module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.NumberTheory.GaussSum | {
"line": 368,
"column": 6
} | {
"line": 368,
"column": 12
} | {
"line": 369,
"column": 4
} | [
{
"pp": "case refine_1\nF : Type u_1\ninst✝¹ : Fintype F\ninst✝ : Field F\nhF : ringChar F ≠ 2\nhp2 : ∀ (n : ℕ), 2 ^ n ≠ 0\nn : ℕ+\nhp : Nat.Prime (ringChar F)\nhc : Fintype.card F = ringChar F ^ ↑n\nFF : Type u_1 := CyclotomicField 8 F\nhchar : ringChar F = ringChar FF\nFFp : Nat.Prime (ringChar FF)\nthis : Fa... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.GaussSum | {
"line": 370,
"column": 6
} | {
"line": 370,
"column": 12
} | {
"line": 372,
"column": 2
} | [
{
"pp": "case refine_2\nF : Type u_1\ninst✝¹ : Fintype F\ninst✝ : Field F\nhF : ringChar F ≠ 2\nhp2 : ∀ (n : ℕ), 2 ^ n ≠ 0\nn : ℕ+\nhp : Nat.Prime (ringChar F)\nhc : Fintype.card F = ringChar F ^ ↑n\nFF : Type u_1 := CyclotomicField 8 F\nhchar : ringChar F = ringChar FF\nFFp : Nat.Prime (ringChar FF)\nthis : Fa... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.GaussSum | {
"line": 369,
"column": 4
} | {
"line": 370,
"column": 12
} | {
"line": 372,
"column": 2
} | [
{
"pp": "case refine_2\nF : Type u_1\ninst✝¹ : Fintype F\ninst✝ : Field F\nhF : ringChar F ≠ 2\nhp2 : ∀ (n : ℕ), 2 ^ n ≠ 0\nn : ℕ+\nhp : Nat.Prime (ringChar F)\nhc : Fintype.card F = ringChar F ^ ↑n\nFF : Type u_1 := CyclotomicField 8 F\nhchar : ringChar F = ringChar FF\nFFp : Nat.Prime (ringChar FF)\nthis : Fa... | [] | · rw [← map_nsmul_eq_pow ψ₈.char, ψ₈.prim.zmod_char_eq_one_iff]
decide | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Analysis.InnerProductSpace.Positive | {
"line": 368,
"column": 2
} | {
"line": 369,
"column": 22
} | {
"line": 371,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁶ : RCLike 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : InnerProductSpace 𝕜 F\ninst✝¹ : CompleteSpace E\ninst✝ : CompleteSpace F\nT : E →L[𝕜] E\nhT : T.IsPositive\nS : F →L[𝕜] E\n⊢ (adjoint... | [] | convert! hT.conj_adjoint (S†)
rw [adjoint_adjoint] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.InnerProductSpace.Positive | {
"line": 368,
"column": 2
} | {
"line": 369,
"column": 22
} | {
"line": 371,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁶ : RCLike 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : InnerProductSpace 𝕜 F\ninst✝¹ : CompleteSpace E\ninst✝ : CompleteSpace F\nT : E →L[𝕜] E\nhT : T.IsPositive\nS : F →L[𝕜] E\n⊢ (adjoint... | [] | convert! hT.conj_adjoint (S†)
rw [adjoint_adjoint] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.InnerProductSpace.LinearPMap | {
"line": 95,
"column": 27
} | {
"line": 95,
"column": 44
} | {
"line": 95,
"column": 45
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : RCLike 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace 𝕜 F\nT : E →ₗ.[𝕜] F\nS : F →ₗ.[𝕜] E\na✝ b✝ : F\nhx : a✝ ∈ {y | Continuous ⇑((innerₛₗ 𝕜) y ∘ₗ T.toFun)}\nhy : b✝ ∈ {... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : RCLike 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace 𝕜 F\nT : E →ₗ.[𝕜] F\nS : F →ₗ.[𝕜] E\na✝ b✝ : F\nhx : Continuous ⇑((innerₛₗ 𝕜) a✝ ∘ₗ T.toFun)\nhy : Continuous ⇑((innerₛₗ 𝕜) b✝... | Set.mem_setOf_eq, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.InnerProductSpace.LinearPMap | {
"line": 93,
"column": 8
} | {
"line": 93,
"column": 25
} | {
"line": 93,
"column": 26
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : RCLike 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace 𝕜 F\nT : E →ₗ.[𝕜] F\nS : F →ₗ.[𝕜] E\n⊢ 0 ∈ {y | Continuous ⇑((innerₛₗ 𝕜) y ∘ₗ T.toFun)}",
"ppTerm": "?m.129",
... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : RCLike 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace 𝕜 F\nT : E →ₗ.[𝕜] F\nS : F →ₗ.[𝕜] E\n⊢ Continuous ⇑((innerₛₗ 𝕜) 0 ∘ₗ T.toFun)"
] | Set.mem_setOf_eq, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.InnerProductSpace.LinearPMap | {
"line": 97,
"column": 8
} | {
"line": 97,
"column": 25
} | {
"line": 97,
"column": 26
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : RCLike 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace 𝕜 F\nT : E →ₗ.[𝕜] F\nS : F →ₗ.[𝕜] E\na : 𝕜\nx : F\nhx : x ∈ {y | Continuous ⇑((innerₛₗ 𝕜) y ∘ₗ T.toFun)}\n⊢ a • x ... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : RCLike 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace 𝕜 F\nT : E →ₗ.[𝕜] F\nS : F →ₗ.[𝕜] E\na : 𝕜\nx : F\nhx : Continuous ⇑((innerₛₗ 𝕜) x ∘ₗ T.toFun)\n⊢ Continuous ⇑((innerₛₗ 𝕜) (a... | Set.mem_setOf_eq, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.InnerProductSpace.LinearPMap | {
"line": 98,
"column": 4
} | {
"line": 98,
"column": 32
} | {
"line": 100,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : RCLike 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace 𝕜 F\nT : E →ₗ.[𝕜] F\nS : F →ₗ.[𝕜] E\na : 𝕜\nx : F\nhx : Continuous ⇑((innerₛₗ 𝕜) x ∘ₗ T.toFun)\n⊢ Continuous ⇑(((s... | [] | exact hx.const_smul (conj a) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Analysis.InnerProductSpace.LinearPMap | {
"line": 318,
"column": 2
} | {
"line": 319,
"column": 96
} | {
"line": 320,
"column": 2
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁵ : RCLike 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : InnerProductSpace 𝕜 F\nT : E →ₗ.[𝕜] F\ninst✝ : CompleteSpace E\nhT : Dense ↑T.domain\nx : F × E\nhx : x ∈ T.graph.adjoint\nhx' : x.1 =... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁵ : RCLike 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : InnerProductSpace 𝕜 F\nT : E →ₗ.[𝕜] F\ninst✝ : CompleteSpace E\nhT : Dense ↑T.domain\nx : F × E\nhx' : x.1 = 0\nhx : ∀ a ∈ T.domain, ⟪a, x.2⟫ = 0\... | simp only [mem_adjoint_iff, mem_graph_iff, Subtype.exists, exists_and_left, exists_eq_left, hx',
inner_zero_right, zero_sub, neg_eq_zero, forall_exists_index, forall_apply_eq_imp_iff] at hx | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Topology.MetricSpace.HausdorffDimension | {
"line": 115,
"column": 2
} | {
"line": 118,
"column": 59
} | {
"line": 120,
"column": 0
} | [
{
"pp": "X : Type u_2\ninst✝² : EMetricSpace X\ninst✝¹ : MeasurableSpace X\ninst✝ : BorelSpace X\ns : Set X\nd : ℝ≥0\nh : ↑d < dimH s\n⊢ μH[↑d] s = ∞",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Real",
