module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Data.Seq.Basic | {
"line": 204,
"column": 6
} | {
"line": 204,
"column": 17
} | {
"line": 204,
"column": 18
} | [
{
"pp": "case succ.some\nα : Type u\nm : ℕ\nih : ∀ {s : Seq α}, (take m s).length ≤ m\ns : Seq α\nx : α\nr : Seq α\n⊢ (match some (x, r) with\n | none => []\n | some (x, r) => x :: take m r).length ≤\n m + 1",
"ppTerm": "?succ.some",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"case succ.some\nα : Type u\nm : ℕ\nih : ∀ {s : Seq α}, (take m s).length ≤ m\ns : Seq α\nx : α\nr : Seq α\n⊢ (take m r).length ≤ m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Seq.Computation | {
"line": 631,
"column": 19
} | {
"line": 631,
"column": 30
} | {
"line": 631,
"column": 31
} | [
{
"pp": "case think\nα : Type u\nβ : Type v\nf : α → β\ns✝ : Computation α\nc₁ c₂ : Computation β\nh : c₁ = c₂ ∨ ∃ s, c₁ = s.bind (pure ∘ f) ∧ c₂ = map f s\ns : Computation α\n⊢ BisimO (fun c₁ c₂ ↦ c₁ = c₂ ∨ ∃ s, c₁ = s.bind (pure ∘ f) ∧ c₂ = map f s) (s.think.bind (pure ∘ f)).destruct\n (map f s.think).dest... | [
"case think\nα : Type u\nβ : Type v\nf : α → β\ns✝ : Computation α\nc₁ c₂ : Computation β\nh : c₁ = c₂ ∨ ∃ s, c₁ = s.bind (pure ∘ f) ∧ c₂ = map f s\ns : Computation α\n⊢ s.bind (pure ∘ f) = map f s ∨ ∃ s_1, s.bind (pure ∘ f) = s_1.bind (pure ∘ f) ∧ map f s = map f s_1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Seq.Computation | {
"line": 636,
"column": 2
} | {
"line": 636,
"column": 13
} | {
"line": 636,
"column": 14
} | [
{
"pp": "α : Type u\ns : Computation α\n⊢ s.bind pure = s",
"ppTerm": "?m.5",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\ns : Computation α\n⊢ s.bind pure = s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.ContinuedFractions.Translations | {
"line": 46,
"column": 31
} | {
"line": 46,
"column": 54
} | {
"line": 46,
"column": 54
} | [
{
"pp": "α : Type u_1\ng : GenContFract α\nn : ℕ\n⊢ g.s.get? n = none ↔ g.partNums.get? n = none",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"GenContFract.s",
"Eq.mpr",
"congrArg",
"id",
"GenContFract.Pair",
"Option.none",
"Iff",
"propext... | [
"α : Type u_1\ng : GenContFract α\nn : ℕ\n⊢ g.s.get? n = none ↔ g.s.get? n = none"
] | partNum_none_iff_s_none | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.ContinuedFractions.Translations | {
"line": 62,
"column": 2
} | {
"line": 62,
"column": 46
} | {
"line": 62,
"column": 47
} | [
{
"pp": "α : Type u_1\ng : GenContFract α\nn : ℕ\na : α\nnth_partNum_eq : g.partNums.get? n = some a\n⊢ ∃ gp, g.s.get? n = some gp ∧ gp.a = a",
"ppTerm": "?m.13",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ng : GenContFract α\nn : ℕ\na : α\nnth_partNum_eq : g.partNums.get? n = some a\n⊢ ∃ gp, g.s.get? n = some gp ∧ gp.a = a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.ContinuedFractions.Translations | {
"line": 67,
"column": 2
} | {
"line": 67,
"column": 46
} | {
"line": 67,
"column": 47
} | [
{
"pp": "α : Type u_1\ng : GenContFract α\nn : ℕ\nb : α\nnth_partDen_eq : g.partDens.get? n = some b\n⊢ ∃ gp, g.s.get? n = some gp ∧ gp.b = b",
"ppTerm": "?m.13",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ng : GenContFract α\nn : ℕ\nb : α\nnth_partDen_eq : g.partDens.get? n = some b\n⊢ ∃ gp, g.s.get? n = some gp ∧ gp.b = b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Seq.Computation | {
"line": 654,
"column": 19
} | {
"line": 654,
"column": 39
} | {
"line": 654,
"column": 40
} | [
{
"pp": "case think\nα : Type u\nβ : Type v\nγ : Type w\ns✝ : Computation α\nf : α → Computation β\ng : β → Computation γ\nc₁ c₂ : Computation γ\nh : c₁ = c₂ ∨ ∃ s, c₁ = (s.bind f).bind g ∧ c₂ = s.bind fun x ↦ (f x).bind g\ns : Computation α\n⊢ BisimO (fun c₁ c₂ ↦ c₁ = c₂ ∨ ∃ s, c₁ = (s.bind f).bind g ∧ c₂ = s.... | [
"case think\nα : Type u\nβ : Type v\nγ : Type w\ns✝ : Computation α\nf : α → Computation β\ng : β → Computation γ\nc₁ c₂ : Computation γ\nh : c₁ = c₂ ∨ ∃ s, c₁ = (s.bind f).bind g ∧ c₂ = s.bind fun x ↦ (f x).bind g\ns : Computation α\n⊢ ((s.bind f).bind g = s.bind fun x ↦ (f x).bind g) ∨\n ∃ s_1, (s.bind f).bind... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Seq.Basic | {
"line": 299,
"column": 22
} | {
"line": 299,
"column": 33
} | {
"line": 299,
"column": 34
} | [
{
"pp": "case bisim.nil.nil.cons\nα : Type u\ns t u✝ : Seq α\nx✝ : α\nu : Seq α\n⊢ BisimO (fun s1 s2 ↦ ∃ s t u, s1 = (s.append t).append u ∧ s2 = s.append (t.append u))\n ((nil.append nil).append (cons x✝ u)).destruct (nil.append (nil.append (cons x✝ u))).destruct",
"ppTerm": "?bisim.nil.nil.cons",
"... | [
"case bisim.nil.nil.cons\nα : Type u\ns t u✝ : Seq α\nx✝ : α\nu : Seq α\n⊢ ∃ s t u_1, u = (s.append t).append u_1 ∧ u = s.append (t.append u_1)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Seq.Basic | {
"line": 300,
"column": 20
} | {
"line": 300,
"column": 31
} | {
"line": 300,
"column": 32
} | [
{
"pp": "case bisim.nil.cons\nα : Type u\ns t✝ u✝ u : Seq α\nx✝ : α\nt : Seq α\n⊢ BisimO (fun s1 s2 ↦ ∃ s t u, s1 = (s.append t).append u ∧ s2 = s.append (t.append u))\n ((nil.append (cons x✝ t)).append u).destruct (nil.append ((cons x✝ t).append u)).destruct",
"ppTerm": "?bisim.nil.cons",
"assigned"... | [
"case bisim.nil.cons\nα : Type u\ns t✝ u✝ u : Seq α\nx✝ : α\nt : Seq α\n⊢ ∃ s t_1 u_1, t.append u = (s.append t_1).append u_1 ∧ t.append u = s.append (t_1.append u_1)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Seq.Basic | {
"line": 301,
"column": 18
} | {
"line": 301,
"column": 29
} | {
"line": 301,
"column": 30
} | [
{
"pp": "case bisim.cons\nα : Type u\ns✝ t✝ u✝ t u : Seq α\nx✝ : α\ns : Seq α\n⊢ BisimO (fun s1 s2 ↦ ∃ s t u, s1 = (s.append t).append u ∧ s2 = s.append (t.append u))\n (((cons x✝ s).append t).append u).destruct ((cons x✝ s).append (t.append u)).destruct",
"ppTerm": "?bisim.cons",
"assigned": true,
... | [
"case bisim.cons\nα : Type u\ns✝ t✝ u✝ t u : Seq α\nx✝ : α\ns : Seq α\n⊢ ∃ s_1 t_1 u_1,\n (s.append t).append u = (s_1.append t_1).append u_1 ∧ s.append (t.append u) = s_1.append (t_1.append u_1)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Seq.Basic | {
