module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Geometry.Euclidean.Simplex | {
"line": 94,
"column": 55
} | {
"line": 94,
"column": 61
} | {
"line": 94,
"column": 61
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle ℝ P\nh : Simplex.AcuteAngled t\n⊢ 2 ≠ 0",
"ppTerm": "?m.168",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"in... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Euclidean.Simplex | {
"line": 94,
"column": 55
} | {
"line": 94,
"column": 61
} | {
"line": 94,
"column": 61
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle ℝ P\nh : Simplex.AcuteAngled t\n⊢ 2 ≠ 0",
"ppTerm": "?m.168",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"in... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Euclidean.Simplex | {
"line": 95,
"column": 31
} | {
"line": 95,
"column": 37
} | {
"line": 95,
"column": 37
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle ℝ P\nh : Simplex.AcuteAngled t\n⊢ 2 ≠ 0",
"ppTerm": "?m.172",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"in... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Geometry.Euclidean.Simplex | {
"line": 95,
"column": 31
} | {
"line": 95,
"column": 37
} | {
"line": 95,
"column": 37
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle ℝ P\nh : Simplex.AcuteAngled t\n⊢ 2 ≠ 0",
"ppTerm": "?m.172",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"in... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Euclidean.Simplex | {
"line": 95,
"column": 31
} | {
"line": 95,
"column": 37
} | {
"line": 95,
"column": 37
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle ℝ P\nh : Simplex.AcuteAngled t\n⊢ 2 ≠ 0",
"ppTerm": "?m.172",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"in... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Euclidean.Simplex | {
"line": 95,
"column": 43
} | {
"line": 95,
"column": 49
} | {
"line": 95,
"column": 49
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle ℝ P\nh : Simplex.AcuteAngled t\n⊢ 2 ≠ 1",
"ppTerm": "?m.173",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"in... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Geometry.Euclidean.Simplex | {
"line": 95,
"column": 43
} | {
"line": 95,
"column": 49
} | {
"line": 95,
"column": 49
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle ℝ P\nh : Simplex.AcuteAngled t\n⊢ 2 ≠ 1",
"ppTerm": "?m.173",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"in... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Euclidean.Simplex | {
"line": 95,
"column": 43
} | {
"line": 95,
"column": 49
} | {
"line": 95,
"column": 49
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle ℝ P\nh : Simplex.AcuteAngled t\n⊢ 2 ≠ 1",
"ppTerm": "?m.173",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"in... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Euclidean.Simplex | {
"line": 95,
"column": 55
} | {
"line": 95,
"column": 61
} | {
"line": 95,
"column": 61
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle ℝ P\nh : Simplex.AcuteAngled t\n⊢ 0 ≠ 1",
"ppTerm": "?m.174",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"in... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Geometry.Euclidean.Simplex | {
"line": 95,
"column": 55
} | {
"line": 95,
"column": 61
} | {
"line": 95,
"column": 61
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle ℝ P\nh : Simplex.AcuteAngled t\n⊢ 0 ≠ 1",
"ppTerm": "?m.174",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"in... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Euclidean.Simplex | {
"line": 95,
"column": 55
} | {
"line": 95,
"column": 61
} | {
"line": 95,
"column": 61
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle ℝ P\nh : Simplex.AcuteAngled t\n⊢ 0 ≠ 1",
"ppTerm": "?m.174",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"in... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.MetricSpace.Similarity | {
"line": 323,
"column": 39
} | {
"line": 323,
"column": 74
} | {
"line": 323,
"column": 74
} | [
{
"pp": "case h.«2».«1»\nP₁ : Type u_3\nP₂ : Type u_4\ninst✝¹ : PseudoMetricSpace P₁\ninst✝ : PseudoMetricSpace P₂\na b c : P₁\na' b' c' : P₂\nh_ne : dist a b ≠ 0\nh_ne' : dist a' b' ≠ 0\nheq1 : dist a b * dist b' c' = dist b c * dist a' b'\nheq2 : dist a b * dist c' a' = dist c a * dist a' b'\nr : ℝ := dist a ... | [
"case h.«2».«1»\nP₁ : Type u_3\nP₂ : Type u_4\ninst✝¹ : PseudoMetricSpace P₁\ninst✝ : PseudoMetricSpace P₂\na b c : P₁\na' b' c' : P₂\nh_ne : dist a b ≠ 0\nh_ne' : dist a' b' ≠ 0\nheq1 : dist a b * dist b' c' = dist b c * dist a' b'\nheq2 : dist a b * dist c' a' = dist c a * dist a' b'\nr : ℝ := dist a b / dist a' ... | rw [dist_self, dist_self, mul_zero] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Topology.MetricSpace.Similarity | {
"line": 323,
"column": 39
} | {
"line": 323,
"column": 74
} | {
"line": 323,
"column": 74
} | [
{
"pp": "case h.«2».«2»\nP₁ : Type u_3\nP₂ : Type u_4\ninst✝¹ : PseudoMetricSpace P₁\ninst✝ : PseudoMetricSpace P₂\na b c : P₁\na' b' c' : P₂\nh_ne : dist a b ≠ 0\nh_ne' : dist a' b' ≠ 0\nheq1 : dist a b * dist b' c' = dist b c * dist a' b'\nheq2 : dist a b * dist c' a' = dist c a * dist a' b'\nr : ℝ := dist a ... | [] | rw [dist_self, dist_self, mul_zero] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Geometry.Euclidean.Sphere.Power | {
"line": 93,
"column": 16
} | {
"line": 93,
"column": 35
} | {
"line": 93,
"column": 35
} | [
{
"pp": "V : Type u_1\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\nP : Type u_2\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\na b p q : P\nhp : p ∈ line[ℝ, a, b]\nhq : dist a q = dist b q\nm : P := midpoint ℝ a b\nh1 : m -ᵥ p - (m -ᵥ a) = a -ᵥ p\nh1' : m -ᵥ a - (m -ᵥ p) = p -ᵥ a\nh2 :... | [
"V : Type u_1\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\nP : Type u_2\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\na b p q : P\nhp : p ∈ line[ℝ, a, b]\nhq : dist a q = dist b q\nm : P := midpoint ℝ a b\nh1 : m -ᵥ p - (m -ᵥ a) = a -ᵥ p\nh1' : m -ᵥ a - (m -ᵥ p) = p -ᵥ a\nh2 : m -ᵥ q - (m... | dist_eq_norm_vsub V | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Sphere.Power | {
"line": 93,
"column": 16
} | {
"line": 93,
"column": 35
} | {
"line": 93,
"column": 35
} | [
{
"pp": "V : Type u_1\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\nP : Type u_2\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\na b p q : P\nhp : p ∈ line[ℝ, a, b]\nhq : dist a q = dist b q\nm : P := midpoint ℝ a b\nh1 : m -ᵥ p - (m -ᵥ a) = a -ᵥ p\nh1' : m -ᵥ a - (m -ᵥ p) = p -ᵥ a\nh2 :... | [
"V : Type u_1\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\nP : Type u_2\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\na b p q : P\nhp : p ∈ line[ℝ, a, b]\nhq : dist a q = dist b q\nm : P := midpoint ℝ a b\nh1 : m -ᵥ p - (m -ᵥ a) = a -ᵥ p\nh1' : m -ᵥ a - (m -ᵥ p) = p -ᵥ a\nh2 : m -ᵥ q - (m... | dist_eq_norm_vsub V | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Sphere.Power | {
"line": 93,
"column": 16
} | {
"line": 93,
"column": 35
} | {
"line": 93,
"column": 35
} | [
{
"pp": "V : Type u_1\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\nP : Type u_2\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\na b p q : P\nhp : p ∈ line[ℝ, a, b]\nhq : dist a q = dist b q\nm : P := midpoint ℝ a b\nh1 : m -ᵥ p - (m -ᵥ a) = a -ᵥ p\nh1' : m -ᵥ a - (m -ᵥ p) = p -ᵥ a\nh2 :... | [
"V : Type u_1\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\nP : Type u_2\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\na b p q : P\nhp : p ∈ line[ℝ, a, b]\nhq : dist a q = dist b q\nm : P := midpoint ℝ a b\nh1 : m -ᵥ p - (m -ᵥ a) = a -ᵥ p\nh1' : m -ᵥ a - (m -ᵥ p) = p -ᵥ a\nh2 : m -ᵥ q - (m... | dist_eq_norm_vsub V | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Sphere.Power | {