"ENNReal.ofNNReal",
"MeasureTheory.Measure",
"Preorder.toLT"... | [] | simp only [dimH_def, lt_iSup_iff] at h
rcases h with ⟨d', hsd', hdd'⟩
rw [ENNReal.coe_lt_coe, ← NNReal.coe_lt_coe] at hdd'
exact top_unique (hsd' ▸ hausdorffMeasure_mono hdd'.le _) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.MetricSpace.HausdorffDimension | {
"line": 115,
"column": 2
} | {
"line": 118,
"column": 59
} | {
"line": 120,
"column": 0
} | [
{
"pp": "X : Type u_2\ninst✝² : EMetricSpace X\ninst✝¹ : MeasurableSpace X\ninst✝ : BorelSpace X\ns : Set X\nd : ℝ≥0\nh : ↑d < dimH s\n⊢ μH[↑d] s = ∞",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Real",
"ENNReal.ofNNReal",
"MeasureTheory.Measure",
"Preorder.toLT"... | [] | simp only [dimH_def, lt_iSup_iff] at h
rcases h with ⟨d', hsd', hdd'⟩
rw [ENNReal.coe_lt_coe, ← NNReal.coe_lt_coe] at hdd'
exact top_unique (hsd' ▸ hausdorffMeasure_mono hdd'.le _) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Euclidean.Volume.Measure | {
"line": 237,
"column": 2
} | {
"line": 237,
"column": 36
} | {
"line": 238,
"column": 2
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝¹⁷ : EMetricSpace X\ninst✝¹⁶ : MeasurableSpace X\ninst✝¹⁵ : BorelSpace X\ninst✝¹⁴ : EMetricSpace Y\ninst✝¹³ : MeasurableSpace Y\ninst✝¹² : BorelSpace Y\nV : Type u_3\nP : Type u_4\ninst✝¹¹ : NormedAddCommGroup V\ninst✝¹⁰ : InnerProductSpace ℝ V\ninst✝⁹ : MeasurableSpace... | [
"X : Type u_1\nY : Type u_2\ninst✝¹⁷ : EMetricSpace X\ninst✝¹⁶ : MeasurableSpace X\ninst✝¹⁵ : BorelSpace X\ninst✝¹⁴ : EMetricSpace Y\ninst✝¹³ : MeasurableSpace Y\ninst✝¹² : BorelSpace Y\nV : Type u_3\nP : Type u_4\ninst✝¹¹ : NormedAddCommGroup V\ninst✝¹⁰ : InnerProductSpace ℝ V\ninst✝⁹ : MeasurableSpace V\ninst✝⁸ :... | rw [euclideanHausdorffMeasure_def] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Geometry.Euclidean.Volume.Measure | {
"line": 242,
"column": 2
} | {
"line": 242,
"column": 36
} | {
"line": 243,
"column": 2
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝¹⁶ : EMetricSpace X\ninst✝¹⁵ : MeasurableSpace X\ninst✝¹⁴ : BorelSpace X\ninst✝¹³ : EMetricSpace Y\ninst✝¹² : MeasurableSpace Y\ninst✝¹¹ : BorelSpace Y\nV : Type u_3\nP : Type u_4\ninst✝¹⁰ : NormedAddCommGroup V\ninst✝⁹ : InnerProductSpace ℝ V\ninst✝⁸ : MeasurableSpace ... | [
"X : Type u_1\nY : Type u_2\ninst✝¹⁶ : EMetricSpace X\ninst✝¹⁵ : MeasurableSpace X\ninst✝¹⁴ : BorelSpace X\ninst✝¹³ : EMetricSpace Y\ninst✝¹² : MeasurableSpace Y\ninst✝¹¹ : BorelSpace Y\nV : Type u_3\nP : Type u_4\ninst✝¹⁰ : NormedAddCommGroup V\ninst✝⁹ : InnerProductSpace ℝ V\ninst✝⁸ : MeasurableSpace V\ninst✝⁷ : ... | rw [euclideanHausdorffMeasure_def] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Geometry.Euclidean.Volume.Measure | {
"line": 247,
"column": 2
} | {
"line": 247,
"column": 36
} | {
"line": 248,
"column": 2
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝¹⁶ : EMetricSpace X\ninst✝¹⁵ : MeasurableSpace X\ninst✝¹⁴ : BorelSpace X\ninst✝¹³ : EMetricSpace Y\ninst✝¹² : MeasurableSpace Y\ninst✝¹¹ : BorelSpace Y\nV : Type u_3\nP : Type u_4\ninst✝¹⁰ : NormedAddCommGroup V\ninst✝⁹ : InnerProductSpace ℝ V\ninst✝⁸ : MeasurableSpace ... | [
"X : Type u_1\nY : Type u_2\ninst✝¹⁶ : EMetricSpace X\ninst✝¹⁵ : MeasurableSpace X\ninst✝¹⁴ : BorelSpace X\ninst✝¹³ : EMetricSpace Y\ninst✝¹² : MeasurableSpace Y\ninst✝¹¹ : BorelSpace Y\nV : Type u_3\nP : Type u_4\ninst✝¹⁰ : NormedAddCommGroup V\ninst✝⁹ : InnerProductSpace ℝ V\ninst✝⁸ : MeasurableSpace V\ninst✝⁷ : ... | rw [euclideanHausdorffMeasure_def] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.FunctionalSpaces.SobolevInequality | {
"line": 634,
"column": 6
} | {
"line": 634,
"column": 57
} | {
"line": 635,
"column": 6
} | [
{
"pp": "F : Type u_3\ninst✝⁸ : NormedAddCommGroup F\ninst✝⁷ : NormedSpace ℝ F\nE : Type u_4\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : MeasurableSpace E\ninst✝³ : BorelSpace E\ninst✝² : FiniteDimensional ℝ E\nμ : Measure E\ninst✝¹ : μ.IsAddHaarMeasure\ninst✝ : FiniteDimensional ℝ F\nu :... | [
"F : Type u_3\ninst✝⁸ : NormedAddCommGroup F\ninst✝⁷ : NormedSpace ℝ F\nE : Type u_4\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : MeasurableSpace E\ninst✝³ : BorelSpace E\ninst✝² : FiniteDimensional ℝ E\nμ : Measure E\ninst✝¹ : μ.IsAddHaarMeasure\ninst✝ : FiniteDimensional ℝ F\nu : E → F\nhu :... | simp_rw [C₂, C₁, C, e, SNormLESNormFDerivOfEqConst] | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | Mathlib.Tactic.tacticSimp_rw___ |
Mathlib.Topology.MetricSpace.HausdorffDimension | {
"line": 419,
"column": 47
} | {
"line": 420,
"column": 81
} | {
"line": 422,
"column": 0
} | [
{
"pp": "𝕜 : Type u_4\nE : Type u_5\nF : Type u_6\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\ne : E ≃L[𝕜] F\ns : Set E\n⊢ dimH s ≤ dimH (⇑e '' s)",
"ppTerm": "?m.52",
"assigned": true,
"use... | [] | by
simpa only [e.symm_image_image] using e.symm.lipschitz.dimH_image_le (e '' s) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Topology.MetricSpace.HausdorffDimension | {
"line": 448,
"column": 65
} | {
"line": 448,
"column": 84
} | {
"line": 448,
"column": 85
} | [
{
"pp": "case inr.refine_1\nι : Type u_1\ninst✝ : Fintype ι\nx : ι → ℝ\nr : ℝ\nhr : 0 < r\nh✝ : Nonempty ι\nthis : μH[↑(Fintype.card ι)] (Metric.ball x r) = ENNReal.ofReal ((2 * r) ^ Fintype.card ι)\n⊢ μH[↑↑(Fintype.card ι)] (Metric.ball x r) ≠ 0",
"ppTerm": "?inr.refine_1",
"assigned": true,
"usedC... | [
"case inr.refine_1\nι : Type u_1\ninst✝ : Fintype ι\nx : ι → ℝ\nr : ℝ\nhr : 0 < r\nh✝ : Nonempty ι\nthis : μH[↑(Fintype.card ι)] (Metric.ball x r) = ENNReal.ofReal ((2 * r) ^ Fintype.card ι)\n⊢ μH[↑(Fintype.card ι)] (Metric.ball x r) ≠ 0"
] | NNReal.coe_natCast, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Topology.MetricSpace.HausdorffDimension | {
"line": 448,
"column": 65
} | {
"line": 448,
"column": 84
} | {
"line": 448,
"column": 85
} | [
{
"pp": "case inr.refine_2\nι : Type u_1\ninst✝ : Fintype ι\nx : ι → ℝ\nr : ℝ\nhr : 0 < r\nh✝ : Nonempty ι\nthis : μH[↑(Fintype.card ι)] (Metric.ball x r) = ENNReal.ofReal ((2 * r) ^ Fintype.card ι)\n⊢ μH[↑↑(Fintype.card ι)] (Metric.ball x r) ≠ ∞",
"ppTerm": "?inr.refine_2",
"assigned": true,
"usedC... | [