"line": 313,
"column": 4
} | {
"line": 313,
"column": 15
} | {
"line": 313,
"column": 16
} | [
{
"pp": "case nil\nα : Type u\ns₂ : Seq α\na : α\nss : Seq α\nh : a ∈ ss\nb : α\ns' : Seq α\no : a = b ∨ ∀ {s₁ : Seq α}, a ∈ s₁.append s₂ → s₁.append s₂ = s' → a ∈ s₁ ∨ a ∈ s₂\nm : a ∈ nil.append s₂\ne✝ : nil.append s₂ = cons b s'\n⊢ a ∈ s₂",
"ppTerm": "?nil",
"assigned": false,
"usedConstants": [],... | [
"case nil\nα : Type u\ns₂ : Seq α\na : α\nss : Seq α\nh : a ∈ ss\nb : α\ns' : Seq α\no : a = b ∨ ∀ {s₁ : Seq α}, a ∈ s₁.append s₂ → s₁.append s₂ = s' → a ∈ s₁ ∨ a ∈ s₂\nm : a ∈ nil.append s₂\ne✝ : nil.append s₂ = cons b s'\n⊢ a ∈ s₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Seq.Basic | {
"line": 317,
"column": 44
} | {
"line": 317,
"column": 55
} | {
"line": 317,
"column": 56
} | [
{
"pp": "α : Type u\ns₂ : Seq α\na : α\nss : Seq α\nh : a ∈ ss\nb : α\ns' : Seq α\no : a = b ∨ ∀ {s₁ : Seq α}, a ∈ s₁.append s₂ → s₁.append s₂ = s' → a ∈ s₁ ∨ a ∈ s₂\nc : α\nt₁ : Seq α\nm : a ∈ (cons c t₁).append s₂\ne : (cons c t₁).append s₂ = cons b s'\nthis : ((cons c t₁).append s₂).destruct = (cons b s').de... | [
"α : Type u\ns₂ : Seq α\na : α\nss : Seq α\nh : a ∈ ss\nb : α\ns' : Seq α\no : a = b ∨ ∀ {s₁ : Seq α}, a ∈ s₁.append s₂ → s₁.append s₂ = s' → a ∈ s₁ ∨ a ∈ s₂\nc : α\nt₁ : Seq α\nm : a ∈ (cons c t₁).append s₂\ne : (cons c t₁).append s₂ = cons b s'\nthis : ((cons c t₁).append s₂).destruct = (cons b s').destruct\n⊢ a ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Seq.Basic | {
"line": 320,
"column": 59
} | {
"line": 320,
"column": 70
} | {
"line": 320,
"column": 71
} | [
{
"pp": "α : Type u\ns₂ : Seq α\na : α\nss : Seq α\nh : a ∈ ss\nb : α\ns' : Seq α\no : a = b ∨ ∀ {s₁ : Seq α}, a ∈ s₁.append s₂ → s₁.append s₂ = s' → a ∈ s₁ ∨ a ∈ s₂\nc : α\nt₁ : Seq α\nm✝ : a ∈ (cons c t₁).append s₂\ne : (cons c t₁).append s₂ = cons b s'\nthis : ((cons c t₁).append s₂).destruct = (cons b s').d... | [
"α : Type u\ns₂ : Seq α\na : α\nss : Seq α\nh : a ∈ ss\nb : α\ns' : Seq α\no : a = b ∨ ∀ {s₁ : Seq α}, a ∈ s₁.append s₂ → s₁.append s₂ = s' → a ∈ s₁ ∨ a ∈ s₂\nc : α\nt₁ : Seq α\nm✝ : a ∈ (cons c t₁).append s₂\ne : (cons c t₁).append s₂ = cons b s'\nthis : ((cons c t₁).append s₂).destruct = (cons b s').destruct\nm :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.ContinuedFractions.ContinuantsRecurrence | {
"line": 66,
"column": 2
} | {
"line": 68,
"column": 41
} | {
"line": 69,
"column": 2
} | [
{
"pp": "K : Type u_1\ng : GenContFract K\nn : ℕ\ninst✝ : DivisionRing K\ngp : Pair K\npredB : K\nsucc_nth_s_eq : g.s.get? (n + 1) = some gp\nsucc_nth_den_eq : g.dens (n + 1) = predB\nppredConts : Pair K\nnth_conts_eq : g.conts n = ppredConts\nnth_den_eq : g.dens n = ppredConts.b\n⊢ g.dens (n + 2) = gp.b * pred... | [
"K : Type u_1\ng : GenContFract K\nn : ℕ\ninst✝ : DivisionRing K\ngp : Pair K\nsucc_nth_s_eq : g.s.get? (n + 1) = some gp\nppredConts : Pair K\nnth_conts_eq : g.conts n = ppredConts\nnth_den_eq : g.dens n = ppredConts.b\npredConts : Pair K\nsucc_nth_conts_eq : g.conts (n + 1) = predConts\nsucc_nth_den_eq : g.dens (... | obtain ⟨predConts, succ_nth_conts_eq, ⟨rfl⟩⟩ :
∃ conts, g.conts (n + 1) = conts ∧ conts.b = predB :=
exists_conts_b_of_den succ_nth_den_eq | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Data.Seq.Basic | {
"line": 414,
"column": 18
} | {
"line": 414,
"column": 29
} | {
"line": 414,
"column": 30
} | [
{
"pp": "case nil.cons\nα : Type u\nβ : Type v\nf : α → β\ns t✝ : Seq α\nx✝ : α\nt : Seq α\n⊢ BisimO (fun s1 s2 ↦ ∃ s t, s1 = map f (s.append t) ∧ s2 = (map f s).append (map f t))\n (map f (nil.append (cons x✝ t))).destruct ((map f nil).append (map f (cons x✝ t))).destruct",
"ppTerm": "?nil.cons",
"a... | [
"case nil.cons\nα : Type u\nβ : Type v\nf : α → β\ns t✝ : Seq α\nx✝ : α\nt : Seq α\n⊢ ∃ s t_1, map f t = map f (s.append t_1) ∧ map f t = (map f s).append (map f t_1)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Seq.Basic | {
"line": 415,
"column": 16
} | {
"line": 415,
"column": 27
} | {
"line": 415,
"column": 28
} | [
{
"pp": "case cons\nα : Type u\nβ : Type v\nf : α → β\ns✝ t✝ t : Seq α\nx✝ : α\ns : Seq α\n⊢ BisimO (fun s1 s2 ↦ ∃ s t, s1 = map f (s.append t) ∧ s2 = (map f s).append (map f t))\n (map f ((cons x✝ s).append t)).destruct ((map f (cons x✝ s)).append (map f t)).destruct",
"ppTerm": "?cons",
"assigned":... | [
"case cons\nα : Type u\nβ : Type v\nf : α → β\ns✝ t✝ t : Seq α\nx✝ : α\ns : Seq α\n⊢ ∃ s_1 t_1, map f (s.append t) = map f (s_1.append t_1) ∧ (map f s).append (map f t) = (map f s_1).append (map f t_1)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Seq.Basic | {
"line": 451,
"column": 8
} | {
"line": 451,
"column": 87
} | {
"line": 452,
"column": 10
} | [
{
"pp": "case cons\nα : Type u\na✝ : α\ns : Seq α\nS✝ : Seq (Seq1 α)\ns1 s2 : Seq α\nh : s1 = s2 ∨ ∃ a s S, s1 = (cons (a, s) S).join ∧ s2 = cons a (s.append S.join)\na : α\nS : Seq (Seq1 α)\nx✝ : α\ns✝ : Seq α\n⊢ BisimO (fun s1 s2 ↦ s1 = s2 ∨ ∃ a s S, s1 = (cons (a, s) S).join ∧ s2 = cons a (s.append S.join))\... | [
"case cons\nα : Type u\na✝ : α\ns : Seq α\nS✝ : Seq (Seq1 α)\ns1 s2 : Seq α\nh : s1 = s2 ∨ ∃ a s S, s1 = (cons (a, s) S).join ∧ s2 = cons a (s.append S.join)\na : α\nS : Seq (Seq1 α)\nx✝ : α\ns✝ : Seq α\n⊢ (cons (x✝, s✝) S).join = cons x✝ (s✝.append S.join) ∨\n ∃ a s S_1, (cons (x✝, s✝) S).join = (cons (a, s) S_... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Seq.Basic | {
"line": 468,
"column": 10
} | {
"line": 468,
"column": 21
} | {
"line": 468,
"column": 22
} | [
{
"pp": "case bisim.nil.nil.cons\nα : Type u\nS T✝ T : Seq (Seq1 α)\na : α\ns : Seq α\n⊢ BisimO (fun s1 s2 ↦ ∃ s S T, s1 = s.append (S.append T).join ∧ s2 = s.append (S.join.append T.join))\n (nil.append (nil.append (cons (a, s) T)).join).destruct (nil.append (nil.join.append (cons (a, s) T).join)).destruct"... | [
