module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.LinearAlgebra.Matrix.Rank | {
"line": 451,
"column": 2
} | {
"line": 451,
"column": 68
} | {
"line": 452,
"column": 4
} | [
{
"pp": "m : Type um\nn : Type un\nR : Type uR\ninst✝⁵ : Fintype n\ninst✝⁴ : Fintype m\ninst✝³ : Field R\ninst✝² : PartialOrder R\ninst✝¹ : StarRing R\ninst✝ : StarOrderedRing R\nA : Matrix m n R\n⊢ (A * Aᴴ).rank = A.rank",
"ppTerm": "?m.24",
"assigned": false,
"usedConstants": [],
"usedFVars": ... | [
"m : Type um\nn : Type un\nR : Type uR\ninst✝⁵ : Fintype n\ninst✝⁴ : Fintype m\ninst✝³ : Field R\ninst✝² : PartialOrder R\ninst✝¹ : StarRing R\ninst✝ : StarOrderedRing R\nA : Matrix m n R\n⊢ (A * Aᴴ).rank = A.rank"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.SymplecticGroup | {
"line": 373,
"column": 8
} | {
"line": 373,
"column": 15
} | {
"line": 373,
"column": 16
} | [
{
"pp": "l : Type u_1\nR : Type u_2\ninst✝³ : DecidableEq l\ninst✝² : Fintype l\ninst✝¹ : CommRing R\ninst✝ : IsLocalRing R\nM : Matrix (l ⊕ l) (l ⊕ l) R\nhM : M ∈ symplecticGroup l R\nA : Matrix l l R := M.toBlocks₁₁\nB : Matrix l l R := M.toBlocks₁₂\nC : Matrix l l R := M.toBlocks₂₁\nD : Matrix l l R := M.toB... | [
"l : Type u_1\nR : Type u_2\ninst✝³ : DecidableEq l\ninst✝² : Fintype l\ninst✝¹ : CommRing R\ninst✝ : IsLocalRing R\nM : Matrix (l ⊕ l) (l ⊕ l) R\nhM : M ∈ symplecticGroup l R\nA : Matrix l l R := M.toBlocks₁₁\nB : Matrix l l R := M.toBlocks₁₂\nC : Matrix l l R := M.toBlocks₂₁\nD : Matrix l l R := M.toBlocks₂₂\nX :... | Lx_mul, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Lie.Classical | {
"line": 151,
"column": 2
} | {
"line": 151,
"column": 63
} | {
"line": 151,
"column": 64
} | [
{
"pp": "n : Type u_1\nR : Type u₂\ninst✝³ : CommRing R\ninst✝² : DecidableEq n\ninst✝¹ : Fintype n\ninst✝ : Nontrivial R\nh : 1 < Fintype.card n\ni j : n\nhij : i ≠ j\nA : ↥(sl n R) := (single i j hij) 1\nB : ↥(sl n R) := (single j i ⋯) 1\nc : IsLieAbelian ↥(sl n R)\nc' : ↑A * ↑B = ↑B * ↑A\n⊢ False",
"ppTe... | [
"n : Type u_1\nR : Type u₂\ninst✝³ : CommRing R\ninst✝² : DecidableEq n\ninst✝¹ : Fintype n\ninst✝ : Nontrivial R\nh : 1 < Fintype.card n\ni j : n\nhij : i ≠ j\nA : ↥(sl n R) := (single i j hij) 1\nB : ↥(sl n R) := (single j i ⋯) 1\nc : IsLieAbelian ↥(sl n R)\nc' : ↑A * ↑B = ↑B * ↑A\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Classical | {
"line": 193,
"column": 13
} | {
"line": 193,
"column": 36
} | {
"line": 193,
"column": 37
} | [
{
"pp": "p : Type u_2\nq : Type u_3\nR : Type u₂\ninst✝⁴ : DecidableEq p\ninst✝³ : DecidableEq q\ninst✝² : CommRing R\ninst✝¹ : Fintype p\ninst✝ : Fintype q\ni : R\nhi : i * i = -1\nx y : p ⊕ q\n⊢ (Pso p q R i * Pso p q R (-i)) x y = 1 x y",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
... | [
"case inl\np : Type u_2\nq : Type u_3\nR : Type u₂\ninst✝⁴ : DecidableEq p\ninst✝³ : DecidableEq q\ninst✝² : CommRing R\ninst✝¹ : Fintype p\ninst✝ : Fintype q\ni : R\nhi : i * i = -1\ny : p ⊕ q\nx : p\n⊢ (Pso p q R i * Pso p q R (-i)) (Sum.inl x) y = 1 (Sum.inl x) y",
"case inr\np : Type u_2\nq : Type u_3\nR : Ty... | rcases x with ⟨x⟩ | ⟨x⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.LinearAlgebra.Matrix.Rank | {
"line": 493,
"column": 2
} | {
"line": 493,
"column": 56
} | {
"line": 493,
"column": 57
} | [
{
"pp": "m : Type um\nn : Type un\nR : Type uR\ninst✝⁴ : Fintype n\ninst✝³ : Field R\ninst✝² : LinearOrder R\ninst✝¹ : IsStrictOrderedRing R\ninst✝ : Fintype m\nA : Matrix m n R\n⊢ (A * Aᵀ).rank = A.rank",
"ppTerm": "?m.21",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals... | [
"m : Type um\nn : Type un\nR : Type uR\ninst✝⁴ : Fintype n\ninst✝³ : Field R\ninst✝² : LinearOrder R\ninst✝¹ : IsStrictOrderedRing R\ninst✝ : Fintype m\nA : Matrix m n R\n⊢ (A * Aᵀ).rank = A.rank"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Cochain | {
"line": 76,
"column": 2
} | {
"line": 76,
"column": 63
} | {
"line": 76,
"column": 64
} | [
{
"pp": "R : Type u_1\ninst✝⁴ : CommRing R\nL : Type u_2\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\nM : Type u_3\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\na : ↥(twoCochain R L M)\nx y : L\n⊢ (a y) x + (a x) y = 0",
"ppTerm": "?m.28",
"assigned": false,
"usedConstants": [],
"usedFVars": []... | [
"R : Type u_1\ninst✝⁴ : CommRing R\nL : Type u_2\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\nM : Type u_3\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\na : ↥(twoCochain R L M)\nx y : L\n⊢ (a y) x + (a x) y = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Classical | {
"line": 212,
"column": 13
} | {
"line": 212,
"column": 36
} | {
"line": 212,
"column": 37
} | [
{
"pp": "p : Type u_2\nq : Type u_3\nR : Type u₂\ninst✝⁴ : DecidableEq p\ninst✝³ : DecidableEq q\ninst✝² : CommRing R\ninst✝¹ : Fintype p\ninst✝ : Fintype q\ni : R\nhi : i * i = -1\nx y : p ⊕ q\n⊢ ((Pso p q R i)ᵀ * indefiniteDiagonal p q R * Pso p q R i) x y = 1 x y",
"ppTerm": "?m.42",
"assigned": true... | [
"case inl\np : Type u_2\nq : Type u_3\nR : Type u₂\ninst✝⁴ : DecidableEq p\ninst✝³ : DecidableEq q\ninst✝² : CommRing R\ninst✝¹ : Fintype p\ninst✝ : Fintype q\ni : R\nhi : i * i = -1\ny : p ⊕ q\nx : p\n⊢ ((Pso p q R i)ᵀ * indefiniteDiagonal p q R * Pso p q R i) (Sum.inl x) y = 1 (Sum.inl x) y",
"case inr\np : Typ... | rcases x with ⟨x⟩ | ⟨x⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.Algebra.Lie.Basis | {
"line": 339,
"column": 49
} | {
"line": 339,
"column": 73
} | {
"line": 339,
"column": 74
} | [
{
"pp": "ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁶ : Finite ι\ninst✝⁵ : CommRing R\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra R L\nb : Basis ι R L\ninst✝² : Fintype ι\ninst✝¹ : IsDomain R\ninst✝ : CharZero R\nx : L\nhx : x ∈ b.borelUpper\n⊢ x ∈ lieSpan R L (range b.e)",
"ppTerm": "?m.81",
"assigned... | [
"ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁶ : Finite ι\ninst✝⁵ : CommRing R\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra R L\nb : Basis ι R L\ninst✝² : Fintype ι\ninst✝¹ : IsDomain R\ninst✝ : CharZero R\nx : L\nhx : x ∈ b.borelUpper\n⊢ x ∈ lieSpan R L (range b.e)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 365,
"column": 8
} | {
"line": 365,
"column": 19
} | {
"line": 365,
"column": 20
} | [
{
"pp": "case refine_1\nι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁶ : Finite ι\ninst✝⁵ : CommRing R\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra R L\nb : Basis ι R L\ninst✝² : Fintype ι\ninst✝¹ : IsDomain R\ninst✝ : CharZero R\nx u v✝ : L\nhx✝ : u ∈ lieSpan R L (range b.e)\nhy✝ : v✝ ∈ lieSpan R L (range b.e)\n... | [
"case refine_1\nι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁶ : Finite ι\ninst✝⁵ : CommRing R\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra R L\nb : Basis ι R L\ninst✝² : Fintype ι\ninst✝¹ : IsDomain R\ninst✝ : CharZero R\nx u v✝ : L\nhx✝ : u ∈ lieSpan R L (range b.e)\nhy✝ : v✝ ∈ lieSpan R L (range b.e)\nhu : u ∈ ⨆ n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 368,
"column": 8
} | {
"line": 368,
"column": 19
} | {
"line": 368,
"column": 20
} | [
{
"pp": "case h\nι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁶ : Finite ι\ninst✝⁵ : CommRing R\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra R L\nb : Basis ι R L\ninst✝² : Fintype ι\ninst✝¹ : IsDomain R\ninst✝ : CharZero R\nx u v : L\nhx✝ : u ∈ lieSpan R L (range b.e)\nhy✝ : v ∈ lieSpan R L (range b.e)\nhu : u ∈ ... | [
"case h\nι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁶ : Finite ι\ninst✝⁵ : CommRing R\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra R L\nb : Basis ι R L\ninst✝² : Fintype ι\ninst✝¹ : IsDomain R\ninst✝ : CharZero R\nx u v : L\nhx✝ : u ∈ lieSpan R L (range b.e)\nhy✝ : v ∈ lieSpan R L (range b.e)\nhu : u ∈ ⨆ n, ⨆ (_ : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.DirectSum | {
"line": 112,
"column": 6
} | {
"line": 112,
"column": 51
} | {
"line": 113,
"column": 4
} | [
{
"pp": "R : Type u\nι : Type v\ninst✝² : CommRing R\nL : ι → Type w\ninst✝¹ : (i : ι) → LieRing (L i)\ninst✝ : (i : ι) → LieAlgebra R (L i)\nx y z : ⨁ (i : ι), L i\ni✝ : ι\n⊢ (zipWith (fun x x_1 y ↦ ⁅x_1, y⁆) ⋯ x (y + z)) i✝ =\n (zipWith (fun x x_1 y ↦ ⁅x_1, y⁆) ⋯ x y + zipWith (fun x x_1 y ↦ ⁅x_1, y⁆) ⋯ x ... | [] | simp only [zipWith_apply, add_apply, lie_add] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Lie.Basis | {
"line": 412,
"column": 33
} | {
"line": 412,
"column": 50
} | {
"line": 412,
"column": 51
} | [
{
"pp": "ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁷ : Finite ι\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\nb : Basis ι R L\ninst✝³ : Fintype ι\ninst✝² : IsDomain R\ninst✝¹ : CharZero R\ninst✝ : IsTorsionFree R L\nU : LieSubmodule R (↥b.cartan) L := ⨆ n, ⨆ (_ : n ≠ 0), rootSpace b.ca... | [
"ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁷ : Finite ι\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\nb : Basis ι R L\ninst✝³ : Fintype ι\ninst✝² : IsDomain R\ninst✝¹ : CharZero R\ninst✝ : IsTorsionFree R L\nU : LieSubmodule R (↥b.cartan) L := ⨆ n, ⨆ (_ : n ≠ 0), rootSpace b.cartan (∑ i, n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 416,