"case inr.refine_2\nι : Type u_1\ninst✝ : Fintype ι\nx : ι → ℝ\nr : ℝ\nhr : 0 < r\nh✝ : Nonempty ι\nthis : μH[↑(Fintype.card ι)] (Metric.ball x r) = ENNReal.ofReal ((2 * r) ^ Fintype.card ι)\n⊢ μH[↑(Fintype.card ι)] (Metric.ball x r) ≠ ∞"
] | NNReal.coe_natCast, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.MeasureTheory.Measure.Hausdorff | {
"line": 601,
"column": 2
} | {
"line": 601,
"column": 54
} | {
"line": 601,
"column": 55
} | [
{
"pp": "case inr\nX : Type u_2\ninst✝² : EMetricSpace X\ninst✝¹ : MeasurableSpace X\ninst✝ : BorelSpace X\nd₁ d₂ : ℝ\nh✝ : d₁ ≤ d₂\ns : Set X\nh : d₁ < d₂\n⊢ μH[d₂] s ≤ μH[d₁] s",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"MeasureTheory.Measure",
"MeasureTheory.Measure.haus... | [
"case inr.inl\nX : Type u_2\ninst✝² : EMetricSpace X\ninst✝¹ : MeasurableSpace X\ninst✝ : BorelSpace X\nd₁ d₂ : ℝ\nh✝ : d₁ ≤ d₂\ns : Set X\nh : d₁ < d₂\nhs : μH[d₂] s = 0\n⊢ μH[d₂] s ≤ μH[d₁] s",
"case inr.inr\nX : Type u_2\ninst✝² : EMetricSpace X\ninst✝¹ : MeasurableSpace X\ninst✝ : BorelSpace X\nd₁ d₂ : ℝ\nh✝ ... | rcases hausdorffMeasure_zero_or_top h s with hs | hs | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.Analysis.InnerProductSpace.NormDet | {
"line": 194,
"column": 4
} | {
"line": 194,
"column": 8
} | {
"line": 195,
"column": 4
} | [
{
"pp": "case neg\n𝕜 : Type u_1\nU : Type u_2\nV : Type u_3\ninst✝⁷ : RCLike 𝕜\ninst✝⁶ : NormedAddCommGroup U\ninst✝⁵ : InnerProductSpace 𝕜 U\ninst✝⁴ : FiniteDimensional 𝕜 U\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace 𝕜 V\nι : Type u_5\ninst✝¹ : Fintype ι\ninst✝ : DecidableEq ι\nf : U →ₗ[𝕜]... | [
"case neg\n𝕜 : Type u_1\nU : Type u_2\nV : Type u_3\ninst✝⁷ : RCLike 𝕜\ninst✝⁶ : NormedAddCommGroup U\ninst✝⁵ : InnerProductSpace 𝕜 U\ninst✝⁴ : FiniteDimensional 𝕜 U\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace 𝕜 V\nι : Type u_5\ninst✝¹ : Fintype ι\ninst✝ : DecidableEq ι\nf : U →ₗ[𝕜] V\nbu : Ort... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Analysis.InnerProductSpace.OfNorm | {
"line": 169,
"column": 60
} | {
"line": 176,
"column": 72
} | {
"line": 178,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\ninst✝³ : RCLike 𝕜\nE : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : InnerProductSpaceable E\nr : ℝ\n⊢ innerProp' E ↑r",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"IsDenseEmbedding.toIsDenseInducing",
"Eq.mpr",
"No... | [] | by
intro x y
revert r
rw [← funext_iff]
refine Rat.isDenseEmbedding_coe_real.dense.equalizer ?_ ?_ (funext fun X => ?_)
· exact (continuous_ofReal.smul continuous_const).inner_ continuous_const
· exact (continuous_conj.comp continuous_ofReal).mul continuous_const
· simp only [Function.comp_apply, RCLike.o... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.InnerProductSpace.NormDet | {
"line": 279,
"column": 6
} | {
"line": 279,
"column": 69
} | {
"line": 280,
"column": 6
} | [
{
"pp": "case pos\n𝕜 : Type u_1\nU : Type u_2\nV : Type u_3\ninst✝⁶ : RCLike 𝕜\ninst✝⁵ : NormedAddCommGroup U\ninst✝⁴ : InnerProductSpace 𝕜 U\ninst✝³ : FiniteDimensional 𝕜 U\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace 𝕜 V\ninst✝ : CompleteSpace V\nf : U →L[𝕜] V\nthis✝ : CompleteSpace U\nthi... | [
"case pos\n𝕜 : Type u_1\nU : Type u_2\nV : Type u_3\ninst✝⁶ : RCLike 𝕜\ninst✝⁵ : NormedAddCommGroup U\ninst✝⁴ : InnerProductSpace 𝕜 U\ninst✝³ : FiniteDimensional 𝕜 U\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace 𝕜 V\ninst✝ : CompleteSpace V\nf : U →L[𝕜] V\nthis✝ : CompleteSpace U\nthis : Complete... | ContinuousLinearMap.comp_assoc (ContinuousLinearMap.adjoint _), | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.InnerProductSpace.Reproducing | {
"line": 158,
"column": 2
} | {
"line": 158,
"column": 62
} | {
"line": 159,
"column": 2
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁷ : RCLike 𝕜\nX : Type u_2\nV : Type u_3\ninst✝⁶ : NormedAddCommGroup V\ninst✝⁵ : InnerProductSpace 𝕜 V\nH : Type u_4\ninst✝⁴ : NormedAddCommGroup H\ninst✝³ : InnerProductSpace 𝕜 H\ninst✝² : RKHS 𝕜 H X V\ninst✝¹ : CompleteSpace H\ninst✝ : CompleteSpace V\nf : H\nfin : f ∈ (span ... | [
"𝕜 : Type u_1\ninst✝⁷ : RCLike 𝕜\nX : Type u_2\nV : Type u_3\ninst✝⁶ : NormedAddCommGroup V\ninst✝⁵ : InnerProductSpace 𝕜 V\nH : Type u_4\ninst✝⁴ : NormedAddCommGroup H\ninst✝³ : InnerProductSpace 𝕜 H\ninst✝² : RKHS 𝕜 H X V\ninst✝¹ : CompleteSpace H\ninst✝ : CompleteSpace V\nf : H\nfin : f ∈ (span 𝕜 {x | ∃ x_... | refine inner_right_of_mem_orthogonal (subset_closure ?_) fin | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.InnerProductSpace.NormDet | {
"line": 287,
"column": 4
} | {
"line": 287,
"column": 8
} | {
"line": 288,
"column": 4
} | [
{
"pp": "𝕜 : Type u_1\nU : Type u_2\nV : Type u_3\ninst✝⁶ : RCLike 𝕜\ninst✝⁵ : NormedAddCommGroup U\ninst✝⁴ : InnerProductSpace 𝕜 U\ninst✝³ : FiniteDimensional 𝕜 U\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace 𝕜 V\ninst✝ : CompleteSpace V\nf : U →L[𝕜] V\nthis✝ : CompleteSpace U\nthis : Comple... | [
"𝕜 : Type u_1\nU : Type u_2\nV : Type u_3\ninst✝⁶ : RCLike 𝕜\ninst✝⁵ : NormedAddCommGroup U\ninst✝⁴ : InnerProductSpace 𝕜 U\ninst✝³ : FiniteDimensional 𝕜 U\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace 𝕜 V\ninst✝ : CompleteSpace V\nf : U →L[𝕜] V\nthis✝ : CompleteSpace U\nthis : CompleteSpace ↥(↑f... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Analysis.InnerProductSpace.NormDet | {
"line": 320,
"column": 4
} | {
"line": 320,
"column": 8
} | {
"line": 321,
"column": 4
} | [
{
"pp": "𝕜 : Type u_1\nU : Type u_2\nV : Type u_3\ninst✝⁷ : RCLike 𝕜\ninst✝⁶ : NormedAddCommGroup U\ninst✝⁵ : InnerProductSpace 𝕜 U\ninst✝⁴ : FiniteDimensional 𝕜 U\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace 𝕜 V\nι : Type u_5\ninst✝¹ : Fintype ι\ninst✝ : DecidableEq ι\nf : U →ₗ[𝕜] V\nb : Or... | [
"𝕜 : Type u_1\nU : Type u_2\nV : Type u_3\ninst✝⁷ : RCLike 𝕜\ninst✝⁶ : NormedAddCommGroup U\ninst✝⁵ : InnerProductSpace 𝕜 U\ninst✝⁴ : FiniteDimensional 𝕜 U\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace 𝕜 V\nι : Type u_5\ninst✝¹ : Fintype ι\ninst✝ : DecidableEq ι\nf : U →ₗ[𝕜] V\nb : OrthonormalBas... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Analysis.InnerProductSpace.StarOrder | {