"line": 93,
"column": 16
} | {
"line": 93,
"column": 35
} | {
"line": 93,
"column": 35
} | [
{
"pp": "V : Type u_1\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\nP : Type u_2\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\na b p q : P\nhp : p ∈ line[ℝ, a, b]\nhq : dist a q = dist b q\nm : P := midpoint ℝ a b\nh1 : m -ᵥ p - (m -ᵥ a) = a -ᵥ p\nh1' : m -ᵥ a - (m -ᵥ p) = p -ᵥ a\nh2 :... | [
"V : Type u_1\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\nP : Type u_2\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\na b p q : P\nhp : p ∈ line[ℝ, a, b]\nhq : dist a q = dist b q\nm : P := midpoint ℝ a b\nh1 : m -ᵥ p - (m -ᵥ a) = a -ᵥ p\nh1' : m -ᵥ a - (m -ᵥ p) = p -ᵥ a\nh2 : m -ᵥ q - (m... | dist_eq_norm_vsub V | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.Similarity | {
"line": 110,
"column": 39
} | {
"line": 110,
"column": 74
} | {
"line": 110,
"column": 74
} | [
{
"pp": "case h.«0».«0»\nV₁ : Type u_2\nV₂ : Type u_3\nP₁ : Type u_4\nP₂ : Type u_5\ninst✝⁷ : NormedAddCommGroup V₁\ninst✝⁶ : NormedAddCommGroup V₂\ninst✝⁵ : InnerProductSpace ℝ V₁\ninst✝⁴ : InnerProductSpace ℝ V₂\ninst✝³ : MetricSpace P₁\ninst✝² : MetricSpace P₂\ninst✝¹ : NormedAddTorsor V₁ P₁\ninst✝ : NormedA... | [] | rw [dist_self, dist_self, mul_zero] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Geometry.Euclidean.Similarity | {
"line": 110,
"column": 39
} | {
"line": 110,
"column": 74
} | {
"line": 110,
"column": 74
} | [
{
"pp": "case h.«0».«1»\nV₁ : Type u_2\nV₂ : Type u_3\nP₁ : Type u_4\nP₂ : Type u_5\ninst✝⁷ : NormedAddCommGroup V₁\ninst✝⁶ : NormedAddCommGroup V₂\ninst✝⁵ : InnerProductSpace ℝ V₁\ninst✝⁴ : InnerProductSpace ℝ V₂\ninst✝³ : MetricSpace P₁\ninst✝² : MetricSpace P₂\ninst✝¹ : NormedAddTorsor V₁ P₁\ninst✝ : NormedA... | [
"case h.«0».«1»\nV₁ : Type u_2\nV₂ : Type u_3\nP₁ : Type u_4\nP₂ : Type u_5\ninst✝⁷ : NormedAddCommGroup V₁\ninst✝⁶ : NormedAddCommGroup V₂\ninst✝⁵ : InnerProductSpace ℝ V₁\ninst✝⁴ : InnerProductSpace ℝ V₂\ninst✝³ : MetricSpace P₁\ninst✝² : MetricSpace P₂\ninst✝¹ : NormedAddTorsor V₁ P₁\ninst✝ : NormedAddTorsor V₂ ... | rw [dist_self, dist_self, mul_zero] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Geometry.Euclidean.Sphere.Ptolemy | {
"line": 61,
"column": 2
} | {
"line": 61,
"column": 51
} | {
"line": 62,
"column": 2
} | [
{
"pp": "V : Type u_1\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\nP : Type u_2\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\na b c d p : P\nh : Cospherical {a, b, c, d}\nhapc : ∠ a p c = π\nhbpd : ∠ b p d = π\nh' : Cospherical {a, c, b, d}\nhmul : dist a p * dist c p = dist b p * dis... | [
"V : Type u_1\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\nP : Type u_2\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\na b c d p : P\nh : Cospherical {a, b, c, d}\nhapc : ∠ a p c = π\nhbpd : ∠ b p d = π\nh' : Cospherical {a, c, b, d}\nhmul : dist a p * dist c p = dist b p * dist d p\nhbp :... | have hbp := left_dist_ne_zero_of_angle_eq_pi hbpd | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Geometry.Euclidean.Similarity | {
"line": 110,
"column": 39
} | {
"line": 110,
"column": 74
} | {
"line": 110,
"column": 74
} | [
{
"pp": "case h.«0».«2»\nV₁ : Type u_2\nV₂ : Type u_3\nP₁ : Type u_4\nP₂ : Type u_5\ninst✝⁷ : NormedAddCommGroup V₁\ninst✝⁶ : NormedAddCommGroup V₂\ninst✝⁵ : InnerProductSpace ℝ V₁\ninst✝⁴ : InnerProductSpace ℝ V₂\ninst✝³ : MetricSpace P₁\ninst✝² : MetricSpace P₂\ninst✝¹ : NormedAddTorsor V₁ P₁\ninst✝ : NormedA... | [
"case h.«0».«2»\nV₁ : Type u_2\nV₂ : Type u_3\nP₁ : Type u_4\nP₂ : Type u_5\ninst✝⁷ : NormedAddCommGroup V₁\ninst✝⁶ : NormedAddCommGroup V₂\ninst✝⁵ : InnerProductSpace ℝ V₁\ninst✝⁴ : InnerProductSpace ℝ V₂\ninst✝³ : MetricSpace P₁\ninst✝² : MetricSpace P₂\ninst✝¹ : NormedAddTorsor V₁ P₁\ninst✝ : NormedAddTorsor V₂ ... | rw [dist_self, dist_self, mul_zero] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Geometry.Euclidean.Similarity | {
"line": 110,
"column": 39
} | {
"line": 110,
"column": 74
} | {
"line": 110,
"column": 74
} | [
{
"pp": "case h.«1».«0»\nV₁ : Type u_2\nV₂ : Type u_3\nP₁ : Type u_4\nP₂ : Type u_5\ninst✝⁷ : NormedAddCommGroup V₁\ninst✝⁶ : NormedAddCommGroup V₂\ninst✝⁵ : InnerProductSpace ℝ V₁\ninst✝⁴ : InnerProductSpace ℝ V₂\ninst✝³ : MetricSpace P₁\ninst✝² : MetricSpace P₂\ninst✝¹ : NormedAddTorsor V₁ P₁\ninst✝ : NormedA... | [
"case h.«1».«0»\nV₁ : Type u_2\nV₂ : Type u_3\nP₁ : Type u_4\nP₂ : Type u_5\ninst✝⁷ : NormedAddCommGroup V₁\ninst✝⁶ : NormedAddCommGroup V₂\ninst✝⁵ : InnerProductSpace ℝ V₁\ninst✝⁴ : InnerProductSpace ℝ V₂\ninst✝³ : MetricSpace P₁\ninst✝² : MetricSpace P₂\ninst✝¹ : NormedAddTorsor V₁ P₁\ninst✝ : NormedAddTorsor V₂ ... | rw [dist_self, dist_self, mul_zero] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Geometry.Euclidean.Similarity | {
"line": 110,
"column": 39
} | {
"line": 110,
"column": 74
} | {
"line": 110,
"column": 74
} | [
{
"pp": "case h.«1».«1»\nV₁ : Type u_2\nV₂ : Type u_3\nP₁ : Type u_4\nP₂ : Type u_5\ninst✝⁷ : NormedAddCommGroup V₁\ninst✝⁶ : NormedAddCommGroup V₂\ninst✝⁵ : InnerProductSpace ℝ V₁\ninst✝⁴ : InnerProductSpace ℝ V₂\ninst✝³ : MetricSpace P₁\ninst✝² : MetricSpace P₂\ninst✝¹ : NormedAddTorsor V₁ P₁\ninst✝ : NormedA... | [] | rw [dist_self, dist_self, mul_zero] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Geometry.Euclidean.Similarity | {
"line": 110,
"column": 39
} | {
"line": 110,
"column": 74
} | {
"line": 110,
"column": 74
} | [
{
"pp": "case h.«1».«2»\nV₁ : Type u_2\nV₂ : Type u_3\nP₁ : Type u_4\nP₂ : Type u_5\ninst✝⁷ : NormedAddCommGroup V₁\ninst✝⁶ : NormedAddCommGroup V₂\ninst✝⁵ : InnerProductSpace ℝ V₁\ninst✝⁴ : InnerProductSpace ℝ V₂\ninst✝³ : MetricSpace P₁\ninst✝² : MetricSpace P₂\ninst✝¹ : NormedAddTorsor V₁ P₁\ninst✝ : NormedA... | [
"case h.«1».«2»\nV₁ : Type u_2\nV₂ : Type u_3\nP₁ : Type u_4\nP₂ : Type u_5\ninst✝⁷ : NormedAddCommGroup V₁\ninst✝⁶ : NormedAddCommGroup V₂\ninst✝⁵ : InnerProductSpace ℝ V₁\ninst✝⁴ : InnerProductSpace ℝ V₂\ninst✝³ : MetricSpace P₁\ninst✝² : MetricSpace P₂\ninst✝¹ : NormedAddTorsor V₁ P₁\ninst✝ : NormedAddTorsor V₂ ... | rw [dist_self, dist_self, mul_zero] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Geometry.Euclidean.Similarity | {
"line": 110,
"column": 39
} | {
"line": 110,
"column": 74
} | {
"line": 110,
"column": 74
} | [
{
"pp": "case h.«2».«0»\nV₁ : Type u_2\nV₂ : Type u_3\nP₁ : Type u_4\nP₂ : Type u_5\ninst✝⁷ : NormedAddCommGroup V₁\ninst✝⁶ : NormedAddCommGroup V₂\ninst✝⁵ : InnerProductSpace ℝ V₁\ninst✝⁴ : InnerProductSpace ℝ V₂\ninst✝³ : MetricSpace P₁\ninst✝² : MetricSpace P₂\ninst✝¹ : NormedAddTorsor V₁ P₁\ninst✝ : NormedA... | [
"case h.«2».«0»\nV₁ : Type u_2\nV₂ : Type u_3\nP₁ : Type u_4\nP₂ : Type u_5\ninst✝⁷ : NormedAddCommGroup V₁\ninst✝⁶ : NormedAddCommGroup V₂\ninst✝⁵ : InnerProductSpace ℝ V₁\ninst✝⁴ : InnerProductSpace ℝ V₂\ninst✝³ : MetricSpace P₁\ninst✝² : MetricSpace P₂\ninst✝¹ : NormedAddTorsor V₁ P₁\ninst✝ : NormedAddTorsor V₂ ... | rw [dist_self, dist_self, mul_zero] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Geometry.Euclidean.Similarity | {
"line": 110,
"column": 39
} | {
"line": 110,
"column": 74
} | {
"line": 110,
"column": 74
} | [
{
"pp": "case h.«2».«1»\nV₁ : Type u_2\nV₂ : Type u_3\nP₁ : Type u_4\nP₂ : Type u_5\ninst✝⁷ : NormedAddCommGroup V₁\ninst✝⁶ : NormedAddCommGroup V₂\ninst✝⁵ : InnerProductSpace ℝ V₁\ninst✝⁴ : InnerProductSpace ℝ V₂\ninst✝³ : MetricSpace P₁\ninst✝² : MetricSpace P₂\ninst✝¹ : NormedAddTorsor V₁ P₁\ninst✝ : NormedA... | [