"column": 6
} | {
"line": 416,
"column": 23
} | {
"line": 416,
"column": 24
} | [
{
"pp": "ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁷ : Finite ι\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\nb : Basis ι R L\ninst✝³ : Fintype ι\ninst✝² : IsDomain R\ninst✝¹ : CharZero R\ninst✝ : IsTorsionFree R L\nU : LieSubmodule R (↥b.cartan) L := ⨆ n, ⨆ (_ : n ≠ 0), rootSpace b.ca... | [
"ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁷ : Finite ι\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\nb : Basis ι R L\ninst✝³ : Fintype ι\ninst✝² : IsDomain R\ninst✝¹ : CharZero R\ninst✝ : IsTorsionFree R L\nU : LieSubmodule R (↥b.cartan) L := ⨆ n, ⨆ (_ : n ≠ 0), rootSpace b.cartan (∑ i, n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 420,
"column": 34
} | {
"line": 420,
"column": 45
} | {
"line": 420,
"column": 46
} | [
{
"pp": "ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁷ : Finite ι\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\nb : Basis ι R L\ninst✝³ : Fintype ι\ninst✝² : IsDomain R\ninst✝¹ : CharZero R\ninst✝ : IsTorsionFree R L\nU : LieSubmodule R (↥b.cartan) L := ⨆ n, ⨆ (_ : n ≠ 0), rootSpace b.ca... | [
"ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁷ : Finite ι\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\nb : Basis ι R L\ninst✝³ : Fintype ι\ninst✝² : IsDomain R\ninst✝¹ : CharZero R\ninst✝ : IsTorsionFree R L\nU : LieSubmodule R (↥b.cartan) L := ⨆ n, ⨆ (_ : n ≠ 0), rootSpace b.cartan (∑ i, n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 424,
"column": 33
} | {
"line": 424,
"column": 50
} | {
"line": 424,
"column": 51
} | [
{
"pp": "ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁷ : Finite ι\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\nb : Basis ι R L\ninst✝³ : Fintype ι\ninst✝² : IsDomain R\ninst✝¹ : CharZero R\ninst✝ : IsTorsionFree R L\nU : LieSubmodule R (↥b.cartan) L := ⨆ n, ⨆ (_ : n ≠ 0), rootSpace b.ca... | [
"ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁷ : Finite ι\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\nb : Basis ι R L\ninst✝³ : Fintype ι\ninst✝² : IsDomain R\ninst✝¹ : CharZero R\ninst✝ : IsTorsionFree R L\nU : LieSubmodule R (↥b.cartan) L := ⨆ n, ⨆ (_ : n ≠ 0), rootSpace b.cartan (∑ i, n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.UniversalEnveloping | {
"line": 137,
"column": 2
} | {
"line": 137,
"column": 13
} | {
"line": 137,
"column": 14
} | [
{
"pp": "R : Type u₁\nL : Type u₂\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\nA : Type u₃\ninst✝¹ : Ring A\ninst✝ : Algebra R A\nf : L →ₗ⁅R⁆ A\nx : L\n⊢ ((lift R) f) ((mkAlgHom R L) (ιₜ x)) = f x",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants": [],
"usedFVars": [],... | [
"R : Type u₁\nL : Type u₂\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\nA : Type u₃\ninst✝¹ : Ring A\ninst✝ : Algebra R A\nf : L →ₗ⁅R⁆ A\nx : L\n⊢ ((lift R) f) ((mkAlgHom R L) (ιₜ x)) = f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Free | {
"line": 92,
"column": 2
} | {
"line": 92,
"column": 33
} | {
"line": 92,
"column": 34
} | [
{
"pp": "R : Type u\nX : Type v\ninst✝ : CommRing R\na b : lib R X\nh : Rel R X a b\n⊢ Rel R X (-a) (-b)",
"ppTerm": "?m.9",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u\nX : Type v\ninst✝ : CommRing R\na b : lib R X\nh : Rel R X a b\n⊢ Rel R X (-a) (-b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Free | {
"line": 95,
"column": 2
} | {
"line": 95,
"column": 35
} | {
"line": 95,
"column": 36
} | [
{
"pp": "R : Type u\nX : Type v\ninst✝ : CommRing R\na b c : lib R X\nh : Rel R X b c\n⊢ Rel R X (a - b) (a - c)",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"FreeNonUnitalNonAssocAlgebra",
"congrArg",
"CommSemiring.toSemiring",
"AddMonoid.toAddZe... | [
"R : Type u\nX : Type v\ninst✝ : CommRing R\na b c : lib R X\nh : Rel R X b c\n⊢ Rel R X (a + -b) (a + -c)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Free | {
"line": 98,
"column": 2
} | {
"line": 98,
"column": 35
} | {
"line": 98,
"column": 36
} | [
{
"pp": "R : Type u\nX : Type v\ninst✝ : CommRing R\na b c : lib R X\nh : Rel R X a b\n⊢ Rel R X (a - c) (b - c)",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"FreeNonUnitalNonAssocAlgebra",
"congrArg",
"CommSemiring.toSemiring",
"AddMonoid.toAddZe... | [
"R : Type u\nX : Type v\ninst✝ : CommRing R\na b c : lib R X\nh : Rel R X a b\n⊢ Rel R X (a + -c) (b + -c)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Free | {
"line": 165,
"column": 13
} | {
"line": 165,
"column": 87
} | {
"line": 166,
"column": 2
} | [
{
"pp": "R : Type u\nX : Type v\ninst✝ : CommRing R\n⊢ ∀ (x y z : FreeLieAlgebra R X),\n Quot.map₂ (fun x1 x2 ↦ x1 * x2) ⋯ ⋯ (x + y) z =\n Quot.map₂ (fun x1 x2 ↦ x1 * x2) ⋯ ⋯ x z + Quot.map₂ (fun x1 x2 ↦ x1 * x2) ⋯ ⋯ y z",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"add_mu... | [] | by rintro ⟨a⟩ ⟨b⟩ ⟨c⟩; change Quot.mk _ _ = Quot.mk _ _; simp_rw [add_mul] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Lie.Basis | {
"line": 428,
"column": 6
} | {
"line": 428,
"column": 23
} | {
"line": 428,
"column": 24
} | [
{
"pp": "ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁷ : Finite ι\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\nb : Basis ι R L\ninst✝³ : Fintype ι\ninst✝² : IsDomain R\ninst✝¹ : CharZero R\ninst✝ : IsTorsionFree R L\nU : LieSubmodule R (↥b.cartan) L := ⨆ n, ⨆ (_ : n ≠ 0), rootSpace b.ca... | [
"ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁷ : Finite ι\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\nb : Basis ι R L\ninst✝³ : Fintype ι\ninst✝² : IsDomain R\ninst✝¹ : CharZero R\ninst✝ : IsTorsionFree R L\nU : LieSubmodule R (↥b.cartan) L := ⨆ n, ⨆ (_ : n ≠ 0), rootSpace b.cartan (∑ i, n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 432,
"column": 34
} | {
"line": 432,
"column": 45
} | {
"line": 432,
"column": 46
} | [
{
"pp": "ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁷ : Finite ι\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\nb : Basis ι R L\ninst✝³ : Fintype ι\ninst✝² : IsDomain R\ninst✝¹ : CharZero R\ninst✝ : IsTorsionFree R L\nU : LieSubmodule R (↥b.cartan) L := ⨆ n, ⨆ (_ : n ≠ 0), rootSpace b.ca... | [
"ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁷ : Finite ι\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\nb : Basis ι R L\ninst✝³ : Fintype ι\ninst✝² : IsDomain R\ninst✝¹ : CharZero R\ninst✝ : IsTorsionFree R L\nU : LieSubmodule R (↥b.cartan) L := ⨆ n, ⨆ (_ : n ≠ 0), rootSpace b.cartan (∑ i, n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 437,
"column": 6
} | {
"line": 437,
"column": 23
} | {
"line": 437,
"column": 24
} | [
{
"pp": "ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁷ : Finite ι\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\nb : Basis ι R L\ninst✝³ : Fintype ι\ninst✝² : IsDomain R\ninst✝¹ : CharZero R\ninst✝ : IsTorsionFree R L\nU : LieSubmodule R (↥b.cartan) L := ⨆ n, ⨆ (_ : n ≠ 0), rootSpace b.ca... | [
"ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁷ : Finite ι\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\nb : Basis ι R L\ninst✝³ : Fintype ι\ninst✝² : IsDomain R\ninst✝¹ : CharZero R\ninst✝ : IsTorsionFree R L\nU : LieSubmodule R (↥b.cartan) L := ⨆ n, ⨆ (_ : n ≠ 0), rootSpace b.cartan (∑ i, n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 439,
"column": 6
} | {
"line": 439,
"column": 23
} | {
"line": 439,
"column": 24
} | [
{
"pp": "ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁷ : Finite ι\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\nb : Basis ι R L\ninst✝³ : Fintype ι\ninst✝² : IsDomain R\ninst✝¹ : CharZero R\ninst✝ : IsTorsionFree R L\nU : LieSubmodule R (↥b.cartan) L := ⨆ n, ⨆ (_ : n ≠ 0), rootSpace b.ca... | [
"ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁷ : Finite ι\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\nb : Basis ι R L\ninst✝³ : Fintype ι\ninst✝² : IsDomain R\ninst✝¹ : CharZero R\ninst✝ : IsTorsionFree R L\nU : LieSubmodule R (↥b.cartan) L := ⨆ n, ⨆ (_ : n ≠ 0), rootSpace b.cartan (∑ i, n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 450,
"column": 4
} | {
"line": 450,
"column": 15
} | {
"line": 450,
"column": 16
} | [
{
"pp": "ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁷ : Finite ι\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\nb : Basis ι R L\ninst✝³ : Fintype ι\ninst✝² : IsDomain R\ninst✝¹ : CharZero R\ninst✝ : IsTorsionFree R L\nU : LieSubmodule R (↥b.cartan) L := ⨆ n, ⨆ (_ : n ≠ 0), rootSpace b.ca... | [
"ι : Type u_1\nR : Type u_2\nL : Type u_3\ninst✝⁷ : Finite ι\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\nb : Basis ι R L\ninst✝³ : Fintype ι\ninst✝² : IsDomain R\ninst✝¹ : CharZero R\ninst✝ : IsTorsionFree R L\nU : LieSubmodule R (↥b.cartan) L := ⨆ n, ⨆ (_ : n ≠ 0), rootSpace b.cartan (∑ i, n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 495,
"column": 4
} | {
"line": 495,
"column": 49
} | {
"line": 495,
"column": 50
} | [
{