"line": 67,
"column": 28
} | {
"line": 67,
"column": 32
} | {
"line": 67,
"column": 32
} | [
{
"pp": "𝕜 : Type u_1\nH : Type u_2\ninst✝⁶ : RCLike 𝕜\ninst✝⁵ : NormedAddCommGroup H\ninst✝⁴ : InnerProductSpace 𝕜 H\ninst✝³ : CompleteSpace H\ninst✝² : Algebra ℝ (H →L[𝕜] H)\ninst✝¹ : IsScalarTower ℝ 𝕜 (H →L[𝕜] H)\ninst✝ : ContinuousFunctionalCalculus ℝ (H →L[𝕜] H) IsSelfAdjoint\nf g : H →L[𝕜] H\nh : ... | [
"𝕜 : Type u_1\nH : Type u_2\ninst✝⁶ : RCLike 𝕜\ninst✝⁵ : NormedAddCommGroup H\ninst✝⁴ : InnerProductSpace 𝕜 H\ninst✝³ : CompleteSpace H\ninst✝² : Algebra ℝ (H →L[𝕜] H)\ninst✝¹ : IsScalarTower ℝ 𝕜 (H →L[𝕜] H)\ninst✝ : ContinuousFunctionalCalculus ℝ (H →L[𝕜] H) IsSelfAdjoint\nf g : H →L[𝕜] H\nh : (g - f).IsPo... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.MeasureTheory.Measure.Hausdorff | {
"line": 1065,
"column": 6
} | {
"line": 1065,
"column": 31
} | {
"line": 1065,
"column": 32
} | [
{
"pp": "𝕜 : Type u_4\nE : Type u_5\nP : Type u_6\ninst✝⁶ : NormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : MeasurableSpace P\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor E P\ninst✝ : BorelSpace P\nd : ℝ\nhd : 0 ≤ d\nx : P\nc : 𝕜\nhc : c ≠ 0\ns : Set P\n⊢ μH[d] (⇑((Affi... | [
"𝕜 : Type u_4\nE : Type u_5\nP : Type u_6\ninst✝⁶ : NormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : MeasurableSpace P\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor E P\ninst✝ : BorelSpace P\nd : ℝ\nhd : 0 ≤ d\nx : P\nc : 𝕜\nhc : c ≠ 0\ns : Set P\n⊢ μH[d] (⇑((AffineEquiv.homo... | ← AffineEquiv.image_symm, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.LocallyConvex.ContinuousOfBounded | {
"line": 94,
"column": 2
} | {
"line": 94,
"column": 78
} | {
"line": 96,
"column": 2
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\nE : Type u_3\nF : Type u_4\ninst✝¹¹ : AddCommGroup E\ninst✝¹⁰ : TopologicalSpace E\ninst✝⁹ : IsTopologicalAddGroup E\ninst✝⁸ : AddCommGroup F\ninst✝⁷ : TopologicalSpace F\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : Module 𝕜 E\ninst✝⁴ : ContinuousSMul 𝕜 E\ninst✝³ : No... | [
"𝕜 : Type u_1\n𝕜' : Type u_2\nE : Type u_3\nF : Type u_4\ninst✝¹¹ : AddCommGroup E\ninst✝¹⁰ : TopologicalSpace E\ninst✝⁹ : IsTopologicalAddGroup E\ninst✝⁸ : AddCommGroup F\ninst✝⁷ : TopologicalSpace F\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : Module 𝕜 E\ninst✝⁴ : ContinuousSMul 𝕜 E\ninst✝³ : NormedField 𝕜... | simp_rw [ContinuousAt, map_zero, bE'.tendsto_left_iff, true_and, Set.MapsTo] | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | Mathlib.Tactic.tacticSimp_rw___ |
Mathlib.Analysis.LocallyConvex.PointwiseConvergence | {
"line": 109,
"column": 4
} | {
"line": 109,
"column": 35
} | {
"line": 110,
"column": 4
} | [
{
"pp": "case h\nα : Type u_1\nR : Type u_2\n𝕜₁ : Type u_3\n𝕜₂ : Type u_4\n𝕜₃ : Type u_5\ninst✝¹² : NormedField 𝕜₁\ninst✝¹¹ : NormedField 𝕜₂\ninst✝¹⁰ : NormedField 𝕜₃\nσ : 𝕜₁ →+* 𝕜₂\nτ : 𝕜₃ →+* 𝕜₂\nD : Type u_6\nE : Type u_7\nF : Type u_8\nG : Type u_9\ninst✝⁹ : AddCommGroup E\ninst✝⁸ : TopologicalSpa... | [
"case h\nα : Type u_1\nR : Type u_2\n𝕜₁ : Type u_3\n𝕜₂ : Type u_4\n𝕜₃ : Type u_5\ninst✝¹² : NormedField 𝕜₁\ninst✝¹¹ : NormedField 𝕜₂\ninst✝¹⁰ : NormedField 𝕜₃\nσ : 𝕜₁ →+* 𝕜₂\nτ : 𝕜₃ →+* 𝕜₂\nD : Type u_6\nE : Type u_7\nF : Type u_8\nG : Type u_9\ninst✝⁹ : AddCommGroup E\ninst✝⁸ : TopologicalSpace E\ninst✝⁷... | rw [← Seminorm.finset_sup_smul] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.InnerProductSpace.TwoDim | {
"line": 161,
"column": 4
} | {
"line": 161,
"column": 8
} | {
"line": 162,
"column": 4
} | [
{
"pp": "case e'_2\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : Fact (finrank ℝ E = 2)\no : Orientation ℝ E (Fin 2)\nφ : E ≃ₗᵢ[ℝ] E\nhφ : 0 < LinearMap.det ↑φ.toLinearEquiv\nx y : E\n⊢ o = (map (Fin 2) φ.toLinearEquiv) o",
"ppTerm": "?e'_2",
"assigned": true,
... | [
"case e'_2\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : Fact (finrank ℝ E = 2)\no : Orientation ℝ E (Fin 2)\nφ : E ≃ₗᵢ[ℝ] E\nhφ : 0 < LinearMap.det ↑φ.toLinearEquiv\nx y : E\n⊢ (map (Fin 2) φ.toLinearEquiv) o = o"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Analysis.InnerProductSpace.TwoDim | {
"line": 313,
"column": 4
} | {
"line": 313,
"column": 8
} | {
"line": 314,
"column": 4
} | [
{
"pp": "case e'_3\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : Fact (finrank ℝ E = 2)\no : Orientation ℝ E (Fin 2)\nφ : E ≃ₗᵢ[ℝ] E\nhφ : 0 < LinearMap.det ↑φ.toLinearEquiv\nx : E\n⊢ o = (map (Fin 2) φ.toLinearEquiv) o",
"ppTerm": "?e'_3",
"assigned": true,
"... | [
"case e'_3\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : Fact (finrank ℝ E = 2)\no : Orientation ℝ E (Fin 2)\nφ : E ≃ₗᵢ[ℝ] E\nhφ : 0 < LinearMap.det ↑φ.toLinearEquiv\nx : E\n⊢ (map (Fin 2) φ.toLinearEquiv) o = o"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Analysis.MellinTransform | {
"line": 102,
"column": 2
} | {
"line": 103,
"column": 90
} | {
"line": 105,
"column": 0
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nf : ℝ → E\ns a : ℂ\n⊢ mellin (fun t ↦ ↑t ^ a • f t) s = mellin f (s + a)",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Eq.mpr",
"instClosedIicTopology",
"Real",
"Set.I... | [] | refine setIntegral_congr_fun measurableSet_Ioi fun t ht => ?_
simp_rw [← sub_add_eq_add_sub, cpow_add _ _ (ofReal_ne_zero.2 <| ne_of_gt ht), mul_smul] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.MellinTransform | {
"line": 102,
"column": 2
} | {
"line": 103,
"column": 90
} | {
"line": 105,
"column": 0
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nf : ℝ → E\ns a : ℂ\n⊢ mellin (fun t ↦ ↑t ^ a • f t) s = mellin f (s + a)",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Eq.mpr",
"instClosedIicTopology",
"Real",
"Set.I... | [] | refine setIntegral_congr_fun measurableSet_Ioi fun t ht => ?_
simp_rw [← sub_add_eq_add_sub, cpow_add _ _ (ofReal_ne_zero.2 <| ne_of_gt ht), mul_smul] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.MellinTransform | {
"line": 313,
"column": 24
} | {
"line": 313,
"column": 37
} | {
"line": 313,
"column": 37
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\na b : ℝ\nf : ℝ → E\nhab : a < b\nhf : f =O[𝓝[>] 0] fun x ↦ x ^ (-a)\nthis : log =o[𝓝[>] 0] fun t ↦ t ^ (a - b)\nt : ℝ\nht : t ∈ Ioi 0\n⊢ t ^ (a - b) * t ^ (-a) = t ^ (-b)",