"case h.«2».«1»\nV₁ : Type u_2\nV₂ : Type u_3\nP₁ : Type u_4\nP₂ : Type u_5\ninst✝⁷ : NormedAddCommGroup V₁\ninst✝⁶ : NormedAddCommGroup V₂\ninst✝⁵ : InnerProductSpace ℝ V₁\ninst✝⁴ : InnerProductSpace ℝ V₂\ninst✝³ : MetricSpace P₁\ninst✝² : MetricSpace P₂\ninst✝¹ : NormedAddTorsor V₁ P₁\ninst✝ : NormedAddTorsor V₂ ... | rw [dist_self, dist_self, mul_zero] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Geometry.Euclidean.Similarity | {
"line": 110,
"column": 39
} | {
"line": 110,
"column": 74
} | {
"line": 110,
"column": 74
} | [
{
"pp": "case h.«2».«2»\nV₁ : Type u_2\nV₂ : Type u_3\nP₁ : Type u_4\nP₂ : Type u_5\ninst✝⁷ : NormedAddCommGroup V₁\ninst✝⁶ : NormedAddCommGroup V₂\ninst✝⁵ : InnerProductSpace ℝ V₁\ninst✝⁴ : InnerProductSpace ℝ V₂\ninst✝³ : MetricSpace P₁\ninst✝² : MetricSpace P₂\ninst✝¹ : NormedAddTorsor V₁ P₁\ninst✝ : NormedA... | [] | rw [dist_self, dist_self, mul_zero] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Geometry.Euclidean.MongePoint | {
"line": 441,
"column": 6
} | {
"line": 441,
"column": 65
} | {
"line": 442,
"column": 4
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle ℝ P\ni₁ i₂ : Fin 3\nh : i₁ ≠ i₂\n⊢ dist t.orthocenter ((reflection (affineSpan ℝ (t.points '' {i₁, i₂}))) (circumcenter t)) = circumradius t",
... | [
"V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle ℝ P\ni₁ i₂ : Fin 3\nh : i₁ ≠ i₂\n⊢ dist t.orthocenter ((reflection (affineSpan ℝ (t.points '' {i₁, i₂}))) (circumcenter t)) *\n dist t.orthocenter ((refl... | ← mul_self_inj_of_nonneg dist_nonneg t.circumradius_nonneg, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Euclidean.MongePoint | {
"line": 500,
"column": 2
} | {
"line": 500,
"column": 6
} | {
"line": 501,
"column": 2
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt₁ t₂ : Triangle ℝ P\ni₁ i₂ i₃ j₁ j₂ j₃ : Fin 3\nhi₁₂ : i₁ ≠ i₂\nhi₁₃ : i₁ ≠ i₃\nhi₂₃ : i₂ ≠ i₃\nhj₁₂ : j₁ ≠ j₂\nhj₁₃ : j₁ ≠ j₃\nhj₂₃ : j₂ ≠ j₃\nh₁ : t₂.points... | [
"V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt₁ t₂ : Triangle ℝ P\ni₁ i₂ i₃ j₁ j₂ j₃ : Fin 3\nhi₁₂ : i₁ ≠ i₂\nhi₁₃ : i₁ ≠ i₃\nhi₂₃ : i₂ ≠ i₃\nhj₁₂ : j₁ ≠ j₂\nhj₁₃ : j₁ ≠ j₃\nhj₂₃ : j₂ ≠ j₃\nh₁ : t₂.points j₁ = t₁.ort... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Geometry.Manifold.MFDeriv.Atlas | {
"line": 95,
"column": 97
} | {
"line": 111,
"column": 98
} | {
"line": 113,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\ninst✝ : IsManifold I 1 M\ne : OpenPar... | [] | by
rw [mdifferentiableAt_iff]
refine ⟨(e.continuousOn x hx).continuousAt (e.open_source.mem_nhds hx), ?_⟩
have mem :
I ((chartAt H x : M → H) x) ∈ I.symm ⁻¹' ((chartAt H x).symm ≫ₕ e).source ∩ range I := by
simp only [hx, mfld_simps]
have : (chartAt H x).symm.trans e ∈ contDiffGroupoid 1 I :=
HasGro... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Geometry.Manifold.MFDeriv.UniqueDifferential | {
"line": 125,
"column": 61
} | {
"line": 129,
"column": 52
} | {
"line": 130,
"column": 2
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹¹ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁸ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁷ : TopologicalSpace M\ninst✝⁶ : ChartedSpace H M\nE' : Type u_5\ninst✝⁵ : NormedAddCo... | [] | by
intro z hz
apply (hs z hz.1).inter'
apply (hf z hz.1).preimage_mem_nhdsWithin
exact (isOpen_extChartAt_source y).mem_nhds hz.2 | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary | {
"line": 277,
"column": 2
} | {
"line": 277,
"column": 32
} | {
"line": 278,
"column": 2
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\nn : WithTop ℕ∞\ninst✝ : IsManifold I ... | [
"case inr\n𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\nn : WithTop ℕ∞\ninst✝ : IsManifold I n ... | wlog _ : IsRCLikeNormedField 𝕜 | Mathlib.Tactic._aux_Mathlib_Tactic_WLOG___elabRules_Mathlib_Tactic_wlog_1 | Mathlib.Tactic.wlog |
Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary | {
"line": 335,
"column": 2
} | {
"line": 336,
"column": 28
} | {
"line": 338,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\nn : WithTop ℕ∞\ninst✝ : IsManifold I ... | [] | rw [← I.compl_interior, isClosed_compl_iff]
exact I.isOpen_interior hn | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary | {
"line": 335,
"column": 2
} | {
"line": 336,
"column": 28
} | {
"line": 338,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\nn : WithTop ℕ∞\ninst✝ : IsManifold I ... | [] | rw [← I.compl_interior, isClosed_compl_iff]
exact I.isOpen_interior hn | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary | {
"line": 359,
"column": 2
} | {
"line": 359,
"column": 32
} | {
"line": 360,
"column": 2
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁷ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁶ : TopologicalSpace M\ninst✝⁵ : ChartedSpace H M\nE' : Type u_5\ninst✝⁴ : NormedAddCom... | [
"case inr\n𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁷ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁶ : TopologicalSpace M\ninst✝⁵ : ChartedSpace H M\nE' : Type u_5\ninst✝⁴ : NormedAddCommG... | wlog _ : IsRCLikeNormedField 𝕜 | Mathlib.Tactic._aux_Mathlib_Tactic_WLOG___elabRules_Mathlib_Tactic_wlog_1 | Mathlib.Tactic.wlog |
Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | {
"line": 590,
"column": 2
} | {
"line": 590,
"column": 6
} | {
"line": 591,
"column": 2
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹⁴ : NormedAddCommGroup E\ninst✝¹³ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹² : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹¹ : TopologicalSpace M\ninst✝¹⁰ : ChartedSpace H M\nE' : Type u_5\ninst✝⁹ : NormedA... | [
"𝕜 : Type u_1\ninst✝¹⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹⁴ : NormedAddCommGroup E\ninst✝¹³ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹² : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹¹ : TopologicalSpace M\ninst✝¹⁰ : ChartedSpace H M\nE' : Type u_5\ninst✝⁹ : NormedAddCommGroup ... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | {
"line": 615,
"column": 6
} | {
"line": 615,
"column": 75
} | {
"line": 616,
"column": 4
} | [
{
"pp": "case e_a.hg\n𝕜 : Type u_1\ninst✝¹⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹⁴ : NormedAddCommGroup E\ninst✝¹³ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹² : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹¹ : TopologicalSpace M\ninst✝¹⁰ : ChartedSpace H M\nE' : Type u_5\nins... | [] | exact hf.comp _ (mdifferentiableAt_const.prodMk mdifferentiableAt_id) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | {
"line": 615,
"column": 6
} | {
"line": 615,
"column": 75
} | {
"line": 616,
"column": 4
} | [
{
"pp": "case e_a.hg\n𝕜 : Type u_1\ninst✝¹⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹⁴ : NormedAddCommGroup E\ninst✝¹³ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹² : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹¹ : TopologicalSpace M\ninst✝¹⁰ : ChartedSpace H M\nE' : Type u_5\nins... | [] | exact hf.comp _ (mdifferentiableAt_const.prodMk mdifferentiableAt_id) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | {
"line": 615,
"column": 6
} | {
"line": 615,
"column": 75
} | {
"line": 616,
"column": 4
} | [
{
"pp": "case e_a.hg\n𝕜 : Type u_1\ninst✝¹⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹⁴ : NormedAddCommGroup E\ninst✝¹³ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹² : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹¹ : TopologicalSpace M\ninst✝¹⁰ : ChartedSpace H M\nE' : Type u_5\nins... | [] | exact hf.comp _ (mdifferentiableAt_const.prodMk mdifferentiableAt_id) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Manifold.VectorBundle.MDifferentiable | {
"line": 464,
"column": 4
} | {
"line": 464,
"column": 57
} | {
"line": 465,
"column": 4
} | [
{
"pp": "case insert\n𝕜 : Type u_1\nB : Type u_2\nF : Type u_4\nE : B → Type u_6\ninst✝¹³ : TopologicalSpace B\ninst✝¹² : TopologicalSpace (TotalSpace F E)\ninst✝¹¹ : (x : B) → TopologicalSpace (E x)\ninst✝¹⁰ : NormedAddCommGroup F\ninst✝⁹ : NontriviallyNormedField 𝕜\ninst✝⁸ : NormedSpace 𝕜 F\ninst✝⁷ : Fiber... | [