"pp": "case refine_2\nι : Type u_1\nK : Type u_2\nL : Type u_3\ninst✝⁵ : Fintype ι\ninst✝⁴ : Field K\ninst✝³ : CharZero K\ninst✝² : LieRing L\ninst✝¹ : LieAlgebra K L\ninst✝ : FiniteDimensional K L\nb : Basis ι K L\ni : ι\n⊢ { toFun := ⇑(b.baseSupp i), genWeightSpace_ne_bot' := ⋯ } ∈ root",
"ppTerm": "?re... | [
"case refine_2\nι : Type u_1\nK : Type u_2\nL : Type u_3\ninst✝⁵ : Fintype ι\ninst✝⁴ : Field K\ninst✝³ : CharZero K\ninst✝² : LieRing L\ninst✝¹ : LieAlgebra K L\ninst✝ : FiniteDimensional K L\nb : Basis ι K L\ni : ι\n⊢ ¬b.baseSupp i = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 504,
"column": 49
} | {
"line": 504,
"column": 72
} | {
"line": 504,
"column": 73
} | [
{
"pp": "ι : Type u_1\nK : Type u_2\nL : Type u_3\ninst✝⁷ : Fintype ι\ninst✝⁶ : Field K\ninst✝⁵ : CharZero K\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra K L\ninst✝² : FiniteDimensional K L\nb : Basis ι K L\ninst✝¹ : IsTriangularizable K (↥b.cartan) L\ninst✝ : IsKilling K L\ni j : ι\nhij : b.baseSupp' i = b.baseSup... | [
"ι : Type u_1\nK : Type u_2\nL : Type u_3\ninst✝⁷ : Fintype ι\ninst✝⁶ : Field K\ninst✝⁵ : CharZero K\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra K L\ninst✝² : FiniteDimensional K L\nb : Basis ι K L\ninst✝¹ : IsTriangularizable K (↥b.cartan) L\ninst✝ : IsKilling K L\ni j : ι\nhij : b.baseSupp' i = b.baseSupp' j\n⊢ b.ba... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 522,
"column": 4
} | {
"line": 522,
"column": 57
} | {
"line": 522,
"column": 58
} | [
{
"pp": "ι : Type u_1\nK : Type u_2\nL : Type u_3\ninst✝⁷ : Fintype ι\ninst✝⁶ : Field K\ninst✝⁵ : CharZero K\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra K L\ninst✝² : FiniteDimensional K L\nb : Basis ι K L\ninst✝¹ : IsTriangularizable K (↥b.cartan) L\ninst✝ : IsKilling K L\nχ : ↥root\nthis✝ : ∀ (n : ι → ℕ), ∑ i, n... | [
"ι : Type u_1\nK : Type u_2\nL : Type u_3\ninst✝⁷ : Fintype ι\ninst✝⁶ : Field K\ninst✝⁵ : CharZero K\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra K L\ninst✝² : FiniteDimensional K L\nb : Basis ι K L\ninst✝¹ : IsTriangularizable K (↥b.cartan) L\ninst✝ : IsKilling K L\nχ : ↥root\nthis✝ : ∀ (n : ι → ℕ), ∑ i, n i • b.baseS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 529,
"column": 32
} | {
"line": 529,
"column": 43
} | {
"line": 529,
"column": 44
} | [
{
"pp": "ι : Type u_1\nK : Type u_2\nL : Type u_3\ninst✝⁷ : Fintype ι\ninst✝⁶ : Field K\ninst✝⁵ : CharZero K\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra K L\ninst✝² : FiniteDimensional K L\nb : Basis ι K L\ninst✝¹ : IsTriangularizable K (↥b.cartan) L\ninst✝ : IsKilling K L\nthis : ∀ (n : ι → ℕ), ∑ i, n i • b.baseS... | [
"ι : Type u_1\nK : Type u_2\nL : Type u_3\ninst✝⁷ : Fintype ι\ninst✝⁶ : Field K\ninst✝⁵ : CharZero K\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra K L\ninst✝² : FiniteDimensional K L\nb : Basis ι K L\ninst✝¹ : IsTriangularizable K (↥b.cartan) L\ninst✝ : IsKilling K L\nthis : ∀ (n : ι → ℕ), ∑ i, n i • b.baseSupp i ∈ clos... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 532,
"column": 4
} | {
"line": 532,
"column": 92
} | {
"line": 532,
"column": 93
} | [
{
"pp": "ι : Type u_1\nK : Type u_2\nL : Type u_3\ninst✝⁷ : Fintype ι\ninst✝⁶ : Field K\ninst✝⁵ : CharZero K\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra K L\ninst✝² : FiniteDimensional K L\nb : Basis ι K L\ninst✝¹ : IsTriangularizable K (↥b.cartan) L\ninst✝ : IsKilling K L\nthis : ∀ (n : ι → ℕ), ∑ i, n i • b.baseS... | [
"ι : Type u_1\nK : Type u_2\nL : Type u_3\ninst✝⁷ : Fintype ι\ninst✝⁶ : Field K\ninst✝⁵ : CharZero K\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra K L\ninst✝² : FiniteDimensional K L\nb : Basis ι K L\ninst✝¹ : IsTriangularizable K (↥b.cartan) L\ninst✝ : IsKilling K L\nthis : ∀ (n : ι → ℕ), ∑ i, n i • b.baseSupp i ∈ clos... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 533,
"column": 73
} | {
"line": 533,
"column": 89
} | {
"line": 533,
"column": 90
} | [
{
"pp": "case refine_1\nι : Type u_1\nK : Type u_2\nL : Type u_3\ninst✝⁷ : Fintype ι\ninst✝⁶ : Field K\ninst✝⁵ : CharZero K\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra K L\ninst✝² : FiniteDimensional K L\nb : Basis ι K L\ninst✝¹ : IsTriangularizable K (↥b.cartan) L\ninst✝ : IsKilling K L\nthis : ∀ (n : ι → ℕ), ∑ i... | [
"case refine_1\nι : Type u_1\nK : Type u_2\nL : Type u_3\ninst✝⁷ : Fintype ι\ninst✝⁶ : Field K\ninst✝⁵ : CharZero K\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra K L\ninst✝² : FiniteDimensional K L\nb : Basis ι K L\ninst✝¹ : IsTriangularizable K (↥b.cartan) L\ninst✝ : IsKilling K L\nthis : ∀ (n : ι → ℕ), ∑ i, n i • b.ba... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 533,
"column": 73
} | {
"line": 533,
"column": 89
} | {
"line": 533,
"column": 90
} | [
{
"pp": "case refine_2\nι : Type u_1\nK : Type u_2\nL : Type u_3\ninst✝⁷ : Fintype ι\ninst✝⁶ : Field K\ninst✝⁵ : CharZero K\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra K L\ninst✝² : FiniteDimensional K L\nb : Basis ι K L\ninst✝¹ : IsTriangularizable K (↥b.cartan) L\ninst✝ : IsKilling K L\nthis : ∀ (n : ι → ℕ), ∑ i... | [
"case refine_2\nι : Type u_1\nK : Type u_2\nL : Type u_3\ninst✝⁷ : Fintype ι\ninst✝⁶ : Field K\ninst✝⁵ : CharZero K\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra K L\ninst✝² : FiniteDimensional K L\nb : Basis ι K L\ninst✝¹ : IsTriangularizable K (↥b.cartan) L\ninst✝ : IsKilling K L\nthis : ∀ (n : ι → ℕ), ∑ i, n i • b.ba... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Basis | {
"line": 543,
"column": 63
} | {
"line": 543,
"column": 86
} | {
"line": 543,
"column": 87
} | [
{
"pp": "ι : Type u_1\nK : Type u_2\nL : Type u_3\ninst✝⁷ : Fintype ι\ninst✝⁶ : Field K\ninst✝⁵ : CharZero K\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra K L\ninst✝² : FiniteDimensional K L\nb : Basis ι K L\ninst✝¹ : IsTriangularizable K (↥b.cartan) L\ninst✝ : IsKilling K L\ni j : ι\nhij : b.baseSupp' i = b.baseSup... | [
"ι : Type u_1\nK : Type u_2\nL : Type u_3\ninst✝⁷ : Fintype ι\ninst✝⁶ : Field K\ninst✝⁵ : CharZero K\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra K L\ninst✝² : FiniteDimensional K L\nb : Basis ι K L\ninst✝¹ : IsTriangularizable K (↥b.cartan) L\ninst✝ : IsKilling K L\ni j : ι\nhij : b.baseSupp' i = b.baseSupp' j\n⊢ b.ba... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Semisimple.Lemmas | {
"line": 53,
"column": 6
} | {
"line": 53,
"column": 63
} | {
"line": 53,
"column": 64
} | [
{
"pp": "k : Type u_1\nL : Type u_2\nM : Type u_3\ninst✝¹² : Field k\ninst✝¹¹ : CharZero k\ninst✝¹⁰ : LieRing L\ninst✝⁹ : LieAlgebra k L\ninst✝⁸ : Module.Finite k L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module k M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule k L M\ninst✝³ : Module.Finite k M\ninst✝² : IsIrreduc... | [
"k : Type u_1\nL : Type u_2\nM : Type u_3\ninst✝¹² : Field k\ninst✝¹¹ : CharZero k\ninst✝¹⁰ : LieRing L\ninst✝⁹ : LieAlgebra k L\ninst✝⁸ : Module.Finite k L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module k M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule k L M\ninst✝³ : Module.Finite k M\ninst✝² : IsIrreducible k L M\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Semisimple.Lemmas | {
"line": 54,
"column": 4
} | {
"line": 54,
"column": 15
} | {
"line": 54,
"column": 16
} | [
{
"pp": "k : Type u_1\nL : Type u_2\nM : Type u_3\ninst✝¹² : Field k\ninst✝¹¹ : CharZero k\ninst✝¹⁰ : LieRing L\ninst✝⁹ : LieAlgebra k L\ninst✝⁸ : Module.Finite k L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module k M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule k L M\ninst✝³ : Module.Finite k M\ninst✝² : IsIrreduc... | [
"k : Type u_1\nL : Type u_2\nM : Type u_3\ninst✝¹² : Field k\ninst✝¹¹ : CharZero k\ninst✝¹⁰ : LieRing L\ninst✝⁹ : LieAlgebra k L\ninst✝⁸ : Module.Finite k L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module k M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule k L M\ninst✝³ : Module.Finite k M\ninst✝² : IsIrreducible k L M\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Semisimple.Lemmas | {
"line": 55,
"column": 2
} | {
"line": 59,
"column": 46
} | {
"line": 60,
"column": 2
} | [
{
"pp": "k : Type u_1\nL : Type u_2\nM : Type u_3\ninst✝¹² : Field k\ninst✝¹¹ : CharZero k\ninst✝¹⁰ : LieRing L\ninst✝⁹ : LieAlgebra k L\ninst✝⁸ : Module.Finite k L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module k M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule k L M\ninst✝³ : Module.Finite k M\ninst✝² : IsIrreduc... | [
"k : Type u_1\nL : Type u_2\nM : Type u_3\ninst✝¹² : Field k\ninst✝¹¹ : CharZero k\ninst✝¹⁰ : LieRing L\ninst✝⁹ : LieAlgebra k L\ninst✝⁸ : Module.Finite k L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module k M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule k L M\ninst✝³ : Module.Finite k M\ninst✝² : IsIrreducible k L M\n... | have aux : radical k L = center k L := by
refine le_antisymm (fun x hx ↦ (mem_maxTrivSubmodule k L L x).mpr ?_) (center_le_radical k L)
intro y
simp [← toEnd_eq_zero_iff (R := k) (L := L) (M := M), LieHom.map_lie, hχ _ hx, lie_smul,
(toEnd k L M y).commute_id_right.lie_eq] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Algebra.Lie.Loop | {
