module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 177,
"column": 34
} | {
"line": 177,
"column": 40
} | {
"line": 179,
"column": 0
} | [
{
"pp": "⊢ A 1 = !![2]",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Matrix.of",
"Int.instDecidableEq",
"id",
"Equiv",
"instOfNatNat",
"Int",
"Ca... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 177,
"column": 34
} | {
"line": 177,
"column": 40
} | {
"line": 179,
"column": 0
} | [
{
"pp": "⊢ A 1 = !![2]",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Matrix.of",
"Int.instDecidableEq",
"id",
"Equiv",
"instOfNatNat",
"Int",
"Ca... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 180,
"column": 39
} | {
"line": 180,
"column": 45
} | {
"line": 182,
"column": 0
} | [
{
"pp": "⊢ A 2 = !![2, -1; -1, 2]",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Matrix.of",
"Int.instDecidableEq",
"id",
"Equiv",
"Int.instNegInt",
"in... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 180,
"column": 39
} | {
"line": 180,
"column": 45
} | {
"line": 182,
"column": 0
} | [
{
"pp": "⊢ A 2 = !![2, -1; -1, 2]",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Matrix.of",
"Int.instDecidableEq",
"id",
"Equiv",
"Int.instNegInt",
"in... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 180,
"column": 39
} | {
"line": 180,
"column": 45
} | {
"line": 182,
"column": 0
} | [
{
"pp": "⊢ A 2 = !![2, -1; -1, 2]",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Matrix.of",
"Int.instDecidableEq",
"id",
"Equiv",
"Int.instNegInt",
"in... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 184,
"column": 45
} | {
"line": 184,
"column": 51
} | {
"line": 186,
"column": 0
} | [
{
"pp": "⊢ A 3 = !![2, -1, 0; -1, 2, -1; 0, -1, 2]",
"ppTerm": "?m.64",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Matrix.of",
"Int.instDecidableEq",
"id",
"Equiv",
"Int.instN... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 184,
"column": 45
} | {
"line": 184,
"column": 51
} | {
"line": 186,
"column": 0
} | [
{
"pp": "⊢ A 3 = !![2, -1, 0; -1, 2, -1; 0, -1, 2]",
"ppTerm": "?m.64",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Matrix.of",
"Int.instDecidableEq",
"id",
"Equiv",
"Int.instN... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 184,
"column": 45
} | {
"line": 184,
"column": 51
} | {
"line": 186,
"column": 0
} | [
{
"pp": "⊢ A 3 = !![2, -1, 0; -1, 2, -1; 0, -1, 2]",
"ppTerm": "?m.64",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Matrix.of",
"Int.instDecidableEq",
"id",
"Equiv",
"Int.instN... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 186,
"column": 32
} | {
"line": 186,
"column": 38
} | {
"line": 188,
"column": 0
} | [
{
"pp": "⊢ B 1 = A 1",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Int.instDecidableEq",
"id",
"instOfNatNat",
"Int",
"CartanMatrix.A",
"Fin.fintype",
"Bool.true",
"Nat"... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 186,
"column": 32
} | {
"line": 186,
"column": 38
} | {
"line": 188,
"column": 0
} | [
{
"pp": "⊢ B 1 = A 1",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Int.instDecidableEq",
"id",
"instOfNatNat",
"Int",
"CartanMatrix.A",
"Fin.fintype",
"Bool.true",
"Nat"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 186,
"column": 32
} | {
"line": 186,
"column": 38
} | {
"line": 188,
"column": 0
} | [
{
"pp": "⊢ B 1 = A 1",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Int.instDecidableEq",
"id",
"instOfNatNat",
"Int",
"CartanMatrix.A",
"Fin.fintype",
"Bool.true",
"Nat"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 188,
"column": 32
} | {
"line": 188,
"column": 38
} | {
"line": 190,
"column": 0
} | [
{
"pp": "⊢ C 1 = A 1",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"CartanMatrix.C",
"Int.instDecidableEq",
"id",
"instOfNatNat",
"Int",
"CartanMatrix.A",
"Fin.fintype",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 188,
"column": 32
} | {
"line": 188,
"column": 38
} | {
"line": 190,
"column": 0
} | [
{
"pp": "⊢ C 1 = A 1",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"CartanMatrix.C",
"Int.instDecidableEq",
"id",
"instOfNatNat",
"Int",
"CartanMatrix.A",
"Fin.fintype",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 188,
"column": 32
} | {
"line": 188,
"column": 38
} | {
"line": 190,
"column": 0
} | [
{
"pp": "⊢ C 1 = A 1",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"CartanMatrix.C",
"Int.instDecidableEq",
"id",
"instOfNatNat",
"Int",
"CartanMatrix.A",
"Fin.fintype",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 190,
"column": 32
} | {
"line": 190,
"column": 38
} | {
"line": 192,
"column": 0
} | [
{
"pp": "⊢ D 1 = A 1",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Int.instDecidableEq",
"id",
"instOfNatNat",
"Int",
"CartanMatrix.A",
"Fin.fintype",
"Bool.true",