"case bisim.nil.nil.cons\nα : Type u\nS T✝ T : Seq (Seq1 α)\na : α\ns : Seq α\n⊢ ∃ s_1 S T_1, s.append T.join = s_1.append (S.append T_1).join ∧ s.append T.join = s_1.append (S.join.append T_1.join)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Seq.Basic | {
"line": 471,
"column": 8
} | {
"line": 471,
"column": 19
} | {
"line": 471,
"column": 20
} | [
{
"pp": "case bisim.nil.cons\nα : Type u\nS✝ T✝ T S : Seq (Seq1 α)\na : α\ns : Seq α\n⊢ BisimO (fun s1 s2 ↦ ∃ s S T, s1 = s.append (S.append T).join ∧ s2 = s.append (S.join.append T.join))\n (nil.append ((cons (a, s) S).append T).join).destruct (nil.append ((cons (a, s) S).join.append T.join)).destruct",
... | [
"case bisim.nil.cons\nα : Type u\nS✝ T✝ T S : Seq (Seq1 α)\na : α\ns : Seq α\n⊢ ∃ s_1 S_1 T_1,\n s.append (S.append T).join = s_1.append (S_1.append T_1).join ∧\n s.append (S.join.append T.join) = s_1.append (S_1.join.append T_1.join)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.ContinuedFractions.Determinant | {
"line": 89,
"column": 4
} | {
"line": 89,
"column": 96
} | {
"line": 90,
"column": 2
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\ns : SimpContFract K\nn : ℕ\nnot_terminatedAt_n : ¬(↑s).TerminatedAt n\ni : ℕ\nhi : i < n + 1\ngp : Pair K\ns_ith_eq : (↑s).s.get? i = some gp\n⊢ -((↑s).partNums.get? i).getD 0 = -1",
"ppTerm": "?m.163",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [] | rw [partNum_eq_s_a s_ith_eq, s.property i gp.a <| partNum_eq_s_a s_ith_eq, Option.getD_some] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Seq.Computation | {
"line": 1081,
"column": 16
} | {
"line": 1081,
"column": 27
} | {
"line": 1081,
"column": 28
} | [
{
"pp": "case refine_2.pure\nα : Type u\nβ : Type v\nR : α → β → Prop\nC : Computation α → Computation β → Prop\nH : ∀ {ca : Computation α} {cb : Computation β}, C ca cb → LiftRelAux R C ca.destruct cb.destruct\nca : Computation α\na : α\nha : a ∈ ca\nca' : Computation α\nIH : ∀ (cb : Computation β), C ca' cb →... | [
"case refine_2.pure\nα : Type u\nβ : Type v\nR : α → β → Prop\nC : Computation α → Computation β → Prop\nH : ∀ {ca : Computation α} {cb : Computation β}, C ca cb → LiftRelAux R C ca.destruct cb.destruct\nca : Computation α\na : α\nha : a ∈ ca\nca' : Computation α\nIH : ∀ (cb : Computation β), C ca' cb → LiftRel R c... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Seq.Basic | {
"line": 472,
"column": 18
} | {
"line": 472,
"column": 29
} | {
"line": 472,
"column": 30
} | [
{
"pp": "case bisim.cons\nα : Type u\nS✝ T✝ S T : Seq (Seq1 α)\nx✝ : α\ns : Seq α\n⊢ BisimO (fun s1 s2 ↦ ∃ s S T, s1 = s.append (S.append T).join ∧ s2 = s.append (S.join.append T.join))\n ((cons x✝ s).append (S.append T).join).destruct ((cons x✝ s).append (S.join.append T.join)).destruct",
"ppTerm": "?bi... | [
"case bisim.cons\nα : Type u\nS✝ T✝ S T : Seq (Seq1 α)\nx✝ : α\ns : Seq α\n⊢ ∃ s_1 S_1 T_1,\n s.append (S.append T).join = s_1.append (S_1.append T_1).join ∧\n s.append (S.join.append T.join) = s_1.append (S_1.join.append T_1.join)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Seq.Computation | {
"line": 1082,
"column": 18
} | {
"line": 1082,
"column": 33
} | {
"line": 1082,
"column": 34
} | [
{
"pp": "case refine_2.think\nα : Type u\nβ : Type v\nR : α → β → Prop\nC : Computation α → Computation β → Prop\nH : ∀ {ca : Computation α} {cb : Computation β}, C ca cb → LiftRelAux R C ca.destruct cb.destruct\nca : Computation α\na : α\nha : a ∈ ca\nca' : Computation α\nIH : ∀ (cb : Computation β), C ca' cb ... | [
"case refine_2.think\nα : Type u\nβ : Type v\nR : α → β → Prop\nC : Computation α → Computation β → Prop\nH : ∀ {ca : Computation α} {cb : Computation β}, C ca cb → LiftRelAux R C ca.destruct cb.destruct\nca : Computation α\na : α\nha : a ∈ ca\nca' : Computation α\nIH : ∀ (cb : Computation β), C ca' cb → LiftRel R ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.ContinuedFractions.Computation.Translations | {
"line": 118,
"column": 2
} | {
"line": 118,
"column": 60
} | {
"line": 118,
"column": 61
} | [
{
"pp": "K : Type u_1\ninst✝² : DivisionRing K\ninst✝¹ : LinearOrder K\ninst✝ : FloorRing K\nv : K\nn : ℕ\nifp_n : IntFractPair K\nseq_nth_eq : IntFractPair.stream v n = some ifp_n\nleft✝ : ifp_n.fr ≠ 0\nstream_succ_nth_eq : IntFractPair.stream v (n + 1) = some (IntFractPair.of ifp_n.fr⁻¹)\nsucc_nth_fr_eq_zero ... | [
"K : Type u_1\ninst✝² : DivisionRing K\ninst✝¹ : LinearOrder K\ninst✝ : FloorRing K\nv : K\nn : ℕ\nifp_n : IntFractPair K\nseq_nth_eq : IntFractPair.stream v n = some ifp_n\nleft✝ : ifp_n.fr ≠ 0\nstream_succ_nth_eq : IntFractPair.stream v (n + 1) = some (IntFractPair.of ifp_n.fr⁻¹)\nsucc_nth_fr_eq_zero : (IntFractP... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.ContinuedFractions.Computation.Translations | {
"line": 222,
"column": 4
} | {
"line": 222,
"column": 15
} | {
"line": 222,
"column": 16
} | [
{
"pp": "K : Type u_1\ninst✝² : DivisionRing K\ninst✝¹ : LinearOrder K\ninst✝ : FloorRing K\nv : K\nn : ℕ\ngp_n : Pair K\ns_nth_eq :\n (match (IntFractPair.of v, Stream'.Seq.tail ⟨IntFractPair.stream v, ⋯⟩) with\n | (h, s) => { h := ↑h.b, s := Stream'.Seq.map (fun p ↦ { a := 1, b := ↑p.b }) s }).s.get... | [
"K : Type u_1\ninst✝² : DivisionRing K\ninst✝¹ : LinearOrder K\ninst✝ : FloorRing K\nv : K\nn : ℕ\ngp_n : Pair K\ns_nth_eq :\n (match (IntFractPair.of v, Stream'.Seq.tail ⟨IntFractPair.stream v, ⋯⟩) with\n | (h, s) => { h := ↑h.b, s := Stream'.Seq.map (fun p ↦ { a := 1, b := ↑p.b }) s }).s.get?\n n =... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.DvdSequence | {
"line": 84,
"column": 2
} | {
"line": 84,
"column": 52
} | {
"line": 84,
"column": 53
} | [
{
"pp": "f : ℕ → ℕ\nhf : IsStrongDvdSequence f\na b : ℕ\nhab : a ∣ b\n⊢ f a ∣ f b",
"ppTerm": "?m.10",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"f : ℕ → ℕ\nhf : IsStrongDvdSequence f\na b : ℕ\nhab : a ∣ b\n⊢ f a ∣ f b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Seq.Basic | {
"line": 821,
"column": 2
} | {
"line": 821,
"column": 20
} | {
"line": 821,
"column": 21
} | [
{
