module stringlengths 16 90 | startPos dict | endPos dict | goals listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 366
values | kind stringclasses 370
values |
|---|---|---|---|---|---|---|
Mathlib.FieldTheory.PurelyInseparable.PerfectClosure | {
"line": 406,
"column": 2
} | {
"line": 406,
"column": 13
} | [
{
"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\na : E\nhsep : IsSeparable F a\n⊢ minpoly F ((frobenius E q) a) = Polynomial.map (frobenius F q) (minpoly F a)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 143,
"column": 2
} | {
"line": 143,
"column": 28
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 152,
"column": 2
} | {
"line": 152,
"column": 28
} | [
{
"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)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 156,
"column": 2
} | {
"line": 156,
"column": 13
} | [
{
"pp": "E : Type v\ninst✝¹ : Field E\nL : Type w\ninst✝ : Field L\nA : Subfield E\nf : L →+* E\nB : Subfield L\n⊢ (comap f A).relfinrank B = A.relfinrank (map f B)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 160,
"column": 2
} | {
"line": 160,
"column": 67
} | [
{
"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)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 164,
"column": 2
} | {
"line": 164,
"column": 28
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 167,
"column": 2
} | {
"line": 167,
"column": 13
} | [
{
"pp": "E : Type v\ninst✝¹ : Field E\nL : Type w\ninst✝ : Field L\nA : Subfield E\nf : L →+* E\n⊢ finrank (↥(comap f A)) L = A.relfinrank f.fieldRange",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 171,
"column": 2
} | {
"line": 171,
"column": 13
} | [
{
"pp": "E : Type v\ninst✝¹ : Field E\nL : Type w\ninst✝ : Field L\nA B : Subfield E\nf : E →+* L\n⊢ (map f A).relfinrank (map f B) = A.relfinrank B",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 184,
"column": 2
} | {
"line": 184,
"column": 28
} | [
{
"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)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 188,
"column": 2
} | {
"line": 188,
"column": 13
} | [
{
"pp": "E : Type v\ninst✝¹ : Field E\nL : Type w\ninst✝ : Field L\nA B : Subfield E\nf : L →+* E\n⊢ (comap f A).relfinrank (comap f B) = A.relfinrank (B ⊓ f.fieldRange)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 193,
"column": 2
} | {
"line": 193,
"column": 37
} | [
{
"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)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 198,
"column": 2
} | {
"line": 198,
"column": 28
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 202,
"column": 2
} | {
"line": 202,
"column": 13
} | [
{
"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⊢ (comap f A).relfinrank (comap f B) = A.relfinrank B",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 213,
"column": 2
} | {
"line": 213,
"column": 13
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 218,
"column": 2
} | {
"line": 218,
"column": 13
} | [
{
"pp": "E : Type v\ninst✝¹ : Field E\nL : Type w\ninst✝ : Field L\nA B : Subfield E\nf : L →+* E\nh : Function.Surjective ⇑f\n⊢ (comap f A).relfinrank (comap f B) = A.relfinrank B",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 242,
"column": 2
} | {
"line": 242,
"column": 13
} | [
{
"pp": "E : Type v\ninst✝ : Field E\nA B C : Subfield E\nh1 : A ≤ B\nh2 : B ≤ C\n⊢ A.relfinrank B * B.relfinrank C = A.relfinrank C",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 250,
"column": 2
} | {
"line": 250,
"column": 13
} | [
{
"pp": "E : Type v\ninst✝ : Field E\nA B C : Subfield E\n⊢ A.relfinrank (B ⊓ C) * B.relfinrank C = (A ⊓ B).relfinrank C",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 255,
"column": 2
} | {
"line": 255,
"column": 37
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 260,
"column": 2
} | {
"line": 260,
"column": 13
} | [
{
"pp": "E : Type v\ninst✝ : Field E\nA B C : Subfield E\nh : B ≤ C\n⊢ A.relfinrank B * B.relfinrank C = (A ⊓ B).relfinrank C",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 265,
"column": 2
} | {
"line": 265,
"column": 37
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 270,
"column": 2
} | {
"line": 270,
"column": 13
} | [
{
"pp": "E : Type v\ninst✝ : Field E\nA B C : Subfield E\nh : A ≤ B\n⊢ A.relfinrank (B ⊓ C) * B.relfinrank C = A.relfinrank C",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 357,
"column": 2
} | {
"line": 357,
"column": 28
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 360,
"column": 2
} | {
"line": 360,
"column": 13
} | [
{
"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 : IntermediateField F E\nf : L →ₐ[F] E\n⊢ finrank (↥(comap f A)) L = A.relfinrank f.fieldRange",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 368,
"column": 2
} | {
"line": 368,
"column": 28
} | [
{
"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)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 372,
"column": 2
} | {
"line": 372,
"column": 13
} | [
{