"case insert\n𝕜 : Type u_1\nB : Type u_2\nF : Type u_4\nE : B → Type u_6\ninst✝¹³ : TopologicalSpace B\ninst✝¹² : TopologicalSpace (TotalSpace F E)\ninst✝¹¹ : (x : B) → TopologicalSpace (E x)\ninst✝¹⁰ : NormedAddCommGroup F\ninst✝⁹ : NontriviallyNormedField 𝕜\ninst✝⁸ : NormedSpace 𝕜 F\ninst✝⁷ : FiberBundle F E\n... | simp only [Finset.mem_insert, forall_eq_or_imp] at hs | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Geometry.Manifold.VectorBundle.Hom | {
"line": 222,
"column": 2
} | {
"line": 236,
"column": 10
} | {
"line": 238,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\nF₁ : Type u_2\nF₂ : Type u_3\nB₁ : Type u_4\nB₂ : Type u_5\nM : Type u_6\nE₁ : B₁ → Type u_7\nE₂ : B₂ → Type u_8\ninst✝³¹ : NontriviallyNormedField 𝕜\ninst✝³⁰ : (x : B₁) → AddCommGroup (E₁ x)\ninst✝²⁹ : (x : B₁) → Module 𝕜 (E₁ x)\ninst✝²⁸ : NormedAddCommGroup F₁\ninst✝²⁷ : NormedSpace ... | [] | rw [← contMDiffWithinAt_insert_self] at hϕ hv hb₂ ⊢
rw [contMDiffWithinAt_totalSpace] at hv ⊢
refine ⟨hb₂, ?_⟩
apply (ContMDiffWithinAt.clm_apply hϕ hv.2).congr_of_eventuallyEq_of_mem ?_ (mem_insert m₀ s)
have A : ∀ᶠ m in 𝓝[insert m₀ s] m₀, b₁ m ∈ (trivializationAt F₁ E₁ (b₁ m₀)).baseSet := by
apply hv.1.c... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Manifold.VectorBundle.Hom | {
"line": 222,
"column": 2
} | {
"line": 236,
"column": 10
} | {
"line": 238,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\nF₁ : Type u_2\nF₂ : Type u_3\nB₁ : Type u_4\nB₂ : Type u_5\nM : Type u_6\nE₁ : B₁ → Type u_7\nE₂ : B₂ → Type u_8\ninst✝³¹ : NontriviallyNormedField 𝕜\ninst✝³⁰ : (x : B₁) → AddCommGroup (E₁ x)\ninst✝²⁹ : (x : B₁) → Module 𝕜 (E₁ x)\ninst✝²⁸ : NormedAddCommGroup F₁\ninst✝²⁷ : NormedSpace ... | [] | rw [← contMDiffWithinAt_insert_self] at hϕ hv hb₂ ⊢
rw [contMDiffWithinAt_totalSpace] at hv ⊢
refine ⟨hb₂, ?_⟩
apply (ContMDiffWithinAt.clm_apply hϕ hv.2).congr_of_eventuallyEq_of_mem ?_ (mem_insert m₀ s)
have A : ∀ᶠ m in 𝓝[insert m₀ s] m₀, b₁ m ∈ (trivializationAt F₁ E₁ (b₁ m₀)).baseSet := by
apply hv.1.c... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Manifold.ContMDiffMFDeriv | {
"line": 149,
"column": 2
} | {
"line": 149,
"column": 74
} | {
"line": 150,
"column": 2
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁵ : NontriviallyNormedField 𝕜\nm n : WithTop ℕ∞\nE : Type u_2\ninst✝¹⁴ : NormedAddCommGroup E\ninst✝¹³ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹² : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹¹ : TopologicalSpace M\ninst✝¹⁰ : ChartedSpace H M\nE' : Type u_5... | [
"𝕜 : Type u_1\ninst✝¹⁵ : NontriviallyNormedField 𝕜\nm n : WithTop ℕ∞\nE : Type u_2\ninst✝¹⁴ : NormedAddCommGroup E\ninst✝¹³ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹² : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹¹ : TopologicalSpace M\ninst✝¹⁰ : ChartedSpace H M\nE' : Type u_5\ninst✝⁹ : N... | filter_upwards [h2f, h4f, h2g, self_mem_nhdsWithin] with x hx h'x h2 hxt | Mathlib.Tactic._aux_Mathlib_Order_Filter_Defs___elabRules_Mathlib_Tactic_filterUpwards_1 | Mathlib.Tactic.filterUpwards |
Mathlib.Geometry.Manifold.VectorField.LieBracket | {
"line": 229,
"column": 4
} | {
"line": 233,
"column": 11
} | {
"line": 234,
"column": 2
} | [
{
"pp": "case e_6.hW\n𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nH : Type u_2\ninst✝⁴ : TopologicalSpace H\nE : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace H M\ns : Set M\nx : M\nV W V₁ ... | [] | apply nhdsWithin_mono _ inter_subset_left
filter_upwards [(continuousAt_extChartAt_symm x).continuousWithinAt.preimage_mem_nhdsWithin''
hW (by simp)] with y hy
simp only [mpullbackWithin_apply]
congr 1 | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Manifold.VectorField.LieBracket | {
"line": 229,
"column": 4
} | {
"line": 233,
"column": 11
} | {
"line": 234,
"column": 2
} | [
{
"pp": "case e_6.hW\n𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nH : Type u_2\ninst✝⁴ : TopologicalSpace H\nE : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace H M\ns : Set M\nx : M\nV W V₁ ... | [] | apply nhdsWithin_mono _ inter_subset_left
filter_upwards [(continuousAt_extChartAt_symm x).continuousWithinAt.preimage_mem_nhdsWithin''
hW (by simp)] with y hy
simp only [mpullbackWithin_apply]
congr 1 | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Manifold.Instances.Sphere | {
"line": 507,
"column": 2
} | {
"line": 507,
"column": 6
} | {
"line": 508,
"column": 2
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\nn : ℕ\ninst✝ : Fact (finrank ℝ E = n + 1)\nv : ↑(sphere 0 1)\nU : ↥(ℝ ∙ ↑(-v))ᗮ ≃ₗᵢ[ℝ] EuclideanSpace ℝ (Fin n) := (OrthonormalBasis.fromOrthogonalSpanSingleton n ⋯).repr\nthis : HasFDerivAt (stereoInvFunAux (-↑v) ∘ Subtype.va... | [
"E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\nn : ℕ\ninst✝ : Fact (finrank ℝ E = n + 1)\nv : ↑(sphere 0 1)\nU : ↥(ℝ ∙ ↑(-v))ᗮ ≃ₗᵢ[ℝ] EuclideanSpace ℝ (Fin n) := ⋯\nthis : HasFDerivAt (stereoInvFunAux (-↑v) ∘ Subtype.val) (ℝ ∙ ↑(-v))ᗮ.subtypeL (U.symm 0)\n⊢ (↑((ℝ ∙ ↑(-v))ᗮ.subtypeL ∘S... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Geometry.Manifold.IntegralCurve.Transform | {
"line": 122,
"column": 2
} | {
"line": 122,
"column": 26
} | {
"line": 123,
"column": 2
} | [
{
"pp": "E : Type u_1\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\nH : Type u_2\ninst✝² : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace H M\nγ : ℝ → M\nv : (x : M) → TangentSpace I x\ns : Set ℝ\na : ℝ\nha : a ≠ 0\nhγ : IsMIntegralCur... | [
"case e'_10\nE : Type u_1\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\nH : Type u_2\ninst✝² : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace H M\nγ : ℝ → M\nv : (x : M) → TangentSpace I x\ns : Set ℝ\na : ℝ\nha : a ≠ 0\nhγ : IsMIntegralCur... | convert! hγ.comp_mul a⁻¹ | Mathlib.Tactic._aux_Mathlib_Tactic_Convert___macroRules_Mathlib_Tactic_convert!_1 | Mathlib.Tactic.convert! |
Mathlib.Geometry.Manifold.IntegralCurve.Transform | {
"line": 155,
"column": 2
} | {
"line": 155,
"column": 26
} | {
"line": 156,
"column": 2
} | [
{
"pp": "E : Type u_1\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\nH : Type u_2\ninst✝² : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace H M\nγ : ℝ → M\nv : (x : M) → TangentSpace I x\na : ℝ\nha : a ≠ 0\nhγ : IsMIntegralCurve (γ ∘ fun... | [
"case e'_10\nE : Type u_1\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\nH : Type u_2\ninst✝² : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace H M\nγ : ℝ → M\nv : (x : M) → TangentSpace I x\na : ℝ\nha : a ≠ 0\nhγ : IsMIntegralCurve (γ ∘ fun... | convert! hγ.comp_mul a⁻¹ | Mathlib.Tactic._aux_Mathlib_Tactic_Convert___macroRules_Mathlib_Tactic_convert!_1 | Mathlib.Tactic.convert! |
Mathlib.Geometry.Manifold.IntegralCurve.UniformTime | {
"line": 146,
"column": 4
} | {
"line": 146,
"column": 45
} | {
"line": 147,
"column": 4
} | [
{
"pp": "case neg\nE : Type u_1\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\nH : Type u_2\ninst✝⁵ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝⁴ : TopologicalSpace M\ninst✝³ : ChartedSpace H M\ninst✝² : IsManifold I 1 M\ninst✝¹ : T2Space M\nγ γ' : ℝ → M\nv : (x : M) → Tangen... | [
"case neg\nE : Type u_1\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\nH : Type u_2\ninst✝⁵ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝⁴ : TopologicalSpace M\ninst✝³ : ChartedSpace H M\ninst✝² : IsManifold I 1 M\ninst✝¹ : T2Space M\nγ γ' : ℝ → M\nv : (x : M) → TangentSpace I x\n... | rw [mem_union, or_iff_not_imp_left] at ht | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Geometry.Manifold.Riemannian.PathELength | {
"line": 107,