"Nat"... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 190,
"column": 32
} | {
"line": 190,
"column": 38
} | {
"line": 192,
"column": 0
} | [
{
"pp": "⊢ D 1 = A 1",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Int.instDecidableEq",
"id",
"instOfNatNat",
"Int",
"CartanMatrix.A",
"Fin.fintype",
"Bool.true",
"Nat"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 190,
"column": 32
} | {
"line": 190,
"column": 38
} | {
"line": 192,
"column": 0
} | [
{
"pp": "⊢ D 1 = A 1",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Int.instDecidableEq",
"id",
"instOfNatNat",
"Int",
"CartanMatrix.A",
"Fin.fintype",
"Bool.true",
"Nat"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 193,
"column": 37
} | {
"line": 193,
"column": 43
} | {
"line": 195,
"column": 0
} | [
{
"pp": "⊢ D 2 = !![2, 0; 0, 2]",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Matrix.of",
"Int.instDecidableEq",
"id",
"Equiv",
"instOfNatNat",
"Int",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 193,
"column": 37
} | {
"line": 193,
"column": 43
} | {
"line": 195,
"column": 0
} | [
{
"pp": "⊢ D 2 = !![2, 0; 0, 2]",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Matrix.of",
"Int.instDecidableEq",
"id",
"Equiv",
"instOfNatNat",
"Int",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 193,
"column": 37
} | {
"line": 193,
"column": 43
} | {
"line": 195,
"column": 0
} | [
{
"pp": "⊢ D 2 = !![2, 0; 0, 2]",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Matrix.of",
"Int.instDecidableEq",
"id",
"Equiv",
"instOfNatNat",
"Int",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 196,
"column": 39
} | {
"line": 196,
"column": 45
} | {
"line": 198,
"column": 0
} | [
{
"pp": "⊢ B 2 = !![2, -2; -1, 2]",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Matrix.of",
"Int.instDecidableEq",
"id",
"Equiv",
"Int.instNegInt",
"in... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 196,
"column": 39
} | {
"line": 196,
"column": 45
} | {
"line": 198,
"column": 0
} | [
{
"pp": "⊢ B 2 = !![2, -2; -1, 2]",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Matrix.of",
"Int.instDecidableEq",
"id",
"Equiv",
"Int.instNegInt",
"in... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 196,
"column": 39
} | {
"line": 196,
"column": 45
} | {
"line": 198,
"column": 0
} | [
{
"pp": "⊢ B 2 = !![2, -2; -1, 2]",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Matrix.of",
"Int.instDecidableEq",
"id",
"Equiv",
"Int.instNegInt",
"in... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 199,
"column": 39
} | {
"line": 199,
"column": 45
} | {
"line": 201,
"column": 0
} | [
{
"pp": "⊢ C 2 = !![2, -1; -2, 2]",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"CartanMatrix.C",
"Matrix.of",
"Int.instDecidableEq",
"id",
"Equiv",
"In... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 199,
"column": 39
} | {
"line": 199,
"column": 45
} | {
"line": 201,
"column": 0
} | [
{
"pp": "⊢ C 2 = !![2, -1; -2, 2]",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"CartanMatrix.C",
"Matrix.of",
"Int.instDecidableEq",
"id",
"Equiv",
"In... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 199,
"column": 39
} | {
"line": 199,
"column": 45
} | {
"line": 201,
"column": 0
} | [
{
"pp": "⊢ C 2 = !![2, -1; -2, 2]",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"CartanMatrix.C",
"Matrix.of",
"Int.instDecidableEq",
"id",
"Equiv",
"In... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 203,
"column": 45
} | {
"line": 203,
"column": 51
} | {
"line": 205,
"column": 0
} | [
{
"pp": "⊢ D 3 = !![2, -1, -1; -1, 2, 0; -1, 0, 2]",
"ppTerm": "?m.64",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Matrix.of",
"Int.instDecidableEq",
"id",
"Equiv",
"Int.instN... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 203,
"column": 45
} | {
"line": 203,
"column": 51
} | {
"line": 205,
"column": 0
} | [
{
"pp": "⊢ D 3 = !![2, -1, -1; -1, 2, 0; -1, 0, 2]",
"ppTerm": "?m.64",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Matrix.of",
"Int.instDecidableEq",
"id",
"Equiv",
"Int.instN... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 203,
"column": 45
} | {
"line": 203,
"column": 51
} | {
"line": 205,
"column": 0
} | [
{
"pp": "⊢ D 3 = !![2, -1, -1; -1, 2, 0; -1, 0, 2]",
"ppTerm": "?m.64",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Matrix.of",
"Int.instDecidableEq",
"id",
"Equiv",
"Int.instN... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 205,
"column": 61
} | {
"line": 205,
"column": 67
} | {
"line": 207,
"column": 0
} | [
{
"pp": "⊢ (reindex ((↑[0, 1]).formPerm ⋯) ((↑[0, 1]).formPerm ⋯)) (D 3) = A 3",
"ppTerm": "?m.44",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Equiv.instEquivLike",
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"instDecidableEqFin",
"Int.instDec... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 205,