"ppTerm": "?m.197",
"assigned": true,
"usedCon... | [
"E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\na b : ℝ\nf : ℝ → E\nhab : a < b\nhf : f =O[𝓝[>] 0] fun x ↦ x ^ (-a)\nthis : log =o[𝓝[>] 0] fun t ↦ t ^ (a - b)\nt : ℝ\nht : t ∈ Ioi 0\n⊢ t ^ (a - b + -a) = t ^ (-b)"
] | ← rpow_add ht | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Analysis.SpecialFunctions.Trigonometric.EulerSineProd | {
"line": 201,
"column": 4
} | {
"line": 201,
"column": 35
} | {
"line": 202,
"column": 4
} | [
{
"pp": "case inr.succ\nz : ℂ\nhz : z ≠ 0\nn : ℕ\nhn :\n Complex.sin (↑π * z) =\n ((↑π * z * ∏ j ∈ Finset.range n, (1 - z ^ 2 / (↑j + 1) ^ 2)) *\n ∫ (x : ℝ) in 0..π / 2, Complex.cos (2 * z * ↑x) * ↑(cos x) ^ (2 * n)) /\n ↑(∫ (x : ℝ) in 0..π / 2, cos x ^ (2 * n))\n⊢ Complex.sin (↑π * z) =\n ((... | [
"case inr.succ\nz : ℂ\nhz : z ≠ 0\nn : ℕ\nhn :\n Complex.sin (↑π * z) =\n ((↑π * z * ∏ j ∈ Finset.range n, (1 - z ^ 2 / (↑j + 1) ^ 2)) *\n ∫ (x : ℝ) in 0..π / 2, Complex.cos (2 * z * ↑x) * ↑(cos x) ^ (2 * n)) /\n ↑(∫ (x : ℝ) in 0..π / 2, cos x ^ (2 * n))\n⊢ ((↑π * z * ∏ j ∈ Finset.range n, (1 - z ^ ... | rw [hn, Finset.prod_range_succ] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup | {
"line": 248,
"column": 8
} | {
"line": 249,
"column": 12
} | {
"line": 250,
"column": 4
} | [
{
"pp": "case refine_1.inr\nf : ℝ → ℝ\nx : ℝ\nhf_conv : ConvexOn ℝ (Ioi 0) f\nhf_feq : ∀ {y : ℝ}, 0 < y → f (y + 1) = f y + log y\nhx : 0 < x\nthis : ∀ (m : ℕ), ↑m < x → x ≤ ↑m + 1 → Tendsto (logGammaSeq x) atTop (𝓝 (f x - f 1))\nh✝ : 1 ≤ x\n⊢ ↑⌈x - 1⌉₊ < x",
"ppTerm": "?refine_1.inr",
"assigned": true... | [] | convert! Nat.ceil_lt_add_one (by linarith : 0 ≤ x - 1)
abel | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup | {
"line": 248,
"column": 8
} | {
"line": 249,
"column": 12
} | {
"line": 250,
"column": 4
} | [
{
"pp": "case refine_1.inr\nf : ℝ → ℝ\nx : ℝ\nhf_conv : ConvexOn ℝ (Ioi 0) f\nhf_feq : ∀ {y : ℝ}, 0 < y → f (y + 1) = f y + log y\nhx : 0 < x\nthis : ∀ (m : ℕ), ↑m < x → x ≤ ↑m + 1 → Tendsto (logGammaSeq x) atTop (𝓝 (f x - f 1))\nh✝ : 1 ≤ x\n⊢ ↑⌈x - 1⌉₊ < x",
"ppTerm": "?refine_1.inr",
"assigned": true... | [] | convert! Nat.ceil_lt_add_one (by linarith : 0 ≤ x - 1)
abel | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.SpecialFunctions.Gamma.Beta | {
"line": 245,
"column": 4
} | {
"line": 245,
"column": 46
} | {
"line": 246,
"column": 4
} | [
{
"pp": "case e_a.e_a.e_a\ns : ℂ\nn : ℕ\nhn : n ≠ 0\n⊢ ∏ x ∈ Finset.range n, (s + 1 + ↑x) = ∏ k ∈ Finset.range n, (s + ↑(k + 1))",
"ppTerm": "?e_a.e_a.e_a✝",
"assigned": true,
"usedConstants": [
"Complex.commRing",
"Finset",
"Membership.mem",
"instOfNatNat",
"Finset.pro... | [
"case e_a.e_a.e_a\ns : ℂ\nn : ℕ\nhn : n ≠ 0\nx : ℕ\nx✝ : x ∈ Finset.range n\n⊢ s + 1 + ↑x = s + ↑(x + 1)"
] | refine Finset.prod_congr rfl fun x _ => ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.SpecialFunctions.Gamma.Beta | {
"line": 276,
"column": 6
} | {
"line": 276,
"column": 26
} | {
"line": 276,
"column": 26
} | [
{
"pp": "s : ℂ\nhs : 0 < s.re\n⊢ Tendsto (fun n ↦ ∫ (x : ℝ) in 0..↑n, ↑((1 - x / ↑n) ^ n) * ↑x ^ (s - 1)) atTop (𝓝 (Gamma s))",
"ppTerm": "?m.47",
"assigned": true,
"usedConstants": [
"instInnerProductSpaceRealComplex",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCom... | [
"s : ℂ\nhs : 0 < s.re\n⊢ Tendsto (fun n ↦ ∫ (x : ℝ) in 0..↑n, ↑((1 - x / ↑n) ^ n) * ↑x ^ (s - 1)) atTop (𝓝 s.GammaIntegral)"
] | Gamma_eq_integral hs | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup | {
"line": 357,
"column": 2
} | {
"line": 357,
"column": 6
} | {
"line": 358,
"column": 2
} | [
{
"pp": "case e'_6\n⊢ Ici 2 = Ioi 0 ∩ Ici 2",
"ppTerm": "?e'_6",
"assigned": true,
"usedConstants": [
"Real",
"Set.Ioi",
"Set.Ici",
"Real.instZero",
"PartialOrder.toPreorder",
"Nat.instAtLeastTwoHAddOfNat",
"SemilatticeInf.toPartialOrder",
"DistribLatt... | [
"case e'_6\n⊢ Ioi 0 ∩ Ici 2 = Ici 2"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Analysis.Normed.Affine.Ceva | {
"line": 50,
"column": 2
} | {
"line": 50,
"column": 74
} | {
"line": 51,
"column": 2
} | [
{
"pp": "𝕜 : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : SeminormedAddCommGroup V\ninst✝³ : NormedField 𝕜\ninst✝² : NormedSpace 𝕜 V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle 𝕜 P\np : Fin 3 → P\np' : P\nhp0 : ∀ (i : Fin 3), p i ≠ t.points (i + 2)\nhp : ∀ (i : Fin 3), p i ∈ line[𝕜... | [
"𝕜 : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : SeminormedAddCommGroup V\ninst✝³ : NormedField 𝕜\ninst✝² : NormedSpace 𝕜 V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle 𝕜 P\np : Fin 3 → P\np' : P\nhp0 : ∀ (i : Fin 3), p i ≠ t.points (i + 2)\nhp : ∀ (i : Fin 3), p i ∈ line[𝕜, t.points (... | have aux (i) : dist (p i) (t.points (i + 2)) ≠ 0 := by simpa using hp0 i | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Analysis.SpecialFunctions.Gamma.Beta | {
"line": 380,
"column": 2
} | {
"line": 381,
"column": 75
} | {
"line": 382,
"column": 2
} | [
{
"pp": "z : ℂ\nn : ℕ\nhn : n ≠ 0\naux : ∀ (a b c d : ℂ), a * b * (c * d) = a * c * (b * d)\n⊢ ↑n ^ z * ↑n ^ (1 - z) * ↑n ! ^ 2 /\n ((∏ j ∈ Finset.range (n + 1), (z + ↑j)) * ∏ j ∈ Finset.range (n + 1), (1 - z + ↑j)) =\n ↑n / (↑n + 1 - z) * (1 / (z * ∏ j ∈ Finset.range n, (1 - z ^ 2 / (↑j + 1) ^ 2)))",
... | [
"z : ℂ\nn : ℕ\nhn : n ≠ 0\naux : ∀ (a b c d : ℂ), a * b * (c * d) = a * c * (b * d)\nthis : ↑n ^ z * ↑n ^ (1 - z) = ↑n\n⊢ ↑n ^ z * ↑n ^ (1 - z) * ↑n ! ^ 2 /\n ((∏ j ∈ Finset.range (n + 1), (z + ↑j)) * ∏ j ∈ Finset.range (n + 1), (1 - z + ↑j)) =\n ↑n / (↑n + 1 - z) * (1 / (z * ∏ j ∈ Finset.range n, (1 - z ^ ... | have : (n : ℂ) ^ z * (n : ℂ) ^ (1 - z) = n := by
rw [← cpow_add _ _ (Nat.cast_ne_zero.mpr hn), add_sub_cancel, cpow_one] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.LinearAlgebra.AffineSpace.Ceva | {
"line": 147,
"column": 2
} | {
"line": 148,
"column": 82
} | {
"line": 149,
"column": 2
} | [
{
"pp": "case inr\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\np' : P\nhp' : ∀ (i : Fin 3), p' ∈ line[k, t.points i, (AffineMap.lineMap (t.points (i + 1)) (t.poin... | [
"case inr\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i + 2... | obtain ⟨w', hw', rfl, h⟩ :=