"pp": "α : Type u\nR : α → α → Prop\nhd : α\ntl : Seq α\nh : ∀ (i j : ℕ), i < j → ∀ x ∈ (Seq.cons hd tl).get? i, ∀ y ∈ (Seq.cons hd tl).get? j, R x y\nx : α\nn : ℕ\nhx : some x = tl.get? n\n⊢ R hd x",
"ppTerm": "?m.49",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": ... | [
"α : Type u\nR : α → α → Prop\nhd : α\ntl : Seq α\nh : ∀ (i j : ℕ), i < j → ∀ x ∈ (Seq.cons hd tl).get? i, ∀ y ∈ (Seq.cons hd tl).get? j, R x y\nx : α\nn : ℕ\nhx : some x = tl.get? n\n⊢ R hd x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Seq.Basic | {
"line": 831,
"column": 2
} | {
"line": 831,
"column": 13
} | {
"line": 831,
"column": 14
} | [
{
"pp": "α : Type u\nR : α → α → Prop\nhd tl_hd : α\ntl_tl : Seq α\nh : ∀ (i j : ℕ), i < j → ∀ x ∈ (cons hd (cons tl_hd tl_tl)).get? i, ∀ y ∈ (cons hd (cons tl_hd tl_tl)).get? j, R x y\n⊢ R hd tl_hd",
"ppTerm": "?m.5",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"α : Type u\nR : α → α → Prop\nhd tl_hd : α\ntl_tl : Seq α\nh : ∀ (i j : ℕ), i < j → ∀ x ∈ (cons hd (cons tl_hd tl_tl)).get? i, ∀ y ∈ (cons hd (cons tl_hd tl_tl)).get? j, R x y\n⊢ R hd tl_hd"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.ContinuedFractions.Computation.CorrectnessTerminating | {
"line": 110,
"column": 6
} | {
"line": 110,
"column": 63
} | {
"line": 110,
"column": 64
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\ninst✝¹ : LinearOrder K\nv : K\nn : ℕ\ninst✝ : FloorRing K\ng : GenContFract K := of v\nifp_zero : IntFractPair K\nstream_zero_eq : IntFractPair.stream v 0 = some ifp_zero\n⊢ IntFractPair.of v = ifp_zero",
"ppTerm": "?m.56",
"assigned": false,
"usedConstants":... | [
"K : Type u_1\ninst✝² : Field K\ninst✝¹ : LinearOrder K\nv : K\nn : ℕ\ninst✝ : FloorRing K\ng : GenContFract K := of v\nifp_zero : IntFractPair K\nstream_zero_eq : IntFractPair.stream v 0 = some ifp_zero\n⊢ IntFractPair.of v = ifp_zero"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Seq.Basic | {
"line": 1021,
"column": 8
} | {
"line": 1021,
"column": 25
} | {
"line": 1021,
"column": 26
} | [
{
"pp": "case bisim.nil.cons\nα : Type u\nβ : Type v\nf : α → β\nS✝ S : Seq (Seq1 α)\na : α\ns : Seq α\n⊢ BisimO (fun s1 s2 ↦ ∃ s S, s1 = s.append (Seq.map f S.join) ∧ s2 = s.append (Seq.map (map f) S).join)\n (nil.append (Seq.map f (Seq.cons (a, s) S).join)).destruct\n (nil.append (Seq.map (map f) (Seq.c... | [
"case bisim.nil.cons\nα : Type u\nβ : Type v\nf : α → β\nS✝ S : Seq (Seq1 α)\na : α\ns : Seq α\n⊢ ∃ s_1 S_1,\n (Seq.map f s).append (Seq.map f S.join) = s_1.append (Seq.map f S_1.join) ∧\n (Seq.map f s).append (Seq.map (map f) S).join = s_1.append (Seq.map (map f) S_1).join"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Seq.Basic | {
"line": 1022,
"column": 18
} | {
"line": 1022,
"column": 29
} | {
"line": 1022,
"column": 30
} | [
{
"pp": "case bisim.cons\nα : Type u\nβ : Type v\nf : α → β\nS✝ S : Seq (Seq1 α)\nx✝ : β\ns : Seq β\n⊢ BisimO (fun s1 s2 ↦ ∃ s S, s1 = s.append (Seq.map f S.join) ∧ s2 = s.append (Seq.map (map f) S).join)\n ((Seq.cons x✝ s).append (Seq.map f S.join)).destruct ((Seq.cons x✝ s).append (Seq.map (map f) S).join)... | [
"case bisim.cons\nα : Type u\nβ : Type v\nf : α → β\nS✝ S : Seq (Seq1 α)\nx✝ : β\ns : Seq β\n⊢ ∃ s_1 S_1,\n s.append (Seq.map f S.join) = s_1.append (Seq.map f S_1.join) ∧\n s.append (Seq.map (map f) S).join = s_1.append (Seq.map (map f) S_1).join"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Seq.Basic | {
"line": 1023,
"column": 4
} | {
"line": 1023,
"column": 15
} | {
"line": 1023,
"column": 16
} | [
{
"pp": "case r\nα : Type u\nβ : Type v\nf : α → β\nS : Seq (Seq1 α)\n⊢ ∃ s S_1,\n Seq.map f S.join = s.append (Seq.map f S_1.join) ∧ (Seq.map (map f) S).join = s.append (Seq.map (map f) S_1).join",
"ppTerm": "?r",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"case r\nα : Type u\nβ : Type v\nf : α → β\nS : Seq (Seq1 α)\n⊢ ∃ s S_1,\n Seq.map f S.join = s.append (Seq.map f S_1.join) ∧ (Seq.map (map f) S).join = s.append (Seq.map (map f) S_1).join"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Seq.Basic | {
"line": 1044,
"column": 17
} | {
"line": 1044,
"column": 28
} | {
"line": 1044,
"column": 29
} | [
{
"pp": "case bisim.nil.cons.nil\nα : Type u\nSS✝ SS : Seq (Seq1 (Seq1 α))\nS : Seq (Seq1 α)\nx : α\n⊢ BisimO (fun s1 s2 ↦ ∃ s SS, s1 = s.append SS.join.join ∧ s2 = s.append (Seq.map join SS).join)\n (nil.append (Seq.cons ((x, nil), S) SS).join.join).destruct\n (nil.append (Seq.map join (Seq.cons ((x, nil... | [
"case bisim.nil.cons.nil\nα : Type u\nSS✝ SS : Seq (Seq1 (Seq1 α))\nS : Seq (Seq1 α)\nx : α\n⊢ ∃ s SS_1,\n S.join.append SS.join.join = s.append SS_1.join.join ∧\n S.join.append (Seq.map join SS).join = s.append (Seq.map join SS_1).join"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Seq.Basic | {
"line": 1045,
"column": 22
} | {
"line": 1045,
"column": 33
} | {
"line": 1045,
"column": 34
} | [
{
"pp": "case bisim.nil.cons.cons\nα : Type u\nSS✝ SS : Seq (Seq1 (Seq1 α))\nS : Seq (Seq1 α)\nx✝ x : α\ns : Seq α\n⊢ BisimO (fun s1 s2 ↦ ∃ s SS, s1 = s.append SS.join.join ∧ s2 = s.append (Seq.map join SS).join)\n (nil.append (Seq.cons ((x✝, Seq.cons x s), S) SS).join.join).destruct\n (nil.append (Seq.ma... | [
"case bisim.nil.cons.cons\nα : Type u\nSS✝ SS : Seq (Seq1 (Seq1 α))\nS : Seq (Seq1 α)\nx✝ x : α\ns : Seq α\n⊢ ∃ s_1 SS_1,\n Seq.cons x (s.append (S.join.append SS.join.join)) = s_1.append SS_1.join.join ∧\n Seq.cons x (s.append (S.join.append (Seq.map join SS).join)) = s_1.append (Seq.map join SS_1).join"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Seq.Basic | {
"line": 1046,
"column": 18
} | {
"line": 1046,
"column": 29
} | {
"line": 1046,
"column": 30
} | [
{
"pp": "case bisim.cons\nα : Type u\nSS✝ SS : Seq (Seq1 (Seq1 α))\nx✝ : α\ns : Seq α\n⊢ BisimO (fun s1 s2 ↦ ∃ s SS, s1 = s.append SS.join.join ∧ s2 = s.append (Seq.map join SS).join)\n ((Seq.cons x✝ s).append SS.join.join).destruct ((Seq.cons x✝ s).append (Seq.map join SS).join).destruct",
"ppTerm": "?b... | [