"column": 2
} | {
"line": 107,
"column": 6
} | {
"line": 108,
"column": 2
} | [
{
"pp": "E : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\nH : Type u_2\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\ninst✝ : (x : M) → ENorm (TangentSpace I x)\na b c : ℝ\nγ : ℝ → M\nh : a ≤ b\nh' : b ≤ c\n⊢ ... | [
"E : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\nH : Type u_2\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\ninst✝ : (x : M) → ENorm (TangentSpace I x)\na b c : ℝ\nγ : ℝ → M\nh : a ≤ b\nh' : b ≤ c\n⊢ pathELength ... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Geometry.Manifold.Riemannian.PathELength | {
"line": 122,
"column": 11
} | {
"line": 122,
"column": 43
} | {
"line": 122,
"column": 43
} | [
{
"pp": "E : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\nH : Type u_2\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\ninst✝ : (x : M) → ENorm (TangentSpace I x)\na b : ℝ\nh : Fact (a < b)\nγ : ↑(Icc a b) → M\n... | [
"E : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\nH : Type u_2\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\ninst✝ : (x : M) → ENorm (TangentSpace I x)\na b : ℝ\nh : Fact (a < b)\nγ : ↑(Icc a b) → M\n⊢ ∫⁻ (t : ↑(... | ← mfderivWithin_comp_projIcc_one | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Geometry.Manifold.IntegralCurve.ExistUnique | {
"line": 137,
"column": 2
} | {
"line": 174,
"column": 84
} | {
"line": 176,
"column": 0
} | [
{
"pp": "E : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\nH : Type u_2\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\ninst✝ : IsManifold I 1 M\nγ γ' : ℝ → M\nv : (x : M) → TangentSpace I x\nt₀ : ℝ\nhγt₀ : I.Is... | [] | set v' : E → E := fun x ↦
tangentCoordChange I ((extChartAt I (γ t₀)).symm x) (γ t₀) ((extChartAt I (γ t₀)).symm x)
(v ((extChartAt I (γ t₀)).symm x)) with hv'
-- extract a set `s` on which `v'` is Lipschitz
rw [contMDiffAt_iff] at hv
obtain ⟨_, hv⟩ := hv
obtain ⟨K, s, hs, hlip⟩ : ∃ K, ∃ s ∈ 𝓝 _, Lip... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Manifold.IntegralCurve.ExistUnique | {
"line": 137,
"column": 2
} | {
"line": 174,
"column": 84
} | {
"line": 176,
"column": 0
} | [
{
"pp": "E : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\nH : Type u_2\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_3\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\ninst✝ : IsManifold I 1 M\nγ γ' : ℝ → M\nv : (x : M) → TangentSpace I x\nt₀ : ℝ\nhγt₀ : I.Is... | [] | set v' : E → E := fun x ↦
tangentCoordChange I ((extChartAt I (γ t₀)).symm x) (γ t₀) ((extChartAt I (γ t₀)).symm x)
(v ((extChartAt I (γ t₀)).symm x)) with hv'
-- extract a set `s` on which `v'` is Lipschitz
rw [contMDiffAt_iff] at hv
obtain ⟨_, hv⟩ := hv
obtain ⟨K, s, hs, hlip⟩ : ∃ K, ∃ s ∈ 𝓝 _, Lip... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Manifold.VectorField.LieBracket | {
"line": 984,
"column": 4
} | {
"line": 984,
"column": 8
} | {
"line": 985,
"column": 4
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁷ : NontriviallyNormedField 𝕜\nH : Type u_2\ninst✝⁶ : TopologicalSpace H\nE : Type u_3\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\ninst✝¹ : IsManifold I (minSmoothness ... | [
"𝕜 : Type u_1\ninst✝⁷ : NontriviallyNormedField 𝕜\nH : Type u_2\ninst✝⁶ : TopologicalSpace H\nE : Type u_3\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\ninst✝¹ : IsManifold I (minSmoothness 𝕜 3) M\nins... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Geometry.Manifold.VectorField.LieBracket | {
"line": 1004,
"column": 4
} | {
"line": 1004,
"column": 8
} | {
"line": 1005,
"column": 4
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁷ : NontriviallyNormedField 𝕜\nH : Type u_2\ninst✝⁶ : TopologicalSpace H\nE : Type u_3\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\ninst✝¹ : IsManifold I (minSmoothness ... | [
"𝕜 : Type u_1\ninst✝⁷ : NontriviallyNormedField 𝕜\nH : Type u_2\ninst✝⁶ : TopologicalSpace H\nE : Type u_3\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\ninst✝¹ : IsManifold I (minSmoothness 𝕜 3) M\nins... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Geometry.Manifold.VectorBundle.LocalFrame | {
"line": 237,
"column": 48
} | {
"line": 241,
"column": 21
} | {
"line": 243,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁹ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁸ : TopologicalSpace M\ninst✝⁷ : ChartedSpace H M\nF : Type u_5\ninst✝⁶ : NormedAddCo... | [] | by
by_cases hxe : x ∈ u
· simp [coeff, hxe]
simp_all only [toBasisAt]
· simp [coeff, hxe] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Geometry.Manifold.VectorField.LieBracket | {
"line": 1024,
"column": 4
} | {
"line": 1024,
"column": 8
} | {
"line": 1025,
"column": 4
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁷ : NontriviallyNormedField 𝕜\nH : Type u_2\ninst✝⁶ : TopologicalSpace H\nE : Type u_3\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\ninst✝¹ : IsManifold I (minSmoothness ... | [
"𝕜 : Type u_1\ninst✝⁷ : NontriviallyNormedField 𝕜\nH : Type u_2\ninst✝⁶ : TopologicalSpace H\nE : Type u_3\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\ninst✝¹ : IsManifold I (minSmoothness 𝕜 3) M\nins... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Geometry.Polygon.Basic | {
"line": 87,
"column": 37
} | {
"line": 87,
"column": 43
} | {
"line": 87,
"column": 44
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁵ : Ring R\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module R V\ninst✝² : AddTorsor V P\ninst✝¹ : Nontrivial R\nm : ℕ\ninst✝ : NeZero m.succ\npoly : Polygon P m.succ\nh : HasNondegenerateVertices R poly\ni : Fin m.succ\n⊢ 0 ≠ 1",
"ppTerm": "?m.65",
"assig... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Geometry.Polygon.Basic | {
"line": 87,
"column": 37
} | {
"line": 87,
"column": 43
} | {
"line": 87,
"column": 44
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁵ : Ring R\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module R V\ninst✝² : AddTorsor V P\ninst✝¹ : Nontrivial R\nm : ℕ\ninst✝ : NeZero m.succ\npoly : Polygon P m.succ\nh : HasNondegenerateVertices R poly\ni : Fin m.succ\n⊢ 0 ≠ 1",
"ppTerm": "?m.65",
"assig... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Polygon.Basic | {
"line": 87,
"column": 37
} | {
"line": 87,
"column": 43
} | {
"line": 87,
"column": 44
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁵ : Ring R\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module R V\ninst✝² : AddTorsor V P\ninst✝¹ : Nontrivial R\nm : ℕ\ninst✝ : NeZero m.succ\npoly : Polygon P m.succ\nh : HasNondegenerateVertices R poly\ni : Fin m.succ\n⊢ 0 ≠ 1",
"ppTerm": "?m.65",
"assig... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Polygon.Basic | {
"line": 94,
"column": 31
} | {
"line": 94,
"column": 37
} | {
"line": 94,
"column": 38
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\nn : ℕ\ninst✝⁵ : Ring R\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module R V\ninst✝² : AddTorsor V P\ninst✝¹ : Nontrivial R\ninst✝ : NeZero 2\npoly : Polygon P 2\nh : HasNondegenerateVertices R poly\nthis : 2 ≤ 2\nhlt : 2 < 3\n⊢ 0 ≠ 2",
"ppTerm": "?m.90",
"assi... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Geometry.Polygon.Basic | {
"line": 94,
"column": 31
} | {
"line": 94,
"column": 37
} | {
"line": 94,
"column": 38
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\nn : ℕ\ninst✝⁵ : Ring R\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module R V\ninst✝² : AddTorsor V P\ninst✝¹ : Nontrivial R\ninst✝ : NeZero 2\npoly : Polygon P 2\nh : HasNondegenerateVertices R poly\nthis : 2 ≤ 2\nhlt : 2 < 3\n⊢ 0 ≠ 2",
"ppTerm": "?m.90",
"assi... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Polygon.Basic | {
"line": 94,
"column": 31
