module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Data.Matrix.Reflection | {
"line": 104,
"column": 6
} | {
"line": 109,
"column": 11
} | {
"line": 111,
"column": 0
} | [
{
"pp": "α : Type u_1\nm n : ℕ\nA : Matrix (Fin m) (Fin (n + 1)) α\ni : Fin (n + 1)\nj : Fin m\n⊢ A.transposeᵣ i j = Aᵀ i j",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instNeZeroNatHAdd_1",
"FinVec.map",
"Matrix.submatrix",
"Equiv.instEquivLike"... | [] | simp_rw [transposeᵣ, transposeᵣ_eq]
refine i.cases ?_ fun i => ?_
· dsimp
rw [FinVec.map_eq, Function.comp_apply]
· simp only [of_apply, Matrix.cons_val_succ]
rfl | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Normed.Lp.ProdLp | {
"line": 388,
"column": 4
} | {
"line": 388,
"column": 37
} | {
"line": 389,
"column": 4
} | [
{
"pp": "p : ℝ≥0∞\n𝕜 : Type u_1\nα : Type u_2\nβ : Type u_3\nhp : Fact (1 ≤ p)\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\nf g : WithLp p (α × β)\n⊢ edist f g = ENNReal.ofReal (dist f g)",
"ppTerm": "?m.103",
"assigned": true,
"usedConstants": [
"WithLp",
"PseudoEMetricS... | [
"case inl\n𝕜 : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\nhp : Fact (1 ≤ ∞)\nf g : WithLp ∞ (α × β)\n⊢ edist f g = ENNReal.ofReal (dist f g)",
"case inr\np : ℝ≥0∞\n𝕜 : Type u_1\nα : Type u_2\nβ : Type u_3\nhp : Fact (1 ≤ p)\ninst✝¹ : PseudoMetricSpace α\nins... | rcases p.dichotomy with (rfl | h) | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.Analysis.Normed.Lp.PiLp | {
"line": 160,
"column": 19
} | {
"line": 160,
"column": 36
} | {
"line": 160,
"column": 36
} | [
{
"pp": "p : ℝ≥0∞\nι : Type u_2\nβ : ι → Type u_4\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → Zero (β i)\ni : ι\na : β i\n⊢ Pi.single i a i = a",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"id",
"Pi.single",
"Pi.single_eq_same",
"... | [
"p : ℝ≥0∞\nι : Type u_2\nβ : ι → Type u_4\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → Zero (β i)\ni : ι\na : β i\n⊢ a = a"
] | Pi.single_eq_same | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Normed.Lp.ProdLp | {
"line": 402,
"column": 2
} | {
"line": 402,
"column": 35
} | {
"line": 403,
"column": 2
} | [
{
"pp": "p : ℝ≥0∞\nα : Type u_2\nβ : Type u_3\nhp : Fact (1 ≤ p)\ninst✝¹ : PseudoEMetricSpace α\ninst✝ : PseudoEMetricSpace β\nx y : WithLp p (α × β)\n⊢ edist x.fst y.fst ≤ edist x y ∧ edist x.snd y.snd ≤ edist x y",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"WithLp",
"Pseu... | [
"case inl\nα : Type u_2\nβ : Type u_3\ninst✝¹ : PseudoEMetricSpace α\ninst✝ : PseudoEMetricSpace β\nhp : Fact (1 ≤ ∞)\nx y : WithLp ∞ (α × β)\n⊢ edist x.fst y.fst ≤ edist x y ∧ edist x.snd y.snd ≤ edist x y",
"case inr\np : ℝ≥0∞\nα : Type u_2\nβ : Type u_3\nhp : Fact (1 ≤ p)\ninst✝¹ : PseudoEMetricSpace α\ninst✝ ... | rcases p.dichotomy with (rfl | h) | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.LinearAlgebra.UnitaryGroup | {
"line": 194,
"column": 20
} | {
"line": 194,
"column": 61
} | {
"line": 195,
"column": 4
} | [
{
"pp": "n : Type u\ninst✝³ : DecidableEq n\ninst✝² : Fintype n\nα : Type v\ninst✝¹ : CommRing α\ninst✝ : StarRing α\nA✝ : Matrix n n α\nA : ↥(unitaryGroup n α)\nx : n → α\n⊢ (toLin' (A⁻¹ * A)) x = x",
"ppTerm": "?m.180",
"assigned": true,
"usedConstants": [
"Matrix.UnitaryGroup.toLin'_one",
... | [] | rw [inv_mul_cancel, toLin'_one, id_apply] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.LinearAlgebra.UnitaryGroup | {
"line": 194,
"column": 20
} | {
"line": 194,
"column": 61
} | {
"line": 195,
"column": 4
} | [
{
"pp": "n : Type u\ninst✝³ : DecidableEq n\ninst✝² : Fintype n\nα : Type v\ninst✝¹ : CommRing α\ninst✝ : StarRing α\nA✝ : Matrix n n α\nA : ↥(unitaryGroup n α)\nx : n → α\n⊢ (toLin' (A⁻¹ * A)) x = x",
"ppTerm": "?m.180",
"assigned": true,
"usedConstants": [
"Matrix.UnitaryGroup.toLin'_one",
... | [] | rw [inv_mul_cancel, toLin'_one, id_apply] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.UnitaryGroup | {
"line": 194,
"column": 20
} | {
"line": 194,
"column": 61
} | {
"line": 195,
"column": 4
} | [
{
"pp": "n : Type u\ninst✝³ : DecidableEq n\ninst✝² : Fintype n\nα : Type v\ninst✝¹ : CommRing α\ninst✝ : StarRing α\nA✝ : Matrix n n α\nA : ↥(unitaryGroup n α)\nx : n → α\n⊢ (toLin' (A⁻¹ * A)) x = x",
"ppTerm": "?m.180",
"assigned": true,
"usedConstants": [
"Matrix.UnitaryGroup.toLin'_one",
... | [] | rw [inv_mul_cancel, toLin'_one, id_apply] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Normed.Lp.ProdLp | {
"line": 430,
"column": 2
} | {
"line": 430,
"column": 35
} | {
"line": 431,
"column": 2
} | [
{
"pp": "p : ℝ≥0∞\nα : Type u_2\nβ : Type u_3\nhp : Fact (1 ≤ p)\ninst✝¹ : PseudoEMetricSpace α\ninst✝ : PseudoEMetricSpace β\nx y : WithLp p (α × β)\n⊢ edist x y ≤ ↑(2 ^ (1 / p).toReal) * edist x.ofLp y.ofLp",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"WithLp",
"NonAssocSe... | [
"case inl\nα : Type u_2\nβ : Type u_3\ninst✝¹ : PseudoEMetricSpace α\ninst✝ : PseudoEMetricSpace β\nhp : Fact (1 ≤ ∞)\nx y : WithLp ∞ (α × β)\n⊢ edist x y ≤ ↑(2 ^ (1 / ∞).toReal) * edist x.ofLp y.ofLp",
"case inr\np : ℝ≥0∞\nα : Type u_2\nβ : Type u_3\nhp : Fact (1 ≤ p)\ninst✝¹ : PseudoEMetricSpace α\ninst✝ : Pseu... | rcases p.dichotomy with (rfl | h) | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.Analysis.Normed.Lp.PiLp | {
"line": 442,
"column": 6
} | {
"line": 442,
"column": 39
} | {
"line": 443,
"column": 6
} | [
{
"pp": "p : ℝ≥0∞\n𝕜 : Type u_1\nι : Type u_2\nα : ι → Type u_3\nβ : ι → Type u_4\ninst✝³ : Fact (1 ≤ p)\ninst✝² : (i : ι) → PseudoMetricSpace (α i)\ninst✝¹ : (i : ι) → PseudoEMetricSpace (β i)\ninst✝ : Fintype ι\nf g : PiLp p α\n⊢ 0 ≤ dist f g",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants"... | [
"case inl\n𝕜 : Type u_1\nι : Type u_2\nα : ι → Type u_3\nβ : ι → Type u_4\ninst✝³ : (i : ι) → PseudoMetricSpace (α i)\ninst✝² : (i : ι) → PseudoEMetricSpace (β i)\ninst✝¹ : Fintype ι\ninst✝ : Fact (1 ≤ ∞)\nf g : PiLp ∞ α\n⊢ 0 ≤ dist f g",
"case inr\np : ℝ≥0∞\n𝕜 : Type u_1\nι : Type u_2\nα : ι → Type u_3\nβ : ι ... | rcases p.dichotomy with (rfl | h) | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.Analysis.Normed.Lp.PiLp | {
"line": 451,
"column": 4
} | {
"line": 451,
"column": 37
} | {
"line": 452,
"column": 4
} | [
{
"pp": "p : ℝ≥0∞\n𝕜 : Type u_1\nι : Type u_2\nα : ι → Type u_3\nβ : ι → Type u_4\ninst✝³ : Fact (1 ≤ p)\ninst✝² : (i : ι) → PseudoMetricSpace (α i)\ninst✝¹ : (i : ι) → PseudoEMetricSpace (β i)\ninst✝ : Fintype ι\nf g : PiLp p α\n⊢ edist f g = ENNReal.ofReal (dist f g)",
"ppTerm": "?m.110",
"assigned":... | [
"case inl\n𝕜 : Type u_1\nι : Type u_2\nα : ι → Type u_3\nβ : ι → Type u_4\ninst✝³ : (i : ι) → PseudoMetricSpace (α i)\ninst✝² : (i : ι) → PseudoEMetricSpace (β i)\ninst✝¹ : Fintype ι\ninst✝ : Fact (1 ≤ ∞)\nf g : PiLp ∞ α\n⊢ edist f g = ENNReal.ofReal (dist f g)",
"case inr\np : ℝ≥0∞\n𝕜 : Type u_1\nι : Type u_2\... | rcases p.dichotomy with (rfl | h) | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.Analysis.Normed.Lp.ProdLp | {
"line": 677,
"column": 4
} | {
"line": 677,
"column": 37
} | {
"line": 678,
"column": 4
} | [
{
"pp": "p : ℝ≥0∞\n𝕜 : Type u_1\nα : Type u_2\nβ : Type u_3\nhp : Fact (1 ≤ p)\ninst✝¹ : SeminormedAddCommGroup α\ninst✝ : SeminormedAddCommGroup β\nx y : WithLp p (α × β)\n⊢ dist x y = ‖-x + y‖",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"WithLp",
"Norm.norm",