"case bisim.cons\nα : Type u\nSS✝ SS : Seq (Seq1 (Seq1 α))\nx✝ : α\ns : Seq α\n⊢ ∃ s_1 SS_1,\n s.append SS.join.join = s_1.append SS_1.join.join ∧\n s.append (Seq.map join SS).join = s_1.append (Seq.map join SS_1).join"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Seq.Basic | {
"line": 1047,
"column": 4
} | {
"line": 1047,
"column": 15
} | {
"line": 1047,
"column": 16
} | [
{
"pp": "case r\nα : Type u\nSS : Seq (Seq1 (Seq1 α))\n⊢ ∃ s SS_1, SS.join.join = s.append SS_1.join.join ∧ (Seq.map join SS).join = s.append (Seq.map join SS_1).join",
"ppTerm": "?r",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case r\nα : Type u\nSS : Seq (Seq1 (Seq1 α))\n⊢ ∃ s SS_1, SS.join.join = s.append SS_1.join.join ∧ (Seq.map join SS).join = s.append (Seq.map join SS_1).join"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.ContinuedFractions.Computation.CorrectnessTerminating | {
"line": 146,
"column": 8
} | {
"line": 146,
"column": 82
} | {
"line": 146,
"column": 83
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\ninst✝¹ : LinearOrder K\nv : K\nn✝ : ℕ\ninst✝ : FloorRing K\ng : GenContFract K := of v\nn : ℕ\nifp_succ_n : IntFractPair K\nsucc_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n\nifp_n : IntFractPair K\nnth_stream_eq : IntFractPair.stream v n = some ifp_n\... | [
"K : Type u_1\ninst✝² : Field K\ninst✝¹ : LinearOrder K\nv : K\nn✝ : ℕ\ninst✝ : FloorRing K\ng : GenContFract K := of v\nn : ℕ\nifp_succ_n : IntFractPair K\nsucc_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n\nifp_n : IntFractPair K\nnth_stream_eq : IntFractPair.stream v n = some ifp_n\nnth_fract_n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Seq.Basic | {
"line": 1057,
"column": 2
} | {
"line": 1057,
"column": 39
} | {
"line": 1058,
"column": 2
} | [
{
"pp": "α : Type u\nβ : Type v\nγ : Type w\nf : α → Seq1 β\ng : β → Seq1 γ\na : α\ns : Seq α\n⊢ (join (map g (f a), Seq.map (map g ∘ f) s)).join = join ((map g (f a)).join, Seq.map join (Seq.map (map g ∘ f) s))",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"Function.comp",
"... | [
"α : Type u\nβ : Type v\nγ : Type w\nf : α → Seq1 β\ng : β → Seq1 γ\na : α\ns : Seq α\nSS : Seq (Seq1 (Seq1 γ))\n⊢ (join (map g (f a), SS)).join = join ((map g (f a)).join, Seq.map join SS)"
] | generalize Seq.map (map g ∘ f) s = SS | Lean.Elab.Tactic.evalGeneralize | Lean.Parser.Tactic.generalize |
Mathlib.Data.Nat.Fib.Basic | {
"line": 211,
"column": 57
} | {
"line": 211,
"column": 65
} | {
"line": 211,
"column": 66
} | [
{
"pp": "n : ℕ\n⊢ n.fastFib = fib n",
"ppTerm": "?m.2",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"id",
"Prod.fst",
"Nat.fastFibAux",
"Nat.fib",
"Nat.fastFib.eq_1",
"Nat",
"Nat.fastFib",
"Eq"
],
"usedFVars": [
... | [
"n : ℕ\n⊢ n.fastFibAux.1 = fib n"
] | fastFib, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.ContinuedFractions.Computation.TerminatesIffRat | {
"line": 72,
"column": 66
} | {
"line": 72,
"column": 82
} | {
"line": 73,
"column": 8
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\ninst✝¹ : LinearOrder K\ninst✝ : FloorRing K\nv : K\ng : GenContFract K := of v\nIH : ∀ m < 0, ∃ conts, (of v).contsAux m = Pair.map Rat.cast conts\nthis : ∃ gp, { a := 1, b := 0 } = Pair.map Rat.cast gp\n⊢ ∃ conts, (of v).contsAux 0 = Pair.map Rat.cast conts",
"ppTer... | [] | simpa [contsAux] | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Algebra.ContinuedFractions.Computation.TerminatesIffRat | {
"line": 72,
"column": 66
} | {
"line": 72,
"column": 82
} | {
"line": 73,
"column": 8
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\ninst✝¹ : LinearOrder K\ninst✝ : FloorRing K\nv : K\ng : GenContFract K := of v\nIH : ∀ m < 0, ∃ conts, (of v).contsAux m = Pair.map Rat.cast conts\nthis : ∃ gp, { a := 1, b := 0 } = Pair.map Rat.cast gp\n⊢ ∃ conts, (of v).contsAux 0 = Pair.map Rat.cast conts",
"ppTer... | [] | simpa [contsAux] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.ContinuedFractions.Computation.TerminatesIffRat | {
"line": 72,
"column": 66
} | {
"line": 72,
"column": 82
} | {
"line": 73,
"column": 8
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\ninst✝¹ : LinearOrder K\ninst✝ : FloorRing K\nv : K\ng : GenContFract K := of v\nIH : ∀ m < 0, ∃ conts, (of v).contsAux m = Pair.map Rat.cast conts\nthis : ∃ gp, { a := 1, b := 0 } = Pair.map Rat.cast gp\n⊢ ∃ conts, (of v).contsAux 0 = Pair.map Rat.cast conts",
"ppTer... | [] | simpa [contsAux] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.ContinuedFractions.Computation.TerminatesIffRat | {
"line": 76,
"column": 68
} | {
"line": 76,
"column": 84
} | {
"line": 77,
"column": 8
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\ninst✝¹ : LinearOrder K\ninst✝ : FloorRing K\nv : K\ng : GenContFract K := of v\nIH : ∀ m < 0 + 1, ∃ conts, (of v).contsAux m = Pair.map Rat.cast conts\nthis : ∃ conts, { a := g.h, b := 1 } = Pair.map Rat.cast conts\n⊢ ∃ conts, (of v).contsAux (0 + 1) = Pair.map Rat.cast ... | [] | simpa [contsAux] | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Algebra.ContinuedFractions.Computation.TerminatesIffRat | {
"line": 76,
"column": 68
} | {
"line": 76,
"column": 84
} | {
"line": 77,
"column": 8
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\ninst✝¹ : LinearOrder K\ninst✝ : FloorRing K\nv : K\ng : GenContFract K := of v\nIH : ∀ m < 0 + 1, ∃ conts, (of v).contsAux m = Pair.map Rat.cast conts\nthis : ∃ conts, { a := g.h, b := 1 } = Pair.map Rat.cast conts\n⊢ ∃ conts, (of v).contsAux (0 + 1) = Pair.map Rat.cast ... | [] | simpa [contsAux] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.ContinuedFractions.Computation.TerminatesIffRat | {
"line": 76,
"column": 68
} | {
"line": 76,
"column": 84
} | {
"line": 77,
"column": 8
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\ninst✝¹ : LinearOrder K\ninst✝ : FloorRing K\nv : K\ng : GenContFract K := of v\nIH : ∀ m < 0 + 1, ∃ conts, (of v).contsAux m = Pair.map Rat.cast conts\nthis : ∃ conts, { a := g.h, b := 1 } = Pair.map Rat.cast conts\n⊢ ∃ conts, (of v).contsAux (0 + 1) = Pair.map Rat.cast ... | [] | simpa [contsAux] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.ContinuedFractions.ConvergentsEquiv | {