"line": 105,
"column": 47
} | {
"line": 105,
"column": 58
} | {
"line": 105,
"column": 59
} | [
{
"pp": "R : Type u_1\nA : Type u_2\nL : Type u_3\ninst✝⁵ : CommRing R\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra R L\ninst✝² : AddCommGroup A\ninst✝¹ : DistribSMul A R\ninst✝ : SMulCommClass A R R\nΦ : LinearMap.BilinForm R L\nf : loopAlgebra R A L\nF : loopAlgebra R A L ≃ₗ[R] A →₀ L := toFinsupp R A L\nx y : lo... | [
"R : Type u_1\nA : Type u_2\nL : Type u_3\ninst✝⁵ : CommRing R\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra R L\ninst✝² : AddCommGroup A\ninst✝¹ : DistribSMul A R\ninst✝ : SMulCommClass A R R\nΦ : LinearMap.BilinForm R L\nf : loopAlgebra R A L\nF : loopAlgebra R A L ≃ₗ[R] A →₀ L := toFinsupp R A L\nx y : loopAlgebra R ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Semisimple.Lemmas | {
"line": 77,
"column": 2
} | {
"line": 77,
"column": 26
} | {
"line": 77,
"column": 27
} | [
{
"pp": "k : Type u_1\nL : Type u_2\nM : Type u_3\ninst✝¹² : Field k\ninst✝¹¹ : CharZero k\ninst✝¹⁰ : LieRing L\ninst✝⁹ : LieAlgebra k L\ninst✝⁸ : Module.Finite k L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module k M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule k L M\ninst✝³ : Module.Finite k M\ninst✝² : IsIrreduc... | [
"k : Type u_1\nL : Type u_2\nM : Type u_3\ninst✝¹² : Field k\ninst✝¹¹ : CharZero k\ninst✝¹⁰ : LieRing L\ninst✝⁹ : LieAlgebra k L\ninst✝⁸ : Module.Finite k L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module k M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule k L M\ninst✝³ : Module.Finite k M\ninst✝² : IsIrreducible k L M\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Semisimple.Lemmas | {
"line": 87,
"column": 16
} | {
"line": 87,
"column": 27
} | {
"line": 87,
"column": 28
} | [
{
"pp": "case mem\nL : Type u_2\nM : Type u_3\ninst✝⁶ : LieRing L\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : LieRingModule L M\nR : Type u_4\ninst✝³ : CommRing R\ninst✝² : LieAlgebra R L\ninst✝¹ : Module R M\ninst✝ : LieModule R L M\ns : Set L\nhs : ∀ x ∈ s, (trace R M) ((toEnd R L M) x) = 0\nx u : L\nhu : u ∈ s\n⊢ (tr... | [
"case mem\nL : Type u_2\nM : Type u_3\ninst✝⁶ : LieRing L\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : LieRingModule L M\nR : Type u_4\ninst✝³ : CommRing R\ninst✝² : LieAlgebra R L\ninst✝¹ : Module R M\ninst✝ : LieModule R L M\ns : Set L\nhs : ∀ x ∈ s, (trace R M) ((toEnd R L M) x) = 0\nx u : L\nhu : u ∈ s\n⊢ (trace R M) ((t... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Loop | {
"line": 134,
"column": 77
} | {
"line": 134,
"column": 93
} | {
"line": 134,
"column": 94
} | [
{
"pp": "R : Type u_1\nA : Type u_2\nL : Type u_3\ninst✝⁵ : CommRing R\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra R L\ninst✝² : CommRing A\ninst✝¹ : IsAddTorsionFree R\ninst✝ : Algebra A R\nΦ : LinearMap.BilinForm R L\nhΦ : Φ.IsSymm\nf : loopAlgebra R A L\nF : loopAlgebra R A L ≃ₗ[R] A →₀ L := toFinsupp R A L\ns ... | [
"R : Type u_1\nA : Type u_2\nL : Type u_3\ninst✝⁵ : CommRing R\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra R L\ninst✝² : CommRing A\ninst✝¹ : IsAddTorsionFree R\ninst✝ : Algebra A R\nΦ : LinearMap.BilinForm R L\nhΦ : Φ.IsSymm\nf : loopAlgebra R A L\nF : loopAlgebra R A L ≃ₗ[R] A →₀ L := toFinsupp R A L\ns : Finset A :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 112,
"column": 4
} | {
"line": 112,
"column": 15
} | {
"line": 112,
"column": 16
} | [
{
"pp": "case h1\nα : Type u_1\ninst✝ : DecidableEq α\nl : List α\nhl : l.attach.Nodup\nhn : 2 ≤ l.attach.length\n⊢ ∀ σ ∈ [l.attach.formPerm], σ.IsCycle",
"ppTerm": "?h1",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"congrArg",
"Membership.mem",
"id",
... | [
"case h1\nα : Type u_1\ninst✝ : DecidableEq α\nl : List α\nhl : l.attach.Nodup\nhn : 2 ≤ l.attach.length\n⊢ l.attach.formPerm.IsCycle"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 160,
"column": 2
} | {
"line": 160,
"column": 36
} | {
"line": 160,
"column": 37
} | [
{
"pp": "case mk\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\ns : Cycle α\nx✝ : α\nh : Nodup (Quot.mk ⇑(IsRotated.setoid α) [x✝])\nhn : Nontrivial (Quot.mk ⇑(IsRotated.setoid α) [x✝])\n⊢ False",
"ppTerm": "?mk",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals... | [
"case mk\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\ns : Cycle α\nx✝ : α\nh : Nodup (Quot.mk ⇑(IsRotated.setoid α) [x✝])\nhn : Nontrivial (Quot.mk ⇑(IsRotated.setoid α) [x✝])\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 165,
"column": 2
} | {
"line": 165,
"column": 13
} | {
"line": 165,
"column": 14
} | [
{
"pp": "case h\nα : Type u_1\ninst✝ : DecidableEq α\nx : α\na✝ : List α\nh : Nodup (Quot.mk (⇑(IsRotated.setoid α)) a✝)\nhx : x ∉ Quot.mk (⇑(IsRotated.setoid α)) a✝\n⊢ (formPerm (Quot.mk (⇑(IsRotated.setoid α)) a✝) h) x = x",
"ppTerm": "?h",
"assigned": true,
"usedConstants": [
"Equiv.instEqu... | [
"case h\nα : Type u_1\ninst✝ : DecidableEq α\nx : α\na✝ : List α\nh : Nodup (Quot.mk (⇑(IsRotated.setoid α)) a✝)\nhx : x ∉ Quot.mk (⇑(IsRotated.setoid α)) a✝\n⊢ a✝.formPerm x = x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Loop | {
"line": 137,
"column": 25
} | {
"line": 137,
"column": 36
} | {
"line": 137,
"column": 37
} | [
{
"pp": "R : Type u_1\nA : Type u_2\nL : Type u_3\ninst✝⁵ : CommRing R\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra R L\ninst✝² : CommRing A\ninst✝¹ : IsAddTorsionFree R\ninst✝ : Algebra A R\nΦ : LinearMap.BilinForm R L\nhΦ : Φ.IsSymm\nf : loopAlgebra R A L\nF : loopAlgebra R A L ≃ₗ[R] A →₀ L := toFinsupp R A L\ns ... | [
"R : Type u_1\nA : Type u_2\nL : Type u_3\ninst✝⁵ : CommRing R\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra R L\ninst✝² : CommRing A\ninst✝¹ : IsAddTorsionFree R\ninst✝ : Algebra A R\nΦ : LinearMap.BilinForm R L\nhΦ : Φ.IsSymm\nf : loopAlgebra R A L\nF : loopAlgebra R A L ≃ₗ[R] A →₀ L := toFinsupp R A L\ns : Finset A :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 175,
"column": 2
} | {
"line": 175,
"column": 13
} | {
"line": 175,
"column": 14
} | [
{
"pp": "case h\nα : Type u_1\ninst✝ : DecidableEq α\na✝ : List α\nh : Nodup (Quot.mk (⇑(IsRotated.setoid α)) a✝)\n⊢ (reverse (Quot.mk (⇑(IsRotated.setoid α)) a✝)).formPerm ⋯ = (formPerm (Quot.mk (⇑(IsRotated.setoid α)) a✝) h)⁻¹",
"ppTerm": "?h",
"assigned": true,
"usedConstants": [
"Iff.mpr",... | [
"case h\nα : Type u_1\ninst✝ : DecidableEq α\na✝ : List α\nh : Nodup (Quot.mk (⇑(IsRotated.setoid α)) a✝)\n⊢ a✝.reverse.formPerm = a✝.formPerm⁻¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 182,
"column": 2
} | {
"line": 182,
"column": 13
} | {
"line": 182,
"column": 14
} | [
{
"pp": "case h\nα : Type u_2\ninst✝ : DecidableEq α\na₁✝ a₂✝ : List α\nhs : Nodup (Quotient.mk'' a₁✝)\nhs' : Nodup (Quotient.mk'' a₂✝)\n⊢ formPerm (Quotient.mk'' a₁✝) hs = formPerm (Quotient.mk'' a₂✝) hs' ↔\n Quotient.mk'' a₁✝ = Quotient.mk'' a₂✝ ∨ length (Quotient.mk'' a₁✝) ≤ 1 ∧ length (Quotient.mk'' a₂✝)... | [
"case h\nα : Type u_2\ninst✝ : DecidableEq α\na₁✝ a₂✝ : List α\nhs : Nodup (Quotient.mk'' a₁✝)\nhs' : Nodup (Quotient.mk'' a₂✝)\n⊢ a₁✝.formPerm = a₂✝.formPerm ↔ a₁✝ ~r a₂✝ ∨ a₁✝.length ≤ 1 ∧ a₂✝.length ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 209,
"column": 2
} | {
"line": 209,
"column": 35
} | {
"line": 209,
"column": 36
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx y : α\nH : p.toList x = [y]\n⊢ False",
"ppTerm": "?m.8",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx y : α\nH : p.toList x = [y]\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 234,
"column": 4
} | {
"line": 234,
"column": 15
} | {
"line": 234,
"column": 16
} | [
{
"pp": "case mpr\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx y : α\nh : p.SameCycle x y\nhx : x ∈ p.support\n⊢ ∃ m < (p.cycleOf x).support.card, (p ^ m) x = y",
"ppTerm": "?mpr",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case mpr\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx y : α\nh : p.SameCycle x y\nhx : x ∈ p.support\n⊢ ∃ m < (p.cycleOf x).support.card, (p ^ m) x = y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 273,
"column": 33
} | {
"line": 273,
"column": 44
} | {
"line": 273,
"column": 45
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx y : α\nhy✝ : y ∈ p.toList x\nhy : p.SameCycle x y ∧ x ∈ p.support\nk : ℕ\nhk : k < (p.cycleOf x).support.card\nhk' : (p ^ k) x = y\n⊢ k < (p.toList x).length",
"ppTerm": "?m.54",
"assigned": true,
"usedConstants": [
... | [
"α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx y : α\nhy✝ : y ∈ p.toList x\nhy : p.SameCycle x y ∧ x ∈ p.support\nk : ℕ\nhk : k < (p.cycleOf x).support.card\nhk' : (p ^ k) x = y\n⊢ k < (p.cycleOf x).support.card"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 282,
"column": 2
} | {
"line": 282,
"column": 19
} | {
"line": 283,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx : α\nk : ℕ\n⊢ p.toList ((p ^ k) x) = (p.toList x).rotate k",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Equiv.Perm.toList",
"List.ext_getElem",
"Equiv.instEquivLike",
"Equiv.Perm.ins... | [