"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 : IntermediateField F E\nf : L →ₐ[F] E\nB : IntermediateField F L\n⊢ (comap f A).relfinrank B = A.relfinrank (map f B)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 380,
"column": 2
} | {
"line": 380,
"column": 28
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 384,
"column": 2
} | {
"line": 384,
"column": 13
} | [
{
"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 : E →ₐ[F] L\n⊢ (map f A).relfinrank (map f B) = A.relfinrank B",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 394,
"column": 2
} | {
"line": 394,
"column": 28
} | [
{
"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)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 398,
"column": 2
} | {
"line": 398,
"column": 13
} | [
{
"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\n⊢ (comap f A).relfinrank (comap f B) = A.relfinrank (B ⊓ f.fieldRange)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 402,
"column": 2
} | {
"line": 402,
"column": 37
} | [
{
"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)",
"use... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 407,
"column": 2
} | {
"line": 407,
"column": 28
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 411,
"column": 2
} | {
"line": 411,
"column": 13
} | [
{
"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⊢ (comap f A).relfinrank (comap f B) = A.relfinrank B",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 421,
"column": 2
} | {
"line": 421,
"column": 13
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 426,
"column": 2
} | {
"line": 426,
"column": 13
} | [
{
"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 : Function.Surjective ⇑f\n⊢ (comap f A).relfinrank (comap f B) = A.relfinrank B",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 434,
"column": 2
} | {
"line": 434,
"column": 13
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝² : Field F\ninst✝¹ : Field E\ninst✝ : Algebra F E\nA B : IntermediateField F E\nh : A ≤ B\n⊢ A.relfinrank B * finrank (↥B) E = finrank (↥A) E",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 444,
"column": 2
} | {
"line": 444,
"column": 13
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝² : Field F\ninst✝¹ : Field E\ninst✝ : Algebra F E\nA B : IntermediateField F E\nh : A ≤ B\n⊢ finrank F ↥A * A.relfinrank B = finrank F ↥B",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 468,
"column": 2
} | {
"line": 468,
"column": 13
} | [
{
"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\nh1 : A ≤ B\nh2 : B ≤ C\n⊢ A.relfinrank B * B.relfinrank C = A.relfinrank C",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 475,
"column": 2
} | {
"line": 475,
"column": 13
} | [
{
"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\n⊢ A.relfinrank (B ⊓ C) * B.relfinrank C = (A ⊓ B).relfinrank C",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 480,
"column": 2
} | {
"line": 480,
"column": 37
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 485,
"column": 2
} | {
"line": 485,
"column": 13
} | [
{
"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.relfinrank B * B.relfinrank C = (A ⊓ B).relfinrank C",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 490,
"column": 2
} | {
"line": 490,
"column": 37
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Relrank | {
"line": 495,
"column": 2
} | {
"line": 495,
"column": 13
} | [
{
"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.relfinrank (B ⊓ C) * B.relfinrank C = A.relfinrank C",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.RatFunc.Luroth | {
"line": 74,
"column": 4
} | {
"line": 74,
"column": 15
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"Algebra.algebraMap",
"AddGroupWithOne.toAddGroup",
"congrArg",
"CommSemirin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.RatFunc.Luroth | {
"line": 105,
"column": 41
} | {
"line": 105,
"column": 52
} | [
{
"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",
"usedConstants": [
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Polynomial.algebraOfAlgebra",
"Rin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.RatFunc.Luroth | {
"line": 348,
"column": 4
} | {
"line": 348,
"column": 76
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.RatFunc.Luroth | {
"line": 452,
"column": 12
} | {
"line": 452,
"column": 23
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.RatFunc.Luroth | {
"line": 453,
"column": 7
} | {
"line": 453,
"column": 18
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Diffeology.Basic | {
"line": 326,
"column": 4
} | {
"line": 326,
"column": 53
} | [
{
"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... | 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.Geometry.Euclidean.Altitude | {
"line": 167,
"column": 6
} | {
"line": 167,
"column": 17
} | [
{
"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⊢... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Altitude | {
"line": 170,
"column": 31
} | {
"line": 170,
"column": 42
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Altitude | {