"line": 126,
"column": 4
} | {
"line": 126,
"column": 34
} | {
"line": 128,
"column": 0
} | [
{
"pp": "case some\nK : Type u_1\nn : ℕ\ns : Stream'.Seq (Pair K)\ninst✝ : DivisionRing K\nm : ℕ\nm_lt_n : m < n\nval✝ : Pair K\ns_succ_nth_eq : s.get? (n + 1) = some val✝\ngp_n : Pair K\ns_nth_eq : s.get? n = some gp_n\n⊢ (squashSeq s n).get? m = s.get? m",
"ppTerm": "?some",
"assigned": true,
"use... | [] | simp [*, squashSeq, m_lt_n.ne] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.ContinuedFractions.Computation.ApproximationCorollaries | {
"line": 120,
"column": 2
} | {
"line": 120,
"column": 68
} | {
"line": 120,
"column": 69
} | [
{
"pp": "K : Type u_1\nv : K\ninst✝⁶ : Field K\ninst✝⁵ : LinearOrder K\ninst✝⁴ : IsStrictOrderedRing K\ninst✝³ : FloorRing K\ninst✝² : Archimedean K\ninst✝¹ : TopologicalSpace K\ninst✝ : OrderTopology K\n⊢ Filter.Tendsto (of v).convs Filter.atTop (𝓝 v)",
"ppTerm": "?m.21",
"assigned": true,
"usedCo... | [
"K : Type u_1\nv : K\ninst✝⁶ : Field K\ninst✝⁵ : LinearOrder K\ninst✝⁴ : IsStrictOrderedRing K\ninst✝³ : FloorRing K\ninst✝² : Archimedean K\ninst✝¹ : TopologicalSpace K\ninst✝ : OrderTopology K\n⊢ ∀ (ε : K), 0 < ε → ∃ a, ∀ (b : ℕ), a ≤ b → |v - (of v).convs b| < ε"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.ContinuedFractions.Computation.Approximations | {
"line": 119,
"column": 6
} | {
"line": 119,
"column": 76
} | {
"line": 119,
"column": 77
} | [
{
"pp": "K : Type u_1\nv : K\nn : ℕ\ninst✝² : Field K\ninst✝¹ : LinearOrder K\ninst✝ : FloorRing K\nifp_succ_n : IntFractPair K\nsucc_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n\nb✝ : ℤ\nifp_n_fr : K\nnth_stream_eq : IntFractPair.stream v n = some { b := b✝, fr := ifp_n_fr }\nthis✝ : ↑⌊{ b :... | [
"K : Type u_1\nv : K\nn : ℕ\ninst✝² : Field K\ninst✝¹ : LinearOrder K\ninst✝ : FloorRing K\nifp_succ_n : IntFractPair K\nsucc_nth_stream_eq : IntFractPair.stream v (n + 1) = some ifp_succ_n\nb✝ : ℤ\nifp_n_fr : K\nnth_stream_eq : IntFractPair.stream v n = some { b := b✝, fr := ifp_n_fr }\nthis✝ : ↑⌊{ b := b✝, fr := ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.ContinuedFractions.ConvergentsEquiv | {
"line": 236,
"column": 10
} | {
"line": 243,
"column": 76
} | {
"line": 243,
"column": 76
} | [
{
"pp": "case succ.succ.succ\nK : Type u_1\ng : GenContFract K\ninst✝ : DivisionRing K\nn' m'' : ℕ\nIH : ∀ m < m'' + 1 + 1, m ≤ n' + 1 → g.contsAux m = (g.squashGCF (n' + 1)).contsAux m\nm_le_n : m'' + 1 + 1 ≤ n' + 1\n⊢ g.contsAux (m'' + 1 + 1) = (g.squashGCF (n' + 1)).contsAux (m'' + 1 + 1)",
"ppTerm": "?s... | [] | · -- get some inequalities to instantiate the IH for m'' and m'' + 1
have m'_lt_n : m'' + 1 < n' + 1 := m_le_n
have succ_m''th_contsAux_eq := IH (m'' + 1) (lt_add_one (m'' + 1)) m'_lt_n.le
have : m'' < m'' + 2 := lt_add_of_pos_right m'' zero_lt_two
have m''th_contsAux_eq ... | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Algebra.DirectSum.AddChar | {
"line": 36,
"column": 2
} | {
"line": 36,
"column": 26
} | {
"line": 36,
"column": 27
} | [
{
"pp": "ι : Type u_1\nR : Type u_2\nG : ι → Type u_3\ninst✝² : DecidableEq ι\ninst✝¹ : (i : ι) → AddCommGroup (G i)\ninst✝ : CommMonoid R\nψ χ : (i : ι) → AddChar (G i) R\nh : (fun ψ i ↦ toAddMonoidHomEquiv (ψ i)) ψ = (fun ψ i ↦ toAddMonoidHomEquiv (ψ i)) χ\n⊢ ψ = χ",
"ppTerm": "?m.48",
"assigned": tru... | [
"ι : Type u_1\nR : Type u_2\nG : ι → Type u_3\ninst✝² : DecidableEq ι\ninst✝¹ : (i : ι) → AddCommGroup (G i)\ninst✝ : CommMonoid R\nψ χ : (i : ι) → AddChar (G i) R\nh : (fun ψ i ↦ toAddMonoidHomEquiv (ψ i)) ψ = (fun ψ i ↦ toAddMonoidHomEquiv (ψ i)) χ\n⊢ ∀ (x : ι), ψ x = χ x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.CubicDiscriminant | {
"line": 250,
"column": 6
} | {
"line": 250,
"column": 17
} | {
"line": 250,
"column": 18
} | [
{
"pp": "case inr.a\nR : Type u_1\nS : Type u_2\nF : Type u_3\nK : Type u_4\nP Q : Cubic R\na b c d a' b' c' d' : R\ninst✝ : Semiring R\nf : { p // p.degree ≤ 3 }\nn : ℕ\nhn : 3 < n\n⊢ 3 < ↑n",
"ppTerm": "?inr.a",
"assigned": true,
"usedConstants": [
"WithBot.addMonoidWithOne",
"WithBot.... | [
"case inr.a\nR : Type u_1\nS : Type u_2\nF : Type u_3\nK : Type u_4\nP Q : Cubic R\na b c d a' b' c' d' : R\ninst✝ : Semiring R\nf : { p // p.degree ≤ 3 }\nn : ℕ\nhn : 3 < n\n⊢ 3 < n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.CubicDiscriminant | {
"line": 260,
"column": 2
} | {
"line": 260,
"column": 36
} | {
"line": 260,
"column": 37
} | [
{
"pp": "R : Type u_1\nP : Cubic R\ninst✝ : Semiring R\nha : P.a = 0\n⊢ P.toPoly.degree ≤ 2",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"WithBot.instPreorder",
"Eq.mpr",
"Polynomial.C",
"WithBot",
"HMul.hMul",
"congrArg",
"Nat.instAtLeastTwoHAd... | [
"R : Type u_1\nP : Cubic R\ninst✝ : Semiring R\nha : P.a = 0\n⊢ (C P.b * X ^ 2 + C P.c * X + C P.d).degree ≤ 2"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.CubicDiscriminant | {
"line": 273,
"column": 2
} | {
"line": 273,
"column": 39
} | {
"line": 273,
"column": 40
} | [
{
"pp": "R : Type u_1\nP : Cubic R\ninst✝ : Semiring R\nha : P.a = 0\nhb : P.b = 0\n⊢ P.toPoly.degree ≤ 1",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"WithBot.instPreorder",
"Eq.mpr",
"Polynomial.C",
"WithBot",
"HMul.hMul",
"Nat.instOne",
"cong... | [
"R : Type u_1\nP : Cubic R\ninst✝ : Semiring R\nha : P.a = 0\nhb : P.b = 0\n⊢ (C P.c * X + C P.d).degree ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.CubicDiscriminant | {
"line": 286,
"column": 2
} | {
"line": 286,
"column": 42
} | {
"line": 286,
"column": 43
} | [
{
"pp": "R : Type u_1\nP : Cubic R\ninst✝ : Semiring R\nha : P.a = 0\nhb : P.b = 0\nhc : P.c = 0\n⊢ P.toPoly.degree ≤ 0",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"WithBot.instPreorder",
"Eq.mpr",
"Polynomial.C",
"Nat.instMulZeroClass",
"WithBot",
"... | [
"R : Type u_1\nP : Cubic R\ninst✝ : Semiring R\nha : P.a = 0\nhb : P.b = 0\nhc : P.c = 0\n⊢ (C P.d).degree ≤ 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.CubicDiscriminant | {
"line": 319,
"column": 2