"Real... | [
"case inl\n𝕜 : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝¹ : SeminormedAddCommGroup α\ninst✝ : SeminormedAddCommGroup β\nhp : Fact (1 ≤ ∞)\nx y : WithLp ∞ (α × β)\n⊢ dist x y = ‖-x + y‖",
"case inr\np : ℝ≥0∞\n𝕜 : Type u_1\nα : Type u_2\nβ : Type u_3\nhp : Fact (1 ≤ p)\ninst✝¹ : SeminormedAddCommGroup α\ninst✝ ... | rcases p.dichotomy with (rfl | h) | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.Analysis.Normed.Lp.ProdLp | {
"line": 760,
"column": 43
} | {
"line": 760,
"column": 52
} | {
"line": 760,
"column": 53
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝¹ : SeminormedAddCommGroup α\ninst✝ : SeminormedAddCommGroup β\nf : WithLp ∞ (α × β)\n⊢ max ‖f.ofLp.1‖₊ ‖f.ofLp.2‖₊ = max ‖f.fst‖₊ ‖f.snd‖₊",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"WithLp.ofLp_fst",
"congrArg",
... | [
"α : Type u_2\nβ : Type u_3\ninst✝¹ : SeminormedAddCommGroup α\ninst✝ : SeminormedAddCommGroup β\nf : WithLp ∞ (α × β)\n⊢ max ‖f.fst‖₊ ‖f.ofLp.2‖₊ = max ‖f.fst‖₊ ‖f.snd‖₊"
] | ofLp_fst, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Normed.Lp.PiLp | {
"line": 468,
"column": 2
} | {
"line": 468,
"column": 35
} | {
"line": 469,
"column": 2
} | [
{
"pp": "p : ℝ≥0∞\nι : Type u_2\nβ : ι → Type u_4\ninst✝² : Fact (1 ≤ p)\ninst✝¹ : (i : ι) → PseudoEMetricSpace (β i)\ninst✝ : Fintype ι\nx y : PiLp p β\ni : ι\n⊢ edist (x.ofLp i) (y.ofLp i) ≤ edist x y",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"PseudoEMetricSpace.toWeakPseudoE... | [
"case inl\nι : Type u_2\nβ : ι → Type u_4\ninst✝² : (i : ι) → PseudoEMetricSpace (β i)\ninst✝¹ : Fintype ι\ni : ι\ninst✝ : Fact (1 ≤ ∞)\nx y : PiLp ∞ β\n⊢ edist (x.ofLp i) (y.ofLp i) ≤ edist x y",
"case inr\np : ℝ≥0∞\nι : Type u_2\nβ : ι → Type u_4\ninst✝² : Fact (1 ≤ p)\ninst✝¹ : (i : ι) → PseudoEMetricSpace (β ... | rcases p.dichotomy with (rfl | h) | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.Analysis.Normed.Lp.PiLp | {
"line": 487,
"column": 2
} | {
"line": 487,
"column": 35
} | {
"line": 488,
"column": 2
} | [
{
"pp": "p : ℝ≥0∞\nι : Type u_2\nβ : ι → Type u_4\ninst✝² : Fact (1 ≤ p)\ninst✝¹ : (i : ι) → PseudoEMetricSpace (β i)\ninst✝ : Fintype ι\nx y : WithLp p ((i : ι) → β i)\n⊢ edist x y ≤ ↑(↑(Fintype.card ι) ^ (1 / p).toReal) * edist x.ofLp y.ofLp",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": ... | [
"case inl\nι : Type u_2\nβ : ι → Type u_4\ninst✝² : (i : ι) → PseudoEMetricSpace (β i)\ninst✝¹ : Fintype ι\ninst✝ : Fact (1 ≤ ∞)\nx y : WithLp ∞ ((i : ι) → β i)\n⊢ edist x y ≤ ↑(↑(Fintype.card ι) ^ (1 / ∞).toReal) * edist x.ofLp y.ofLp",
"case inr\np : ℝ≥0∞\nι : Type u_2\nβ : ι → Type u_4\ninst✝² : Fact (1 ≤ p)\n... | rcases p.dichotomy with (rfl | h) | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.Analysis.Normed.Lp.PiLp | {
"line": 684,
"column": 4
} | {
"line": 684,
"column": 37
} | {
"line": 685,
"column": 4
} | [
{
"pp": "p : ℝ≥0∞\n𝕜 : Type u_1\nι : Type u_2\nα : ι → Type u_3\nβ : ι → Type u_4\nhp : Fact (1 ≤ p)\ninst✝¹ : Fintype ι\ninst✝ : (i : ι) → SeminormedAddCommGroup (β i)\nx y : PiLp p β\n⊢ dist x y = ‖-x + y‖",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"WithLp",
"PiLp.instN... | [
"case inl\n𝕜 : Type u_1\nι : Type u_2\nα : ι → Type u_3\nβ : ι → Type u_4\ninst✝¹ : Fintype ι\ninst✝ : (i : ι) → SeminormedAddCommGroup (β i)\nhp : Fact (1 ≤ ∞)\nx y : PiLp ∞ β\n⊢ dist x y = ‖-x + y‖",
"case inr\np : ℝ≥0∞\n𝕜 : Type u_1\nι : Type u_2\nα : ι → Type u_3\nβ : ι → Type u_4\nhp : Fact (1 ≤ p)\ninst✝¹... | rcases p.dichotomy with (rfl | h) | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.Analysis.Normed.Lp.PiLp | {
"line": 688,
"column": 16
} | {
"line": 688,
"column": 34
} | {
"line": 688,
"column": 34
} | [
{
"pp": "p : ℝ≥0∞\n𝕜 : Type u_1\nι : Type u_2\nα : ι → Type u_3\nβ : ι → Type u_4\nhp✝ : Fact (1 ≤ p)\ninst✝¹ : Fintype ι\ninst✝ : (i : ι) → SeminormedAddCommGroup (β i)\nx y : PiLp p β\nh : 1 ≤ ∞.toReal\nhp : p = ∞\n⊢ False",
"ppTerm": "?m.51",
"assigned": true,
"usedConstants": [
"Real.inst... | [
"p : ℝ≥0∞\n𝕜 : Type u_1\nι : Type u_2\nα : ι → Type u_3\nβ : ι → Type u_4\nhp✝ : Fact (1 ≤ p)\ninst✝¹ : Fintype ι\ninst✝ : (i : ι) → SeminormedAddCommGroup (β i)\nx y : PiLp p β\nh : 1 ≤ 0\nhp : p = ∞\n⊢ False"
] | ENNReal.toReal_top | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Normed.Lp.PiLp | {
"line": 870,
"column": 4
} | {
"line": 870,
"column": 37
} | {
"line": 871,
"column": 4
} | [
{
"pp": "p : ℝ≥0∞\n𝕜 : Type u_1\nι : Type u_2\nα : ι → Type u_3\nβ : ι → Type u_4\nhp : Fact (1 ≤ p)\ninst✝⁸ : Fintype ι\ninst✝⁷ : Semiring 𝕜\ninst✝⁶ : (i : ι) → SeminormedAddCommGroup (α i)\ninst✝⁵ : (i : ι) → SeminormedAddCommGroup (β i)\ninst✝⁴ : (i : ι) → Module 𝕜 (α i)\ninst✝³ : (i : ι) → Module 𝕜 (β i... | [
"case inl\n𝕜 : Type u_1\nι : Type u_2\nα : ι → Type u_3\nβ : ι → Type u_4\ninst✝⁸ : Fintype ι\ninst✝⁷ : Semiring 𝕜\ninst✝⁶ : (i : ι) → SeminormedAddCommGroup (α i)\ninst✝⁵ : (i : ι) → SeminormedAddCommGroup (β i)\ninst✝⁴ : (i : ι) → Module 𝕜 (α i)\ninst✝³ : (i : ι) → Module 𝕜 (β i)\nc : 𝕜\nι' : Type u_5\ninst✝... | rcases p.dichotomy with (rfl | h) | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.MeasureTheory.Measure.Lebesgue.Basic | {
"line": 140,
"column": 89
} | {
"line": 141,
"column": 77
} | {
"line": 143,
"column": 0
} | [
{
"pp": "a r : ℝ\n⊢ volume (closedBall a r) = ofReal (2 * r)",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"sub_add",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real",
"MeasureTheory.Measure",
"HMul.hMul",
"ENNReal.ofReal",
"cong... | [] | by
rw [closedBall_eq_Icc, volume_Icc, ← sub_add, add_sub_cancel_left, two_mul] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.MeasureTheory.Measure.Lebesgue.Basic | {
"line": 151,
"column": 26
} | {
"line": 151,
"column": 38
} | {
"line": 151,
"column": 39
} | [
{
"pp": "case inl\na : ℝ\n⊢ volume univ = 2 * ∞",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"MeasureTheory.Measure",
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"Set.univ",
"MeasureTheory.MeasureSpace.toMeasurable... | [
"case inl\na : ℝ\n⊢ ∞ = 2 * ∞"
] | volume_univ, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.MeasureTheory.Measure.Lebesgue.Basic | {
"line": 162,
"column": 32
} | {
"line": 162,
"column": 44
} | {
"line": 162,
"column": 45
} | [
{
"pp": "case inl\na : ℝ\n⊢ volume univ = 2 * ∞",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"MeasureTheory.Measure",
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"Set.univ",
"MeasureTheory.MeasureSpace.toMeasurable... | [
"case inl\na : ℝ\n⊢ ∞ = 2 * ∞"
] | volume_univ, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.MeasureTheory.Measure.Lebesgue.Basic | {
"line": 266,
"column": 2
} | {
"line": 266,
"column": 92
} | {
"line": 268,
"column": 0
} | [
{
"pp": "ι : Type u_1\ninst✝ : Fintype ι\na b : ι → ℝ\nh : a ≤ b\n⊢ (volume (univ.pi fun i ↦ Ioc (a i) (b i))).toReal = ∏ i, (b i - a i)",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"Set.Ioc",
"Real.instLE",
"Real"... | [] | simp only [volume_pi_Ioc, ENNReal.toReal_prod, ENNReal.toReal_ofReal (sub_nonneg.2 (h _))] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.MeasureTheory.Measure.Lebesgue.Basic | {
"line": 266,
"column": 2
} | {
"line": 266,
"column": 92
} | {
"line": 268,
"column": 0
} | [
{
