign = (o.oangle y z).sign\n⊢ (o.oangle 0 x).sign =... | [
"case inl.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 z : V\nh : InnerProductGeometry.angle 0 x = InnerProductGeometry.angle y z\nhs : (o.oangle 0 x).sign = (o.oangle y z).sign\n⊢ (o.oangle y z).sign = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 602,
"column": 8
} | {
"line": 602,
"column": 19
} | {
"line": 602,
"column": 20
} | [
{
"pp": "case inl.inr\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)\nw y z : V\nh : InnerProductGeometry.angle w 0 = InnerProductGeometry.angle y z\nhs : (o.oangle w 0).sign = (o.oangle y z).sign\n⊢ (o.oangle w 0).sign =... | [
"case inl.inr\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)\nw y z : V\nh : InnerProductGeometry.angle w 0 = InnerProductGeometry.angle y z\nhs : (o.oangle w 0).sign = (o.oangle y z).sign\n⊢ (o.oangle y z).sign = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 603,
"column": 8
} | {
"line": 603,
"column": 19
} | {
"line": 603,
"column": 20
} | [
{
"pp": "case inr.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)\nw x z : V\nh : InnerProductGeometry.angle w x = InnerProductGeometry.angle 0 z\nhs : (o.oangle w x).sign = (o.oangle 0 z).sign\n⊢ (o.oangle w x).sign =... | [
"case inr.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)\nw x z : V\nh : InnerProductGeometry.angle w x = InnerProductGeometry.angle 0 z\nhs : (o.oangle w x).sign = (o.oangle 0 z).sign\n⊢ (o.oangle w x).sign = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 604,
"column": 8
} | {
"line": 604,
"column": 19
} | {
"line": 604,
"column": 20
} | [
{
"pp": "case inr.inr\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)\nw x y : V\nh : InnerProductGeometry.angle w x = InnerProductGeometry.angle y 0\nhs : (o.oangle w x).sign = (o.oangle y 0).sign\n⊢ (o.oangle w x).sign =... | [
"case inr.inr\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)\nw x y : V\nh : InnerProductGeometry.angle w x = InnerProductGeometry.angle y 0\nhs : (o.oangle w x).sign = (o.oangle y 0).sign\n⊢ (o.oangle w x).sign = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 608,
"column": 8
} | {
"line": 608,
"column": 19
} | {
"line": 608,
"column": 20
} | [
{
"pp": "case inl.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 z : V\nhsyz : (o.oangle y z).sign = 0\nh : InnerProductGeometry.angle 0 x = InnerProductGeometry.angle y z\nhs : (o.oangle 0 x).sign = (o.oangle y ... | [
"case inl.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 z : V\nhsyz : (o.oangle y z).sign = 0\nh : InnerProductGeometry.angle 0 x = InnerProductGeometry.angle y z\nhs : (o.oangle 0 x).sign = (o.oangle y z).sign\nhsw... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 609,
"column": 8
} | {
"line": 609,
"column": 19
} | {
"line": 609,
"column": 20
} | [
{
"pp": "case inl.inr\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)\nw y z : V\nhsyz : (o.oangle y z).sign = 0\nh : InnerProductGeometry.angle w 0 = InnerProductGeometry.angle y z\nhs : (o.oangle w 0).sign = (o.oangle y ... | [
"case inl.inr\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)\nw y z : V\nhsyz : (o.oangle y z).sign = 0\nh : InnerProductGeometry.angle w 0 = InnerProductGeometry.angle y z\nhs : (o.oangle w 0).sign = (o.oangle y z).sign\nhsw... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 610,
"column": 8
} | {
"line": 610,
"column": 19
} | {
"line": 610,
"column": 20
} | [
{
"pp": "case inr.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)\nw x z : V\nhswx : (o.oangle w x).sign = 0\nh : InnerProductGeometry.angle w x = InnerProductGeometry.angle 0 z\nhs : (o.oangle w x).sign = (o.oangle 0 ... | [