} | {
"line": 94,
"column": 37
} | {
"line": 94,
"column": 38
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\nn : ℕ\ninst✝⁵ : Ring R\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module R V\ninst✝² : AddTorsor V P\ninst✝¹ : Nontrivial R\ninst✝ : NeZero 2\npoly : Polygon P 2\nh : HasNondegenerateVertices R poly\nthis : 2 ≤ 2\nhlt : 2 < 3\n⊢ 0 ≠ 2",
"ppTerm": "?m.90",
"assi... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Manifold.VectorField.LieBracket | {
"line": 1041,
"column": 2
} | {
"line": 1041,
"column": 57
} | {
"line": 1042,
"column": 2
} | [
{
"pp": "case e_6\n𝕜 : Type u_1\ninst✝⁷ : NontriviallyNormedField 𝕜\nH : Type u_2\ninst✝⁶ : TopologicalSpace H\nE : Type u_3\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\ninst✝¹ : IsManifold I (minS... | [
"case e_6.hs\n𝕜 : Type u_1\ninst✝⁷ : NontriviallyNormedField 𝕜\nH : Type u_2\ninst✝⁶ : TopologicalSpace H\nE : Type u_3\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\ninst✝¹ : IsManifold I (minSmoothness... | apply leibniz_identity_lieBracketWithin (E := E) le_rfl | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.GroupTheory.Commensurable | {
"line": 98,
"column": 8
} | {
"line": 98,
"column": 25
} | {
"line": 98,
"column": 26
} | [
{
"pp": "G : Type u_1\ninst✝ : Group G\nH : Subgroup G\na✝ b✝ : ConjAct G\nha : a✝ ∈ {g | (g • H).Commensurable H}\nhb : b✝ ∈ {g | (g • H).Commensurable H}\n⊢ a✝ * b✝ ∈ {g | (g • H).Commensurable H}",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHSMul",
"H... | [
"G : Type u_1\ninst✝ : Group G\nH : Subgroup G\na✝ b✝ : ConjAct G\nha : a✝ ∈ {g | (g • H).Commensurable H}\nhb : b✝ ∈ {g | (g • H).Commensurable H}\n⊢ ((a✝ * b✝) • H).Commensurable H"
] | Set.mem_setOf_eq, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.Commensurable | {
"line": 96,
"column": 21
} | {
"line": 96,
"column": 38
} | {
"line": 96,
"column": 39
} | [
{
"pp": "G : Type u_1\ninst✝ : Group G\nH : Subgroup G\n⊢ 1 ∈ {g | (g • H).Commensurable H}",
"ppTerm": "?m.47",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"instHSMul",
"Monoid.toMulOneClass",
"congrArg",
"setOf",
"Membership.mem",
... | [
"G : Type u_1\ninst✝ : Group G\nH : Subgroup G\n⊢ (1 • H).Commensurable H"
] | Set.mem_setOf_eq, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.Commensurable | {
"line": 100,
"column": 24
} | {
"line": 100,
"column": 41
} | {
"line": 100,
"column": 42
} | [
{
"pp": "G : Type u_1\ninst✝ : Group G\nH : Subgroup G\nx✝¹ : ConjAct G\nx✝ : x✝¹ ∈ {g | (g • H).Commensurable H}\n⊢ x✝¹⁻¹ ∈ {g | (g • H).Commensurable H}",
"ppTerm": "?m.61",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHSMul",
"DivInvOneMonoid.toInvOneClass",
"congrA... | [
"G : Type u_1\ninst✝ : Group G\nH : Subgroup G\nx✝¹ : ConjAct G\nx✝ : x✝¹ ∈ {g | (g • H).Commensurable H}\n⊢ (x✝¹⁻¹ • H).Commensurable H"
] | Set.mem_setOf_eq, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.SpecificGroups.KleinFour | {
"line": 152,
"column": 6
} | {
"line": 152,
"column": 10
} | {
"line": 153,
"column": 6
} | [
{
"pp": "case neg\nG : Type u_1\ninst✝⁴ : Group G\ninst✝³ : IsKleinFour G\nG₁ : Type u_2\nG₂ : Type u_3\ninst✝² : Group G₁\ninst✝¹ : Group G₂\ninst✝ : IsKleinFour G₁\ne : G₁ ≃ G₂\nhe : e 1 = 1\nh : Monoid.exponent G₂ = 2\n_inst₁ : Fintype G₁ := Fintype.ofFinite G₁\n_inst₂ : Fintype G₂ := Fintype.ofEquiv G₁ e\nx... | [
"case neg\nG : Type u_1\ninst✝⁴ : Group G\ninst✝³ : IsKleinFour G\nG₁ : Type u_2\nG₂ : Type u_3\ninst✝² : Group G₁\ninst✝¹ : Group G₂\ninst✝ : IsKleinFour G₁\ne : G₁ ≃ G₂\nhe : e 1 = 1\nh : Monoid.exponent G₂ = 2\n_inst₁ : Fintype G₁ := ⋯\n_inst₂ : Fintype G₂ := ⋯\nx y : G₁\nhx : e x ≠ 1\nhy : e y ≠ 1\nhxy : e x ≠ ... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.GroupTheory.SpecificGroups.Dihedral | {
"line": 220,
"column": 4
} | {
"line": 221,
"column": 29
} | {
"line": 222,
"column": 2
} | [
{
"pp": "case inr.a.sr\nn : ℕ\nhn : NeZero n\nm : ZMod n\n⊢ sr m ^ lcm n 2 = 1",
"ppTerm": "?inr.a.sr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"Dvd.dvd",
"Monoid.toMulOneClass",
"congrArg",
"dvd_lcm_right",
"DihedralGroup.instGroup",
... | [] | · rw [← orderOf_dvd_iff_pow_eq_one, orderOf_sr]
exact dvd_lcm_right n 2 | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.GroupTheory.SpecificGroups.Dihedral | {
"line": 225,
"column": 6
} | {
"line": 225,
"column": 58
} | {
"line": 226,
"column": 6
} | [
{
"pp": "case hcb\nn : ℕ\nhn : NeZero n\n⊢ 2 ∣ Monoid.exponent (DihedralGroup n)",
"ppTerm": "?hcb",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Dvd.dvd",
"ZMod.commRing",
"CommSemiring.toSemiring",
"HEq.refl",
"semigroupDvd",
"Dvd",
"Monoid.order_... | [
"case e'_3\nn : ℕ\nhn : NeZero n\n⊢ 2 = orderOf (sr 0)"
] | convert! Monoid.order_dvd_exponent (sr (0 : ZMod n)) | Mathlib.Tactic._aux_Mathlib_Tactic_Convert___macroRules_Mathlib_Tactic_convert!_1 | Mathlib.Tactic.convert! |
Mathlib.GroupTheory.SpecificGroups.Dihedral | {
"line": 238,
"column": 46
} | {
"line": 238,
"column": 52
} | {
"line": 238,
"column": 52
} | [
{
"pp": "⊢ ∀ (a b : DihedralGroup 1), a * b = b * a",
"ppTerm": "?m.55",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"of_decide_eq_true",
"Monoid.toMulOneClass",
"instDecidableEqDihedralGroup",
"DihedralGroup.instGroup",
"id",
"MulOne.toMul",
"Di... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.GroupTheory.SpecificGroups.Dihedral | {
"line": 238,
"column": 46
} | {
"line": 238,
"column": 52
} | {
"line": 238,
"column": 52
} | [
{
"pp": "⊢ ∀ (a b : DihedralGroup 1), a * b = b * a",
"ppTerm": "?m.55",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"of_decide_eq_true",
"Monoid.toMulOneClass",
"instDecidableEqDihedralGroup",
"DihedralGroup.instGroup",
"id",
"MulOne.toMul",
"Di... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.GroupTheory.SpecificGroups.Dihedral | {
"line": 238,
"column": 46
} | {
"line": 238,
"column": 52
} | {
"line": 238,
"column": 52
} | [
{
"pp": "⊢ ∀ (a b : DihedralGroup 1), a * b = b * a",
"ppTerm": "?m.55",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"of_decide_eq_true",
"Monoid.toMulOneClass",
"instDecidableEqDihedralGroup",
"DihedralGroup.instGroup",
"id",
"MulOne.toMul",
"Di... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.GroupTheory.SpecificGroups.Dihedral | {
"line": 238,
"column": 46
} | {
"line": 238,
"column": 52
} | {
"line": 238,
"column": 52
} | [
{
"pp": "⊢ ∀ (a b : DihedralGroup 2), a * b = b * a",
"ppTerm": "?m.60",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"of_decide_eq_true",
"Monoid.toMulOneClass",
"instDecidableEqDihedralGroup",
"DihedralGroup.instGroup",
"id",
"MulOne.toMul",
"Di... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.GroupTheory.SpecificGroups.Dihedral | {
"line": 238,
"column": 46
} | {
"line": 238,
"column": 52
} | {
"line": 238,
"column": 52
} | [
{
"pp": "⊢ ∀ (a b : DihedralGroup 2), a * b = b * a",
"ppTerm": "?m.60",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"of_decide_eq_true",
"Monoid.toMulOneClass",
"instDecidableEqDihedralGroup",
"DihedralGroup.instGroup",
"id",
"MulOne.toMul",
"Di... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.GroupTheory.SpecificGroups.Dihedral | {
"line": 238,
"column": 46
} | {
"line": 238,
"column": 52
} | {
"line": 238,
"column": 52
} | [
{
"pp": "⊢ ∀ (a b : DihedralGroup 2), a * b = b * a",
"ppTerm": "?m.60",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"of_decide_eq_true",
"Monoid.toMulOneClass",
"instDecidableEqDihedralGroup",
"DihedralGroup.instGroup",
"id",
"MulOne.toMul",
"Di... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.GroupTheory.Congruence.Star | {
"line": 28,
"column": 17
} | {
"line": 30,
"column": 39
} | {
"line": 32,
"column": 0
} | [
{