"column": 61
} | {
"line": 205,
"column": 67
} | {
"line": 207,
"column": 0
} | [
{
"pp": "⊢ (reindex ((↑[0, 1]).formPerm ⋯) ((↑[0, 1]).formPerm ⋯)) (D 3) = A 3",
"ppTerm": "?m.44",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Equiv.instEquivLike",
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"instDecidableEqFin",
"Int.instDec... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 205,
"column": 61
} | {
"line": 205,
"column": 67
} | {
"line": 207,
"column": 0
} | [
{
"pp": "⊢ (reindex ((↑[0, 1]).formPerm ⋯) ((↑[0, 1]).formPerm ⋯)) (D 3) = A 3",
"ppTerm": "?m.44",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Equiv.instEquivLike",
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"instDecidableEqFin",
"Int.instDec... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 210,
"column": 48
} | {
"line": 210,
"column": 54
} | {
"line": 214,
"column": 0
} | [
{
"pp": "⊢ D 4 = !![2, -1, 0, 0; -1, 2, -1, -1; 0, -1, 2, 0; 0, -1, 0, 2]",
"ppTerm": "?m.99",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Matrix.of",
"Int.instDecidableEq",
"id",
"E... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 210,
"column": 48
} | {
"line": 210,
"column": 54
} | {
"line": 214,
"column": 0
} | [
{
"pp": "⊢ D 4 = !![2, -1, 0, 0; -1, 2, -1, -1; 0, -1, 2, 0; 0, -1, 0, 2]",
"ppTerm": "?m.99",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Matrix.of",
"Int.instDecidableEq",
"id",
"E... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 210,
"column": 48
} | {
"line": 210,
"column": 54
} | {
"line": 214,
"column": 0
} | [
{
"pp": "⊢ D 4 = !![2, -1, 0, 0; -1, 2, -1, -1; 0, -1, 2, 0; 0, -1, 0, 2]",
"ppTerm": "?m.99",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Matrix.of",
"Int.instDecidableEq",
"id",
"E... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 216,
"column": 71
} | {
"line": 216,
"column": 77
} | {
"line": 218,
"column": 0
} | [
{
"pp": "case «0»\n⊢ E₆ ((fun i ↦ i) ⟨0, ⋯⟩) ((fun i ↦ i) ⟨0, ⋯⟩) = 2",
"ppTerm": "?«0»",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Nat.le_refl",
"Int.instDecidableEq",
"Fin.mk",
"id",
"instOfNatNat",
"Int",
"Nat.le_of_lt",
"Bool... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 216,
"column": 71
} | {
"line": 216,
"column": 77
} | {
"line": 218,
"column": 0
} | [
{
"pp": "case «1»\n⊢ E₆ ((fun i ↦ i) ⟨1, ⋯⟩) ((fun i ↦ i) ⟨1, ⋯⟩) = 2",
"ppTerm": "?«1»",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Nat.le_refl",
"Int.instDecidableEq",
"Fin.mk",
"id",
"instOfNatNat",
"Int",
"Nat.le_of_lt",
"Bool... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 216,
"column": 71
} | {
"line": 216,
"column": 77
} | {
"line": 218,
"column": 0
} | [
{
"pp": "case «2»\n⊢ E₆ ((fun i ↦ i) ⟨2, ⋯⟩) ((fun i ↦ i) ⟨2, ⋯⟩) = 2",
"ppTerm": "?«2»",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Nat.le_refl",
"Int.instDecidableEq",
"Fin.mk",
"id",
"instOfNatNat",
"Int",
"Nat.le_of_lt",
"Bool... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 216,
"column": 71
} | {
"line": 216,
"column": 77
} | {
"line": 218,
"column": 0
} | [
{
"pp": "case «3»\n⊢ E₆ ((fun i ↦ i) ⟨3, ⋯⟩) ((fun i ↦ i) ⟨3, ⋯⟩) = 2",
"ppTerm": "?«3»",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Nat.le_refl",
"Int.instDecidableEq",
"Fin.mk",
"id",
"instOfNatNat",
"Int",
"Nat.le_of_lt",
"Bool... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 216,
"column": 71
} | {
"line": 216,
"column": 77
} | {
"line": 218,
"column": 0
} | [
{
"pp": "case «4»\n⊢ E₆ ((fun i ↦ i) ⟨4, ⋯⟩) ((fun i ↦ i) ⟨4, ⋯⟩) = 2",
"ppTerm": "?«4»",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Nat.le_refl",
"Int.instDecidableEq",
"Fin.mk",
"id",
"instOfNatNat",
"Int",
"Nat.le_of_lt",
"Bool... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 216,
"column": 71
} | {
"line": 216,
"column": 77
} | {
"line": 218,
"column": 0
} | [
{
"pp": "case «5»\n⊢ E₆ ((fun i ↦ i) ⟨5, ⋯⟩) ((fun i ↦ i) ⟨5, ⋯⟩) = 2",
"ppTerm": "?«5»",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Nat.le_refl",
"Int.instDecidableEq",
"Fin.mk",
"id",
"instOfNatNat",
"Int",
"Bool.true",
"instOfN... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 218,
"column": 71
} | {
"line": 218,
"column": 77
} | {
"line": 220,
"column": 0
} | [
{
"pp": "case «0»\n⊢ E₇ ((fun i ↦ i) ⟨0, ⋯⟩) ((fun i ↦ i) ⟨0, ⋯⟩) = 2",
"ppTerm": "?«0»",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"CartanMatrix.E₇",
"Nat.le_refl",
"Int.instDecidableEq",
"Fin.mk",
"id",
"instOfNatNat",
"Int",
"N... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 218,
"column": 71
} | {
"line": 218,
"column": 77
} | {
"line": 220,
"column": 0
} | [
{
"pp": "case «1»\n⊢ E₇ ((fun i ↦ i) ⟨1, ⋯⟩) ((fun i ↦ i) ⟨1, ⋯⟩) = 2",
"ppTerm": "?«1»",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"CartanMatrix.E₇",