"pp": "ι : Type u_1\ninst✝ : Fintype ι\na b : ι → ℝ\nh : a ≤ b\n⊢ (volume (univ.pi fun i ↦ Ioc (a i) (b i))).toReal = ∏ i, (b i - a i)",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"Set.Ioc",
"Real.instLE",
"Real"... | [] | simp only [volume_pi_Ioc, ENNReal.toReal_prod, ENNReal.toReal_ofReal (sub_nonneg.2 (h _))] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.MeasureTheory.Measure.Lebesgue.Basic | {
"line": 266,
"column": 2
} | {
"line": 266,
"column": 92
} | {
"line": 268,
"column": 0
} | [
{
"pp": "ι : Type u_1\ninst✝ : Fintype ι\na b : ι → ℝ\nh : a ≤ b\n⊢ (volume (univ.pi fun i ↦ Ioc (a i) (b i))).toReal = ∏ i, (b i - a i)",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"Set.Ioc",
"Real.instLE",
"Real"... | [] | simp only [volume_pi_Ioc, ENNReal.toReal_prod, ENNReal.toReal_ofReal (sub_nonneg.2 (h _))] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Normed.Lp.PiLp | {
"line": 1019,
"column": 4
} | {
"line": 1019,
"column": 29
} | {
"line": 1020,
"column": 4
} | [
{
"pp": "case top\nι : Type u_2\nβ : ι → Type u_4\ninst✝² : Fintype ι\ninst✝¹ : (i : ι) → SeminormedAddCommGroup (β i)\ninst✝ : DecidableEq ι\ni : ι\nb : β i\nthis : Nonempty ι\nhp : Fact (1 ≤ ∞)\n⊢ ‖single ∞ i b‖₊ = ‖b‖₊",
"ppTerm": "?top",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"case top\nι : Type u_2\nβ : ι → Type u_4\ninst✝² : Fintype ι\ninst✝¹ : (i : ι) → SeminormedAddCommGroup (β i)\ninst✝ : DecidableEq ι\ni : ι\nb : β i\nthis : Nonempty ι\nhp : Fact (1 ≤ ∞)\n⊢ ⨆ i_1, ‖(single ∞ i b).ofLp i_1‖₊ = ‖b‖₊"
] | simp_rw [nnnorm_eq_ciSup] | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | Mathlib.Tactic.tacticSimp_rw___ |
Mathlib.MeasureTheory.Measure.Haar.OfBasis | {
"line": 65,
"column": 2
} | {
"line": 65,
"column": 7
} | {
"line": 67,
"column": 0
} | [
{
"pp": "ι : Type u_1\nE : Type u_3\ninst✝² : Fintype ι\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℝ E\nb : Basis ι ℝ E\nx : E\n⊢ (∃ t, ∀ (x_1 : ι), (0 ≤ t x_1 ∧ t x_1 ≤ 1) ∧ (b.repr x) x_1 = t x_1) ↔ ∀ (i : ι), 0 ≤ (b.repr x) i ∧ (b.repr x) i ≤ 1",
"ppTerm": "?m.67",
"assigned": true,
"usedConstants"... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.MeasureTheory.Measure.Haar.OfBasis | {
"line": 243,
"column": 6
} | {
"line": 243,
"column": 11
} | {
"line": 244,
"column": 4
} | [
{
"pp": "case h.left.left\nι : Type u_1\nι' : Type u_2\nE : Type u_3\nF : Type u_4\ninst✝⁵ : Fintype ι\ninst✝⁴ : Fintype ι'\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ E\ninst✝ : NormedSpace ℝ F\nv : Basis ι ℝ E\nw : Basis ι' ℝ F\nx : E × F\nt : ι → ℝ\nht1 : t ∈ Icc 0 1... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.MeasureTheory.Measure.Haar.OfBasis | {
"line": 245,
"column": 6
} | {
"line": 245,
"column": 11
} | {
"line": 246,
"column": 2
} | [
{
"pp": "case h.left.right\nι : Type u_1\nι' : Type u_2\nE : Type u_3\nF : Type u_4\ninst✝⁵ : Fintype ι\ninst✝⁴ : Fintype ι'\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ E\ninst✝ : NormedSpace ℝ F\nv : Basis ι ℝ E\nw : Basis ι' ℝ F\nx : E × F\nt : ι → ℝ\nht1 : t ∈ Icc 0 ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.BoxIntegral.Box.Basic | {
"line": 327,
"column": 6
} | {
"line": 327,
"column": 43
} | {
"line": 328,
"column": 6
} | [
{
"pp": "ι : Type u_1\nI✝ J✝ : Box ι\nx y : ι → ℝ\nI J : WithBot (Box ι)\n⊢ I ⊓ J ≤ I",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"WithBot.instPreorder",
"Eq.mpr",
"Real",
"WithBot",
"congrArg",
"BoxIntegral.Box.WithBot.inf",
"PartialOrder.toPr... | [
"ι : Type u_1\nI✝ J✝ : Box ι\nx y : ι → ℝ\nI J : WithBot (Box ι)\n⊢ ↑I ∩ ↑J ⊆ ↑I"
] | rw [← withBotCoe_subset_iff, coe_inf] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.BoxIntegral.Box.Basic | {
"line": 330,
"column": 6
} | {
"line": 330,
"column": 43
} | {
"line": 331,
"column": 6
} | [
{
"pp": "ι : Type u_1\nI✝ J✝ : Box ι\nx y : ι → ℝ\nI J : WithBot (Box ι)\n⊢ I ⊓ J ≤ J",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"WithBot.instPreorder",
"Eq.mpr",
"Real",
"WithBot",
"congrArg",
"BoxIntegral.Box.WithBot.inf",
"PartialOrder.toPr... | [
"ι : Type u_1\nI✝ J✝ : Box ι\nx y : ι → ℝ\nI J : WithBot (Box ι)\n⊢ ↑I ∩ ↑J ⊆ ↑J"
] | rw [← withBotCoe_subset_iff, coe_inf] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.BoxIntegral.Box.SubboxInduction | {
"line": 138,
"column": 2
} | {
"line": 138,
"column": 15
} | {
"line": 139,
"column": 2
} | [
{
"pp": "ι : Type u_1\np : Box ι → Prop\nI : Box ι\nH_nhds :\n ∀ z ∈ Box.Icc I,\n ∃ U ∈ 𝓝[Box.Icc I] z,\n ∀ J ≤ I,\n ∀ (m : ℕ),\n z ∈ Box.Icc J → Box.Icc J ⊆ U → (∀ (i : ι), J.upper i - J.lower i = (I.upper i - I.lower i) / 2 ^ m) → p J\nhpI : ¬p I\ns : Box ι → Set ι\nhs : ∀ J ≤ I, ¬p ... | [
"ι : Type u_1\np : Box ι → Prop\nI : Box ι\nH_nhds :\n ∀ z ∈ Box.Icc I,\n ∃ U ∈ 𝓝[Box.Icc I] z,\n ∀ J ≤ I,\n ∀ (m : ℕ),\n z ∈ Box.Icc J → Box.Icc J ⊆ U → (∀ (i : ι), J.upper i - J.lower i = (I.upper i - I.lower i) / 2 ^ m) → p J\nhpI : ¬p I\ns : Box ι → Set ι\nhs : ∀ J ≤ I, ¬p J → ¬p (J.sp... | clear_value J | Lean.Elab.Tactic.evalClearValue | Lean.Parser.Tactic.clearValue |
Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar | {
"line": 593,
"column": 6
} | {
"line": 593,
"column": 28
} | {
"line": 593,
"column": 28
} | [
{
"pp": "E : Type u_1\ninst✝¹² : NormedAddCommGroup E\ninst✝¹¹ : NormedSpace ℝ E\ninst✝¹⁰ : MeasurableSpace E\ninst✝⁹ : BorelSpace E\ninst✝⁸ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝⁷ : μ.IsAddHaarMeasure\ns : Set E\nι : Type u_2\nG : Type u_3\ninst✝⁶ : Fintype ι\ninst✝⁵ : DecidableEq ι\ninst✝⁴ : NormedAddC... | [
"E : Type u_1\ninst✝¹² : NormedAddCommGroup E\ninst✝¹¹ : NormedSpace ℝ E\ninst✝¹⁰ : MeasurableSpace E\ninst✝⁹ : BorelSpace E\ninst✝⁸ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝⁷ : μ.IsAddHaarMeasure\ns : Set E\nι : Type u_2\nG : Type u_3\ninst✝⁶ : Fintype ι\ninst✝⁵ : DecidableEq ι\ninst✝⁴ : NormedAddCommGroup G\n... | AlternatingMap.measure | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar | {
"line": 596,
"column": 6
} | {
"line": 596,
"column": 28
} | {
"line": 596,
"column": 28
} | [
{
"pp": "E : Type u_1\ninst✝¹² : NormedAddCommGroup E\ninst✝¹¹ : NormedSpace ℝ E\ninst✝¹⁰ : MeasurableSpace E\ninst✝⁹ : BorelSpace E\ninst✝⁸ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝⁷ : μ.IsAddHaarMeasure\ns : Set E\nι : Type u_2\nG : Type u_3\ninst✝⁶ : Fintype ι\ninst✝⁵ : DecidableEq ι\ninst✝⁴ : NormedAddC... | [
"E : Type u_1\ninst✝¹² : NormedAddCommGroup E\ninst✝¹¹ : NormedSpace ℝ E\ninst✝¹⁰ : MeasurableSpace E\ninst✝⁹ : BorelSpace E\ninst✝⁸ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝⁷ : μ.IsAddHaarMeasure\ns : Set E\nι : Type u_2\nG : Type u_3\ninst✝⁶ : Fintype ι\ninst✝⁵ : DecidableEq ι\ninst✝⁴ : NormedAddCommGroup G\n... | AlternatingMap.measure | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.BoxIntegral.Partition.Basic | {
"line": 266,
"column": 4
} | {
"line": 266,
"column": 32
} | {
"line": 267,
"column": 4
} | [
{
"pp": "ι : Type u_1\nI J✝ J₁ J₂ : Box ι\nπ π₁ π₂ : Prepartition I\nx : ι → ℝ\nπi : (J : Box ι) → Prepartition J\nJ : Box ι\nhJ : ∃ a ∈ π, J ∈ πi a\n⊢ J ≤ I",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"BoxIntegral.Prepartition",
"Membership.mem",
"Exists",
"LE.... | [
"ι : Type u_1\nI J✝ J₁ J₂ : Box ι\nπ π₁ π₂ : Prepartition I\nx : ι → ℝ\nπi : (J : Box ι) → Prepartition J\nJ J' : Box ι\nhJ' : J' ∈ π\nhJ : J ∈ πi J'\n⊢ J ≤ I"