} | {
"line": 319,
"column": 36
} | {
"line": 319,
"column": 37
} | [
{
"pp": "R : Type u_1\nP : Cubic R\ninst✝ : Semiring R\nha : P.a = 0\n⊢ P.toPoly.natDegree ≤ 2",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Polynomial.C",
"HMul.hMul",
"congrArg",
"Cubic.of_a_eq_zero",
"RingHom",
"id",
"Cubic.c"... | [
"R : Type u_1\nP : Cubic R\ninst✝ : Semiring R\nha : P.a = 0\n⊢ (C P.b * X ^ 2 + C P.c * X + C P.d).natDegree ≤ 2"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.CubicDiscriminant | {
"line": 332,
"column": 2
} | {
"line": 332,
"column": 39
} | {
"line": 332,
"column": 40
} | [
{
"pp": "R : Type u_1\nP : Cubic R\ninst✝ : Semiring R\nha : P.a = 0\nhb : P.b = 0\n⊢ P.toPoly.natDegree ≤ 1",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Polynomial.C",
"HMul.hMul",
"congrArg",
"Cubic.of_b_eq_zero",
"RingHom",
"id",
... | [
"R : Type u_1\nP : Cubic R\ninst✝ : Semiring R\nha : P.a = 0\nhb : P.b = 0\n⊢ (C P.c * X + C P.d).natDegree ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.ContinuedFractions.Computation.Approximations | {
"line": 313,
"column": 8
} | {
"line": 313,
"column": 19
} | {
"line": 313,
"column": 20
} | [
{
"pp": "K : Type u_1\nv : K\nn : ℕ\ninst✝³ : Field K\ninst✝² : LinearOrder K\ninst✝¹ : IsStrictOrderedRing K\ninst✝ : FloorRing K\ng : GenContFract K := of v\nnot_terminated : ¬g.partDens.TerminatedAt n\nb : K\nnth_partDen_eq : g.partDens.get? n = some b\nthis : 1 ≤ b\n⊢ g.dens n ≤ b * g.dens n",
"ppTerm":... | [
"K : Type u_1\nv : K\nn : ℕ\ninst✝³ : Field K\ninst✝² : LinearOrder K\ninst✝¹ : IsStrictOrderedRing K\ninst✝ : FloorRing K\ng : GenContFract K := of v\nnot_terminated : ¬g.partDens.TerminatedAt n\nb : K\nnth_partDen_eq : g.partDens.get? n = some b\nthis : 1 ≤ b\n⊢ g.dens n ≤ b * g.dens n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.CubicDiscriminant | {
"line": 427,
"column": 2
} | {
"line": 430,
"column": 68
} | {
"line": 431,
"column": 2
} | [
{
"pp": "F : Type u_3\nK : Type u_4\nP : Cubic F\ninst✝¹ : Field F\ninst✝ : Field K\nφ : F →+* K\nx y z : K\nha : P.a ≠ 0\nh3 : (map φ P).roots = {x, y, z}\n⊢ (map φ P).toPoly = C (φ P.a) * (X - C x) * (X - C y) * (X - C z)",
"ppTerm": "?m.83",
"assigned": true,
"usedConstants": [
"Iff.mpr",
... | [
"F : Type u_3\nK : Type u_4\nP : Cubic F\ninst✝¹ : Field F\ninst✝ : Field K\nφ : F →+* K\nx y z : K\nha : P.a ≠ 0\nh3 : (map φ P).roots = {x, y, z}\n⊢ C (φ P.a) * (Multiset.map (fun x ↦ X - C x) {x, y, z}).prod = C (φ P.a) * (X - C x) * (X - C y) * (X - C z)"
] | rw [map_toPoly,
Splits.eq_prod_roots <|
(splits_iff_roots_eq_three ha).mpr <| Exists.intro x <| Exists.intro y <| Exists.intro z h3,
leadingCoeff_map, leadingCoeff_of_a_ne_zero ha, ← map_roots, h3] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.CubicDiscriminant | {
"line": 468,
"column": 54
} | {
"line": 468,
"column": 76
} | {
"line": 468,
"column": 76
} | [
{
"pp": "F : Type u_3\nK : Type u_4\nP : Cubic F\ninst✝¹ : Field F\ninst✝ : Field K\nφ : F →+* K\nx y z : K\nha : P.a ≠ 0\nh3 : (map φ P).roots = {x, y, z}\n⊢ (φ P.a * -(x + y + z)) ^ 2 * (φ P.a * (x * y + x * z + y * z)) ^ 2 -\n 4 * φ P.a * (φ P.a * (x * y + x * z + y * z)) ^ 3 -\n 4 * (φ P... | [
"F : Type u_3\nK : Type u_4\nP : Cubic F\ninst✝¹ : Field F\ninst✝ : Field K\nφ : F →+* K\nx y z : K\nha : P.a ≠ 0\nh3 : (map φ P).roots = {x, y, z}\n⊢ (φ P.a * -(x + y + z)) ^ 2 * (φ P.a * (x * y + x * z + y * z)) ^ 2 -\n 4 * φ P.a * (φ P.a * (x * y + x * z + y * z)) ^ 3 -\n 4 * (φ P.a * -(x + y... | d_eq_three_roots ha h3 | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.TensorProduct.Free | {
"line": 83,
"column": 2
} | {
"line": 83,
"column": 13
} | {
"line": 83,
"column": 14
} | [
{
"pp": "R : Type u_1\nA : Type u_2\nM : Type uM\nι : Type uι\ninst✝⁴ : CommSemiring R\ninst✝³ : Semiring A\ninst✝² : Algebra R A\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nb : Basis ι R M\na : A\ni : ι\n⊢ a • (basis A b) i = a ⊗ₜ[R] b i",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
... | [
"R : Type u_1\nA : Type u_2\nM : Type uM\nι : Type uι\ninst✝⁴ : CommSemiring R\ninst✝³ : Semiring A\ninst✝² : Algebra R A\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nb : Basis ι R M\na : A\ni : ι\n⊢ a • 1 ⊗ₜ[R] b i = a ⊗ₜ[R] b i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Congruence.BigOperators | {
"line": 31,
"column": 4
} | {
"line": 31,
"column": 50
} | {
"line": 31,
"column": 51
} | [
{
"pp": "case nil\nι : Type u_1\nM : Type u_2\ninst✝ : MulOneClass M\nc : Con M\nf g : ι → M\nh : ∀ x ∈ [], c (f x) (g x)\n⊢ c (List.map f []).prod (List.map g []).prod",
"ppTerm": "?nil",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"List.map",
"id",
"MulOne.toMul",
... | [
"case nil\nι : Type u_1\nM : Type u_2\ninst✝ : MulOneClass M\nc : Con M\nf g : ι → M\nh : ∀ x ∈ [], c (f x) (g x)\n⊢ c 1 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Congruence.BigOperators | {
"line": 47,
"column": 12
} | {
"line": 47,
"column": 23
} | {
"line": 47,
"column": 24
} | [
{
"pp": "case mk\nι : Type u_1\nM : Type u_2\ninst✝ : CommMonoid M\nc : Con M\ns : Multiset ι\nf g : ι → M\na✝ : List ι\nh : ∀ x ∈ Quot.mk (⇑(List.isSetoid ι)) a✝, c (f x) (g x)\n⊢ c (Multiset.map f (Quot.mk (⇑(List.isSetoid ι)) a✝)).prod (Multiset.map g (Quot.mk (⇑(List.isSetoid ι)) a✝)).prod",
"ppTerm": "... | [
"case mk\nι : Type u_1\nM : Type u_2\ninst✝ : CommMonoid M\nc : Con M\ns : Multiset ι\nf g : ι → M\na✝ : List ι\nh : ∀ x ∈ Quot.mk (⇑(List.isSetoid ι)) a✝, c (f x) (g x)\n⊢ c (List.map f a✝).prod (List.map g a✝).prod"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Congruence.BigOperators | {
"line": 53,
"column": 2
} | {
"line": 53,
"column": 13
} | {
"line": 53,
"column": 14
} | [
{
"pp": "ι : Type u_1\nM : Type u_2\ninst✝ : CommMonoid M\nc : Con M\ns : Multiset ι\nf : ι → M\n⊢ ↑(Multiset.map f s).prod = (Multiset.map (fun i ↦ ↑(f i)) s).prod",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"ι : Type u_1\nM : Type u_2\ninst✝ : CommMonoid M\nc : Con M\ns : Multiset ι\nf : ι → M\n⊢ ↑(Multiset.map f s).prod = (Multiset.map (fun i ↦ ↑(f i)) s).prod"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Idempotents | {