t.independent.exists_affineCombination_eq_smul_eq_of_fintype (by simp) hw hp'w | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Analysis.Normed.Affine.MazurUlam | {
"line": 58,
"column": 6
} | {
"line": 60,
"column": 54
} | {
"line": 64,
"column": 2
} | [] | [] | dist (e z) z ≤ dist (e z) x + dist x z := dist_triangle (e z) x z
_ = dist (e x) (e z) + dist x z := by rw [hx, dist_comm]
_ = dist x z + dist x z := by rw [e.dist_eq x z] | Lean.Elab.Tactic._aux_Mathlib_Tactic_Widget_Calc___elabRules_Lean_calcTactic_1 | Lean.calcSteps |
Mathlib.Analysis.SpecialFunctions.Gamma.Beta | {
"line": 432,
"column": 14
} | {
"line": 432,
"column": 27
} | {
"line": 432,
"column": 28
} | [
{
"pp": "case pos\ns : ℂ\nhs : ∀ (m : ℕ), s ≠ -↑m\nh_im : s.im = 0\nthis : s = ↑s.re\n⊢ Gamma ↑s.re ≠ 0",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Complex.instZero",
"Complex.Gamma",
"id",
"Ne",
"Complex.ofReal",
"... | [
"case pos\ns : ℂ\nhs : ∀ (m : ℕ), s ≠ -↑m\nh_im : s.im = 0\nthis : s = ↑s.re\n⊢ ↑(Real.Gamma s.re) ≠ 0"
] | Gamma_ofReal, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.SpecialFunctions.Gamma.Beta | {
"line": 572,
"column": 17
} | {
"line": 572,
"column": 30
} | {
"line": 572,
"column": 31
} | [
{
"pp": "s : ℂ\nh1 : AnalyticOnNhd ℂ (fun z ↦ (Gamma z)⁻¹ * (Gamma (z + 1 / 2))⁻¹) univ\nh2 : AnalyticOnNhd ℂ (fun z ↦ (Gamma (2 * z))⁻¹ * 2 ^ (2 * z - 1) / ↑√π) univ\nh3 : Tendsto ofReal (𝓝[≠] 1) (𝓝[≠] 1)\nt : ℝ\nht : 0 < t\n⊢ (Gamma ↑t * Gamma (↑t + 1 / 2))⁻¹ = (Gamma (2 * ↑t))⁻¹ * 2 ^ (2 * ↑t - 1) / ↑√π",
... | [
"s : ℂ\nh1 : AnalyticOnNhd ℂ (fun z ↦ (Gamma z)⁻¹ * (Gamma (z + 1 / 2))⁻¹) univ\nh2 : AnalyticOnNhd ℂ (fun z ↦ (Gamma (2 * z))⁻¹ * 2 ^ (2 * z - 1) / ↑√π) univ\nh3 : Tendsto ofReal (𝓝[≠] 1) (𝓝[≠] 1)\nt : ℝ\nht : 0 < t\n⊢ (↑(Real.Gamma t) * Gamma (↑t + 1 / 2))⁻¹ = (Gamma (2 * ↑t))⁻¹ * 2 ^ (2 * ↑t - 1) / ↑√π"
] | Gamma_ofReal, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.SpecialFunctions.Gamma.Beta | {
"line": 572,
"column": 75
} | {
"line": 572,
"column": 88
} | {
"line": 572,
"column": 89
} | [
{
"pp": "s : ℂ\nh1 : AnalyticOnNhd ℂ (fun z ↦ (Gamma z)⁻¹ * (Gamma (z + 1 / 2))⁻¹) univ\nh2 : AnalyticOnNhd ℂ (fun z ↦ (Gamma (2 * z))⁻¹ * 2 ^ (2 * z - 1) / ↑√π) univ\nh3 : Tendsto ofReal (𝓝[≠] 1) (𝓝[≠] 1)\nt : ℝ\nht : 0 < t\n⊢ (↑(Real.Gamma t) * Gamma ↑(t + 1 / 2))⁻¹ = (Gamma (2 * ↑t))⁻¹ * 2 ^ (2 * ↑t - 1) /... | [
"s : ℂ\nh1 : AnalyticOnNhd ℂ (fun z ↦ (Gamma z)⁻¹ * (Gamma (z + 1 / 2))⁻¹) univ\nh2 : AnalyticOnNhd ℂ (fun z ↦ (Gamma (2 * z))⁻¹ * 2 ^ (2 * z - 1) / ↑√π) univ\nh3 : Tendsto ofReal (𝓝[≠] 1) (𝓝[≠] 1)\nt : ℝ\nht : 0 < t\n⊢ (↑(Real.Gamma t) * ↑(Real.Gamma (t + 1 / 2)))⁻¹ = (Gamma (2 * ↑t))⁻¹ * 2 ^ (2 * ↑t - 1) / ↑√π"... | Gamma_ofReal, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.SpecialFunctions.Gamma.Beta | {
"line": 574,
"column": 58
} | {
"line": 574,
"column": 71
} | {
"line": 575,
"column": 4
} | [
{
"pp": "s : ℂ\nh1 : AnalyticOnNhd ℂ (fun z ↦ (Gamma z)⁻¹ * (Gamma (z + 1 / 2))⁻¹) univ\nh2 : AnalyticOnNhd ℂ (fun z ↦ (Gamma (2 * z))⁻¹ * 2 ^ (2 * z - 1) / ↑√π) univ\nh3 : Tendsto ofReal (𝓝[≠] 1) (𝓝[≠] 1)\nt : ℝ\nht : 0 < t\n⊢ (Gamma ↑(2 * t))⁻¹ * (↑(2 ^ (1 - 2 * t)))⁻¹ * (↑√π)⁻¹ = (Gamma ↑(2 * t))⁻¹ * 2 ^ (... | [
"s : ℂ\nh1 : AnalyticOnNhd ℂ (fun z ↦ (Gamma z)⁻¹ * (Gamma (z + 1 / 2))⁻¹) univ\nh2 : AnalyticOnNhd ℂ (fun z ↦ (Gamma (2 * z))⁻¹ * 2 ^ (2 * z - 1) / ↑√π) univ\nh3 : Tendsto ofReal (𝓝[≠] 1) (𝓝[≠] 1)\nt : ℝ\nht : 0 < t\n⊢ (↑(Real.Gamma (2 * t)))⁻¹ * (↑(2 ^ (1 - 2 * t)))⁻¹ * (↑√π)⁻¹ = (↑(Real.Gamma (2 * t)))⁻¹ * 2 ^... | Gamma_ofReal, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 143,
"column": 19
} | {
"line": 143,
"column": 25
} | {
"line": 143,
"column": 26
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ 0 ≠ 1",
"ppTerm": "?m.181",
"assigned": true,
"usedConstants": [
"in... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 143,
"column": 19
} | {
"line": 143,
"column": 25
} | {
"line": 143,
"column": 26
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ 0 ≠ 1",
"ppTerm": "?m.181",
"assigned": true,
"usedConstants": [
"in... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 143,
"column": 19
} | {
"line": 143,
"column": 25
} | {
"line": 143,
"column": 26
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ 0 ≠ 1",
"ppTerm": "?m.181",
"assigned": true,
"usedConstants": [
"in... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 143,
"column": 49
} | {
"line": 143,
"column": 55
} | {
"line": 143,
"column": 56
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ 0 ≠ 2",
"ppTerm": "?m.189",
"assigned": true,
"usedConstants": [
"in... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 143,
"column": 49
} | {
"line": 143,
"column": 55
} | {
"line": 143,
"column": 56
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ 0 ≠ 2",
"ppTerm": "?m.189",
"assigned": true,
"usedConstants": [
"in... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 143,
"column": 49
} | {
"line": 143,
"column": 55
} | {
"line": 143,
"column": 56
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ 0 ≠ 2",
"ppTerm": "?m.189",
"assigned": true,
"usedConstants": [
"in... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 143,
"column": 79
} | {
"line": 143,
"column": 85
} | {
"line": 143,
"column": 85
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ ¬(0 = 0 ∧ 1 = 2)",
"ppTerm": "?m.190",
"assigned": true,
"usedConstants": ... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 143,
"column": 79
} | {
"line": 143,
"column": 85
} | {
"line": 143,
"column": 85
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ ¬(0 = 0 ∧ 1 = 2)",
"ppTerm": "?m.190",
"assigned": true,
"usedConstants": ... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 143,
"column": 79
} | {
"line": 143,
"column": 85
} | {
"line": 143,
"column": 85
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ ¬(0 = 0 ∧ 1 = 2)",
"ppTerm": "?m.190",
"assigned": true,
"usedConstants": ... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 143,
"column": 91
} | {
"line": 143,
"column": 97
} | {
"line": 143,
"column": 97
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ ¬(0 = 2 ∧ 1 = 0)",
"ppTerm": "?m.191",
"assigned": true,