] | rcases hJ with ⟨J', hJ', hJ⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.Algebra.Module.ZLattice.Basic | {
"line": 565,
"column": 6
} | {
"line": 565,
"column": 68
} | {
"line": 566,
"column": 6
} | [
{
"pp": "K : Type u_1\ninst✝⁹ : NormedField K\ninst✝⁸ : LinearOrder K\ninst✝⁷ : IsStrictOrderedRing K\ninst✝⁶ : HasSolidNorm K\ninst✝⁵ : FloorRing K\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace K E\ninst✝² : FiniteDimensional K E\ninst✝¹ : ProperSpace E\nL : Submodule ℤ E\ninst✝ : Discrete... | [
"K : Type u_1\ninst✝⁹ : NormedField K\ninst✝⁸ : LinearOrder K\ninst✝⁷ : IsStrictOrderedRing K\ninst✝⁶ : HasSolidNorm K\ninst✝⁵ : FloorRing K\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace K E\ninst✝² : FiniteDimensional K E\ninst✝¹ : ProperSpace E\nL : Submodule ℤ E\ninst✝ : DiscreteTopology ↥L\... | rw [Set.toFinset_sdiff, Finset.sdiff_eq_empty_iff_subset] at h | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.InnerProductSpace.PiL2 | {
"line": 723,
"column": 16
} | {
"line": 723,
"column": 36
} | {
"line": 723,
"column": 37
} | [
{
"pp": "ι : Type u_1\n𝕜 : Type u_3\ninst✝³ : RCLike 𝕜\nE : Type u_4\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : Fintype ι\nv : ι → E\nhon : Orthonormal 𝕜 v\nhsp : ⊤ ≤ span 𝕜 (range v)\n⊢ ⇑(OrthonormalBasis.mk hon hsp) = v",
"ppTerm": "?m.32",
"assigned": true,
"used... | [
"ι : Type u_1\n𝕜 : Type u_3\ninst✝³ : RCLike 𝕜\nE : Type u_4\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : Fintype ι\nv : ι → E\nhon : Orthonormal 𝕜 v\nhsp : ⊤ ≤ span 𝕜 (range v)\n⊢ ⇑((Basis.mk ⋯ hsp).toOrthonormalBasis ⋯) = v"
] | OrthonormalBasis.mk, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Module.ZLattice.Basic | {
"line": 583,
"column": 6
} | {
"line": 583,
"column": 69
} | {
"line": 584,
"column": 6
} | [
{
"pp": "K : Type u_1\ninst✝⁹ : NormedField K\ninst✝⁸ : LinearOrder K\ninst✝⁷ : IsStrictOrderedRing K\ninst✝⁶ : HasSolidNorm K\ninst✝⁵ : FloorRing K\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace K E\ninst✝² : FiniteDimensional K E\ninst✝¹ : ProperSpace E\nL : Submodule ℤ E\ninst✝ : Discrete... | [
"K : Type u_1\ninst✝⁹ : NormedField K\ninst✝⁸ : LinearOrder K\ninst✝⁷ : IsStrictOrderedRing K\ninst✝⁶ : HasSolidNorm K\ninst✝⁵ : FloorRing K\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace K E\ninst✝² : FiniteDimensional K E\ninst✝¹ : ProperSpace E\nL : Submodule ℤ E\ninst✝ : DiscreteTopology ↥L\... | rw [Set.mapsTo_inter, Set.mapsTo_univ_iff, Set.mapsTo_univ_iff] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.BoxIntegral.Partition.Split | {
"line": 175,
"column": 79
} | {
"line": 176,
"column": 64
} | {
"line": 178,
"column": 0
} | [
{
"pp": "ι : Type u_1\nI : Box ι\ni : ι\nx : ℝ\n⊢ (split I i x).iUnion = ↑I",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Real.instLE",
"Real",
"WithBot",
"Preorder.toLT",
"Iff.of_eq",
"congrArg",
"BoxIntegral.Box.toSet",
"BoxIntegral.Prepa... | [] | by
simp [split, ← inter_union_distrib_left, ← setOf_or, le_or_gt] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.InnerProductSpace.PiL2 | {
"line": 1227,
"column": 83
} | {
"line": 1229,
"column": 6
} | {
"line": 1231,
"column": 0
} | [
{
"pp": "𝕜 : Type u_3\ninst✝³ : RCLike 𝕜\nV : Type u_7\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace 𝕜 V\ninst✝ : FiniteDimensional 𝕜 V\nS : Submodule 𝕜 V\nL : ↥S →ₗᵢ[𝕜] V\ns : ↥S\n⊢ L.extend ↑s = L s",
"ppTerm": "?m.44",
"assigned": true,
"usedConstants": [
"LinearIsometry"... | [] | by
simp only [LinearIsometry.extend, ← LinearIsometry.coe_toLinearMap]
simp | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Module.ZLattice.Basic | {
"line": 665,
"column": 2
} | {
"line": 675,
"column": 32
} | {
"line": 677,
"column": 0
} | [
{
"pp": "E : Type u_4\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : FiniteDimensional ℝ E\ns : Set E\nhs : DiscreteTopology ↥(span ℤ s)\n⊢ Set.finrank ℝ s = Set.finrank ℤ s",
"ppTerm": "?m.44",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Eq.mpr",
"Submodule... | [] | let F := span ℝ s
let L : Submodule ℤ (span ℝ s) := comap (F.restrictScalars ℤ).subtype (span ℤ s)
let f := Submodule.comapSubtypeEquivOfLe (span_le_restrictScalars ℤ ℝ s)
have : DiscreteTopology L := by
let e : span ℤ s ≃L[ℤ] L :=
⟨f.symm, continuous_of_discreteTopology, Isometry.continuous fun _ ↦ con... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Module.ZLattice.Basic | {
"line": 665,
"column": 2
} | {
"line": 675,
"column": 32
} | {
"line": 677,
"column": 0
} | [
{
"pp": "E : Type u_4\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : FiniteDimensional ℝ E\ns : Set E\nhs : DiscreteTopology ↥(span ℤ s)\n⊢ Set.finrank ℝ s = Set.finrank ℤ s",
"ppTerm": "?m.44",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Eq.mpr",
"Submodule... | [] | let F := span ℝ s
let L : Submodule ℤ (span ℝ s) := comap (F.restrictScalars ℤ).subtype (span ℤ s)
let f := Submodule.comapSubtypeEquivOfLe (span_le_restrictScalars ℤ ℝ s)
have : DiscreteTopology L := by
let e : span ℤ s ≃L[ℤ] L :=
⟨f.symm, continuous_of_discreteTopology, Isometry.continuous fun _ ↦ con... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.InnerProductSpace.PiL2 | {
"line": 1334,
"column": 28
} | {
"line": 1334,
"column": 33
} | {
"line": 1334,
"column": 33
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\n𝕜 : Type u_3\ninst✝⁸ : RCLike 𝕜\nE : Type u_4\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : InnerProductSpace 𝕜 E\nF : Type u_5\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : InnerProductSpace ℝ F\nF' : Type u_6\ninst✝³ : NormedAddCommGroup F'\ninst✝² : InnerProductSpace ℝ F'\ninst... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.InnerProductSpace.PiL2 | {
"line": 1334,
"column": 28
} | {
"line": 1334,
"column": 33
} | {
"line": 1334,
"column": 33
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\n𝕜 : Type u_3\ninst✝⁸ : RCLike 𝕜\nE : Type u_4\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : InnerProductSpace 𝕜 E\nF : Type u_5\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : InnerProductSpace ℝ F\nF' : Type u_6\ninst✝³ : NormedAddCommGroup F'\ninst✝² : InnerProductSpace ℝ F'\ninst... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.InnerProductSpace.PiL2 | {
"line": 1334,
"column": 28
} | {
"line": 1334,
"column": 33
} | {
"line": 1334,
"column": 33
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\n𝕜 : Type u_3\ninst✝⁸ : RCLike 𝕜\nE : Type u_4\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : InnerProductSpace 𝕜 E\nF : Type u_5\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : InnerProductSpace ℝ F\nF' : Type u_6\ninst✝³ : NormedAddCommGroup F'\ninst✝² : InnerProductSpace ℝ F'\ninst... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.InnerProductSpace.PiL2 | {
"line": 1343,
"column": 78
} | {
"line": 1343,
"column": 83
} | {
"line": 1343,
"column": 83
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\n𝕜 : Type u_3\ninst✝⁸ : RCLike 𝕜\nE : Type u_4\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : InnerProductSpace 𝕜 E\nF : Type u_5\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : InnerProductSpace ℝ F\nF' : Type u_6\ninst✝³ : NormedAddCommGroup F'\ninst✝² : InnerProductSpace ℝ F'\ninst... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.InnerProductSpace.PiL2 | {
"line": 1343,
"column": 78
} | {
"line": 1343,
"column": 83
} | {
"line": 1343,