"Nat.le_refl",
"Int.instDecidableEq",
"Fin.mk",
"id",
"instOfNatNat",
"Int",
"N... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 218,
"column": 71
} | {
"line": 218,
"column": 77
} | {
"line": 220,
"column": 0
} | [
{
"pp": "case «2»\n⊢ E₇ ((fun i ↦ i) ⟨2, ⋯⟩) ((fun i ↦ i) ⟨2, ⋯⟩) = 2",
"ppTerm": "?«2»",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"CartanMatrix.E₇",
"Nat.le_refl",
"Int.instDecidableEq",
"Fin.mk",
"id",
"instOfNatNat",
"Int",
"N... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 218,
"column": 71
} | {
"line": 218,
"column": 77
} | {
"line": 220,
"column": 0
} | [
{
"pp": "case «3»\n⊢ E₇ ((fun i ↦ i) ⟨3, ⋯⟩) ((fun i ↦ i) ⟨3, ⋯⟩) = 2",
"ppTerm": "?«3»",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"CartanMatrix.E₇",
"Nat.le_refl",
"Int.instDecidableEq",
"Fin.mk",
"id",
"instOfNatNat",
"Int",
"N... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 218,
"column": 71
} | {
"line": 218,
"column": 77
} | {
"line": 220,
"column": 0
} | [
{
"pp": "case «4»\n⊢ E₇ ((fun i ↦ i) ⟨4, ⋯⟩) ((fun i ↦ i) ⟨4, ⋯⟩) = 2",
"ppTerm": "?«4»",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"CartanMatrix.E₇",
"Nat.le_refl",
"Int.instDecidableEq",
"Fin.mk",
"id",
"instOfNatNat",
"Int",
"N... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 218,
"column": 71
} | {
"line": 218,
"column": 77
} | {
"line": 220,
"column": 0
} | [
{
"pp": "case «5»\n⊢ E₇ ((fun i ↦ i) ⟨5, ⋯⟩) ((fun i ↦ i) ⟨5, ⋯⟩) = 2",
"ppTerm": "?«5»",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"CartanMatrix.E₇",
"Nat.le_refl",
"Int.instDecidableEq",
"Fin.mk",
"id",
"instOfNatNat",
"Int",
"N... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 218,
"column": 71
} | {
"line": 218,
"column": 77
} | {
"line": 220,
"column": 0
} | [
{
"pp": "case «6»\n⊢ E₇ ((fun i ↦ i) ⟨6, ⋯⟩) ((fun i ↦ i) ⟨6, ⋯⟩) = 2",
"ppTerm": "?«6»",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"CartanMatrix.E₇",
"Nat.le_refl",
"Int.instDecidableEq",
"Fin.mk",
"id",
"instOfNatNat",
"Int",
"B... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 220,
"column": 71
} | {
"line": 220,
"column": 77
} | {
"line": 222,
"column": 0
} | [
{
"pp": "case «0»\n⊢ E₈ ((fun i ↦ i) ⟨0, ⋯⟩) ((fun i ↦ i) ⟨0, ⋯⟩) = 2",
"ppTerm": "?«0»",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Nat.le_refl",
"Int.instDecidableEq",
"Fin.mk",
"id",
"CartanMatrix.E₈",
"instOfNatNat",
"Int",
"N... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 271,
"column": 2
} | {
"line": 278,
"column": 51
} | {
"line": 280,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx y : α\nhy : y ∈ p.toList x\n⊢ (p.toList x).next y hy = p y",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Equiv.Perm.SameCycle.exists_pow_eq_of_mem_support",
"Equiv.Perm.mem_toList_iff",
"Eq... | [] | rw [mem_toList_iff] at hy
obtain ⟨k, hk, hk'⟩ := hy.left.exists_pow_eq_of_mem_support hy.right
rw [← getElem_toList p x k (by simpa using hk)] at hk'
simp_rw [← hk']
rw [next_getElem _ (nodup_toList _ _), getElem_toList, getElem_toList, ← mul_apply, ← pow_succ']
simp_rw [length_toList]
rw [← pow_mod_orderOf... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 220,
"column": 71
} | {
"line": 220,
"column": 77
} | {
"line": 222,
"column": 0
} | [
{
"pp": "case «1»\n⊢ E₈ ((fun i ↦ i) ⟨1, ⋯⟩) ((fun i ↦ i) ⟨1, ⋯⟩) = 2",
"ppTerm": "?«1»",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Nat.le_refl",
"Int.instDecidableEq",
"Fin.mk",
"id",
"CartanMatrix.E₈",
"instOfNatNat",
"Int",
"N... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 220,
"column": 71
} | {
"line": 220,
"column": 77
} | {
"line": 222,
"column": 0
} | [
{
"pp": "case «2»\n⊢ E₈ ((fun i ↦ i) ⟨2, ⋯⟩) ((fun i ↦ i) ⟨2, ⋯⟩) = 2",
"ppTerm": "?«2»",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Nat.le_refl",
"Int.instDecidableEq",
"Fin.mk",
"id",
"CartanMatrix.E₈",
"instOfNatNat",
"Int",
"N... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 220,
"column": 71
} | {
"line": 220,
"column": 77
} | {
"line": 222,
"column": 0
} | [
{
"pp": "case «3»\n⊢ E₈ ((fun i ↦ i) ⟨3, ⋯⟩) ((fun i ↦ i) ⟨3, ⋯⟩) = 2",
"ppTerm": "?«3»",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Nat.le_refl",
"Int.instDecidableEq",
"Fin.mk",
"id",
"CartanMatrix.E₈",
"instOfNatNat",
"Int",
"N... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 220,
"column": 71
} | {
"line": 220,
"column": 77
} | {
"line": 222,
"column": 0
} | [
{
"pp": "case «4»\n⊢ E₈ ((fun i ↦ i) ⟨4, ⋯⟩) ((fun i ↦ i) ⟨4, ⋯⟩) = 2",
"ppTerm": "?«4»",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Nat.le_refl",
"Int.instDecidableEq",
"Fin.mk",
"id",
"CartanMatrix.E₈",
"instOfNatNat",
"Int",
"N... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 220,
"column": 71
} | {
"line": 220,
"column": 77
} | {