"usedConstants": ... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 143,
"column": 91
} | {
"line": 143,
"column": 97
} | {
"line": 143,
"column": 97
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ ¬(0 = 2 ∧ 1 = 0)",
"ppTerm": "?m.191",
"assigned": true,
"usedConstants": ... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 143,
"column": 91
} | {
"line": 143,
"column": 97
} | {
"line": 143,
"column": 97
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ ¬(0 = 2 ∧ 1 = 0)",
"ppTerm": "?m.191",
"assigned": true,
"usedConstants": ... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 144,
"column": 19
} | {
"line": 144,
"column": 25
} | {
"line": 144,
"column": 26
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ 0 ≠ 1",
"ppTerm": "?m.215",
"assigned": true,
"usedConstants": [
"in... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 144,
"column": 19
} | {
"line": 144,
"column": 25
} | {
"line": 144,
"column": 26
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ 0 ≠ 1",
"ppTerm": "?m.215",
"assigned": true,
"usedConstants": [
"in... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 144,
"column": 19
} | {
"line": 144,
"column": 25
} | {
"line": 144,
"column": 26
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ 0 ≠ 1",
"ppTerm": "?m.215",
"assigned": true,
"usedConstants": [
"in... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 144,
"column": 49
} | {
"line": 144,
"column": 55
} | {
"line": 144,
"column": 56
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ 1 ≠ 2",
"ppTerm": "?m.223",
"assigned": true,
"usedConstants": [
"in... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 144,
"column": 49
} | {
"line": 144,
"column": 55
} | {
"line": 144,
"column": 56
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ 1 ≠ 2",
"ppTerm": "?m.223",
"assigned": true,
"usedConstants": [
"in... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 144,
"column": 49
} | {
"line": 144,
"column": 55
} | {
"line": 144,
"column": 56
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ 1 ≠ 2",
"ppTerm": "?m.223",
"assigned": true,
"usedConstants": [
"in... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 144,
"column": 79
} | {
"line": 144,
"column": 85
} | {
"line": 144,
"column": 85
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ ¬(0 = 1 ∧ 1 = 2)",
"ppTerm": "?m.224",
"assigned": true,
"usedConstants": ... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 144,
"column": 79
} | {
"line": 144,
"column": 85
} | {
"line": 144,
"column": 85
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ ¬(0 = 1 ∧ 1 = 2)",
"ppTerm": "?m.224",
"assigned": true,
"usedConstants": ... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 144,
"column": 79
} | {
"line": 144,
"column": 85
} | {
"line": 144,
"column": 85
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ ¬(0 = 1 ∧ 1 = 2)",
"ppTerm": "?m.224",
"assigned": true,
"usedConstants": ... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 144,
"column": 91
} | {
"line": 144,
"column": 97
} | {
"line": 144,
"column": 97
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ ¬(0 = 2 ∧ 1 = 1)",
"ppTerm": "?m.225",
"assigned": true,
"usedConstants": ... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 144,
"column": 91
} | {
"line": 144,
"column": 97
} | {
"line": 144,
"column": 97
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ ¬(0 = 2 ∧ 1 = 1)",
"ppTerm": "?m.225",
"assigned": true,
"usedConstants": ... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 144,
"column": 91
} | {
"line": 144,
"column": 97
} | {
"line": 144,
"column": 97
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ ¬(0 = 2 ∧ 1 = 1)",
"ppTerm": "?m.225",
"assigned": true,
"usedConstants": ... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 145,
"column": 19
} | {
"line": 145,
"column": 25
} | {
"line": 145,
"column": 26
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ 0 ≠ 2",
"ppTerm": "?m.247",
"assigned": true,
"usedConstants": [
"in... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 145,
"column": 19
} | {
"line": 145,
"column": 25
} | {
"line": 145,
"column": 26
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ 0 ≠ 2",
"ppTerm": "?m.247",
"assigned": true,
"usedConstants": [
"in... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 145,
"column": 19
} | {
"line": 145,
"column": 25
} | {
"line": 145,
"column": 26
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ 0 ≠ 2",
"ppTerm": "?m.247",
"assigned": true,
"usedConstants": [
"in... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 145,
"column": 49
} | {
"line": 145,
"column": 55
} | {
"line": 145,
"column": 56
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ 1 ≠ 2",
"ppTerm": "?m.255",
"assigned": true,
"usedConstants": [
"in... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 145,
"column": 49
} | {
"line": 145,
"column": 55
} | {
"line": 145,
"column": 56
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ 1 ≠ 2",
"ppTerm": "?m.255",
"assigned": true,
"usedConstants": [
"in... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 145,
"column": 49
} | {
"line": 145,
"column": 55
} | {
"line": 145,
"column": 56
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ 1 ≠ 2",
"ppTerm": "?m.255",
"assigned": true,
"usedConstants": [
"in... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 145,
"column": 79
} | {
"line": 145,
"column": 85
} | {
"line": 145,
"column": 85
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ ¬(0 = 1 ∧ 2 = 2)",
"ppTerm": "?m.256",
"assigned": true,
"usedConstants": ... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 145,
"column": 79
} | {
"line": 145,
"column": 85
} | {
"line": 145,
"column": 85
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ ¬(0 = 1 ∧ 2 = 2)",
"ppTerm": "?m.256",
"assigned": true,
"usedConstants": ... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 145,
"column": 79
} | {
"line": 145,
"column": 85
} | {
"line": 145,
"column": 85
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ ¬(0 = 1 ∧ 2 = 2)",
"ppTerm": "?m.256",
"assigned": true,
"usedConstants": ... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 145,
"column": 91
} | {