"column": 83
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\n𝕜 : Type u_3\ninst✝⁸ : RCLike 𝕜\nE : Type u_4\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : InnerProductSpace 𝕜 E\nF : Type u_5\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : InnerProductSpace ℝ F\nF' : Type u_6\ninst✝³ : NormedAddCommGroup F'\ninst✝² : InnerProductSpace ℝ F'\ninst... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.InnerProductSpace.PiL2 | {
"line": 1343,
"column": 78
} | {
"line": 1343,
"column": 83
} | {
"line": 1343,
"column": 83
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\n𝕜 : Type u_3\ninst✝⁸ : RCLike 𝕜\nE : Type u_4\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : InnerProductSpace 𝕜 E\nF : Type u_5\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : InnerProductSpace ℝ F\nF' : Type u_6\ninst✝³ : NormedAddCommGroup F'\ninst✝² : InnerProductSpace ℝ F'\ninst... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Oscillation | {
"line": 145,
"column": 6
} | {
"line": 145,
"column": 73
} | {
"line": 146,
"column": 4
} | [
{
"pp": "case right\nE : Type u\nF : Type v\ninst✝¹ : PseudoEMetricSpace F\ninst✝ : PseudoEMetricSpace E\nK : Set E\nf : E → F\nD : Set E\nε : ℝ≥0∞\ncomp : IsCompact K\nhK : ∀ x ∈ K, oscillationWithin f D x < ε\nS : ℝ → Set E := fun r ↦ {x | ∃ a > r, ediam (f '' (eball x (ENNReal.ofReal a) ∩ D)) ≤ ε}\nS_open : ... | [] | exact (S_antitone _ r (IsWF.min_le Tfin.isWF T_nonempty hr.1)) hr.2 | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Analysis.BoxIntegral.UnitPartition | {
"line": 171,
"column": 2
} | {
"line": 171,
"column": 81
} | {
"line": 172,
"column": 2
} | [
{
"pp": "ι : Type u_1\nn : ℕ\ninst✝ : NeZero n\nν ν' : ι → ℤ\n⊢ (∃ x ∈ ↑(box n ν), x ∈ ↑(box n ν')) ↔ ν = ν'",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Real",
"BoxIntegral.unitPartition.tag_mem",
"BoxIntegral.Box.toSet",
"BoxIntegral.unitPartition.tag",
... | [
"ι : Type u_1\nn : ℕ\ninst✝ : NeZero n\nν ν' : ι → ℤ\nx✝ : ∃ x ∈ ↑(box n ν), x ∈ ↑(box n ν')\nx : ι → ℝ\nhx : x ∈ ↑(box n ν)\nhx' : x ∈ ↑(box n ν')\n⊢ ν = ν'"
] | refine ⟨fun ⟨x, hx, hx'⟩ ↦ ?_, fun h ↦ ⟨tag n ν, tag_mem n ν, h ▸ tag_mem n ν⟩⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.BoxIntegral.Basic | {
"line": 432,
"column": 2
} | {
"line": 432,
"column": 71
} | {
"line": 434,
"column": 0
} | [
{
"pp": "ι : Type u\nE : Type v\nF : Type w\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\nI : Box ι\nπ : TaggedPrepartition I\ninst✝ : Fintype ι\nl : IntegrationParams\nf : (ι → ℝ) → E\nvol : ι →ᵇᵃ[⊤] E →L[ℝ] F\nc : ℝ≥0\nε : ℝ\nh : Integrable ... | [] | exact (hasIntegral_iff.1 h.hasIntegral ε h₀).choose_spec.2 c _ hπ hπp | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Analysis.InnerProductSpace.ProdL2 | {
"line": 78,
"column": 2
} | {
"line": 78,
"column": 7
} | {
"line": 80,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\nι₁ : Type u_2\nι₂ : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁶ : RCLike 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : InnerProductSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace 𝕜 F\ninst✝¹ : Fintype ι₁\ninst✝ : Fintype ι₂\nv : OrthonormalBasis ι₁ 𝕜 E\nw : Orthono... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Module.ZLattice.Covolume | {
"line": 237,
"column": 28
} | {
"line": 237,
"column": 42
} | {
"line": 237,
"column": 43
} | [
{
"pp": "case e_a\nE : Type u_1\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\nL : Submodule ℤ E\ninst✝⁵ : DiscreteTopology ↥L\ninst✝⁴ : IsZLattice ℝ L\nι : Type u_2\ninst✝³ : Fintype ι\nb : Basis ι ℤ ↥L\ninst✝² : FiniteDimensional ℝ E\ninst✝¹ : MeasurableSpace E\ninst✝ : BorelSpace E\ns : Set E\nhs₁... | [
"case e_a\nE : Type u_1\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\nL : Submodule ℤ E\ninst✝⁵ : DiscreteTopology ↥L\ninst✝⁴ : IsZLattice ℝ L\nι : Type u_2\ninst✝³ : Fintype ι\nb : Basis ι ℤ ↥L\ninst✝² : FiniteDimensional ℝ E\ninst✝¹ : MeasurableSpace E\ninst✝ : BorelSpace E\ns : Set E\nhs₁ : Bornology... | Set.mem_image, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Algebra.Module.ZLattice.Covolume | {
"line": 242,
"column": 4
} | {
"line": 242,
"column": 93
} | {
"line": 243,
"column": 2
} | [
{
"pp": "case refine_2\nE : Type u_1\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\nL : Submodule ℤ E\ninst✝⁵ : DiscreteTopology ↥L\ninst✝⁴ : IsZLattice ℝ L\nι : Type u_2\ninst✝³ : Fintype ι\nb : Basis ι ℤ ↥L\ninst✝² : FiniteDimensional ℝ E\ninst✝¹ : MeasurableSpace E\ninst✝ : BorelSpace E\ns : Set E... | [] | exact Bornology.IsVonNBounded.image hs₁ ((b.ofZLatticeBasis ℝ).equivFunL : E →L[ℝ] ι → ℝ) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Analysis.PSeries | {
"line": 411,
"column": 8
} | {
"line": 411,
"column": 33
} | {
"line": 412,
"column": 8
} | [
{
"pp": "case h\nα : Type u_1\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nk n x : ℕ\nhx : x ∈ Ioo k n\n⊢ x ∈ Ioc k (max (k + 1) n)",
"ppTerm": "?h",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"Finset",
"Nat.instLocallyFiniteOrder",
"Me... | [
"case h\nα : Type u_1\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nk n x : ℕ\nhx : k < x ∧ x < n\n⊢ x ∈ Ioc k (max (k + 1) n)"
] | simp only [mem_Ioo] at hx | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Module.ZLattice.Summable | {
"line": 50,
"column": 28
} | {
"line": 50,
"column": 87
} | {
"line": 50,
"column": 87
} | [
{
"pp": "E : Type u_1\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : FiniteDimensional ℝ E\nL : Submodule ℤ E\ninst✝¹ : DiscreteTopology ↥L\nι : Type u_2\nb : Basis ι ℤ ↥L\nthis :\n ∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [FiniteDimensional ℝ E] {L : Submod... | [] | by simpa using! H ⟨⟨x.1, Submodule.subset_span x.2⟩, x.2⟩ i | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Module.ZLattice.Covolume | {
"line": 283,
"column": 30
} | {
"line": 283,
"column": 44
} | {
"line": 283,
"column": 45
} | [
{
"pp": "case e_a\nE : Type u_1\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\nL : Submodule ℤ E\ninst✝⁶ : DiscreteTopology ↥L\ninst✝⁵ : IsZLattice ℝ L\nι : Type u_2\ninst✝⁴ : Fintype ι\nb : Basis ι ℤ ↥L\ninst✝³ : FiniteDimensional ℝ E\ninst✝² : MeasurableSpace E\ninst✝¹ : BorelSpace E\ninst✝ : Nonem... | [
"case e_a\nE : Type u_1\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\nL : Submodule ℤ E\ninst✝⁶ : DiscreteTopology ↥L\ninst✝⁵ : IsZLattice ℝ L\nι : Type u_2\ninst✝⁴ : Fintype ι\nb : Basis ι ℤ ↥L\ninst✝³ : FiniteDimensional ℝ E\ninst✝² : MeasurableSpace E\ninst✝¹ : BorelSpace E\ninst✝ : Nonempty ι\nX : S... | Set.mem_image, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Algebra.Module.ZLattice.Summable | {
"line": 177,
"column": 4
} | {
"line": 177,
"column": 85
} | {
"line": 178,
"column": 4
} | [
{
"pp": "E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : FiniteDimensional ℝ E\nL : Submodule ℤ E\ninst✝ : DiscreteTopology ↥L\nh✝ : Nontrivial ↥L\nI : Type u_1 := Free.ChooseBasisIndex ℤ ↥L\nthis : Fintype I\nb : Basis I ℤ ↥L := Free.chooseBasis ℤ ↥L\nd : ℕ := Fintype.card I\nhd... | [
"E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : FiniteDimensional ℝ E\nL : Submodule ℤ E\ninst✝ : DiscreteTopology ↥L\nh✝ : Nontrivial ↥L\nI : Type u_1 := Free.ChooseBasisIndex ℤ ↥L\nthis : Fintype I\nb : Basis I ℤ ↥L := Free.chooseBasis ℤ ↥L\nd : ℕ := Fintype.card I\nhd : d ≠ 0\nε ... | let e : (I → ℤ) ≃ₗ[ℤ] L := (b.repr ≪≫ₗ Finsupp.linearEquivFunOnFinite _ _ _).symm | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLet___1 | Lean.Parser.Tactic.tacticLet__ |