"line": 222,
"column": 0
} | [
{
"pp": "case «5»\n⊢ E₈ ((fun i ↦ i) ⟨5, ⋯⟩) ((fun i ↦ i) ⟨5, ⋯⟩) = 2",
"ppTerm": "?«5»",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Nat.le_refl",
"Int.instDecidableEq",
"Fin.mk",
"id",
"CartanMatrix.E₈",
"instOfNatNat",
"Int",
"N... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 220,
"column": 71
} | {
"line": 220,
"column": 77
} | {
"line": 222,
"column": 0
} | [
{
"pp": "case «6»\n⊢ E₈ ((fun i ↦ i) ⟨6, ⋯⟩) ((fun i ↦ i) ⟨6, ⋯⟩) = 2",
"ppTerm": "?«6»",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Nat.le_refl",
"Int.instDecidableEq",
"Fin.mk",
"id",
"CartanMatrix.E₈",
"instOfNatNat",
"Int",
"N... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 220,
"column": 71
} | {
"line": 220,
"column": 77
} | {
"line": 222,
"column": 0
} | [
{
"pp": "case «7»\n⊢ E₈ ((fun i ↦ i) ⟨7, ⋯⟩) ((fun i ↦ i) ⟨7, ⋯⟩) = 2",
"ppTerm": "?«7»",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Nat.le_refl",
"Int.instDecidableEq",
"Fin.mk",
"id",
"CartanMatrix.E₈",
"instOfNatNat",
"Int",
"B... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.GroupTheory.Perm.Cycle.Concrete | {
"line": 271,
"column": 2
} | {
"line": 278,
"column": 51
} | {
"line": 280,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx y : α\nhy : y ∈ p.toList x\n⊢ (p.toList x).next y hy = p y",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Equiv.Perm.SameCycle.exists_pow_eq_of_mem_support",
"Equiv.Perm.mem_toList_iff",
"Eq... | [] | rw [mem_toList_iff] at hy
obtain ⟨k, hk, hk'⟩ := hy.left.exists_pow_eq_of_mem_support hy.right
rw [← getElem_toList p x k (by simpa using hk)] at hk'
simp_rw [← hk']
rw [next_getElem _ (nodup_toList _ _), getElem_toList, getElem_toList, ← mul_apply, ← pow_succ']
simp_rw [length_toList]
rw [← pow_mod_orderOf... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 222,
"column": 71
} | {
"line": 222,
"column": 77
} | {
"line": 224,
"column": 0
} | [
{
"pp": "case «0»\n⊢ F₄ ((fun i ↦ i) ⟨0, ⋯⟩) ((fun i ↦ i) ⟨0, ⋯⟩) = 2",
"ppTerm": "?«0»",
"assigned": true,
"usedConstants": [
"CartanMatrix.F₄",
"of_decide_eq_true",
"Nat.le_refl",
"Int.instDecidableEq",
"Fin.mk",
"id",
"instOfNatNat",
"Int",
"N... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 222,
"column": 71
} | {
"line": 222,
"column": 77
} | {
"line": 224,
"column": 0
} | [
{
"pp": "case «1»\n⊢ F₄ ((fun i ↦ i) ⟨1, ⋯⟩) ((fun i ↦ i) ⟨1, ⋯⟩) = 2",
"ppTerm": "?«1»",
"assigned": true,
"usedConstants": [
"CartanMatrix.F₄",
"of_decide_eq_true",
"Nat.le_refl",
"Int.instDecidableEq",
"Fin.mk",
"id",
"instOfNatNat",
"Int",
"N... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 222,
"column": 71
} | {
"line": 222,
"column": 77
} | {
"line": 224,
"column": 0
} | [
{
"pp": "case «2»\n⊢ F₄ ((fun i ↦ i) ⟨2, ⋯⟩) ((fun i ↦ i) ⟨2, ⋯⟩) = 2",
"ppTerm": "?«2»",
"assigned": true,
"usedConstants": [
"CartanMatrix.F₄",
"of_decide_eq_true",
"Nat.le_refl",
"Int.instDecidableEq",
"Fin.mk",
"id",
"instOfNatNat",
"Int",
"N... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 222,
"column": 71
} | {
"line": 222,
"column": 77
} | {
"line": 224,
"column": 0
} | [
{
"pp": "case «3»\n⊢ F₄ ((fun i ↦ i) ⟨3, ⋯⟩) ((fun i ↦ i) ⟨3, ⋯⟩) = 2",
"ppTerm": "?«3»",
"assigned": true,
"usedConstants": [
"CartanMatrix.F₄",
"of_decide_eq_true",
"Nat.le_refl",
"Int.instDecidableEq",
"Fin.mk",
"id",
"instOfNatNat",
"Int",
"B... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 224,
"column": 71
} | {
"line": 224,
"column": 77
} | {
"line": 227,
"column": 0
} | [
{
"pp": "case «0»\n⊢ G₂ ((fun i ↦ i) ⟨0, ⋯⟩) ((fun i ↦ i) ⟨0, ⋯⟩) = 2",
"ppTerm": "?«0»",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Nat.le_refl",
"CartanMatrix.G₂",
"Int.instDecidableEq",
"Fin.mk",
"id",
"instOfNatNat",
"Int",
"N... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 224,
"column": 71
} | {
"line": 224,
"column": 77
} | {
"line": 227,
"column": 0
} | [
{
"pp": "case «1»\n⊢ G₂ ((fun i ↦ i) ⟨1, ⋯⟩) ((fun i ↦ i) ⟨1, ⋯⟩) = 2",
"ppTerm": "?«1»",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Nat.le_refl",
"CartanMatrix.G₂",
"Int.instDecidableEq",
"Fin.mk",
"id",
"instOfNatNat",
"Int",
"B... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Algebra.Lie.LieTheorem | {
"line": 56,
"column": 2
} | {
"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 ... | [] | rw [mem_weightSpace] at hv ⊢
intro a
rcases eq_or_ne v 0 with (rfl | hv')
· simp only [lie_zero, smul_zero]
suffices χ ⁅z, a⁆ = 0 by
rw [leibniz_lie, hv a, lie_smul, lie_swap_lie, hv, this, zero_smul, neg_zero, zero_add]
let U' : ℕ →o Submodule R V :=
{ toFun n := Submodule.span R {((π z)^i) v | i < n},... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Lie.LieTheorem | {
"line": 56,
"column": 2
} | {
"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 ... | [] | rw [mem_weightSpace] at hv ⊢