"line": 205,
"column": 2
} | {
"line": 205,
"column": 34
} | [
{
"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)",
"usedConstants": [
... | exact orthogonalProjection_mem _ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Geometry.Euclidean.Altitude | {
"line": 350,
"column": 10
} | {
"line": 350,
"column": 21
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine | {
"line": 108,
"column": 2
} | {
"line": 108,
"column": 32
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine | {
"line": 113,
"column": 2
} | {
"line": 113,
"column": 32
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine | {
"line": 118,
"column": 2
} | {
"line": 118,
"column": 29
} | [
{
"pp": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nv₁ v₂ v₃ : V\n⊢ ∠ (-v₁) (-v₂) (-v₃) = ∠ v₁ v₂ v₃",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation | {
"line": 49,
"column": 6
} | {
"line": 53,
"column": 42
} | [
{
"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 +... | 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
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation | {
"line": 118,
"column": 4
} | {
"line": 118,
"column": 57
} | [
{
"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",
"usedConstants": [
"LinearEquiv.det",
"Units.val",
"InnerProductSpace.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Projection | {
"line": 211,
"column": 2
} | {
"line": 211,
"column": 13
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Projection | {
"line": 210,
"column": 76
} | {
"line": 211,
"column": 68
} | [
{
"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.Angle.Unoriented.Affine | {
"line": 386,
"column": 2
} | {
"line": 386,
"column": 31
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Projection | {
"line": 226,
"column": 6
} | {
"line": 226,
"column": 27
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine | {
"line": 399,
"column": 2
} | {
"line": 399,
"column": 31
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Projection | {
"line": 237,
"column": 2
} | {
"line": 237,
"column": 13
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine | {
"line": 426,
"column": 6
} | {
"line": 426,
"column": 17
} | [
{
"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}",
"usedConstants": [
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Real",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine | {
"line": 427,
"column": 6
} | {
"line": 427,
"column": 17
} | [
{
"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}",
"usedConstants": [
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Real",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation | {
"line": 251,
"column": 4
} | {
"line": 251,
"column": 23
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation | {
"line": 249,
"column": 2
} | {
"line": 251,
"column": 55
} | [
{
"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",
"usedConstants": [
"LinearIsometryEquiv.instEquivLike",
"Eq.mpr",
... | · 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.Projection | {
"line": 362,
"column": 6
} | {
"line": 362,
"column": 44
} | [
{
"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... | 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
} | [
{
"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... | s.direction.reflection_eq_self_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Projection | {
"line": 481,
"column": 4
} | {
"line": 481,
"column": 15
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation | {
"line": 361,
"column": 45
} | {
"line": 362,
"column": 85
} | [
{
"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",
"usedConstants": ... | by
rw [← Complex.rotation, ← hf, o.rotation_map, LinearIsometryEquiv.symm_apply_apply] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 107,
"column": 2
} | {
"line": 107,
"column": 18
} | [
{
"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‖",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Norm.norm",
"SeminormedAddGroup.toNorm",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 243,
"column": 2
} | {
"line": 243,
"column": 63
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"Orientation.oangle",
"Real.Angle",... | 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
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"Orientation.oangle",
"Real.Angle",... | 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
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"Orientation.oangle",
"Real.Angle",... | 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.Basic | {
"line": 359,
"column": 2
} | {
"line": 359,
"column": 13
} | [
{
"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",
"usedConstants": [
"Complex.mul_im",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 333,
"column": 4
} | {
"line": 333,
"column": 34
} | [
{
"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... | 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
} | [
{