Mathlib.Analysis.BoxIntegral.Basic | {
"line": 768,
"column": 4
} | {
"line": 771,
"column": 100
} | {
"line": 772,
"column": 2
} | [
{
"pp": "case hb\nι : Type u\nE : Type v\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : Fintype ι\nl : IntegrationParams\ninst✝¹ : CompleteSpace E\nI : Box ι\nf : (ι → ℝ) → E\nhc : ContinuousOn f (Box.Icc I)\nμ : Measure (ι → ℝ)\ninst✝ : IsLocallyFiniteMeasure μ\n⊢ ∃ C, ∀ x ∈ Box.Icc I, ‖f x... | [] | obtain ⟨C, hC⟩ := (NormedSpace.isBounded_iff_subset_smul_closedBall ℝ).1
(I.isCompact_Icc.image_of_continuousOn hc).isBounded
use ‖C‖, fun x hx ↦ by
simpa only [smul_unitClosedBall, mem_closedBall_zero_iff] using hC (Set.mem_image_of_mem f hx) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.BoxIntegral.Basic | {
"line": 768,
"column": 4
} | {
"line": 771,
"column": 100
} | {
"line": 772,
"column": 2
} | [
{
"pp": "case hb\nι : Type u\nE : Type v\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : Fintype ι\nl : IntegrationParams\ninst✝¹ : CompleteSpace E\nI : Box ι\nf : (ι → ℝ) → E\nhc : ContinuousOn f (Box.Icc I)\nμ : Measure (ι → ℝ)\ninst✝ : IsLocallyFiniteMeasure μ\n⊢ ∃ C, ∀ x ∈ Box.Icc I, ‖f x... | [] | obtain ⟨C, hC⟩ := (NormedSpace.isBounded_iff_subset_smul_closedBall ℝ).1
(I.isCompact_Icc.image_of_continuousOn hc).isBounded
use ‖C‖, fun x hx ↦ by
simpa only [smul_unitClosedBall, mem_closedBall_zero_iff] using hC (Set.mem_image_of_mem f hx) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.MonoidAlgebra.PointwiseSMul | {
"line": 65,
"column": 4
} | {
"line": 65,
"column": 9
} | {
"line": 66,
"column": 2
} | [
{
"pp": "G : Type u_1\nP : Type u_2\nR : Type u_3\nV : Type u_4\ninst✝⁴ : Group G\ninst✝³ : MulAction G P\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid V\ninst✝ : SMulWithZero R V\nf : R[G]\nx : P → V\np : P\nhp : ((↑f.coeff.support).smulAntidiagonal (Function.support x) p).Finite\ns : Set (G × P) := ↑(Finset.SM... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.MonoidAlgebra.PointwiseSMul | {
"line": 66,
"column": 64
} | {
"line": 66,
"column": 69
} | {
"line": 67,
"column": 2
} | [
{
"pp": "G : Type u_1\nP : Type u_2\nR : Type u_3\nV : Type u_4\ninst✝⁴ : Group G\ninst✝³ : MulAction G P\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid V\ninst✝ : SMulWithZero R V\nf : R[G]\nx : P → V\np : P\nhp : ((↑f.coeff.support).smulAntidiagonal (Function.support x) p).Finite\ns : Set (G × P) := ↑(Finset.SM... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.MonoidAlgebra.PointwiseSMul | {
"line": 66,
"column": 64
} | {
"line": 66,
"column": 69
} | {
"line": 67,
"column": 2
} | [
{
"pp": "G : Type u_1\nP : Type u_2\nR : Type u_3\nV : Type u_4\ninst✝⁴ : Group G\ninst✝³ : MulAction G P\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid V\ninst✝ : SMulWithZero R V\nf : R[G]\nx : P → V\np : P\nhp : ((↑f.coeff.support).smulAntidiagonal (Function.support x) p).Finite\ns : Set (G × P) := ↑(Finset.SM... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.MonoidAlgebra.PointwiseSMul | {
"line": 66,
"column": 64
} | {
"line": 66,
"column": 69
} | {
"line": 67,
"column": 2
} | [
{
"pp": "G : Type u_1\nP : Type u_2\nR : Type u_3\nV : Type u_4\ninst✝⁴ : Group G\ninst✝³ : MulAction G P\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid V\ninst✝ : SMulWithZero R V\nf : R[G]\nx : P → V\np : P\nhp : ((↑f.coeff.support).smulAntidiagonal (Function.support x) p).Finite\ns : Set (G × P) := ↑(Finset.SM... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.MonoidAlgebra.PointwiseSMul | {
"line": 69,
"column": 71
} | {
"line": 69,
"column": 76
} | {
"line": 70,
"column": 4
} | [
{
"pp": "G : Type u_1\nP : Type u_2\nR : Type u_3\nV : Type u_4\ninst✝⁴ : Group G\ninst✝³ : MulAction G P\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid V\ninst✝ : SMulWithZero R V\nf : R[G]\nx : P → V\np : P\nhp : ((↑f.coeff.support).smulAntidiagonal (Function.support x) p).Finite\ns : Set (G × P) := ↑(Finset.SM... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.MonoidAlgebra.PointwiseSMul | {
"line": 69,
"column": 71
} | {
"line": 69,
"column": 76
} | {
"line": 70,
"column": 4
} | [
{
"pp": "G : Type u_1\nP : Type u_2\nR : Type u_3\nV : Type u_4\ninst✝⁴ : Group G\ninst✝³ : MulAction G P\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid V\ninst✝ : SMulWithZero R V\nf : R[G]\nx : P → V\np : P\nhp : ((↑f.coeff.support).smulAntidiagonal (Function.support x) p).Finite\ns : Set (G × P) := ↑(Finset.SM... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.MonoidAlgebra.PointwiseSMul | {
"line": 69,
"column": 71
} | {
"line": 69,
"column": 76
} | {
"line": 70,
"column": 4
} | [
{
"pp": "G : Type u_1\nP : Type u_2\nR : Type u_3\nV : Type u_4\ninst✝⁴ : Group G\ninst✝³ : MulAction G P\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid V\ninst✝ : SMulWithZero R V\nf : R[G]\nx : P → V\np : P\nhp : ((↑f.coeff.support).smulAntidiagonal (Function.support x) p).Finite\ns : Set (G × P) := ↑(Finset.SM... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.MonoidAlgebra.PointwiseSMul | {
"line": 72,
"column": 6
} | {
"line": 72,
"column": 11
} | {
"line": 73,
"column": 2
} | [
{
"pp": "case inr\nG : Type u_1\nP : Type u_2\nR : Type u_3\nV : Type u_4\ninst✝⁴ : Group G\ninst✝³ : MulAction G P\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid V\ninst✝ : SMulWithZero R V\nf : R[G]\nx : P → V\np : P\nhp : ((↑f.coeff.support).smulAntidiagonal (Function.support x) p).Finite\ns : Set (G × P) := ↑... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.MonoidAlgebra.PointwiseSMul | {
"line": 74,
"column": 2
} | {
"line": 74,
"column": 7
} | {
"line": 76,
"column": 0
} | [
{
"pp": "G : Type u_1\nP : Type u_2\nR : Type u_3\nV : Type u_4\ninst✝⁴ : Group G\ninst✝³ : MulAction G P\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid V\ninst✝ : SMulWithZero R V\nf : R[G]\nx : P → V\np : P\nhp : ((↑f.coeff.support).smulAntidiagonal (Function.support x) p).Finite\ns : Set (G × P) := ↑(Finset.SM... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.MvPolynomial.Comap | {
"line": 65,
"column": 2
} | {
"line": 68,
"column": 24
} | {
"line": 69,
"column": 2
} | [
{
"pp": "σ : Type u_1\nτ : Type u_2\nυ : Type u_3\nR : Type u_4\ninst✝ : CommSemiring R\nf : MvPolynomial σ R →ₐ[R] MvPolynomial τ R\ng : MvPolynomial τ R →ₐ[R] MvPolynomial υ R\nx : υ → R\ni : σ\n⊢ comap (g.comp f) x i = (aeval x) ((aeval fun i ↦ g (X i)) (f (X i)))",
"ppTerm": "?m.70",
"assigned": tru... | [
"σ : Type u_1\nτ : Type u_2\nυ : Type u_3\nR : Type u_4\ninst✝ : CommSemiring R\nf : MvPolynomial σ R →ₐ[R] MvPolynomial τ R\ng : MvPolynomial τ R →ₐ[R] MvPolynomial υ R\nx : υ → R\ni : σ\n⊢ (aeval x) ((aeval fun i ↦ g (X i)) (f (X i))) = comap f (comap g x) i"
] | · apply eval₂Hom_congr rfl rfl
rw [AlgHom.comp_apply]
suffices g = aeval fun i => g (X i) by rw [← this]
exact aeval_unique g | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Data.Nat.Choose.Multinomial | {
"line": 116,
"column": 84
} | {
"line": 116,
"column": 89
} | {
"line": 116,
"column": 89
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\nf g : α → ℕ\ns t : Finset α\nhf : ∀ a ∈ s \\ t, f a = 0\nhg : ∀ a ∈ t \\ s, g a = 0\nhfg : ∀ a ∈ s ∩ t, f a = g a\n⊢ ∀ a ∈ t, a ∉ s → (g a)! = 1",