"case inr.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)\nw x z : V\nhswx : (o.oangle w x).sign = 0\nh : InnerProductGeometry.angle w x = InnerProductGeometry.angle 0 z\nhs : (o.oangle w x).sign = (o.oangle 0 z).sign\nhsy... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 611,
"column": 8
} | {
"line": 611,
"column": 19
} | {
"line": 611,
"column": 20
} | [
{
"pp": "case inr.inr\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)\nw x y : V\nhswx : (o.oangle w x).sign = 0\nh : InnerProductGeometry.angle w x = InnerProductGeometry.angle y 0\nhs : (o.oangle w x).sign = (o.oangle y ... | [
"case inr.inr\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)\nw x y : V\nhswx : (o.oangle w x).sign = 0\nh : InnerProductGeometry.angle w x = InnerProductGeometry.angle y 0\nhs : (o.oangle w x).sign = (o.oangle y 0).sign\nhsy... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine | {
"line": 438,
"column": 6
} | {
"line": 438,
"column": 17
} | {
"line": 438,
"column": 18
} | [
{
"pp": "case refine_2.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\np₁ p₃ : P\n⊢ Collinear ℝ {p₁, p₁, p₃}",
"ppTerm": "?refine_2.inl",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"I... | [
"case refine_2.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\np₁ p₃ : P\n⊢ Collinear ℝ {p₁, p₃}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine | {
"line": 439,
"column": 6
} | {
"line": 439,
"column": 17
} | {
"line": 439,
"column": 18
} | [
{
"pp": "case refine_2.inr.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\np₁ p₃ : P\n⊢ Collinear ℝ {p₁, p₃, p₃}",
"ppTerm": "?refine_2.inr.inl",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"case refine_2.inr.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\np₁ p₃ : P\n⊢ Collinear ℝ {p₁, p₃}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 620,
"column": 6
} | {
"line": 620,
"column": 49
} | {
"line": 620,
"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)\nw x y z : V\nh : InnerProductGeometry.angle w x = InnerProductGeometry.angle y z\nhs : (o.oangle w x).sign = (o.oangle y z).sign\nh0 : (w = 0 ∨ x = 0) ∨ y = 0 ∨ z = ... | [
"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)\nw x y z : V\nh : InnerProductGeometry.angle w x = InnerProductGeometry.angle y z\nhs : (o.oangle w x).sign = (o.oangle y z).sign\nh0 : (w = 0 ∨ x = 0) ∨ y = 0 ∨ z = 0\nhswx : (o... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 623,
"column": 6
} | {
"line": 623,
"column": 49
} | {
"line": 623,
"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)\nw x y z : V\nh : InnerProductGeometry.angle w x = InnerProductGeometry.angle y z\nhs : (o.oangle w x).sign = (o.oangle y z).sign\nh0 : (w = 0 ∨ x = 0) ∨ y = 0 ∨ z = ... | [
"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)\nw x y z : V\nh : InnerProductGeometry.angle w x = InnerProductGeometry.angle y z\nhs : (o.oangle w x).sign = (o.oangle y z).sign\nh0 : (w = 0 ∨ x = 0) ∨ y = 0 ∨ z = 0\nhswx : (o... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 333,
"column": 4
} | {
"line": 333,
"column": 34
} | {
"line": 333,
"column": 35
} | [
{
"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‖ ↔\n ‖p₁ -ᵥ p₂ - (p₃ -ᵥ p₂)‖ * ‖p₁ -ᵥ p₂ - (p₃ -ᵥ p₂)‖ = ‖p₁ -ᵥ p... | [
"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 ‖p₁ -ᵥ p₃‖ * ‖p₁ -ᵥ p₃‖ = ‖p₁ -ᵥ p₂‖ * ‖p₁ -ᵥ p₂‖ + ‖p₃ -ᵥ p₂‖ * ‖p₃ -ᵥ ... | vsub_sub_vsub_cancel_right p₁, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 340,
"column": 68
} | {
"line": 340,
"column": 100
} | {
"line": 341,
"column": 4
} | [
{
"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⊢ InnerProductGeometry.angle (p₂ -ᵥ p₃) (p₁ -ᵥ p₃) = Real.arccos (‖p₂ -ᵥ p₃‖ / ‖p₁ -ᵥ p₃‖)",
"ppTerm": "?m.112"... | [