"case hl\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx : α\nk : ℕ\n⊢ (p.toList ((p ^ k) x)).length = ((p.toList x).rotate k).length",
"case h\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx : α\nk : ℕ\n⊢ ∀ (i : ℕ) (h₁ : i < (p.toList ((p ^ k) x)).length) (h₂ : i <... | apply ext_getElem | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 331,
"column": 4
} | {
"line": 331,
"column": 15
} | {
"line": 331,
"column": 16
} | [
{
"pp": "case hl\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nl : List α\nhl : 2 ≤ l.length\nhn : l.Nodup\nk : Fin l.length\nhx : l.get k ∈ l\nhr : l ~r l.rotate ↑k\n⊢ 2 ≤ (l.rotate ↑k).length",
"ppTerm": "?hl",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
... | [
"case hl\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nl : List α\nhl : 2 ≤ l.length\nhn : l.Nodup\nk : Fin l.length\nhx : l.get k ∈ l\nhr : l ~r l.rotate ↑k\n⊢ 2 ≤ l.length"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 332,
"column": 4
} | {
"line": 332,
"column": 15
} | {
"line": 332,
"column": 16
} | [
{
"pp": "case hn\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nl : List α\nhl : 2 ≤ l.length\nhn : l.Nodup\nk : Fin l.length\nhx : l.get k ∈ l\nhr : l ~r l.rotate ↑k\n⊢ (l.rotate ↑k).Nodup",
"ppTerm": "?hn",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"id",
"Fin.val"... | [
"case hn\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nl : List α\nhl : 2 ≤ l.length\nhn : l.Nodup\nk : Fin l.length\nhx : l.get k ∈ l\nhr : l ~r l.rotate ↑k\n⊢ l.Nodup"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 374,
"column": 2
} | {
"line": 374,
"column": 43
} | {
"line": 374,
"column": 44
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nf : Perm α\nhf : f.IsCycle\nx : α\nhx : f x ≠ x\n⊢ (f.toCycle hf).Nodup",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Equiv.Perm.toList",
"congrArg",
"Equiv.Perm.toCycle",
"id",
... | [
"α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nf : Perm α\nhf : f.IsCycle\nx : α\nhx : f x ≠ x\n⊢ (f.toList x).Nodup"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 410,
"column": 4
} | {
"line": 410,
"column": 94
} | {
"line": 411,
"column": 6
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx✝ : α\nf : { f // f.IsCycle }\nx : α\nhx : ↑f x ≠ x\n⊢ (fun s ↦ ⟨(↑s).formPerm ⋯, ⋯⟩) ((fun f ↦ ⟨(↑f).toCycle ⋯, ⋯⟩) f) = f",
"ppTerm": "?m.72",
"assigned": true,
"usedConstants": [
"Equiv.Perm.instDecidableRelSameC... | [
"α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx✝ : α\nf : { f // f.IsCycle }\nx : α\nhx : ↑f x ≠ x\n⊢ (↑f).cycleOf x = ↑f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 415,
"column": 33
} | {
"line": 415,
"column": 44
} | {
"line": 415,
"column": 45
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx✝ : α\nval✝ : Cycle α\ns : List α\nhn : Cycle.Nodup (Quot.mk (⇑(IsRotated.setoid α)) s)\nht : Cycle.Nontrivial (Quot.mk (⇑(IsRotated.setoid α)) s)\nx : α\nhx : x ∈ Quot.mk (⇑(IsRotated.setoid α)) s\n⊢ 2 ≤ s.length",
"ppTerm": "?m... | [
"α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx✝ : α\nval✝ : Cycle α\ns : List α\nhn : Cycle.Nodup (Quot.mk (⇑(IsRotated.setoid α)) s)\nht : Cycle.Nontrivial (Quot.mk (⇑(IsRotated.setoid α)) s)\nx : α\nhx : x ∈ Quot.mk (⇑(IsRotated.setoid α)) s\n⊢ 2 ≤ s.length"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.LieTheorem | {
"line": 138,
"column": 4
} | {
"line": 138,
"column": 32
} | {
"line": 138,
"column": 33
} | [
{
"pp": "R : Type u_1\nL : Type u_2\nA : Type u_3\nV : Type u_4\ninst✝¹⁹ : CommRing R\ninst✝¹⁸ : IsPrincipalIdealRing R\ninst✝¹⁷ : IsDomain R\ninst✝¹⁶ : CharZero R\ninst✝¹⁵ : LieRing L\ninst✝¹⁴ : LieAlgebra R L\ninst✝¹³ : LieRing A\ninst✝¹² : LieAlgebra R A\ninst✝¹¹ : Bracket L A\ninst✝¹⁰ : Bracket A L\ninst✝⁹ ... | [
"R : Type u_1\nL : Type u_2\nA : Type u_3\nV : Type u_4\ninst✝¹⁹ : CommRing R\ninst✝¹⁸ : IsPrincipalIdealRing R\ninst✝¹⁷ : IsDomain R\ninst✝¹⁶ : CharZero R\ninst✝¹⁵ : LieRing L\ninst✝¹⁴ : LieAlgebra R L\ninst✝¹³ : LieRing A\ninst✝¹² : LieAlgebra R A\ninst✝¹¹ : Bracket L A\ninst✝¹⁰ : Bracket A L\ninst✝⁹ : AddCommGro... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 424,
"column": 8
} | {
"line": 424,
"column": 19
} | {
"line": 424,
"column": 20
} | [
{
"pp": "case mk\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx✝ : α\nval✝ : Cycle α\ns : List α\nhn✝ : Cycle.Nodup (Quot.mk (⇑(IsRotated.setoid α)) s)\nht : Cycle.Nontrivial (Quot.mk (⇑(IsRotated.setoid α)) s)\nx : α\nhl : 2 ≤ s.length\nhn : s.Nodup\nhx : x ∈ s\n⊢ x ∈ s.toFinset",
... | [
"case mk\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx✝ : α\nval✝ : Cycle α\ns : List α\nhn✝ : Cycle.Nodup (Quot.mk (⇑(IsRotated.setoid α)) s)\nht : Cycle.Nontrivial (Quot.mk (⇑(IsRotated.setoid α)) s)\nx : α\nhl : 2 ≤ s.length\nhn : s.Nodup\nhx : x ∈ s\n⊢ x ∈ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 449,
"column": 6
} | {
"line": 449,
"column": 17
} | {
"line": 449,
"column": 18
} | [
{
"pp": "case intro.refine_2.mk.refine_2\nα : Type u_1\ninst✝¹ : Finite α\ninst✝ : DecidableEq α\nval✝ : Fintype α\nx : α\ny✝ : Cycle α\nl : List α\nhn : Cycle.Nodup (Quot.mk (⇑(IsRotated.setoid α)) l)\nhf : (Cycle.formPerm (Quot.mk (⇑(IsRotated.setoid α)) l) hn).IsCycle\nhx : (Cycle.formPerm (Quot.mk (⇑(IsRota... | [
"case intro.refine_2.mk.refine_2\nα : Type u_1\ninst✝¹ : Finite α\ninst✝ : DecidableEq α\nval✝ : Fintype α\nx : α\ny✝ : Cycle α\nl : List α\nhn : Cycle.Nodup (Quot.mk (⇑(IsRotated.setoid α)) l)\nhf : (Cycle.formPerm (Quot.mk (⇑(IsRotated.setoid α)) l) hn).IsCycle\nhx : (Cycle.formPerm (Quot.mk (⇑(IsRotated.setoid α... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 456,
"column": 2
} | {
"line": 456,
"column": 13
} | {
"line": 456,
"column": 14
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Finite α\ninst✝ : DecidableEq α\ns : Cycle α\nhs : s.Nodup\nhf : (s.formPerm hs).IsCycle\nhs' : ∀ (y : Cycle α), (fun s_1 ↦ ∃ (h : s_1.Nodup), s_1.formPerm h = s.formPerm hs) y → y = s\nt : Cycle α\nht : t.Nodup\nht' : (↑⟨t, ht⟩).formPerm ⋯ = s.formPerm hs\n⊢ ⟨t, ht⟩ = ⟨s, hs⟩",
... | [
"α : Type u_1\ninst✝¹ : Finite α\ninst✝ : DecidableEq α\ns : Cycle α\nhs : s.Nodup\nhf : (s.formPerm hs).IsCycle\nhs' : ∀ (y : Cycle α), (fun s_1 ↦ ∃ (h : s_1.Nodup), s_1.formPerm h = s.formPerm hs) y → y = s\nt : Cycle α\nht : t.Nodup\nht' : (↑⟨t, ht⟩).formPerm ⋯ = s.formPerm hs\n⊢ t = s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.LieTheorem | {
"line": 146,
"column": 42
} | {
"line": 146,
"column": 52
} | {
"line": 148,
"column": 0
} | [
{
"pp": "R : Type u_1\nL : Type u_2\nA : Type u_3\nV : Type u_4\ninst✝¹⁹ : CommRing R\ninst✝¹⁸ : IsPrincipalIdealRing R\ninst✝¹⁷ : IsDomain R\ninst✝¹⁶ : CharZero R\ninst✝¹⁵ : LieRing L\ninst✝¹⁴ : LieAlgebra R L\ninst✝¹³ : LieRing A\ninst✝¹² : LieAlgebra R A\ninst✝¹¹ : Bracket L A\ninst✝¹⁰ : Bracket A L\ninst✝⁹ ... | [] | simp [hv'] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Lie.LieTheorem | {
"line": 146,
"column": 42
} | {
"line": 146,
"column": 52
} | {
"line": 148,
"column": 0
} | [
{
"pp": "R : Type u_1\nL : Type u_2\nA : Type u_3\nV : Type u_4\ninst✝¹⁹ : CommRing R\ninst✝¹⁸ : IsPrincipalIdealRing R\ninst✝¹⁷ : IsDomain R\ninst✝¹⁶ : CharZero R\ninst✝¹⁵ : LieRing L\ninst✝¹⁴ : LieAlgebra R L\ninst✝¹³ : LieRing A\ninst✝¹² : LieAlgebra R A\ninst✝¹¹ : Bracket L A\ninst✝¹⁰ : Bracket A L\ninst✝⁹ ... | [] | simp [hv'] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Lie.LieTheorem | {
"line": 146,
"column": 42
} | {
"line": 146,
"column": 52
} | {
"line": 148,
"column": 0
} | [
{
"pp": "R : Type u_1\nL : Type u_2\nA : Type u_3\nV : Type u_4\ninst✝¹⁹ : CommRing R\ninst✝¹⁸ : IsPrincipalIdealRing R\ninst✝¹⁷ : IsDomain R\ninst✝¹⁶ : CharZero R\ninst✝¹⁵ : LieRing L\ninst✝¹⁴ : LieAlgebra R L\ninst✝¹³ : LieRing A\ninst✝¹² : LieAlgebra R A\ninst✝¹¹ : Bracket L A\ninst✝¹⁰ : Bracket A L\ninst✝⁹ ... | [] | simp [hv'] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 466,
"column": 4
} | {
"line": 466,
"column": 15
} | {
"line": 466,
"column": 16
} | [
{
"pp": "case refine_1\nα : Type u_1\ninst✝¹ : Finite α\ninst✝ : DecidableEq α\ns : Cycle α\nhn : s.Nodup\nhf : ((↑⟨s, hn⟩).formPerm ⋯).IsCycle\nhs' : ∀ (y : { s // s.Nodup }), (fun s_1 ↦ (↑s_1).formPerm ⋯ = (↑⟨s, hn⟩).formPerm ⋯) y → y = ⟨s, hn⟩\nH : s.Subsingleton\n⊢ (↑⟨s, hn⟩).formPerm ⋯ = 1",
"ppTerm": ... | [
"case refine_1\nα : Type u_1\ninst✝¹ : Finite α\ninst✝ : DecidableEq α\ns : Cycle α\nhn : s.Nodup\nhf : ((↑⟨s, hn⟩).formPerm ⋯).IsCycle\nhs' : ∀ (y : { s // s.Nodup }), (fun s_1 ↦ (↑s_1).formPerm ⋯ = (↑⟨s, hn⟩).formPerm ⋯) y → y = ⟨s, hn⟩\nH : s.Subsingleton\n⊢ s.formPerm ⋯ = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 467,
"column": 4
} | {
"line": 467,
"column": 15
} | {
"line": 467,
"column": 16
} | [
{
"pp": "case refine_2\nα : Type u_1\ninst✝¹ : Finite α\ninst✝ : DecidableEq α\nf : Perm α\nhf : f.IsCycle\ns : Cycle α\nhn : s.Nodup\nhs : (↑⟨s, hn⟩).formPerm ⋯ = f\nhs' : ∀ (y : { s // s.Nodup }), (fun s ↦ (↑s).formPerm ⋯ = f) y → y = ⟨s, hn⟩\n⊢ (fun s ↦ (↑s).formPerm ⋯ = f) ⟨s, ⋯⟩",
"ppTerm": "?refine_2"... | [