intro a
rcases eq_or_ne v 0 with (rfl | hv')
· simp only [lie_zero, smul_zero]
suffices χ ⁅z, a⁆ = 0 by
rw [leibniz_lie, hv a, lie_smul, lie_swap_lie, hv, this, zero_smul, neg_zero, zero_add]
let U' : ℕ →o Submodule R V :=
{ toFun n := Submodule.span R {((π z)^i) v | i < n},... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Lie.Extension | {
"line": 447,
"column": 19
} | {
"line": 447,
"column": 70
} | {
"line": 447,
"column": 70
} | [
{
"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... | [] | by rw [LieHom.mem_ker, map_sub, sub_eq_zero, h, hs] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Lie.Extension | {
"line": 448,
"column": 19
} | {
"line": 448,
"column": 70
} | {
"line": 448,
"column": 70
} | [
{
"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... | [] | by rw [LieHom.mem_ker, map_sub, sub_eq_zero, h, hs] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 246,
"column": 55
} | {
"line": 246,
"column": 61
} | {
"line": 247,
"column": 0
} | [
{
"pp": "⊢ E₆ᵀ = E₆",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Int.instDecidableEq",
"id",
"instOfNatNat",
"Int",
"Fin.fintype",
"Bool.true",
"Matrix.transpose",
"Nat... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 246,
"column": 55
} | {
"line": 246,
"column": 61
} | {
"line": 247,
"column": 0
} | [
{
"pp": "⊢ E₆ᵀ = E₆",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Int.instDecidableEq",
"id",
"instOfNatNat",
"Int",
"Fin.fintype",
"Bool.true",
"Matrix.transpose",
"Nat... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 246,
"column": 55
} | {
"line": 246,
"column": 61
} | {
"line": 247,
"column": 0
} | [
{
"pp": "⊢ E₆ᵀ = E₆",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Int.instDecidableEq",
"id",
"instOfNatNat",
"Int",
"Fin.fintype",
"Bool.true",
"Matrix.transpose",
"Nat... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 247,
"column": 55
} | {
"line": 247,
"column": 61
} | {
"line": 248,
"column": 0
} | [
{
"pp": "⊢ E₇ᵀ = E₇",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"CartanMatrix.E₇",
"Matrix.decidableEq",
"Matrix",
"Int.instDecidableEq",
"id",
"instOfNatNat",
"Int",
"Fin.fintype",
"Bool.true",
"Matr... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 247,
"column": 55
} | {
"line": 247,
"column": 61
} | {
"line": 248,
"column": 0
} | [
{
"pp": "⊢ E₇ᵀ = E₇",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"CartanMatrix.E₇",
"Matrix.decidableEq",
"Matrix",
"Int.instDecidableEq",
"id",
"instOfNatNat",
"Int",
"Fin.fintype",
"Bool.true",
"Matr... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 247,
"column": 55
} | {
"line": 247,
"column": 61
} | {
"line": 248,
"column": 0
} | [
{
"pp": "⊢ E₇ᵀ = E₇",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"CartanMatrix.E₇",
"Matrix.decidableEq",
"Matrix",
"Int.instDecidableEq",
"id",
"instOfNatNat",
"Int",
"Fin.fintype",
"Bool.true",
"Matr... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 248,
"column": 55
} | {
"line": 248,
"column": 61
} | {
"line": 250,
"column": 0
} | [
{
"pp": "⊢ E₈ᵀ = E₈",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Int.instDecidableEq",
"id",
"CartanMatrix.E₈",
"instOfNatNat",
"Int",
"Fin.fintype",
"Bool.true",
"Matr... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 248,
"column": 55
} | {
"line": 248,
"column": 61
} | {
"line": 250,
"column": 0
} | [
{
"pp": "⊢ E₈ᵀ = E₈",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Int.instDecidableEq",
"id",
"CartanMatrix.E₈",
"instOfNatNat",
"Int",
"Fin.fintype",
"Bool.true",
"Matr... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 248,
"column": 55
} | {
"line": 248,
"column": 61
} | {
"line": 250,
"column": 0
} | [
{
"pp": "⊢ E₈ᵀ = E₈",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Matrix.decidableEq",
"Matrix",
"Int.instDecidableEq",
"id",
"CartanMatrix.E₈",
"instOfNatNat",
"Int",
"Fin.fintype",
"Bool.true",
"Matr... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 256,
"column": 34
} | {
"line": 256,
"column": 40
} | {
"line": 258,
"column": 0
} | [
{
"pp": "⊢ G₂.det = 1",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"instDecidableEqFin",
"CartanMatrix.G₂",
"Int.instDecidableEq",
"id",
"instOfNatNat",
"Int",
"Fin.fintype",
"Bool.true",
"Int.instCommRing",... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 256,
"column": 34
} | {
"line": 256,
"column": 40
} | {
"line": 258,
"column": 0
} | [
{
"pp": "⊢ G₂.det = 1",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"instDecidableEqFin",
"CartanMatrix.G₂",
"Int.instDecidableEq",
"id",
"instOfNatNat",
"Int",
"Fin.fintype",
"Bool.true",
"Int.instCommRing",... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 256,
"column": 34
} | {
"line": 256,
"column": 40
} | {
"line": 258,
"column": 0