"pp": "M : Type u_1\ninst✝¹ : Mul M\ninst✝ : StarMul M\nr : M → M → Prop\nhr : ∀ (a b : M), r a b → r (Star.star a) (Star.star b)\na b w✝ x✝ y✝ z✝ : M\nh1 : Rel r w✝ x✝\nh2 : Rel r y✝ z✝\n⊢ Rel r (Star.star (w✝ * y✝)) (Star.star (x✝ * z✝))",
"ppTerm": "?m.99",
"assigned": true,
"usedConstants": [
... | [] | by
rw [star_mul, star_mul]
exact (h2.star hr).mul (h1.star hr) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.GroupTheory.CommutingProbability | {
"line": 192,
"column": 25
} | {
"line": 192,
"column": 31
} | {
"line": 192,
"column": 31
} | [
{
"pp": "n : ℕ\nh0 : ¬n = 0\nh1 : ¬n = 1\nh2 : Even n\n⊢ Odd 3",
"ppTerm": "?m.92",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Odd",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"Bool",
"Nat.instSemiring",
"Eq.refl",
"OfNat.ofN... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.GroupTheory.CommutingProbability | {
"line": 192,
"column": 25
} | {
"line": 192,
"column": 31
} | {
"line": 192,
"column": 31
} | [
{
"pp": "n : ℕ\nh0 : ¬n = 0\nh1 : ¬n = 1\nh2 : Even n\n⊢ Odd 3",
"ppTerm": "?m.92",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Odd",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"Bool",
"Nat.instSemiring",
"Eq.refl",
"OfNat.ofN... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.GroupTheory.CommutingProbability | {
"line": 192,
"column": 25
} | {
"line": 192,
"column": 31
} | {
"line": 192,
"column": 31
} | [
{
"pp": "n : ℕ\nh0 : ¬n = 0\nh1 : ¬n = 1\nh2 : Even n\n⊢ Odd 3",
"ppTerm": "?m.92",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Odd",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"Bool",
"Nat.instSemiring",
"Eq.refl",
"OfNat.ofN... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.GroupTheory.Coxeter.Basic | {
"line": 475,
"column": 90
} | {
"line": 486,
"column": 49
} | {
"line": 488,
"column": 0
} | [
{
"pp": "B : Type u_1\nW : Type u_3\ninst✝ : Group W\nM : CoxeterMatrix B\ncs : CoxeterSystem M W\ni i' : B\nm : ℕ\n⊢ cs.wordProd (alternatingWord i i' m) = (if Even m then 1 else cs.simple i') * (cs.simple i * cs.simple i') ^ (m / 2)",
"ppTerm": "?m.46",
"assigned": true,
"usedConstants": [
"... | [] | by
induction m with
| zero => simp [alternatingWord]
| succ m ih =>
rw [alternatingWord_succ', wordProd_cons, ih]
by_cases hm : Even m
· have h₁ : ¬ Even (m + 1) := by simp [hm, parity_simps]
have h₂ : (m + 1) / 2 = m / 2 := Nat.succ_div_of_not_dvd <| by rwa [← even_iff_two_dvd]
simp [hm, ... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.GroupTheory.Coxeter.Length | {
"line": 147,
"column": 54
} | {
"line": 147,
"column": 60
} | {
"line": 147,
"column": 61
} | [
{
"pp": "B : Type u_1\nW : Type u_2\ninst✝ : Group W\nM : CoxeterMatrix B\ncs : CoxeterSystem M W\n⊢ 1 + 1 = 0",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"ZMod.commRing",
"CommSemiring.toSemiring",
"ZMod.decidableEq",
"AddGroupWithOne... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.GroupTheory.Coxeter.Length | {
"line": 147,
"column": 54
} | {
"line": 147,
"column": 60
} | {
"line": 147,
"column": 61
} | [
{
"pp": "B : Type u_1\nW : Type u_2\ninst✝ : Group W\nM : CoxeterMatrix B\ncs : CoxeterSystem M W\n⊢ 1 + 1 = 0",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"ZMod.commRing",
"CommSemiring.toSemiring",
"ZMod.decidableEq",
"AddGroupWithOne... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.GroupTheory.Coxeter.Length | {
"line": 147,
"column": 54
} | {
"line": 147,
"column": 60
} | {
"line": 147,
"column": 61
} | [
{
"pp": "B : Type u_1\nW : Type u_2\ninst✝ : Group W\nM : CoxeterMatrix B\ncs : CoxeterSystem M W\n⊢ 1 + 1 = 0",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"ZMod.commRing",
"CommSemiring.toSemiring",
"ZMod.decidableEq",
"AddGroupWithOne... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.GroupTheory.CoprodI | {
"line": 684,
"column": 4
} | {
"line": 684,
"column": 24
} | {
"line": 685,
"column": 4
} | [
{
"pp": "ι : Type u_1\nM : ι → Type u_2\ninst✝ : (i : ι) → Monoid (M i)\nw✝ : Word M\nh✝ : w✝ ≠ empty\ni j : ι\nw : NeWord M i j\nh : w.toWord.toList = w✝.toList\n⊢ ∃ i j w', w'.toWord = w✝",
"ppTerm": "?m.64",
"assigned": true,
"usedConstants": [
"Monoid.CoprodI.NeWord.toWord",
"Monoid.... | [
"ι : Type u_1\nM : ι → Type u_2\ninst✝ : (i : ι) → Monoid (M i)\nw✝ : Word M\nh✝ : w✝ ≠ empty\ni j : ι\nw : NeWord M i j\nh : w.toWord.toList = w✝.toList\n⊢ w.toWord = w✝"
] | refine ⟨i, j, w, ?_⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.GroupTheory.Coxeter.Inversion | {
"line": 318,
"column": 2
} | {
"line": 318,
"column": 33
} | {
"line": 319,
"column": 2
} | [
{
"pp": "B : Type u_1\nW : Type u_2\ninst✝ : Group W\nM : CoxeterMatrix B\ncs : CoxeterSystem M W\nω : List B\nj : ℕ\n⊢ cs.rightInvSeq (drop j ω) = drop j (cs.rightInvSeq ω)",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.recAux",
"HMul.hMul",
"DivInv... | [] | induction j generalizing ω with | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.GroupTheory.DivisibleHull | {
"line": 190,
"column": 2
} | {
"line": 190,
"column": 20
} | {
"line": 191,
"column": 2
} | [
{
"pp": "M : Type u_2\ninst✝ : AddCommGroup M\na : ℚ\nh : 0 ≤ a\nx : DivisibleHull M\n⊢ a • x =\n (have this := ⟨a, h⟩;\n this) •\n x",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Rat.instOfNat",
"LE.le.eq_or_lt",
"Preorder.toLT",
"Rat",
"Parti... | [
"M : Type u_2\ninst✝ : AddCommGroup M\na : ℚ\nh : 0 ≤ a\nx : DivisibleHull M\nthis : 0 = a ∨ 0 < a\n⊢ a • x =\n (have this := ⟨a, h⟩;\n this) •\n x"
] | have := h.eq_or_lt | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.GroupTheory.DivisibleHull | {
"line": 196,
"column": 2
} | {
"line": 196,
"column": 20
} | {
"line": 197,
"column": 2
} | [
{
"pp": "M : Type u_2\ninst✝ : AddCommGroup M\na : ℚ\nh : a ≤ 0\nx : DivisibleHull M\n⊢ a • x =\n -((have this := ⟨-a, ⋯⟩;\n this) •\n x)",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Rat.instOfNat",
"LE.le.eq_or_lt",
"Preorder.toLT",
"Rat",
... | [
"M : Type u_2\ninst✝ : AddCommGroup M\na : ℚ\nh : a ≤ 0\nx : DivisibleHull M\nthis : a = 0 ∨ a < 0\n⊢ a • x =\n -((have this := ⟨-a, ⋯⟩;\n this) •\n x)"
] | have := h.eq_or_lt | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.GroupTheory.CoprodI | {
"line": 906,
"column": 8
} | {
"line": 906,
"column": 46
} | {
"line": 906,
"column": 46
} | [
{
"pp": "ι : Type u_1\nG : Type u_4\ninst✝³ : Group G\nH : ι → Type u_5\ninst✝² : (i : ι) → Group (H i)\nf : (i : ι) → H i →* G\nhcard : 3 ≤ #ι ∨ ∃ i, 3 ≤ #(H i)\nα : Type u_6\ninst✝¹ : MulAction G α\nX : ι → Set α\nhXnonempty : ∀ (i : ι), (X i).Nonempty\nhXdisj : Pairwise (Disjoint on X)\nhpp : Pairwise fun i ... | [
"ι : Type u_1\nG : Type u_4\ninst✝³ : Group G\nH : ι → Type u_5\ninst✝² : (i : ι) → Group (H i)\nf : (i : ι) → H i →* G\nhcard : 3 ≤ #ι ∨ ∃ i, 3 ≤ #(H i)\nα : Type u_6\ninst✝¹ : MulAction G α\nX : ι → Set α\nhXnonempty : ∀ (i : ι), (X i).Nonempty\nhXdisj : Pairwise (Disjoint on X)\nhpp : Pairwise fun i j ↦ ∀ (h : H... | (CoprodI.Word.equiv).forall_congr_left | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.Coxeter.Inversion | {
"line": 459,
"column": 6
} | {
"line": 459,
"column": 55
} | {
"line": 459,
"column": 55
} | [
{
"pp": "B : Type u_1\nW : Type u_2\ninst✝ : Group W\nM : CoxeterMatrix B\ncs : CoxeterSystem M W\ni j : B\np k : ℕ\nh : k + 1 < 2 * p\n⊢ cs.simple (alternatingWord i j (2 * p))[k + 1] = cs.simple (alternatingWord j i (2 * p))[k]",
"ppTerm": "?m.111",
"assigned": true,
"usedConstants": [
"Eq.m... | [
"B : Type u_1\nW : Type u_2\ninst✝ : Group W\nM : CoxeterMatrix B\ncs : CoxeterSystem M W\ni j : B\np k : ℕ\nh : k + 1 < 2 * p\n⊢ cs.simple (alternatingWord j i (2 * p))[k] = cs.simple (alternatingWord j i (2 * p))[k]",