"case refine_2\nα : Type u_1\ninst✝¹ : Finite α\ninst✝ : DecidableEq α\nf : Perm α\nhf : f.IsCycle\ns : Cycle α\nhn : s.Nodup\nhs : (↑⟨s, hn⟩).formPerm ⋯ = f\nhs' : ∀ (y : { s // s.Nodup }), (fun s ↦ (↑s).formPerm ⋯ = f) y → y = ⟨s, hn⟩\n⊢ s.formPerm ⋯ = f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 469,
"column": 4
} | {
"line": 469,
"column": 15
} | {
"line": 469,
"column": 16
} | [
{
"pp": "case refine_3\nα : Type u_1\ninst✝¹ : Finite α\ninst✝ : DecidableEq α\nf : Perm α\nhf : f.IsCycle\ns : Cycle α\nhn : s.Nodup\nhs : (↑⟨s, hn⟩).formPerm ⋯ = f\nhs' : ∀ (y : { s // s.Nodup }), (fun s ↦ (↑s).formPerm ⋯ = f) y → y = ⟨s, hn⟩\nt : Cycle α\nht : t.Nodup\nht' : t.Nontrivial\nht'' : (↑⟨t, ⋯⟩).fo... | [
"case refine_3\nα : Type u_1\ninst✝¹ : Finite α\ninst✝ : DecidableEq α\nf : Perm α\nhf : f.IsCycle\ns : Cycle α\nhn : s.Nodup\nhs : (↑⟨s, hn⟩).formPerm ⋯ = f\nhs' : ∀ (y : { s // s.Nodup }), (fun s ↦ (↑s).formPerm ⋯ = f) y → y = ⟨s, hn⟩\nt : Cycle α\nht : t.Nodup\nht' : t.Nontrivial\nht'' : (↑⟨t, ⋯⟩).formPerm ⋯ = f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.LieTheorem | {
"line": 186,
"column": 4
} | {
"line": 186,
"column": 61
} | {
"line": 186,
"column": 62
} | [
{
"pp": "k : Type u_1\ninst✝¹⁰ : Field k\nL : Type u_2\ninst✝⁹ : LieRing L\ninst✝⁸ : LieAlgebra k L\nV : Type u_3\ninst✝⁷ : AddCommGroup V\ninst✝⁶ : Module k V\ninst✝⁵ : LieRingModule L V\ninst✝⁴ : LieModule k L V\ninst✝³ : CharZero k\ninst✝² : Module.Finite k V\ninst✝¹ : IsTriangularizable k L V\nA : LieIdeal ... | [
"k : Type u_1\ninst✝¹⁰ : Field k\nL : Type u_2\ninst✝⁹ : LieRing L\ninst✝⁸ : LieAlgebra k L\nV : Type u_3\ninst✝⁷ : AddCommGroup V\ninst✝⁶ : Module k V\ninst✝⁵ : LieRingModule L V\ninst✝⁴ : LieModule k L V\ninst✝³ : CharZero k\ninst✝² : Module.Finite k V\ninst✝¹ : IsTriangularizable k L V\nA : LieIdeal k L\nhA✝ : I... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Extension | {
"line": 449,
"column": 4
} | {
"line": 450,
"column": 37
} | {
"line": 450,
"column": 38
} | [
{
"pp": "R : Type u_1\nL : Type u_3\nM : Type u_4\ninst✝⁵ : CommRing R\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra R L\ninst✝² : LieRing M\ninst✝¹ : LieAlgebra R M\ninst✝ : IsLieAbelian M\nE : Extension R M L\ns₁ s₂ : L →ₗ[R] E.L\nhs₁ : LeftInverse ⇑E.proj ⇑s₁\nhs₂ : LeftInverse ⇑E.proj ⇑s₂\nx y : L\ns : L → E.L\n... | [
"R : Type u_1\nL : Type u_3\nM : Type u_4\ninst✝⁵ : CommRing R\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra R L\ninst✝² : LieRing M\ninst✝¹ : LieAlgebra R M\ninst✝ : IsLieAbelian M\nE : Extension R M L\ns₁ s₂ : L →ₗ[R] E.L\nhs₁ : LeftInverse ⇑E.proj ⇑s₁\nhs₂ : LeftInverse ⇑E.proj ⇑s₂\nx y : L\ns : L → E.L\nhs : ∀ (b : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Extension | {
"line": 453,
"column": 4
} | {
"line": 453,
"column": 38
} | {
"line": 453,
"column": 39
} | [
{
"pp": "R : Type u_1\nL : Type u_3\nM : Type u_4\ninst✝⁵ : CommRing R\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra R L\ninst✝² : LieRing M\ninst✝¹ : LieAlgebra R M\ninst✝ : IsLieAbelian M\nE : Extension R M L\ns₁ s₂ : L →ₗ[R] E.L\nhs₁ : LeftInverse ⇑E.proj ⇑s₁\nhs₂ : LeftInverse ⇑E.proj ⇑s₂\nx y : L\ns : L → E.L\n... | [
"R : Type u_1\nL : Type u_3\nM : Type u_4\ninst✝⁵ : CommRing R\ninst✝⁴ : LieRing L\ninst✝³ : LieAlgebra R L\ninst✝² : LieRing M\ninst✝¹ : LieAlgebra R M\ninst✝ : IsLieAbelian M\nE : Extension R M L\ns₁ s₂ : L →ₗ[R] E.L\nhs₁ : LeftInverse ⇑E.proj ⇑s₁\nhs₂ : LeftInverse ⇑E.proj ⇑s₂\nx y : L\ns : L → E.L\nhs : ∀ (b : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 287,
"column": 6
} | {
"line": 287,
"column": 37
} | {
"line": 287,
"column": 38
} | [
{
"pp": "case mpr.inl\nι : Type u_1\ninst✝ : LinearOrder ι\nA : Matrix ι ι ℤ\nhA : A.IsSymm\nh : ∀ ⦃i j : ι⦄, j < i → A i j = 0 ∨ A i j = -1\ni j : ι\nhij✝ : i ≠ j\nhij : i < j\n⊢ A i j = 0 ∨ A i j = -1",
"ppTerm": "?mpr.inl",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoa... | [
"case mpr.inl\nι : Type u_1\ninst✝ : LinearOrder ι\nA : Matrix ι ι ℤ\nhA : A.IsSymm\nh : ∀ ⦃i j : ι⦄, j < i → A i j = 0 ∨ A i j = -1\ni j : ι\nhij✝ : i ≠ j\nhij : i < j\n⊢ A i j = 0 ∨ A i j = -1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.LieTheorem | {
"line": 201,
"column": 4
} | {
"line": 201,
"column": 48
} | {
"line": 201,
"column": 49
} | [
{
"pp": "case h.refine_2\nk : Type u_1\ninst✝¹⁰ : Field k\nL : Type u_2\ninst✝⁹ : LieRing L\ninst✝⁸ : LieAlgebra k L\nV : Type u_3\ninst✝⁷ : AddCommGroup V\ninst✝⁶ : Module k V\ninst✝⁵ : LieRingModule L V\ninst✝⁴ : LieModule k L V\ninst✝³ : CharZero k\ninst✝² : Module.Finite k V\ninst✝¹ : IsTriangularizable k L... | [
"case h.refine_2\nk : Type u_1\ninst✝¹⁰ : Field k\nL : Type u_2\ninst✝⁹ : LieRing L\ninst✝⁸ : LieAlgebra k L\nV : Type u_3\ninst✝⁷ : AddCommGroup V\ninst✝⁶ : Module k V\ninst✝⁵ : LieRingModule L V\ninst✝⁴ : LieModule k L V\ninst✝³ : CharZero k\ninst✝² : Module.Finite k V\ninst✝¹ : IsTriangularizable k L V\nA : LieI... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.LieTheorem | {
"line": 218,
"column": 6
} | {
"line": 218,
"column": 69
} | {
"line": 218,
"column": 70
} | [
{
"pp": "case h\nk : Type u_1\ninst✝¹² : Field k\nV : Type u_3\ninst✝¹¹ : AddCommGroup V\ninst✝¹⁰ : Module k V\ninst✝⁹ : CharZero k\ninst✝⁸ : Module.Finite k V\ninst✝⁷ : Nontrivial V\nL : Type u_4\ninst✝⁶ : LieRing L\ninst✝⁵ : LieAlgebra k L\ninst✝⁴ : LieRingModule L V\ninst✝³ : LieModule k L V\ninst✝² : IsSolv... | [
"case h\nk : Type u_1\ninst✝¹² : Field k\nV : Type u_3\ninst✝¹¹ : AddCommGroup V\ninst✝¹⁰ : Module k V\ninst✝⁹ : CharZero k\ninst✝⁸ : Module.Finite k V\ninst✝⁷ : Nontrivial V\nL : Type u_4\ninst✝⁶ : LieRing L\ninst✝⁵ : LieAlgebra k L\ninst✝⁴ : LieRingModule L V\ninst✝³ : LieModule k L V\ninst✝² : IsSolvable L\ninst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.LieTheorem | {
"line": 253,
"column": 4
} | {
"line": 253,
"column": 15
} | {
"line": 253,
"column": 16
} | [
{
"pp": "case h.refine_2\nk : Type u_1\ninst✝¹¹ : Field k\nL : Type u_2\ninst✝¹⁰ : LieRing L\ninst✝⁹ : LieAlgebra k L\nV : Type u_3\ninst✝⁸ : AddCommGroup V\ninst✝⁷ : Module k V\ninst✝⁶ : LieRingModule L V\ninst✝⁵ : LieModule k L V\ninst✝⁴ : CharZero k\ninst✝³ : Module.Finite k V\ninst✝² : Nontrivial V\ninst✝¹ ... | [
"case h.refine_2\nk : Type u_1\ninst✝¹¹ : Field k\nL : Type u_2\ninst✝¹⁰ : LieRing L\ninst✝⁹ : LieAlgebra k L\nV : Type u_3\ninst✝⁸ : AddCommGroup V\ninst✝⁷ : Module k V\ninst✝⁶ : LieRingModule L V\ninst✝⁵ : LieModule k L V\ninst✝⁴ : CharZero k\ninst✝³ : Module.Finite k V\ninst✝² : Nontrivial V\ninst✝¹ : IsSolvable... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Weights.IsSimple | {
"line": 156,
"column": 51
} | {
"line": 156,
"column": 83
} | {
"line": 156,
"column": 84
} | [
{
"pp": "K : Type u_1\nL : Type u_2\ninst✝⁷ : Field K\ninst✝⁶ : LieRing L\ninst✝⁵ : LieAlgebra K L\ninst✝⁴ : FiniteDimensional K L\nH : LieSubalgebra K L\ninst✝³ : H.IsCartanSubalgebra\ninst✝² : CharZero K\ninst✝¹ : IsKilling K L\ninst✝ : IsTriangularizable K (↥H) L\nI : LieIdeal K L\nx : L\nhxI : x ∈ ↑↑(LieSub... | [
"K : Type u_1\nL : Type u_2\ninst✝⁷ : Field K\ninst✝⁶ : LieRing L\ninst✝⁵ : LieAlgebra K L\ninst✝⁴ : FiniteDimensional K L\nH : LieSubalgebra K L\ninst✝³ : H.IsCartanSubalgebra\ninst✝² : CharZero K\ninst✝¹ : IsKilling K L\ninst✝ : IsTriangularizable K (↥H) L\nI : LieIdeal K L\nx : L\nhxI : x ∈ ↑↑(LieSubmodule.restr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.LinearRecurrence | {
"line": 236,
"column": 4
} | {
"line": 236,
"column": 29
} | {
"line": 236,
"column": 30
} | [
{
"pp": "case mp\nR : Type u_1\ninst✝ : CommRing R\nE : LinearRecurrence R\nq : R\nh : E.IsSolution fun n ↦ q ^ n\n⊢ q ^ E.order - ∑ x, E.coeffs x * q ^ ↑x = 0",
"ppTerm": "?mp",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"Finset.univ",
"AddGroupWithOne.toAdd... | [
"case mp\nR : Type u_1\ninst✝ : CommRing R\nE : LinearRecurrence R\nq : R\nh : E.IsSolution fun n ↦ q ^ n\n⊢ q ^ E.order = ∑ x, E.coeffs x * q ^ ↑x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.ChainOfDivisors | {
"line": 108,
"column": 4
} | {
"line": 108,
"column": 28
} | {
"line": 108,
"column": 29
} | [
{
"pp": "case succ.refine_2.succ\nM : Type u_1\ninst✝¹ : CommMonoidWithZero M\ninst✝ : IsCancelMulZero M\nq : Associates M\nhq : q ≠ 0\nn : ℕ\nhn : n + 1 ≠ 0\nc : Fin (n + 1 + 1) → Associates M\nh₁ : StrictMono c\nh₂ : ∀ {r : Associates M}, r ≤ q ↔ ∃ i, r = c i\nn✝ : ℕ\nhi : n✝ + 1 < n + 1 + 1\nhb : c ⟨n✝ + 1, ... | [
"case succ.refine_2.succ\nM : Type u_1\ninst✝¹ : CommMonoidWithZero M\ninst✝ : IsCancelMulZero M\nq : Associates M\nhq : q ≠ 0\nn : ℕ\nhn : n + 1 ≠ 0\nc : Fin (n + 1 + 1) → Associates M\nh₁ : StrictMono c\nh₂ : ∀ {r : Associates M}, r ≤ q ↔ ∃ i, r = c i\nn✝ : ℕ\nhi : n✝ + 1 < n + 1 + 1\nhb : c ⟨n✝ + 1, hi⟩ < c 1\n⊢... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.ChainOfDivisors | {
"line": 129,
"column": 4
} | {
"line": 129,
"column": 15
} | {
"line": 129,
"column": 16
} | [
{
"pp": "case succ.refine_2.inr.refine_1\nM : Type u_1\ninst✝¹ : CommMonoidWithZero M\ninst✝ : IsCancelMulZero M\nq r : Associates M\nhr : r ∣ q\nn : ℕ\nhn : n + 1 ≠ 0\nc : Fin (n + 1 + 1) → Associates M\nh₁ : StrictMono c\nh₂ : ∀ {r : Associates M}, r ≤ q ↔ ∃ i, r = c i\nj : Fin (n + 1)\nhp : Prime (c j.succ)\... | [