} | [
{
"pp": "⊢ G₂.det = 1",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"instDecidableEqFin",
"CartanMatrix.G₂",
"Int.instDecidableEq",
"id",
"instOfNatNat",
"Int",
"Fin.fintype",
"Bool.true",
"Int.instCommRing",... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 258,
"column": 34
} | {
"line": 258,
"column": 40
} | {
"line": 260,
"column": 0
} | [
{
"pp": "⊢ F₄.det = 1",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"CartanMatrix.F₄",
"of_decide_eq_true",
"instDecidableEqFin",
"Int.instDecidableEq",
"id",
"instOfNatNat",
"Int",
"Fin.fintype",
"Bool.true",
"Int.instCommRing",... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 258,
"column": 34
} | {
"line": 258,
"column": 40
} | {
"line": 260,
"column": 0
} | [
{
"pp": "⊢ F₄.det = 1",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"CartanMatrix.F₄",
"of_decide_eq_true",
"instDecidableEqFin",
"Int.instDecidableEq",
"id",
"instOfNatNat",
"Int",
"Fin.fintype",
"Bool.true",
"Int.instCommRing",... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 258,
"column": 34
} | {
"line": 258,
"column": 40
} | {
"line": 260,
"column": 0
} | [
{
"pp": "⊢ F₄.det = 1",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"CartanMatrix.F₄",
"of_decide_eq_true",
"instDecidableEqFin",
"Int.instDecidableEq",
"id",
"instOfNatNat",
"Int",
"Fin.fintype",
"Bool.true",
"Int.instCommRing",... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 306,
"column": 61
} | {
"line": 306,
"column": 67
} | {
"line": 308,
"column": 0
} | [
{
"pp": "⊢ ∀ ⦃i j : Fin 6⦄, j < i → E₆ i j = 0 ∨ E₆ i j = -1",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"of_decide_eq_true",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"Int.instDecidableEq",
"DistribLattice.toLattice... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 309,
"column": 61
} | {
"line": 309,
"column": 67
} | {
"line": 311,
"column": 0
} | [
{
"pp": "⊢ ∀ ⦃i j : Fin 7⦄, j < i → E₇ i j = 0 ∨ E₇ i j = -1",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"of_decide_eq_true",
"CartanMatrix.E₇",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"Int.instDecidableEq",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 312,
"column": 61
} | {
"line": 312,
"column": 67
} | {
"line": 314,
"column": 0
} | [
{
"pp": "⊢ ∀ ⦃i j : Fin 8⦄, j < i → E₈ i j = 0 ∨ E₈ i j = -1",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"of_decide_eq_true",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"Int.instDecidableEq",
"DistribLattice.toLattice... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 317,
"column": 56
} | {
"line": 317,
"column": 62
} | {
"line": 319,
"column": 0
} | [
{
"pp": "⊢ ¬F₄.IsSimplyLaced",
"ppTerm": "?m.2",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"CartanMatrix.F₄",
"of_decide_eq_true",
"instDecidableEqFin",
"Matrix.IsSimplyLaced",
"id",
"instOfNatNat",
"Fin.fintype",
"Bool.true",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 317,
"column": 56
} | {
"line": 317,
"column": 62
} | {
"line": 319,
"column": 0
} | [
{
"pp": "⊢ ¬F₄.IsSimplyLaced",
"ppTerm": "?m.2",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"CartanMatrix.F₄",
"of_decide_eq_true",
"instDecidableEqFin",
"Matrix.IsSimplyLaced",
"id",
"instOfNatNat",
"Fin.fintype",
"Bool.true",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 317,
"column": 56
} | {
"line": 317,
"column": 62
} | {
"line": 319,
"column": 0
} | [
{
"pp": "⊢ ¬F₄.IsSimplyLaced",
"ppTerm": "?m.2",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"CartanMatrix.F₄",
"of_decide_eq_true",
"instDecidableEqFin",
"Matrix.IsSimplyLaced",
"id",
"instOfNatNat",
"Fin.fintype",
"Bool.true",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 319,
"column": 56
} | {
"line": 319,
"column": 62
} | {
"line": 321,
"column": 0
} | [
{
"pp": "⊢ ¬G₂.IsSimplyLaced",
"ppTerm": "?m.2",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"instDecidableEqFin",
"CartanMatrix.G₂",
"Matrix.IsSimplyLaced",
"id",
"instOfNatNat",
"Fin.fintype",
"Bool.true",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 319,
"column": 56
} | {
"line": 319,
"column": 62
} | {
"line": 321,
"column": 0
} | [
{
"pp": "⊢ ¬G₂.IsSimplyLaced",
"ppTerm": "?m.2",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"instDecidableEqFin",
"CartanMatrix.G₂",
"Matrix.IsSimplyLaced",
"id",
"instOfNatNat",
"Fin.fintype",
"Bool.true",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Matrix.Cartan | {
"line": 319,
"column": 56
} | {
"line": 319,
"column": 62
} | {
"line": 321,
"column": 0
} | [
{
"pp": "⊢ ¬G₂.IsSimplyLaced",
"ppTerm": "?m.2",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"instDecidableEqFin",
"CartanMatrix.G₂",
"Matrix.IsSimplyLaced",
"id",
"instOfNatNat",
"Fin.fintype",