"ppTerm": "?m.55",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"False",
"eq_fals... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Nat.Choose.Multinomial | {
"line": 116,
"column": 84
} | {
"line": 116,
"column": 89
} | {
"line": 116,
"column": 89
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\nf g : α → ℕ\ns t : Finset α\nhf : ∀ a ∈ s \\ t, f a = 0\nhg : ∀ a ∈ t \\ s, g a = 0\nhfg : ∀ a ∈ s ∩ t, f a = g a\n⊢ ∀ a ∈ t, a ∉ s → (g a)! = 1",
"ppTerm": "?m.55",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"False",
"eq_fals... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Nat.Choose.Multinomial | {
"line": 116,
"column": 84
} | {
"line": 116,
"column": 89
} | {
"line": 116,
"column": 89
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\nf g : α → ℕ\ns t : Finset α\nhf : ∀ a ∈ s \\ t, f a = 0\nhg : ∀ a ∈ t \\ s, g a = 0\nhfg : ∀ a ∈ s ∩ t, f a = g a\n⊢ ∀ a ∈ t, a ∉ s → (g a)! = 1",
"ppTerm": "?m.55",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"False",
"eq_fals... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Nat.Choose.Multinomial | {
"line": 117,
"column": 8
} | {
"line": 117,
"column": 13
} | {
"line": 117,
"column": 13
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\nf g : α → ℕ\ns t : Finset α\nhf : ∀ a ∈ s \\ t, f a = 0\nhg : ∀ a ∈ t \\ s, g a = 0\nhfg : ∀ a ∈ s ∩ t, f a = g a\n⊢ ∀ a ∈ s, a ∉ t → (f a)! = 1",
"ppTerm": "?m.56",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"False",
"eq_fals... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Nat.Choose.Multinomial | {
"line": 117,
"column": 8
} | {
"line": 117,
"column": 13
} | {
"line": 117,
"column": 13
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\nf g : α → ℕ\ns t : Finset α\nhf : ∀ a ∈ s \\ t, f a = 0\nhg : ∀ a ∈ t \\ s, g a = 0\nhfg : ∀ a ∈ s ∩ t, f a = g a\n⊢ ∀ a ∈ s, a ∉ t → (f a)! = 1",
"ppTerm": "?m.56",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"False",
"eq_fals... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Nat.Choose.Multinomial | {
"line": 117,
"column": 8
} | {
"line": 117,
"column": 13
} | {
"line": 117,
"column": 13
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\nf g : α → ℕ\ns t : Finset α\nhf : ∀ a ∈ s \\ t, f a = 0\nhg : ∀ a ∈ t \\ s, g a = 0\nhfg : ∀ a ∈ s ∩ t, f a = g a\n⊢ ∀ a ∈ s, a ∉ t → (f a)! = 1",
"ppTerm": "?m.56",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"False",
"eq_fals... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Nat.Choose.Multinomial | {
"line": 117,
"column": 19
} | {
"line": 117,
"column": 24
} | {
"line": 117,
"column": 24
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\nf g : α → ℕ\ns t : Finset α\nhf : ∀ a ∈ s \\ t, f a = 0\nhg : ∀ a ∈ t \\ s, g a = 0\nhfg : ∀ a ∈ s ∩ t, f a = g a\n⊢ ∀ a ∈ t, a ∈ s → (g a)! = (f a)!",
"ppTerm": "?m.57",
"assigned": true,
"usedConstants": [
"congrArg",
"Finset",
"Membe... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Nat.Choose.Multinomial | {
"line": 117,
"column": 19
} | {
"line": 117,
"column": 24
} | {
"line": 117,
"column": 24
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\nf g : α → ℕ\ns t : Finset α\nhf : ∀ a ∈ s \\ t, f a = 0\nhg : ∀ a ∈ t \\ s, g a = 0\nhfg : ∀ a ∈ s ∩ t, f a = g a\n⊢ ∀ a ∈ t, a ∈ s → (g a)! = (f a)!",
"ppTerm": "?m.57",
"assigned": true,
"usedConstants": [
"congrArg",
"Finset",
"Membe... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Nat.Choose.Multinomial | {
"line": 117,
"column": 19
} | {
"line": 117,
"column": 24
} | {
"line": 117,
"column": 24
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\nf g : α → ℕ\ns t : Finset α\nhf : ∀ a ∈ s \\ t, f a = 0\nhg : ∀ a ∈ t \\ s, g a = 0\nhfg : ∀ a ∈ s ∩ t, f a = g a\n⊢ ∀ a ∈ t, a ∈ s → (g a)! = (f a)!",
"ppTerm": "?m.57",
"assigned": true,
"usedConstants": [
"congrArg",
"Finset",
"Membe... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Nat.Choose.Multinomial | {
"line": 132,
"column": 61
} | {
"line": 132,
"column": 78
} | {
"line": 132,
"column": 78
} | [
{
"pp": "case pos\nα : Type u_1\ns : Finset α\na : α\nn : ℕ\ninst✝ : DecidableEq α\nha : a ∈ s\n⊢ n ! = (Pi.single a n a)!",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.instMulZeroClass",
"congrArg",
"id",
"Pi.single",
"Nat.factorial",
... | [
"case pos\nα : Type u_1\ns : Finset α\na : α\nn : ℕ\ninst✝ : DecidableEq α\nha : a ∈ s\n⊢ n ! = n !"
] | Pi.single_eq_same | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.MvPolynomial.Division | {
"line": 229,
"column": 6
} | {
"line": 229,
"column": 24
} | {
"line": 229,
"column": 25
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝¹ : CommSemiring R\ninst✝ : IsLeftCancelAdd R\ni : σ\np q r : MvPolynomial σ R\nh : p = X i * q + r\nhr : ∀ n ∈ r.support, n i = 0\nn : σ →₀ ℕ\n⊢ coeff n q = coeff n (p.divMonomial (Finsupp.single i 1))",
"ppTerm": "?m.46",
"assigned": true,
"usedConstants":... | [
"σ : Type u_1\nR : Type u_2\ninst✝¹ : CommSemiring R\ninst✝ : IsLeftCancelAdd R\ni : σ\np q r : MvPolynomial σ R\nh : p = X i * q + r\nhr : ∀ n ∈ r.support, n i = 0\nn : σ →₀ ℕ\n⊢ coeff n q = coeff (Finsupp.single i 1 + n) p"
] | coeff_divMonomial, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.MvPolynomial.Nilpotent | {
"line": 52,
"column": 4
} | {
"line": 52,
"column": 9
} | {
"line": 53,
"column": 2
} | [
{
"pp": "case pos\nσ : Type u_1\nR : Type u_2\ninst✝ : CommRing R\nn : ℕ\nP : MvPolynomial (Fin n) R\nf : Fin n ↪ σ\nH✝ : ∀ (i : Fin n →₀ ℕ), IsNilpotent (coeff i P)\ni : σ →₀ ℕ\nH : i ∈ Set.range (Finsupp.embDomain f)\n⊢ IsNilpotent (coeff i ((rename ⇑f) P))",
"ppTerm": "?pos✝",
"assigned": true,
"... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.MvPolynomial.Nilpotent | {
"line": 52,
"column": 4
} | {
"line": 52,
"column": 9
} | {
"line": 53,
"column": 2
} | [
{
"pp": "case pos\nσ : Type u_1\nR : Type u_2\ninst✝ : CommRing R\nn : ℕ\nP : MvPolynomial (Fin n) R\nf : Fin n ↪ σ\nH✝ : ∀ (i : Fin n →₀ ℕ), IsNilpotent (coeff i P)\ni : σ →₀ ℕ\nH : i ∈ Set.range (Finsupp.embDomain f)\n⊢ IsNilpotent (coeff i ((rename ⇑f) P))",
"ppTerm": "?pos✝",
"assigned": true,
"... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.MvPolynomial.Nilpotent | {
"line": 52,
"column": 4
} | {
"line": 52,
"column": 9
} | {
"line": 53,
"column": 2
} | [
{
"pp": "case pos\nσ : Type u_1\nR : Type u_2\ninst✝ : CommRing R\nn : ℕ\nP : MvPolynomial (Fin n) R\nf : Fin n ↪ σ\nH✝ : ∀ (i : Fin n →₀ ℕ), IsNilpotent (coeff i P)\ni : σ →₀ ℕ\nH : i ∈ Set.range (Finsupp.embDomain f)\n⊢ IsNilpotent (coeff i ((rename ⇑f) P))",
"ppTerm": "?pos✝",
"assigned": true,
"... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Nat.Choose.Multinomial | {
"line": 378,
"column": 6
} | {
"line": 378,
"column": 59
} | {
"line": 378,
"column": 59
} | [
{
"pp": "ι : Type u_1\ns : Finset ι\nf : ι → ℕ\n⊢ ((2 * ∑ i ∈ s, f i) ^ ∑ i ∈ s, f i) * (∑ i ∈ s, f i)! * ∏ i ∈ s, (f i)! =\n ((∑ i ∈ s, f i) ^ ∑ i ∈ s, f i) * (∑ i ∈ s, f i)! * ∏ i ∈ s, 2 ^ f i * (f i)!",
"ppTerm": "?m.178",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.prod... | [
"ι : Type u_1\ns : Finset ι\nf : ι → ℕ\n⊢ ((∏ i ∈ s, 2 ^ f i) * (∑ i ∈ s, f i) ^ ∑ i ∈ s, f i) * (∑ i ∈ s, f i)! * ∏ i ∈ s, (f i)! =\n ((∑ i ∈ s, f i) ^ ∑ i ∈ s, f i) * (∑ i ∈ s, f i)! * ((∏ x ∈ s, 2 ^ f x) * ∏ x ∈ s, (f x)!)"