"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‖)",
"usedConstants": [... | ← vsub_add_vsub_cancel p₁ p₂ p₃, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 349,
"column": 67
} | {
"line": 349,
"column": 99
} | [
{
"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... | ← 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
} | [
{
"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‖)",
... | ← 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
} | [
{
"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)",
"usedConstants": [
... | ← vsub_add_vsub_cancel p₁ p₂ p₃, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 375,
"column": 13
} | {
"line": 375,
"column": 45
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"Real.ins... | ← vsub_add_vsub_cancel p₁ p₂ p₃, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 384,
"column": 13
} | {
"line": 384,
"column": 45
} | [
{
"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",
"usedConstants": [
"Eq.mp... | ← 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
} | [
{
"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‖",
"usedConstants": [
... | ← vsub_add_vsub_cancel p₁ p₂ p₃, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 401,
"column": 67
} | {
"line": 401,
"column": 99
} | [
{
"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 ... | ← 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
} | [
{
"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‖",
"usedConstants": [
... | ← 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
} | [
{
"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‖",
"usedConstants": [
... | ← 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
} | [
{
"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‖",
"usedConstants": [
... | ← vsub_add_vsub_cancel p₁ p₂ p₃, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 437,
"column": 68
} | {
"line": 437,
"column": 100
} | [
{
"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 ... | ← vsub_add_vsub_cancel p₁ p₂ p₃, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 426,
"column": 25
} | {
"line": 426,
"column": 36
} | [
{
"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",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"N... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 447,
"column": 68
} | {
"line": 447,
"column": 100
} | [
{
"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 -ᵥ p₃‖ / Real.cos (InnerProductGeometry.angle (p₂ -ᵥ p₃) (p₁ -ᵥ p₃)) = ‖p₁ ... | ← vsub_add_vsub_cancel p₁ p₂ p₃, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 429,
"column": 6
} | {
"line": 429,
"column": 47
} | [
{
"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‖",
"usedConstants": [
"Norm.norm",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 457,
"column": 67
} | {
"line": 457,
"column": 99
} | [
{
"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⊢ ‖p₁ -ᵥ p₂‖ / Real.sin (InnerProductGeometry.angle (p₂ -ᵥ p₃) (p₁ -ᵥ p₃)) = ‖p₁ ... | ← vsub_add_vsub_cancel p₁ p₂ p₃, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle | {
"line": 467,
"column": 68
} | {
"line": 467,
"column": 100
} | [
{
"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⊢ ‖p₁ -ᵥ p₂‖ / Real.tan (InnerProductGeometry.angle (p₂ -ᵥ p₃) (p₁ -ᵥ p₃)) = ‖p₂ ... | ← 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
} | [
{
"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",
"usedConstant... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | {
"line": 495,
"column": 2
} | {
"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",
"usedConstan... | by_cases hp₃p₁ : p₃ = p₁ | «_aux_Init_ByCases___macroRules_tacticBy_cases_:__2» | «tacticBy_cases_:_» |
Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle | {
"line": 436,
"column": 2
} | {
"line": 439,
"column": 58
} | [
{
"pp": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nhd2 : Fact (finrank ℝ V = 2)\no : Orientation ℝ V (Fin 2)\nx y : V\nh : o.oangle x y = ↑(π / 2)\nhs : (o.oangle y (y - x)).sign = 1\n⊢ ‖x‖ / (o.oangle y (y - x)).tan = ‖y‖",
"usedConstants": [
"Norm.norm",
"Eq.m... | rw [o.oangle_eq_angle_of_sign_eq_one hs, Real.Angle.tan_coe,
InnerProductGeometry.norm_div_tan_angle_sub_of_inner_eq_zero
(o.inner_rev_eq_zero_of_oangle_eq_pi_div_two h)
(Or.inr (o.left_ne_zero_of_oangle_eq_pi_div_two h))] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle | {
"line": 457,
"column": 6
} | {
"line": 457,
"column": 17
} | [
{
"pp": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nhd2 : Fact (finrank ℝ V = 2)\no : Orientation ℝ V (Fin 2)\nx : V\nh : x ≠ 0\nr : ℝ\nhr : r < 0\n⊢ (o.rotation ↑(π / 2)) x ≠ 0",
"usedConstants": [
"LinearIsometryEquiv.instEquivLike",
"Eq.mpr",
"InnerProdu... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | {
"line": 601,
"column": 8
} | {
"line": 601,
"column": 19
} | [
{
"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 =... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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