"Bool.true",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Lie.LieTheorem | {
"line": 221,
"column": 2
} | {
"line": 221,
"column": 24
} | {
"line": 222,
"column": 2
} | [
{
"pp": "case inr\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 : IsSo... | [
"k : 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✝¹ : IsT... | lift A to LieIdeal k L | Mathlib.Tactic._aux_Mathlib_Tactic_Lift___elabRules_Mathlib_Tactic_lift_1 | Mathlib.Tactic.lift |
Mathlib.Algebra.LinearRecurrence | {
"line": 139,
"column": 26
} | {
"line": 139,
"column": 30
} | {
"line": 139,
"column": 30
} | [
{
"pp": "R : Type u_1\ninst✝ : CommSemiring R\nE : LinearRecurrence R\nu : ↥E.solSpace\nn : ℕ\n⊢ ↑((fun u ↦ ⟨E.mkSol u, ⋯⟩) ((fun u x ↦ ↑u ↑x) u)) n = ↑u n",
"ppTerm": "?m.90",
"assigned": true,
"usedConstants": [
"Pi.Function.module",
"Submodule",
"Semiring.toModule",
"Pi.ad... | [
"R : Type u_1\ninst✝ : CommSemiring R\nE : LinearRecurrence R\nu : ↥E.solSpace\nn : ℕ\n⊢ ↑u n = ↑((fun u ↦ ⟨E.mkSol u, ⋯⟩) ((fun u x ↦ ↑u ↑x) u)) n"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Algebra.Lie.Weights.IsSimple | {
"line": 155,
"column": 17
} | {
"line": 155,
"column": 28
} | {
"line": 155,
"column": 29
} | [
{
"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... | eq_top_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.ChainOfDivisors | {
"line": 223,
"column": 2
} | {
"line": 223,
"column": 74
} | {
"line": 224,
"column": 2
} | [
{
"pp": "M : Type u_1\ninst✝³ : CommMonoidWithZero M\ninst✝² : IsCancelMulZero M\nN : Type u_2\ninst✝¹ : CommMonoidWithZero N\ninst✝ : IsCancelMulZero N\nm : Associates M\nn : Associates N\nd : { l // l ≤ m } ≃o { l // l ≤ n }\nthis : OrderBot { l // l ≤ m } := Subtype.orderBot ⋯\n⊢ ↑(d ⟨1, ⋯⟩) = 1",
"ppTer... | [
"M : Type u_1\ninst✝³ : CommMonoidWithZero M\ninst✝² : IsCancelMulZero M\nN : Type u_2\ninst✝¹ : CommMonoidWithZero N\ninst✝ : IsCancelMulZero N\nm : Associates M\nn : Associates N\nd : { l // l ≤ m } ≃o { l // l ≤ n }\nthis✝ : OrderBot { l // l ≤ m } := Subtype.orderBot ⋯\nthis : OrderBot { l // l ≤ n } := Subtype... | letI : OrderBot { l : Associates N // l ≤ n } := Subtype.orderBot bot_le | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLetI___1 | Lean.Parser.Tactic.tacticLetI__ |
Mathlib.Algebra.Lie.Weights.IsSimple | {
"line": 259,
"column": 4
} | {
"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 (↥... | [
"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 (↥H) L\nx_χ m_... | have h_zero_weight : H.toLieSubmodule.incl y ∈ genWeightSpace L (0 : H → K) := by
apply toLieSubmodule_le_rootSpace_zero
exact y.property | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.RingTheory.FractionalIdeal.Inverse | {
"line": 104,
"column": 35
} | {
"line": 104,
"column": 67
} | {
"line": 104,
"column": 68
} | [
{
"pp": "K : Type u_3\ninst✝⁴ : Field K\nR₁ : Type u_4\ninst✝³ : CommRing R₁\ninst✝² : IsDomain R₁\ninst✝¹ : Algebra R₁ K\ninst✝ : IsFractionRing R₁ K\nx y : K\n⊢ spanSingleton R₁⁰ x * spanSingleton R₁⁰ y⁻¹ = spanSingleton R₁⁰ (x / y)",
"ppTerm": "?m.67",
"assigned": true,
"usedConstants": [
"... | [
"K : Type u_3\ninst✝⁴ : Field K\nR₁ : Type u_4\ninst✝³ : CommRing R₁\ninst✝² : IsDomain R₁\ninst✝¹ : Algebra R₁ K\ninst✝ : IsFractionRing R₁ K\nx y : K\n⊢ spanSingleton R₁⁰ (x * y⁻¹) = spanSingleton R₁⁰ (x / y)"
] | spanSingleton_mul_spanSingleton, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.FractionalIdeal.Inverse | {
"line": 118,
"column": 25
} | {
"line": 118,
"column": 57
} | {
"line": 118,
"column": 58
} | [
{
"pp": "K : Type u_3\ninst✝⁴ : Field K\nR₁ : Type u_4\ninst✝³ : CommRing R₁\ninst✝² : IsDomain R₁\ninst✝¹ : Algebra R₁ K\ninst✝ : IsFractionRing R₁ K\nx : K\nhx : x ≠ 0\n⊢ spanSingleton R₁⁰ x * spanSingleton R₁⁰ x⁻¹ = 1",
"ppTerm": "?m.57",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"K : Type u_3\ninst✝⁴ : Field K\nR₁ : Type u_4\ninst✝³ : CommRing R₁\ninst✝² : IsDomain R₁\ninst✝¹ : Algebra R₁ K\ninst✝ : IsFractionRing R₁ K\nx : K\nhx : x ≠ 0\n⊢ spanSingleton R₁⁰ (x * x⁻¹) = 1"
] | spanSingleton_mul_spanSingleton, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.ChainOfDivisors | {
"line": 295,
"column": 4
} | {
"line": 295,
"column": 76
} | {
"line": 296,
"column": 4
} | [
{
"pp": "case 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 p : Associates M\nn : Associates N\nhn : n ≠ 0\nhp : p ∈ normalizedFactors m\nd : ↑(Set.Iic m... | [
"case 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 p : Associates M\nn : Associates N\nhn : n ≠ 0\nhp : p ∈ normalizedFactors m\nd : ↑(Set.Iic m) ≃o ↑(Set.I... | letI : OrderBot { l : Associates N // l ≤ n } := Subtype.orderBot bot_le | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLetI___1 | Lean.Parser.Tactic.tacticLetI__ |
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