"line": 145,
"column": 97
} | {
"line": 145,
"column": 97
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ ¬(0 = 2 ∧ 2 = 1)",
"ppTerm": "?m.257",
"assigned": true,
"usedConstants": ... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 145,
"column": 91
} | {
"line": 145,
"column": 97
} | {
"line": 145,
"column": 97
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ ¬(0 = 2 ∧ 2 = 1)",
"ppTerm": "?m.257",
"assigned": true,
"usedConstants": ... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 145,
"column": 91
} | {
"line": 145,
"column": 97
} | {
"line": 145,
"column": 97
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\nh : Simplex.Scalene t\n⊢ ¬(0 = 2 ∧ 2 = 1)",
"ppTerm": "?m.257",
"assigned": true,
"usedConstants": ... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.AffineSpace.Ceva | {
"line": 194,
"column": 53
} | {
"line": 194,
"column": 64
} | {
"line": 194,
"column": 64
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i +... | [] | simp [hri1] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.LinearAlgebra.AffineSpace.Ceva | {
"line": 194,
"column": 53
} | {
"line": 194,
"column": 64
} | {
"line": 194,
"column": 64
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i +... | [] | simp [hri1] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.AffineSpace.Ceva | {
"line": 194,
"column": 53
} | {
"line": 194,
"column": 64
} | {
"line": 194,
"column": 64
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i +... | [] | simp [hri1] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Normed.Algebra.GelfandMazur | {
"line": 295,
"column": 2
} | {
"line": 295,
"column": 30
} | {
"line": 296,
"column": 2
} | [
{
"pp": "F : Type u_1\ninst✝³ : NormedRing F\ninst✝² : NormedAlgebra ℝ F\ninst✝¹ : NormOneClass F\ninst✝ : NormMulClass F\nx : F\nz : ℝ × ℝ\nh : IsMinOn (fun x_1 ↦ ‖φ x x_1‖) Set.univ z\nH : ‖φ x z‖ ≠ 0\nw : ℝ × ℝ\n⊢ ‖φ x w‖ = ‖φ x z‖",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"... | [
"F : Type u_1\ninst✝³ : NormedRing F\ninst✝² : NormedAlgebra ℝ F\ninst✝¹ : NormOneClass F\ninst✝ : NormMulClass F\nx : F\nz : ℝ × ℝ\nh : IsMinOn (fun x_1 ↦ ‖φ x x_1‖) Set.univ z\nw : ℝ × ℝ\nM : ℝ := ‖φ x z‖\nH : M ≠ 0\nhM : M = ‖φ x z‖\n⊢ ‖φ x w‖ = M"
] | set M : ℝ := ‖φ x z‖ with hM | Mathlib.Tactic._aux_Mathlib_Tactic_Set___elabRules_Mathlib_Tactic_setTactic_1 | Mathlib.Tactic.setTactic |
Mathlib.Analysis.Normed.Algebra.QuaternionExponential | {
"line": 50,
"column": 2
} | {
"line": 53,
"column": 7
} | {
"line": 54,
"column": 2
} | [
{
"pp": "case calc_1\nq : ℍ\nhq : q.re = 0\nn : ℕ\nhq2 : q ^ 2 = -↑(normSq q)\nk : ℝ := ↑(2 * n)!\n⊢ k⁻¹ • (-↑(normSq q)) ^ n = k⁻¹ • ↑((-1) ^ n * ‖q‖ ^ (2 * n))",
"ppTerm": "?calc_1",
"assigned": true,
"usedConstants": [
"Quaternion.coe",
"Norm.norm",
"Eq.mpr",
"NegZeroClass... | [
"case calc_2\nq : ℍ\nhq : q.re = 0\nn : ℕ\nhq2 : q ^ 2 = -↑(normSq q)\nk : ℝ := ↑(2 * n)!\n⊢ k⁻¹ • ↑((-1) ^ n * ‖q‖ ^ (2 * n)) = ↑((-1) ^ n * ‖q‖ ^ (2 * n) / k)"
] | · congr 1
rw [neg_pow, normSq_eq_norm_mul_self, pow_mul, sq]
push_cast
rfl | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 178,
"column": 42
} | {
"line": 178,
"column": 48
} | {
"line": 178,
"column": 48
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\n⊢ 0 ≠ 1",
"ppTerm": "?m.121",
"assigned": true,
"usedConstants": [
"instDecidableNot",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 178,
"column": 42
} | {
"line": 178,
"column": 48
} | {
"line": 178,
"column": 48
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\n⊢ 0 ≠ 1",
"ppTerm": "?m.121",
"assigned": true,
"usedConstants": [
"instDecidableNot",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 178,
"column": 42
} | {
"line": 178,
"column": 48
} | {
"line": 178,
"column": 48
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\n⊢ 0 ≠ 1",
"ppTerm": "?m.121",
"assigned": true,
"usedConstants": [
"instDecidableNot",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 178,
"column": 54
} | {
"line": 178,
"column": 60
} | {
"line": 178,
"column": 60
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\n⊢ 0 ≠ 2",
"ppTerm": "?m.122",
"assigned": true,
"usedConstants": [
"instDecidableNot",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 178,
"column": 54
} | {
"line": 178,
"column": 60
} | {
"line": 178,
"column": 60
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\n⊢ 0 ≠ 2",
"ppTerm": "?m.122",
"assigned": true,
"usedConstants": [
"instDecidableNot",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 178,
"column": 54
} | {
"line": 178,
"column": 60
} | {
"line": 178,
"column": 60
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\n⊢ 0 ≠ 2",
"ppTerm": "?m.122",
"assigned": true,
"usedConstants": [
"instDecidableNot",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 178,
"column": 66
} | {
"line": 178,
"column": 72
} | {
"line": 178,
"column": 72
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\n⊢ 1 ≠ 2",
"ppTerm": "?m.123",
"assigned": true,
"usedConstants": [
"instDecidableNot",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 178,
"column": 66
} | {
"line": 178,
"column": 72
} | {
"line": 178,
"column": 72
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\n⊢ 1 ≠ 2",
"ppTerm": "?m.123",
"assigned": true,
"usedConstants": [
"instDecidableNot",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 178,
"column": 66
} | {
"line": 178,
"column": 72
} | {
"line": 178,
"column": 72
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nt : Triangle R P\n⊢ 1 ≠ 2",
"ppTerm": "?m.123",
"assigned": true,
"usedConstants": [
"instDecidableNot",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt | {
"line": 241,
"column": 6
} | {
"line": 242,
"column": 16
} | {
"line": 243,
"column": 4
} | [
{
"pp": "𝕜 : Type u_1\nS : Type u_2\nR : Type u_3\nM : Type u_4\ninst✝¹¹ : SeminormedCommRing S\ninst✝¹⁰ : SeminormedRing R\ninst✝⁹ : SeminormedAddCommGroup M\ninst✝⁸ : Algebra S R\ninst✝⁷ : Module S M\ninst✝⁶ : IsBoundedSMul S R\ninst✝⁵ : IsBoundedSMul S M\ninst✝⁴ : Module R M\ninst✝³ : IsBoundedSMul R M\nins... | [] | apply le_add_of_nonneg_right
positivity | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
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