"case succ.refine_2.inr.refine_1\nM : Type u_1\ninst✝¹ : CommMonoidWithZero M\ninst✝ : IsCancelMulZero M\nq r : Associates M\nhr : r ∣ q\nn : ℕ\nhn : n + 1 ≠ 0\nc : Fin (n + 1 + 1) → Associates M\nh₁ : StrictMono c\nh₂ : ∀ {r : Associates M}, r ≤ q ↔ ∃ i, r = c i\nj : Fin (n + 1)\nhp : Prime (c j.succ)\nhp' : c j.s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.ChainOfDivisors | {
"line": 131,
"column": 4
} | {
"line": 131,
"column": 42
} | {
"line": 131,
"column": 43
} | [
{
"pp": "case succ.refine_2.inr.refine_2\nM : Type u_1\ninst✝¹ : CommMonoidWithZero M\ninst✝ : IsCancelMulZero M\nq r : Associates M\nhr : r ∣ q\nn : ℕ\nhn : n + 1 ≠ 0\nc : Fin (n + 1 + 1) → Associates M\nh₁ : StrictMono c\nh₂ : ∀ {r : Associates M}, r ≤ q ↔ ∃ i, r = c i\nj : Fin (n + 1)\nhp : Prime (c j.succ)\... | [
"case succ.refine_2.inr.refine_2\nM : Type u_1\ninst✝¹ : CommMonoidWithZero M\ninst✝ : IsCancelMulZero M\nq r : Associates M\nhr : r ∣ q\nn : ℕ\nhn : n + 1 ≠ 0\nc : Fin (n + 1 + 1) → Associates M\nh₁ : StrictMono c\nh₂ : ∀ {r : Associates M}, r ≤ q ↔ ∃ i, r = c i\nj : Fin (n + 1)\nhp : Prime (c j.succ)\nhp' : c j.s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Weights.IsSimple | {
"line": 182,
"column": 44
} | {
"line": 182,
"column": 80
} | {
"line": 182,
"column": 81
} | [
{
"pp": "K : Type u_1\nL : Type u_2\ninst✝⁷ : Field K\ninst✝⁶ : LieRing L\ninst✝⁵ : LieAlgebra K L\ninst✝⁴ : FiniteDimensional K L\nH : LieSubalgebra K L\ninst✝³ : H.IsCartanSubalgebra\ninst✝² : CharZero K\ninst✝¹ : IsKilling K L\ninst✝ : IsTriangularizable K (↥H) L\nI : LieIdeal K L\nx : L\nhxI : x ∈ ↑↑(LieSub... | [
"K : Type u_1\nL : Type u_2\ninst✝⁷ : Field K\ninst✝⁶ : LieRing L\ninst✝⁵ : LieAlgebra K L\ninst✝⁴ : FiniteDimensional K L\nH : LieSubalgebra K L\ninst✝³ : H.IsCartanSubalgebra\ninst✝² : CharZero K\ninst✝¹ : IsKilling K L\ninst✝ : IsTriangularizable K (↥H) L\nI : LieIdeal K L\nx : L\nhxI : x ∈ ↑↑(LieSubmodule.restr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Weights.IsSimple | {
"line": 185,
"column": 36
} | {
"line": 185,
"column": 68
} | {
"line": 185,
"column": 69
} | [
{
"pp": "K : Type u_1\nL : Type u_2\ninst✝⁷ : Field K\ninst✝⁶ : LieRing L\ninst✝⁵ : LieAlgebra K L\ninst✝⁴ : FiniteDimensional K L\nH : LieSubalgebra K L\ninst✝³ : H.IsCartanSubalgebra\ninst✝² : CharZero K\ninst✝¹ : IsKilling K L\ninst✝ : IsTriangularizable K (↥H) L\nI : LieIdeal K L\nx : L\nhxI : x ∈ ↑↑(LieSub... | [
"K : Type u_1\nL : Type u_2\ninst✝⁷ : Field K\ninst✝⁶ : LieRing L\ninst✝⁵ : LieAlgebra K L\ninst✝⁴ : FiniteDimensional K L\nH : LieSubalgebra K L\ninst✝³ : H.IsCartanSubalgebra\ninst✝² : CharZero K\ninst✝¹ : IsKilling K L\ninst✝ : IsTriangularizable K (↥H) L\nI : LieIdeal K L\nx : L\nhxI : x ∈ ↑↑(LieSubmodule.restr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.FractionalIdeal.Basic | {
"line": 144,
"column": 4
} | {
"line": 144,
"column": 54
} | {
"line": 144,
"column": 55
} | [
{
"pp": "case refine_2\nR : Type u_1\ninst✝³ : CommRing R\nS : Submonoid R\nP : Type u_2\ninst✝² : CommRing P\ninst✝¹ : Algebra R P\ninst✝ : FaithfulSMul R P\nI : FractionalIdeal S P\nreg : IsSMulRegular P I.den\nx✝¹ x✝ : ↥↑I\nhxy : ((DistribSMul.toLinearMap R P I.den).restrict ⋯) x✝¹ = ((DistribSMul.toLinearMa... | [
"case refine_2\nR : Type u_1\ninst✝³ : CommRing R\nS : Submonoid R\nP : Type u_2\ninst✝² : CommRing P\ninst✝¹ : Algebra R P\ninst✝ : FaithfulSMul R P\nI : FractionalIdeal S P\nreg : IsSMulRegular P I.den\nx✝¹ x✝ : ↥↑I\nhxy : ((DistribSMul.toLinearMap R P I.den).restrict ⋯) x✝¹ = ((DistribSMul.toLinearMap R P I.den)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.FractionalIdeal.Basic | {
"line": 260,
"column": 34
} | {
"line": 260,
"column": 45
} | {
"line": 260,
"column": 46
} | [
{
"pp": "R : Type u_1\ninst✝² : CommRing R\nS : Submonoid R\nP : Type u_2\ninst✝¹ : CommRing P\ninst✝ : Algebra R P\nI : Ideal R\n⊢ coeSubmodule P I ≤ 1",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_1\ninst✝² : CommRing R\nS : Submonoid R\nP : Type u_2\ninst✝¹ : CommRing P\ninst✝ : Algebra R P\nI : Ideal R\n⊢ coeSubmodule P I ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.FractionalIdeal.Basic | {
"line": 438,
"column": 20
} | {
"line": 438,
"column": 49
} | {
"line": 438,
"column": 50
} | [
{
"pp": "R : Type u_1\ninst✝² : CommRing R\nS : Submonoid R\nP : Type u_2\ninst✝¹ : CommRing P\ninst✝ : Algebra R P\nI : FractionalIdeal S P\nh : I = 0\nx : P\nhx : x ∈ I\n⊢ x = 0",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_1\ninst✝² : CommRing R\nS : Submonoid R\nP : Type u_2\ninst✝¹ : CommRing P\ninst✝ : Algebra R P\nI : FractionalIdeal S P\nh : I = 0\nx : P\nhx : x ∈ I\n⊢ x = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Weights.IsSimple | {
"line": 261,
"column": 6
} | {
"line": 261,
"column": 22
} | {
"line": 262,
"column": 4
} | [
{
"pp": "K : Type u_1\nL : Type u_2\ninst✝⁷ : Field K\ninst✝⁶ : CharZero K\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra K L\ninst✝³ : FiniteDimensional K L\ninst✝² : IsKilling K L\nH : LieSubalgebra K L\ninst✝¹ : H.IsCartanSubalgebra\ninst✝ : IsTriangularizable K (↥H) L\nq : Submodule K (Dual K ↥H)\nχ : Weight K (↥... | [] | exact y.property | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.RingTheory.ChainOfDivisors | {
"line": 274,
"column": 4
} | {
"line": 274,
"column": 59
} | {
"line": 274,
"column": 60
} | [
{
"pp": "case neg.refine_2\nM : Type u_1\ninst✝⁴ : CommMonoidWithZero M\ninst✝³ : IsCancelMulZero M\nN : Type u_2\ninst✝² : CommMonoidWithZero N\ninst✝¹ : UniqueFactorizationMonoid N\ninst✝ : UniqueFactorizationMonoid M\nm : Associates M\nn : Associates N\nhn : n ≠ 0\nd : ↑(Set.Iic m) ≃o ↑(Set.Iic n)\ns : ℕ\nhs... | [
"case neg.refine_2\nM : Type u_1\ninst✝⁴ : CommMonoidWithZero M\ninst✝³ : IsCancelMulZero M\nN : Type u_2\ninst✝² : CommMonoidWithZero N\ninst✝¹ : UniqueFactorizationMonoid N\ninst✝ : UniqueFactorizationMonoid M\nm : Associates M\nn : Associates N\nhn : n ≠ 0\nd : ↑(Set.Iic m) ≃o ↑(Set.Iic n)\ns : ℕ\nhs : ¬s = 0\nc... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.ChainOfDivisors | {
"line": 275,
"column": 4
} | {
"line": 275,
"column": 18
} | {
"line": 276,
"column": 4
} | [
{
"pp": "case neg.refine_3\nM : Type u_1\ninst✝⁴ : CommMonoidWithZero M\ninst✝³ : IsCancelMulZero M\nN : Type u_2\ninst✝² : CommMonoidWithZero N\ninst✝¹ : UniqueFactorizationMonoid N\ninst✝ : UniqueFactorizationMonoid M\nm : Associates M\nn : Associates N\nhn : n ≠ 0\nd : ↑(Set.Iic m) ≃o ↑(Set.Iic n)\ns : ℕ\nhs... | [
"case neg.refine_3\nM : Type u_1\ninst✝⁴ : CommMonoidWithZero M\ninst✝³ : IsCancelMulZero M\nN : Type u_2\ninst✝² : CommMonoidWithZero N\ninst✝¹ : UniqueFactorizationMonoid N\ninst✝ : UniqueFactorizationMonoid M\nm : Associates M\nn : Associates N\nhn : n ≠ 0\nd : ↑(Set.Iic m) ≃o ↑(Set.Iic n)\ns : ℕ\nhs : ¬s = 0\nc... | rintro ⟨i, hr⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro | Lean.Parser.Tactic.rintro |
Mathlib.RingTheory.ChainOfDivisors | {
"line": 277,
"column": 4
} | {
"line": 277,
"column": 34
} | {
"line": 277,
"column": 35
} | [
{
"pp": "case neg.refine_3\nM : Type u_1\ninst✝⁴ : CommMonoidWithZero M\ninst✝³ : IsCancelMulZero M\nN : Type u_2\ninst✝² : CommMonoidWithZero N\ninst✝¹ : UniqueFactorizationMonoid N\ninst✝ : UniqueFactorizationMonoid M\nm : Associates M\nn : Associates N\nhn : n ≠ 0\nd : ↑(Set.Iic m) ≃o ↑(Set.Iic n)\ns : ℕ\nhs... | [
"case neg.refine_3\nM : Type u_1\ninst✝⁴ : CommMonoidWithZero M\ninst✝³ : IsCancelMulZero M\nN : Type u_2\ninst✝² : CommMonoidWithZero N\ninst✝¹ : UniqueFactorizationMonoid N\ninst✝ : UniqueFactorizationMonoid M\nm : Associates M\nn : Associates N\nhn : n ≠ 0\nd : ↑(Set.Iic m) ≃o ↑(Set.Iic n)\ns : ℕ\nhs : ¬s = 0\nc... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.ChainOfDivisors | {
"line": 337,
"column": 2
} | {
"line": 337,
"column": 36
} | {
"line": 338,
"column": 4
} | [
{
"pp": "M : Type u_1\ninst✝⁴ : CommMonoidWithZero M\ninst✝³ : IsCancelMulZero M\nN : Type u_2\ninst✝² : CommMonoidWithZero N\ninst✝¹ : UniqueFactorizationMonoid N\ninst✝ : UniqueFactorizationMonoid M\nm p : Associates M\nn : Associates N\nhn : n ≠ 0\nhp : p ∈ normalizedFactors m\nd : ↑(Set.Iic m) ≃o ↑(Set.Iic ... | [
"M : Type u_1\ninst✝⁴ : CommMonoidWithZero M\ninst✝³ : IsCancelMulZero M\nN : Type u_2\ninst✝² : CommMonoidWithZero N\ninst✝¹ : UniqueFactorizationMonoid N\ninst✝ : UniqueFactorizationMonoid M\nm p : Associates M\nn : Associates N\nhn : n ≠ 0\nhp : p ∈ normalizedFactors m\nd : ↑(Set.Iic m) ≃o ↑(Set.Iic n)\nthis : D... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Lie.Weights.IsSimple | {
"line": 288,
"column": 6
} | {
"line": 288,
"column": 54
} | {
"line": 288,
"column": 54
} | [
{
"pp": "K : Type u_1\nL : Type u_2\ninst✝⁷ : Field K\ninst✝⁶ : CharZero K\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra K L\ninst✝³ : FiniteDimensional K L\ninst✝² : IsKilling K L\nH : LieSubalgebra K L\ninst✝¹ : H.IsCartanSubalgebra\ninst✝ : IsTriangularizable K (↥H) L\nq : Submodule K (Dual K ↥H)\nχ : Weight K (↥... | [] | exact q.add_mem h_chi_in_q (q.smul_mem (-1) hαq) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.RingTheory.ChainOfDivisors | {