"B : Type u_1\nW : Type u_2\ninst✝ : Group W\nM : CoxeterMatrix B\ncs : CoxeterSystem M W\ni j... | getElem_alternatingWord_swapIndices i j (2 * p) k | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.DoubleCoset | {
"line": 257,
"column": 2
} | {
"line": 257,
"column": 50
} | {
"line": 258,
"column": 2
} | [
{
"pp": "G : Type u_1\ninst✝ : Group G\nH K : Subgroup G\nt : Finset (Quotient ↑H ↑K)\nht : ⋃ q ∈ t, doubleCoset (out q) ↑H ↑K ≠ Set.univ\nx : G\ny : Quotient ↑H ↑K\nhy : y ∈ t\nq : G\nhq : q ∈ doubleCoset (out y) ↑H ↑K\nhx : Quot.mk (⇑(leftRel K)) q = Quot.mk (⇑(leftRel K)) x\n⊢ x ∈ doubleCoset (out y) ↑H ↑K",... | [
"G : Type u_1\ninst✝ : Group G\nH K : Subgroup G\nt : Finset (Quotient ↑H ↑K)\nht : ⋃ q ∈ t, doubleCoset (out q) ↑H ↑K ≠ Set.univ\nx : G\ny : Quotient ↑H ↑K\nhy : y ∈ t\nq : G\nhq : q ∈ doubleCoset (out y) ↑H ↑K\nhx : Quot.mk (⇑(leftRel K)) q = Quot.mk (⇑(leftRel K)) x\n⊢ ∃ x_1 ∈ ↑H, ∃ y ∈ ↑K, x = x_1 * q * y"
] | rw [← doubleCoset_eq_of_mem hq, mem_doubleCoset] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.GroupTheory.DoubleCoset | {
"line": 274,
"column": 2
} | {
"line": 274,
"column": 50
} | {
"line": 275,
"column": 2
} | [
{
"pp": "G : Type u_1\ninst✝ : Group G\nH K : Subgroup G\nt : Finset (Quotient ↑H ↑K)\nht : ⋃ q ∈ t, doubleCoset (out q) ↑H ↑K ≠ Set.univ\nx : G\ny : Quotient ↑H ↑K\nhy : y ∈ t\nq : G\nhq : q ∈ doubleCoset (out y) ↑H ↑K\nhx : Quot.mk (⇑(rightRel H)) q = Quot.mk (⇑(rightRel H)) x\n⊢ x ∈ doubleCoset (out y) ↑H ↑K... | [
"G : Type u_1\ninst✝ : Group G\nH K : Subgroup G\nt : Finset (Quotient ↑H ↑K)\nht : ⋃ q ∈ t, doubleCoset (out q) ↑H ↑K ≠ Set.univ\nx : G\ny : Quotient ↑H ↑K\nhy : y ∈ t\nq : G\nhq : q ∈ doubleCoset (out y) ↑H ↑K\nhx : Quot.mk (⇑(rightRel H)) q = Quot.mk (⇑(rightRel H)) x\n⊢ ∃ x_1 ∈ ↑H, ∃ y ∈ ↑K, x = x_1 * q * y"
] | rw [← doubleCoset_eq_of_mem hq, mem_doubleCoset] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.GroupTheory.Transfer | {
"line": 199,
"column": 4
} | {
"line": 200,
"column": 77
} | {
"line": 201,
"column": 4
} | [
{
"pp": "case neg\nG : Type u_1\ninst✝ : Group G\nH : Subgroup G\ng : G\nhH : ¬H.index = 0\nthis : Fintype (G ⧸ H) := fintypeOfIndexNeZero hH\nkey : ∀ (q : G ⧸ H), g ^ Function.minimalPeriod (fun x ↦ g • x) q ∈ H\n⊢ g ^ H.index ∈ H",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"ins... | [
"case neg\nG : Type u_1\ninst✝ : Group G\nH : Subgroup G\ng : G\nhH : ¬H.index = 0\nthis : Fintype (G ⧸ H) := fintypeOfIndexNeZero hH\nkey : ∀ (q : G ⧸ H), g ^ Function.minimalPeriod (fun x ↦ g • x) q ∈ H\nf : Quotient (orbitRel (↥(zpowers g)) (G ⧸ H)) → ↥(zpowers g) :=\n fun q ↦ ⟨g, ⋯⟩ ^ Function.minimalPeriod (f... | let f : Quotient (orbitRel (zpowers g) (G ⧸ H)) → zpowers g := fun q =>
(⟨g, mem_zpowers g⟩ : zpowers g) ^ Function.minimalPeriod (g • ·) q.out | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLet___1 | Lean.Parser.Tactic.tacticLet__ |
Mathlib.GroupTheory.Schreier | {
"line": 47,
"column": 34
} | {
"line": 47,
"column": 45
} | {
"line": 47,
"column": 46
} | [
{
"pp": "G : Type u_1\ninst✝¹ : CommGroup G\ninst✝ : Group.FG G\nS : Finset G\nhS1 : #S = Group.rank G\nhS2 : closure ↑S = ⊤\nf : ((g : ↥S) → ↥(zpowers ↑g)) →* G := noncommPiCoprod ⋯\n⊢ f.range = ⊤",
"ppTerm": "?m.80",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MonoidHom.range",
... | [
"G : Type u_1\ninst✝¹ : CommGroup G\ninst✝ : Group.FG G\nS : Finset G\nhS1 : #S = Group.rank G\nhS2 : closure ↑S = ⊤\nf : ((g : ↥S) → ↥(zpowers ↑g)) →* G := noncommPiCoprod ⋯\n⊢ ⊤ ≤ f.range"
] | eq_top_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.Schreier | {
"line": 123,
"column": 6
} | {
"line": 123,
"column": 17
} | {
"line": 123,
"column": 18
} | [
{
"pp": "G : Type u_1\ninst✝ : Group G\nH : Subgroup G\nR S : Set G\nhR : IsComplement (↑H) R\nhR1 : 1 ∈ R\nhS : closure S = ⊤\n⊢ closure ((fun g ↦ ⟨g * (↑(hR.toRightFun g))⁻¹, ⋯⟩) '' (R * S)) = ⊤",
"ppTerm": "?m.53",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"Sub... | [
"G : Type u_1\ninst✝ : Group G\nH : Subgroup G\nR S : Set G\nhR : IsComplement (↑H) R\nhR1 : 1 ∈ R\nhS : closure S = ⊤\n⊢ ⊤ ≤ closure ((fun g ↦ ⟨g * (↑(hR.toRightFun g))⁻¹, ⋯⟩) '' (R * S))"
] | eq_top_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.Schreier | {
"line": 122,
"column": 81
} | {
"line": 124,
"column": 76
} | {
"line": 126,
"column": 0
} | [
{
"pp": "G : Type u_1\ninst✝ : Group G\nH : Subgroup G\nR S : Set G\nhR : IsComplement (↑H) R\nhR1 : 1 ∈ R\nhS : closure S = ⊤\n⊢ closure ((fun g ↦ ⟨g * (↑(hR.toRightFun g))⁻¹, ⋯⟩) '' (R * S)) = ⊤",
"ppTerm": "?m.53",
"assigned": true,
"usedConstants": [
"Set.image_image",
"Eq.mpr",
... | [] | by
rw [eq_top_iff, ← map_subtype_le_map_subtype, MonoidHom.map_closure, Set.image_image]
exact (map_subtype_le ⊤).trans (ge_of_eq (closure_mul_image_eq hR hR1 hS)) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.GroupTheory.Nilpotent | {
"line": 340,
"column": 8
} | {
"line": 340,
"column": 19
} | {
"line": 340,
"column": 20
} | [
{
"pp": "case h\nG : Type u_1\ninst✝ : Group G\nn : ℕ\nH : ℕ → Subgroup G\nhH : IsAscendingCentralSeries H\nhn : H n = ⊤\n⊢ upperCentralSeries G n = ⊤",
"ppTerm": "?h",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"eq_top_iff",
"congrArg",
"PartialOrder.toPreorder",
"... | [
"case h\nG : Type u_1\ninst✝ : Group G\nn : ℕ\nH : ℕ → Subgroup G\nhH : IsAscendingCentralSeries H\nhn : H n = ⊤\n⊢ ⊤ ≤ upperCentralSeries G n"
] | eq_top_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.FreeGroup.NielsenSchreier | {
"line": 214,
"column": 59
} | {
"line": 214,
"column": 69
} | {
"line": 214,
"column": 70
} | [
{
"pp": "G : Type u\ninst✝³ : Groupoid G\ninst✝² : IsFreeGroupoid G\nT : WideSubquiver (Symmetrify (Generators G))\ninst✝¹ : Arborescence (WideSubquiver.toType (Symmetrify (Generators G)) T)\nX : Type ?u.18\ninst✝ : Monoid X\nf : End (root' T) →* X\na : G\n⊢ f 1 = 𝟙 ()",
"ppTerm": "?m.51",
"assigned": ... | [
"G : Type u\ninst✝³ : Groupoid G\ninst✝² : IsFreeGroupoid G\nT : WideSubquiver (Symmetrify (Generators G))\ninst✝¹ : Arborescence (WideSubquiver.toType (Symmetrify (Generators G)) T)\nX : Type ?u.18\ninst✝ : Monoid X\nf : End (root' T) →* X\na : G\n⊢ 1 = 𝟙 ()"
] | f.map_one, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.Nilpotent | {
"line": 557,
"column": 8
} | {
"line": 557,
"column": 19
} | {
"line": 557,
"column": 20
} | [
{
"pp": "case mpr\nG : Type u_1\ninst✝ : Group G\nhG : Group.IsNilpotent G\nn : ℕ\nh : nilpotencyClass G ≤ n\n⊢ upperCentralSeries G n = ⊤",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"eq_top_iff",
"congrArg",
"PartialOrder.toPreorder",
"Subgroup.u... | [
"case mpr\nG : Type u_1\ninst✝ : Group G\nhG : Group.IsNilpotent G\nn : ℕ\nh : nilpotencyClass G ≤ n\n⊢ ⊤ ≤ upperCentralSeries G n"
] | eq_top_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.FreeGroup.NielsenSchreier | {
"line": 264,
"column": 8
} | {
"line": 264,
"column": 62
} | {
"line": 265,
"column": 8
} | [
{
"pp": "case pos\nG : Type u\ninst✝³ : Groupoid G\ninst✝² : IsFreeGroupoid G\nT : WideSubquiver (Symmetrify (Generators G))\ninst✝¹ : Arborescence (WideSubquiver.toType (Symmetrify (Generators G)) T)\nX : Type u\ninst✝ : Group X\nf : ↑(wideSubquiverEquivSetTotal (wideSubquiverSymmetrify T))ᶜ → X\nf' : Labellin... | [
"case neg\nG : Type u\ninst✝³ : Groupoid G\ninst✝² : IsFreeGroupoid G\nT : WideSubquiver (Symmetrify (Generators G))\ninst✝¹ : Arborescence (WideSubquiver.toType (Symmetrify (Generators G)) T)\nX : Type u\ninst✝ : Group X\nf : ↑(wideSubquiverEquivSetTotal (wideSubquiverSymmetrify T))ᶜ → X\nf' : Labelling (Generator... | · rw [loopOfHom_eq_id T e h, ← End.one_def, E.map_one] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
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