] | rw [mul_pow, ← prod_pow_eq_pow_sum, prod_mul_distrib] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Nat.Choose.Multinomial | {
"line": 445,
"column": 45
} | {
"line": 445,
"column": 62
} | {
"line": 445,
"column": 62
} | [
{
"pp": "x✝ : ℕ\nl : List ℕ\nsuccEmb : ℕ ↪ ℕ := addRightEmbedding 1\nthis :\n (Finsupp.single 0 x✝ + Finsupp.embDomain succEmb l.toFinsupp).update 0 0 =\n (Finsupp.embDomain succEmb l.toFinsupp).update 0 0\nx : ℕ\n⊢ succEmb x = x + 1",
"ppTerm": "?m.170",
"assigned": true,
"usedConstants": [
... | [] | by simp [succEmb] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.MvPolynomial.NoZeroDivisors | {
"line": 90,
"column": 38
} | {
"line": 90,
"column": 43
} | {
"line": 90,
"column": 43
} | [
{
"pp": "R : Type u_1\nσ : Type u_2\ninst✝¹ : CommSemiring R\ninst✝ : NoZeroDivisors R\nf r : MvPolynomial σ R\nhg : f * r ≠ 0\n⊢ f ≠ 0",
"ppTerm": "?m.44",
"assigned": true,
"usedConstants": [
"False",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"Semigroup.toMul",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.MvPolynomial.NoZeroDivisors | {
"line": 90,
"column": 38
} | {
"line": 90,
"column": 43
} | {
"line": 90,
"column": 43
} | [
{
"pp": "R : Type u_1\nσ : Type u_2\ninst✝¹ : CommSemiring R\ninst✝ : NoZeroDivisors R\nf r : MvPolynomial σ R\nhg : f * r ≠ 0\n⊢ f ≠ 0",
"ppTerm": "?m.44",
"assigned": true,
"usedConstants": [
"False",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"Semigroup.toMul",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.MvPolynomial.NoZeroDivisors | {
"line": 90,
"column": 38
} | {
"line": 90,
"column": 43
} | {
"line": 90,
"column": 43
} | [
{
"pp": "R : Type u_1\nσ : Type u_2\ninst✝¹ : CommSemiring R\ninst✝ : NoZeroDivisors R\nf r : MvPolynomial σ R\nhg : f * r ≠ 0\n⊢ f ≠ 0",
"ppTerm": "?m.44",
"assigned": true,
"usedConstants": [
"False",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"Semigroup.toMul",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.MvPolynomial.NoZeroDivisors | {
"line": 90,
"column": 49
} | {
"line": 90,
"column": 54
} | {
"line": 90,
"column": 54
} | [
{
"pp": "R : Type u_1\nσ : Type u_2\ninst✝¹ : CommSemiring R\ninst✝ : NoZeroDivisors R\nf r : MvPolynomial σ R\nhg : f * r ≠ 0\n⊢ r ≠ 0",
"ppTerm": "?m.45",
"assigned": true,
"usedConstants": [
"False",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"Semigroup.toMul",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.MvPolynomial.NoZeroDivisors | {
"line": 90,
"column": 49
} | {
"line": 90,
"column": 54
} | {
"line": 90,
"column": 54
} | [
{
"pp": "R : Type u_1\nσ : Type u_2\ninst✝¹ : CommSemiring R\ninst✝ : NoZeroDivisors R\nf r : MvPolynomial σ R\nhg : f * r ≠ 0\n⊢ r ≠ 0",
"ppTerm": "?m.45",
"assigned": true,
"usedConstants": [
"False",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"Semigroup.toMul",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.MvPolynomial.NoZeroDivisors | {
"line": 90,
"column": 49
} | {
"line": 90,
"column": 54
} | {
"line": 90,
"column": 54
} | [
{
"pp": "R : Type u_1\nσ : Type u_2\ninst✝¹ : CommSemiring R\ninst✝ : NoZeroDivisors R\nf r : MvPolynomial σ R\nhg : f * r ≠ 0\n⊢ r ≠ 0",
"ppTerm": "?m.45",
"assigned": true,
"usedConstants": [
"False",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"Semigroup.toMul",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.MvPolynomial.MonomialOrder | {
"line": 288,
"column": 2
} | {
"line": 288,
"column": 33
} | {
"line": 289,
"column": 2
} | [
{
"pp": "σ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommSemiring R\nf : MvPolynomial σ R\n⊢ m.degree f = 0 ↔ f.totalDegree = 0",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.instMulZeroClass",
"congrArg",
"MonomialOrder.syn",
"Add... | [
"σ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommSemiring R\nf : MvPolynomial σ R\n⊢ m.toSyn (m.degree f) = m.toSyn 0 ↔ f.totalDegree = 0"
] | rw [← m.toSyn.injective.eq_iff] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Sym.Card | {
"line": 135,
"column": 45
} | {
"line": 135,
"column": 50
} | {
"line": 136,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\ns : Finset α\na b : α\nha : a ∈ s\nhb : b ∈ s\nhab : a ≠ b ∨ b ≠ a\n⊢ {z ∈ s.offDiag | uncurry Sym2.mk z = s(a, b)} = cons (a, b) {(b, a)} ⋯",
"ppTerm": "?m.86",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"Finset.mem_filter... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Sym.Card | {
"line": 136,
"column": 2
} | {
"line": 136,
"column": 7
} | {
"line": 138,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\ns : Finset α\nthis :\n ∀ (a b : α),\n a ∈ s → b ∈ s → ∀ (hab : a ≠ b ∨ b ≠ a), {z ∈ s.offDiag | uncurry Sym2.mk z = s(a, b)} = cons (a, b) {(b, a)} ⋯\n⊢ ∀ (x y : α), s(x, y) ∈ image (uncurry Sym2.mk) s.offDiag → #({a ∈ s.offDiag | uncurry Sym2.mk a = s(x, y)}) =... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.RingTheory.MvPolynomial.MonomialOrder | {
"line": 385,
"column": 2
} | {
"line": 402,
"column": 12
} | {
"line": 404,
"column": 0
} | [
{
"pp": "σ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommSemiring R\nf g : MvPolynomial σ R\n⊢ m.toSyn (m.degree (f * g)) ≤ m.toSyn (m.degree f + m.degree g)",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Finsupp.instHasAntidiagonal",
"Finsupp.instAddZeroClass",
... | [] | classical
rw [degree_le_iff]
intro c
rw [← not_lt, mem_support_iff, not_imp_not]
intro hc
rw [coeff_mul]
apply Finset.sum_eq_zero
rintro ⟨d, e⟩ hde
simp only [Finset.mem_antidiagonal] at hde
dsimp only
by_cases hd : m.degree f ≺[m] d
· rw [m.coeff_eq_zero_of_lt hd, zero_mul]
· suffices m.degree ... | Lean.Elab.Tactic.evalClassical | Lean.Parser.Tactic.classical |
Mathlib.RingTheory.MvPolynomial.MonomialOrder | {
"line": 385,
"column": 2
} | {
"line": 402,
"column": 12
} | {
"line": 404,
"column": 0
} | [
{
"pp": "σ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommSemiring R\nf g : MvPolynomial σ R\n⊢ m.toSyn (m.degree (f * g)) ≤ m.toSyn (m.degree f + m.degree g)",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Finsupp.instHasAntidiagonal",
"Finsupp.instAddZeroClass",
... | [] | classical
rw [degree_le_iff]
intro c
rw [← not_lt, mem_support_iff, not_imp_not]
intro hc
rw [coeff_mul]
apply Finset.sum_eq_zero
rintro ⟨d, e⟩ hde
simp only [Finset.mem_antidiagonal] at hde
dsimp only
by_cases hd : m.degree f ≺[m] d
· rw [m.coeff_eq_zero_of_lt hd, zero_mul]
· suffices m.degree ... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.MvPolynomial.MonomialOrder | {
"line": 385,
"column": 2
} | {
"line": 402,
"column": 12
} | {
"line": 404,
"column": 0
} | [
{
"pp": "σ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommSemiring R\nf g : MvPolynomial σ R\n⊢ m.toSyn (m.degree (f * g)) ≤ m.toSyn (m.degree f + m.degree g)",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Finsupp.instHasAntidiagonal",
"Finsupp.instAddZeroClass",
... | [] | classical
rw [degree_le_iff]
intro c
rw [← not_lt, mem_support_iff, not_imp_not]
intro hc
rw [coeff_mul]
apply Finset.sum_eq_zero
rintro ⟨d, e⟩ hde
simp only [Finset.mem_antidiagonal] at hde
dsimp only
by_cases hd : m.degree f ≺[m] d
· rw [m.coeff_eq_zero_of_lt hd, zero_mul]
· suffices m.degree ... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.MvPolynomial.MonomialOrder | {
"line": 572,
"column": 2
} | {
"line": 572,
"column": 38
} | {
"line": 573,
"column": 2
} | [
{
"pp": "σ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommSemiring R\nf : MvPolynomial σ R\nn : ℕ\nhf : m.Monic f\na✝ : Nontrivial R\n⊢ m.leadingCoeff f ^ n ≠ 0",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"one_pow",
"Eq.mpr",
"NonAssocSemiring.toAddCommMon... | [
"σ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommSemiring R\nf : MvPolynomial σ R\nn : ℕ\nhf : m.Monic f\na✝ : Nontrivial R\n⊢ 1 ≠ 0"
] | rw [hf.leadingCoeff_eq_one, one_pow] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.RingTheory.MvPolynomial.MonomialOrder | {
"line": 722,
"column": 2
} | {
"line": 722,
"column": 7
} | {
"line": 724,
"column": 0
} | [
{
"pp": "σ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommSemiring R\nB : Set (MvPolynomial σ R)\n⊢ m.leadingTerm '' (B \\ {0}) = m.leadingTerm '' B \\ {0}",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"False",
"Nat.instMulZeroClas... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.RingTheory.MvPolynomial.MonomialOrder | {
"line": 722,
"column": 2
} | {
"line": 722,
"column": 7
} | {
"line": 724,
"column": 0
} | [
{
"pp": "σ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommSemiring R\nB : Set (MvPolynomial σ R)\n⊢ m.leadingTerm '' (B \\ {0}) = m.leadingTerm '' B \\ {0}",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"False",
"Nat.instMulZeroClas... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.MvPolynomial.MonomialOrder | {
"line": 722,
"column": 2
} | {
"line": 722,
"column": 7
} | {
"line": 724,
"column": 0
} | [
{
"pp": "σ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommSemiring R\nB : Set (MvPolynomial σ R)\n⊢ m.leadingTerm '' (B \\ {0}) = m.leadingTerm '' B \\ {0}",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"False",
"Nat.instMulZeroClas... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
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