"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 p₂ + (p₂ -ᵥ p₃)) = Real.arccos (‖p₂ -ᵥ p₃‖ / ‖p₁ -ᵥ p₂ + (p₂ -ᵥ p₃)‖)"
] | ← vsub_add_vsub_cancel p₁ p₂ p₃, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 323,
"column": 4
} | {
"line": 323,
"column": 15
} | {
"line": 323,
"column": 16
} | [
{
"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 : ‖p₁ -ᵥ p₂‖ = ‖p₁ -ᵥ p₃‖\n⊢ p₁ -ᵥ p₂ ≠ p₁ -ᵥ p₃",
"ppTerm": "?m... | [
"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⊢ ¬p₂ = p₃"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 349,
"column": 67
} | {
"line": 349,
"column": 99
} | {
"line": 350,
"column": 4
} | [
{
"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⊢ InnerProductGeometry.angle (p₂ -ᵥ p₃) (p₁ -ᵥ p₃) = Real.arcsin (‖p₁ -ᵥ p₂‖ / ‖p... | [
"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 p₂ + (p₂ -ᵥ p₃)) = Real.arcsin (‖p₁ -ᵥ p₂‖ / ‖... | ← vsub_add_vsub_cancel p₁ p₂ p₃, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 358,
"column": 68
} | {
"line": 358,
"column": 100
} | {
"line": 359,
"column": 4
} | [
{
"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⊢ InnerProductGeometry.angle (p₂ -ᵥ p₃) (p₁ -ᵥ p₃) = Real.arctan (‖p₁ -ᵥ p₂‖ / ‖p₂ -ᵥ p₃‖)",
... | [
"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 p₂ + (p₂ -ᵥ p₃)) = Real.arctan (‖p₁ -ᵥ p₂‖ / ‖p₂ -ᵥ p₃‖)"
] | ← vsub_add_vsub_cancel p₁ p₂ p₃, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 367,
"column": 13
} | {
"line": 367,
"column": 45
} | {
"line": 367,
"column": 46
} | [
{
"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 < InnerProductGeometry.angle (p₂ -ᵥ p₃) (p₁ -ᵥ p₃)",
"ppTerm": "?m.148",
... | [
"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 p₂ + (p₂ -ᵥ p₃))"
] | ← vsub_add_vsub_cancel p₁ p₂ p₃, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 691,
"column": 4
} | {
"line": 691,
"column": 15
} | {
"line": 691,
"column": 16
} | [
{
"pp": "case refine_2\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\nhx : x ≠ 0\nhy : y ≠ 0\nh : InnerProductGeometry.angle x y = 0\nha : o.oangle x y = ↑0 ∨ o.oangle x y = -↑0\n⊢ o.oangle x y = 0",
"ppTerm... | [
"case refine_2\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\nhx : x ≠ 0\nhy : y ≠ 0\nh : InnerProductGeometry.angle x y = 0\nha : o.oangle x y = ↑0 ∨ o.oangle x y = -↑0\n⊢ o.oangle x y = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 375,
"column": 13
} | {
"line": 375,
"column": 45
} | {
"line": 375,
"column": 46
} | [
{
"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⊢ InnerProductGeometry.angle (p₂ -ᵥ p₃) (p₁ -ᵥ p₃) ≤ π / 2",
"ppTerm": "?m.101",
"assigned": true,
"use... | [
"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 p₂ + (p₂ -ᵥ p₃)) ≤ π / 2"
] | ← vsub_add_vsub_cancel p₁ p₂ p₃, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 707,
"column": 4
} | {
"line": 707,
"column": 15
} | {
"line": 707,
"column": 16
} | [
{
"pp": "case neg.refine_2\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\nhx : ¬x = 0\nhy : ¬y = 0\nh : InnerProductGeometry.angle x y = π\nha : o.oangle x y = ↑π ∨ o.oangle x y = -↑π\n⊢ o.oangle x y = ↑π",
... | [
"case neg.refine_2\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\nhx : ¬x = 0\nhy : ¬y = 0\nh : InnerProductGeometry.angle x y = π\nha : o.oangle x y = ↑π ∨ o.oangle x y = -↑π\n⊢ o.oangle x y = ↑π"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 384,
"column": 13
} | {
"line": 384,
"column": 45
} | {
"line": 384,
"column": 46
} | [
{
"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⊢ InnerProductGeometry.angle (p₂ -ᵥ p₃) (p₁ -ᵥ p₃) < π / 2",
"ppTerm": "?m.136",
"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\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 p₂ + (p₂ -ᵥ p₃)) < π / 2"