"line": 413,
"column": 2
} | {
"line": 413,
"column": 86
} | {
"line": 413,
"column": 87
} | [
{
"pp": "M : Type u_1\ninst✝⁶ : CommMonoidWithZero M\ninst✝⁵ : IsCancelMulZero M\nN : Type u_2\ninst✝⁴ : CommMonoidWithZero N\ninst✝³ : Subsingleton Mˣ\ninst✝² : Subsingleton Nˣ\ninst✝¹ : UniqueFactorizationMonoid M\ninst✝ : UniqueFactorizationMonoid N\nm p : M\nn : N\nhm : m ≠ 0\nhn : n ≠ 0\nhp : p ∈ normalize... | [
"M : Type u_1\ninst✝⁶ : CommMonoidWithZero M\ninst✝⁵ : IsCancelMulZero M\nN : Type u_2\ninst✝⁴ : CommMonoidWithZero N\ninst✝³ : Subsingleton Mˣ\ninst✝² : Subsingleton Nˣ\ninst✝¹ : UniqueFactorizationMonoid M\ninst✝ : UniqueFactorizationMonoid N\nm p : M\nn : N\nhm : m ≠ 0\nhn : n ≠ 0\nhp : p ∈ normalizedFactors m\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.ChainOfDivisors | {
"line": 423,
"column": 4
} | {
"line": 424,
"column": 69
} | {
"line": 424,
"column": 70
} | [
{
"pp": "M : Type u_1\ninst✝⁶ : CommMonoidWithZero M\ninst✝⁵ : IsCancelMulZero M\nN : Type u_2\ninst✝⁴ : CommMonoidWithZero N\ninst✝³ : Subsingleton Mˣ\ninst✝² : Subsingleton Nˣ\ninst✝¹ : UniqueFactorizationMonoid M\ninst✝ : UniqueFactorizationMonoid N\nm p : M\nn : N\nhm : m ≠ 0\nhn : n ≠ 0\nhp : p ∈ normalize... | [
"M : Type u_1\ninst✝⁶ : CommMonoidWithZero M\ninst✝⁵ : IsCancelMulZero M\nN : Type u_2\ninst✝⁴ : CommMonoidWithZero N\ninst✝³ : Subsingleton Mˣ\ninst✝² : Subsingleton Nˣ\ninst✝¹ : UniqueFactorizationMonoid M\ninst✝ : UniqueFactorizationMonoid N\nm p : M\nn : N\nhm : m ≠ 0\nhn : n ≠ 0\nhp : p ∈ normalizedFactors m\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Ideal.Basic | {
"line": 110,
"column": 8
} | {
"line": 110,
"column": 66
} | {
"line": 110,
"column": 67
} | [
{
"pp": "R : Type u_1\nA : Type u_2\nK : Type u_3\ninst✝⁵ : CommRing R\ninst✝⁴ : CommRing A\ninst✝³ : Field K\ninst✝² : IsDomain A\ninst✝¹ : Algebra A K\ninst✝ : IsFractionRing A K\nh : IsDedekindDomainInv A\nI✝ J✝ I J : FractionalIdeal A⁰ K\nhJ : J ≠ 0\nthis : I / J * J ≤ I\n⊢ I / J ≤ I * J⁻¹",
"ppTerm": "... | [
"R : Type u_1\nA : Type u_2\nK : Type u_3\ninst✝⁵ : CommRing R\ninst✝⁴ : CommRing A\ninst✝³ : Field K\ninst✝² : IsDomain A\ninst✝¹ : Algebra A K\ninst✝ : IsFractionRing A K\nh : IsDedekindDomainInv A\nI✝ J✝ I J : FractionalIdeal A⁰ K\nhJ : J ≠ 0\nthis : I / J * J ≤ I\n⊢ I / J ≤ I * J⁻¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Ideal.Basic | {
"line": 144,
"column": 2
} | {
"line": 144,
"column": 94
} | {
"line": 146,
"column": 2
} | [
{
"pp": "A : Type u_2\ninst✝¹ : CommRing A\ninst✝ : IsDomain A\nh : IsDedekindDomainInv A\nthis : CommGroupWithZero (FractionalIdeal A⁰ (FractionRing A)) := h.commGroupWithZero\nP : Ideal A\nP_ne : P ≠ ⊥\nhP : P.IsPrime\nM : Ideal A\nhM : P < M\nP'_ne : ↑P ≠ 0\n⊢ M = ⊤",
"ppTerm": "?m.72",
"assigned": t... | [
"A : Type u_2\ninst✝¹ : CommRing A\ninst✝ : IsDomain A\nh : IsDedekindDomainInv A\nthis : CommGroupWithZero (FractionalIdeal A⁰ (FractionRing A)) := h.commGroupWithZero\nP : Ideal A\nP_ne : P ≠ ⊥\nhP : P.IsPrime\nM : Ideal A\nhM : P < M\nP'_ne : ↑P ≠ 0\nM'_ne : ↑M ≠ 0\n⊢ M = ⊤"
] | have M'_ne : (M : FractionalIdeal A⁰ (FractionRing A)) ≠ 0 := coeIdeal_ne_zero.mpr hM.ne_bot | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.RingTheory.FractionalIdeal.Operations | {
"line": 172,
"column": 24
} | {
"line": 176,
"column": 20
} | {
"line": 178,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝³ : CommRing R\nS : Submonoid R\nP : Type u_2\ninst✝² : CommRing P\ninst✝¹ : Algebra R P\ninst✝ : IsLocalization S P\nI : Submodule R P\nhI : I.FG\n⊢ IsFractional S I",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
"IsLocalization.IsInteger",
"Eq.mpr... | [] | by
rcases hI with ⟨I, rfl⟩
rcases exist_integer_multiples_of_finset S I with ⟨⟨s, hs1⟩, hs⟩
rw [isFractional_span_iff]
exact ⟨s, hs1, hs⟩ | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.FractionalIdeal.Operations | {
"line": 180,
"column": 47
} | {
"line": 180,
"column": 58
} | {
"line": 180,
"column": 59
} | [
{
"pp": "R : Type u_1\ninst✝² : CommRing R\nS : Submonoid R\nP : Type u_2\ninst✝¹ : CommRing P\ninst✝ : Algebra R P\nI J : FractionalIdeal S P\nx : P\nhx : x ∈ I * J\n⊢ x ∈ ↑I * ↑J",
"ppTerm": "?m.61",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_1\ninst✝² : CommRing R\nS : Submonoid R\nP : Type u_2\ninst✝¹ : CommRing P\ninst✝ : Algebra R P\nI J : FractionalIdeal S P\nx : P\nhx : x ∈ I * J\n⊢ x ∈ ↑I * ↑J"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.FractionalIdeal.Operations | {
"line": 232,
"column": 22
} | {
"line": 232,
"column": 37
} | {
"line": 232,
"column": 38
} | [
{
"pp": "R : Type u_1\ninst✝⁶ : CommRing R\nS : Submonoid R\nP : Type u_2\ninst✝⁵ : CommRing P\ninst✝⁴ : Algebra R P\nP' : Type u_3\ninst✝³ : CommRing P'\ninst✝² : Algebra R P'\ninst✝¹ : IsLocalization S P\ninst✝ : IsLocalization S P'\nI : FractionalIdeal S P\nx : P'\n⊢ x ∈\n (mapEquiv\n (let __sr... | [
"R : Type u_1\ninst✝⁶ : CommRing R\nS : Submonoid R\nP : Type u_2\ninst✝⁵ : CommRing P\ninst✝⁴ : Algebra R P\nP' : Type u_3\ninst✝³ : CommRing P'\ninst✝² : Algebra R P'\ninst✝¹ : IsLocalization S P\ninst✝ : IsLocalization S P'\nI : FractionalIdeal S P\nx : P'\n⊢ x ∈\n map\n (↑(let __src := ringEquivOfRi... | mapEquiv_apply, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.DedekindDomain.Ideal.Basic | {
"line": 282,
"column": 2
} | {
"line": 282,
"column": 22
} | {
"line": 283,
"column": 2
} | [
{
"pp": "A : Type u_2\nK : Type u_3\ninst✝⁴ : CommRing A\ninst✝³ : Field K\ninst✝² : Algebra A K\ninst✝¹ : IsFractionRing A K\ninst✝ : IsDedekindDomain A\nI : Ideal A\nhI0 : I ≠ ⊥\nhI : (↑I * (↑I)⁻¹)⁻¹ ≤ 1\nJ : Ideal A\nhJ : ↑J = ↑I * (↑I)⁻¹\n⊢ ↑I * (↑I)⁻¹ = 1",
"ppTerm": "?m.89",
"assigned": true,
... | [
"case pos\nA : Type u_2\nK : Type u_3\ninst✝⁴ : CommRing A\ninst✝³ : Field K\ninst✝² : Algebra A K\ninst✝¹ : IsFractionRing A K\ninst✝ : IsDedekindDomain A\nI : Ideal A\nhI0 : I ≠ ⊥\nhI : (↑I * (↑I)⁻¹)⁻¹ ≤ 1\nJ : Ideal A\nhJ : ↑J = ↑I * (↑I)⁻¹\nhJ0 : J = ⊥\n⊢ ↑I * (↑I)⁻¹ = 1",
"case neg\nA : Type u_2\nK : Type u_... | by_cases hJ0 : J = ⊥ | «_aux_Init_ByCases___macroRules_tacticBy_cases_:__2» | «tacticBy_cases_:_» |
Mathlib.RingTheory.FractionalIdeal.Operations | {
"line": 239,
"column": 67
} | {
"line": 239,
"column": 82
} | {
"line": 240,
"column": 8
} | [
{
"pp": "R : Type u_1\ninst✝⁶ : CommRing R\nS : Submonoid R\nP : Type u_2\ninst✝⁵ : CommRing P\ninst✝⁴ : Algebra R P\nP' : Type u_3\ninst✝³ : CommRing P'\ninst✝² : Algebra R P'\ninst✝¹ : IsLocalization S P\ninst✝ : IsLocalization S P'\nI : FractionalIdeal S P'\nx : P\n⊢ x ∈\n (mapEquiv\n (let __sr... | [
"R : Type u_1\ninst✝⁶ : CommRing R\nS : Submonoid R\nP : Type u_2\ninst✝⁵ : CommRing P\ninst✝⁴ : Algebra R P\nP' : Type u_3\ninst✝³ : CommRing P'\ninst✝² : Algebra R P'\ninst✝¹ : IsLocalization S P\ninst✝ : IsLocalization S P'\nI : FractionalIdeal S P'\nx : P\n⊢ x ∈\n map\n (↑(let __src := ringEquivOfRi... | mapEquiv_apply, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.FractionalIdeal.Operations | {
"line": 238,
"column": 33
} | {
"line": 241,
"column": 80
} | {
"line": 243,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝⁶ : CommRing R\nS : Submonoid R\nP : Type u_2\ninst✝⁵ : CommRing P\ninst✝⁴ : Algebra R P\nP' : Type u_3\ninst✝³ : CommRing P'\ninst✝² : Algebra R P'\ninst✝¹ : IsLocalization S P\ninst✝ : IsLocalization S P'\nI : FractionalIdeal S P'\nx : P\n⊢ x ∈ (canonicalEquiv S P P').symm I ↔ x ∈ ... | [] | by
rw [mem_canonicalEquiv_apply, canonicalEquiv, mapEquiv_symm, mapEquiv_apply,
mem_map]
exact ⟨fun ⟨y, mem, Eq⟩ => ⟨y, mem, Eq⟩, fun ⟨y, mem, Eq⟩ => ⟨y, mem, Eq⟩⟩ | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.DedekindDomain.Ideal.Basic | {
"line": 303,
"column": 35
} | {
"line": 305,
"column": 28
} | {
"line": 308,
"column": 2
} | [
{
"pp": "A : Type u_2\nK : Type u_3\ninst✝⁴ : CommRing A\ninst✝³ : Field K\ninst✝² : Algebra A K\ninst✝¹ : IsFractionRing A K\ninst✝ : IsDedekindDomain A\nI : Ideal A\nhI0 : I ≠ ⊥\nhJ0 : ¬↑I * (↑I)⁻¹ = 0\nx : K\nhx : x ∈ (↑I * (↑I)⁻¹)⁻¹\nthis : x ∈ integralClosure A K\n⊢ x ∈ 1",
"ppTerm": "?m.86",
"assi... | [] | by
rwa [IsIntegrallyClosed.integralClosure_eq_bot, Algebra.mem_bot, Set.mem_range,
← mem_one_iff] at this | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.FractionalIdeal.Operations | {
"line": 289,
"column": 29
} | {
"line": 289,
"column": 45
} | {
"line": 289,
"column": 46
} | [
{
"pp": "R : Type u_1\ninst✝⁴ : CommRing R\nK : Type u_3\ninst✝³ : Field K\ninst✝² : Algebra R K\ninst✝¹ : IsFractionRing R K\nI : FractionalIdeal R⁰ K\ninst✝ : Nontrivial R\nhI : I ≠ 0\n⊢ ?m.52 < ?m.53",
"ppTerm": "?m.54",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals"... | [
"R : Type u_1\ninst✝⁴ : CommRing R\nK : Type u_3\ninst✝³ : Field K\ninst✝² : Algebra R K\ninst✝¹ : IsFractionRing R K\nI : FractionalIdeal R⁰ K\ninst✝ : Nontrivial R\nhI : I ≠ 0\n⊢ ?m.52 < ?m.53"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.