] | ← vsub_add_vsub_cancel p₁ p₂ p₃, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 392,
"column": 68
} | {
"line": 392,
"column": 100
} | {
"line": 393,
"column": 4
} | [
{
"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 (InnerProductGeometry.angle (p₂ -ᵥ p₃) (p₁ -ᵥ p₃)) = ‖p₂ -ᵥ p₃‖ / ‖p₁ -ᵥ p₃‖",
"ppTerm": "?m.112",
... | [
"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 p₂ + (p₂ -ᵥ p₃))) = ‖p₂ -ᵥ p₃‖ / ‖p₁ -ᵥ p₂ + (p₂ -ᵥ p₃)‖"
] | ← vsub_add_vsub_cancel p₁ p₂ p₃, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 495,
"column": 2
} | {
"line": 495,
"column": 26
} | {
"line": 495,
"column": 26
} | [
{
"pp": "case neg\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)\np₁ p₂ p₃ : P\nh : Wbtw ℝ p₁ p₂ p₃\nhp₂p₁ : ¬p₂ = p₁\n⊢ ∡ p₂ p₁ p₃ = 0",
"ppTerm": "?... | [
"case pos\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)\np₁ p₂ p₃ : P\nh : Wbtw ℝ p₁ p₂ p₃\nhp₂p₁ : ¬p₂ = p₁\nhp₃p₁ : p₃ = p₁\n⊢ ∡ p₂ p₁ p₃ = 0",
"case neg... | by_cases hp₃p₁ : p₃ = p₁ | «_aux_Init_ByCases___macroRules_tacticBy_cases_:__2» | «tacticBy_cases_:_» |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 401,
"column": 67
} | {
"line": 401,
"column": 99
} | {
"line": 402,
"column": 4
} | [
{
"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 (InnerProductGeometry.angle (p₂ -ᵥ p₃) (p₁ -ᵥ p₃)) = ‖p₁ -ᵥ p₂‖ / ‖p₁ ... | [
"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 p₂ + (p₂ -ᵥ p₃))) = ‖p₁ -ᵥ p₂‖ / ‖p₁... | ← vsub_add_vsub_cancel p₁ p₂ p₃, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 409,
"column": 68
} | {
"line": 409,
"column": 100
} | {
"line": 410,
"column": 4
} | [
{
"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 (InnerProductGeometry.angle (p₂ -ᵥ p₃) (p₁ -ᵥ p₃)) = ‖p₁ -ᵥ p₂‖ / ‖p₂ -ᵥ p₃‖",
"ppTerm": "?m.112",
... | [
"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 p₂ + (p₂ -ᵥ p₃))) = ‖p₁ -ᵥ p₂‖ / ‖p₂ -ᵥ p₃‖"
] | ← vsub_add_vsub_cancel p₁ p₂ p₃, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 418,
"column": 68
} | {
"line": 418,
"column": 100
} | {
"line": 419,
"column": 4
} | [
{
"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 (InnerProductGeometry.angle (p₂ -ᵥ p₃) (p₁ -ᵥ p₃)) * ‖p₁ -ᵥ p₃‖ = ‖p₂ -ᵥ p₃‖",
"ppTerm": "?m.112",
... | [
"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 p₂ + (p₂ -ᵥ p₃))) * ‖p₁ -ᵥ p₂ + (p₂ -ᵥ p₃)‖ = ‖p₂ -ᵥ p₃‖"
] | ← vsub_add_vsub_cancel p₁ p₂ p₃, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 427,
"column": 67
} | {
"line": 427,
"column": 99
} | {
"line": 428,
"column": 4
} | [
{
"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 (InnerProductGeometry.angle (p₂ -ᵥ p₃) (p₁ -ᵥ p₃)) * ‖p₁ -ᵥ p₃‖ = ‖p₁ -ᵥ p₂‖",
"ppTerm": "?m.112",
... | [
"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 p₂ + (p₂ -ᵥ p₃))) * ‖p₁ -ᵥ p₂ + (p₂ -ᵥ p₃)‖ = ‖p₁ -ᵥ p₂‖"
] | ← vsub_add_vsub_cancel p₁ p₂ p₃, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 755,
"column": 2
} | {
"line": 755,
"column": 55
} | {
"line": 757,
"column": 0
} | [
{
"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\nhx : ¬x = 0\nhy : ¬y = 0\n⊢ (o.oangle x (-y)).sign = -(o.oangle x y).sign",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
... | [] | rw [o.oangle_neg_right hx hy, Real.Angle.sign_add_pi] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 437,
"column": 68
} | {
"line": 437,
"column": 100
} | {
"line": 438,
"column": 4
} | [
{
"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 (InnerProductGeometry.angle (p₂ -ᵥ p₃) (p₁ -ᵥ p₃)) * ‖p₂ -ᵥ p₃‖ = ‖p₁ ... | [
"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 p₂ + (p₂ -ᵥ p₃))) * ‖p₂ -ᵥ p₃‖ = ‖p₁... | ← vsub_add_vsub_cancel p₁ p₂ p₃, | Lean.Elab.Tactic.evalRewriteSeq | null |
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