"line": 228,
"column": 66
} | {
"line": 228,
"column": 77
} | {
"line": 228,
"column": 78
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝¹ : Ring R\ninst✝ : Ring S\nf : R →+* S\nh : ∀ x ∈ RingHom.ker f, IsNilpotent x\ne₂ : R\nhe₂ : IsIdempotentElem e₂\ne₁ : R\nhe₁ : IsIdempotentElem (f e₁)\nhe₁e₂ : f e₁ * f e₂ = 0\nh✝ : Nontrivial R\na : R := e₁ - e₁ * e₂\nha : f a = f e₁\nha' : a * e₂ = 0\nhx' : a - a ^... | [
"R : Type u_1\nS : Type u_2\ninst✝¹ : Ring R\ninst✝ : Ring S\nf : R →+* S\nh : ∀ x ∈ RingHom.ker f, IsNilpotent x\ne₂ : R\nhe₂ : IsIdempotentElem e₂\ne₁ : R\nhe₁ : IsIdempotentElem (f e₁)\nhe₁e₂ : f e₁ * f e₂ = 0\nh✝ : Nontrivial R\na : R := e₁ - e₁ * e₂\nha : f a = f e₁\nha' : a * e₂ = 0\nhx' : a - a ^ 2 ∈ RingHom... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.GeneralLinearGroup.AlgEquiv | {
"line": 37,
"column": 4
} | {
"line": 37,
"column": 15
} | {
"line": 37,
"column": 16
} | [
{
"pp": "K : Type u_1\nV : Type u_2\nW : Type u_3\ninst✝⁶ : Semifield K\ninst✝⁵ : AddCommMonoid V\ninst✝⁴ : Module K V\ninst✝³ : Projective K V\ninst✝² : AddCommMonoid W\ninst✝¹ : Module K W\ninst✝ : Projective K W\nf : End K V ≃ₐ[K] End K W\nhV : Subsingleton V\na✝ : Nontrivial W\n⊢ ∃ T, f = conjAlgEquiv K T",... | [
"K : Type u_1\nV : Type u_2\nW : Type u_3\ninst✝⁶ : Semifield K\ninst✝⁵ : AddCommMonoid V\ninst✝⁴ : Module K V\ninst✝³ : Projective K V\ninst✝² : AddCommMonoid W\ninst✝¹ : Module K W\ninst✝ : Projective K W\nf : End K V ≃ₐ[K] End K W\nhV : Subsingleton V\na✝ : Nontrivial W\n⊢ ∃ T, f = conjAlgEquiv K T"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Idempotents | {
"line": 252,
"column": 2
} | {
"line": 252,
"column": 13
} | {
"line": 252,
"column": 14
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝¹ : Ring R\ninst✝ : Ring S\nf : R →+* S\nh : ∀ x ∈ RingHom.ker f, IsNilpotent x\ne : S\nhe : e ∈ f.range\nhe' : IsIdempotentElem e\n⊢ ∃ e', IsIdempotentElem e' ∧ f e' = e",
"ppTerm": "?m.31",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"... | [
"R : Type u_1\nS : Type u_2\ninst✝¹ : Ring R\ninst✝ : Ring S\nf : R →+* S\nh : ∀ x ∈ RingHom.ker f, IsNilpotent x\ne : S\nhe : e ∈ f.range\nhe' : IsIdempotentElem e\n⊢ ∃ e', IsIdempotentElem e' ∧ f e' = e"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.Ideal | {
"line": 61,
"column": 4
} | {
"line": 61,
"column": 35
} | {
"line": 61,
"column": 36
} | [
{
"pp": "R : Type u_1\ninst✝³ : Semiring R\nn : Type u_2\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : Nonempty n\nI J : Ideal R\neq : matrix n I = matrix n J\nx : R\nthis : (∀ (x_1 x_2 : n), x ∈ I) ↔ ∀ (x_1 x_2 : n), x ∈ J\n⊢ x ∈ I ↔ x ∈ J",
"ppTerm": "?m.61",
"assigned": false,
"usedConstan... | [
"R : Type u_1\ninst✝³ : Semiring R\nn : Type u_2\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : Nonempty n\nI J : Ideal R\neq : matrix n I = matrix n J\nx : R\nthis : (∀ (x_1 x_2 : n), x ∈ I) ↔ ∀ (x_1 x_2 : n), x ∈ J\n⊢ x ∈ I ↔ x ∈ J"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.GeneralLinearGroup.AlgEquiv | {
"line": 57,
"column": 4
} | {
"line": 57,
"column": 45
} | {
"line": 57,
"column": 46
} | [
{
"pp": "K : Type u_1\nV : Type u_2\nW : Type u_3\ninst✝⁶ : Semifield K\ninst✝⁵ : AddCommMonoid V\ninst✝⁴ : Module K V\ninst✝³ : Projective K V\ninst✝² : AddCommMonoid W\ninst✝¹ : Module K W\ninst✝ : Projective K W\nf : End K V ≃ₐ[K] End K W\nhV : Nontrivial V\nu : V\nhu : u ≠ 0\nv : Dual K V\nhuv : v u ≠ 0\nz ... | [
"K : Type u_1\nV : Type u_2\nW : Type u_3\ninst✝⁶ : Semifield K\ninst✝⁵ : AddCommMonoid V\ninst✝⁴ : Module K V\ninst✝³ : Projective K V\ninst✝² : AddCommMonoid W\ninst✝¹ : Module K W\ninst✝ : Projective K W\nf : End K V ≃ₐ[K] End K W\nhV : Nontrivial V\nu : V\nhu : u ≠ 0\nv : Dual K V\nhuv : v u ≠ 0\nz : W\nhz : ¬(... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.Ideal | {
"line": 144,
"column": 21
} | {
"line": 144,
"column": 32
} | {
"line": 144,
"column": 33
} | [
{
"pp": "R : Type u_1\nn : Type u_2\ninst✝² : NonUnitalNonAssocSemiring R\ninst✝¹ : Fintype n\ninst✝ : DecidableEq n\nc : RingCon R\ni j : n\nx y : R\nh : (matrix n c) (Matrix.single i j x) (Matrix.single i j y)\n⊢ c x y",
"ppTerm": "?m.24",
"assigned": false,
"usedConstants": [],
"usedFVars": [... | [
"R : Type u_1\nn : Type u_2\ninst✝² : NonUnitalNonAssocSemiring R\ninst✝¹ : Fintype n\ninst✝ : DecidableEq n\nc : RingCon R\ni j : n\nx y : R\nh : (matrix n c) (Matrix.single i j x) (Matrix.single i j y)\n⊢ c x y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.Ideal | {
"line": 146,
"column": 4
} | {
"line": 146,
"column": 20
} | {
"line": 146,
"column": 21
} | [
{
"pp": "case inl\nR : Type u_1\nn : Type u_2\ninst✝² : NonUnitalNonAssocSemiring R\ninst✝¹ : Fintype n\ninst✝ : DecidableEq n\nc : RingCon R\ni j : n\nx y : R\nh : c x y\ni' j' : n\nhi : i ≠ i'\n⊢ c (Matrix.single i j x i' j') (Matrix.single i j y i' j')",
"ppTerm": "?inl",
"assigned": true,
"usedC... | [
"case inl\nR : Type u_1\nn : Type u_2\ninst✝² : NonUnitalNonAssocSemiring R\ninst✝¹ : Fintype n\ninst✝ : DecidableEq n\nc : RingCon R\ni j : n\nx y : R\nh : c x y\ni' j' : n\nhi : i ≠ i'\n⊢ c 0 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.Ideal | {
"line": 148,
"column": 4
} | {
"line": 148,
"column": 20
} | {
"line": 148,
"column": 21
} | [
{
"pp": "case inr.inl\nR : Type u_1\nn : Type u_2\ninst✝² : NonUnitalNonAssocSemiring R\ninst✝¹ : Fintype n\ninst✝ : DecidableEq n\nc : RingCon R\ni j : n\nx y : R\nh : c x y\nj' : n\nhj : j ≠ j'\n⊢ c (Matrix.single i j x i j') (Matrix.single i j y i j')",
"ppTerm": "?inr.inl",
"assigned": true,
"us... | [
"case inr.inl\nR : Type u_1\nn : Type u_2\ninst✝² : NonUnitalNonAssocSemiring R\ninst✝¹ : Fintype n\ninst✝ : DecidableEq n\nc : RingCon R\ni j : n\nx y : R\nh : c x y\nj' : n\nhj : j ≠ j'\n⊢ c 0 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.Ideal | {
"line": 149,
"column": 2
} | {
"line": 149,
"column": 13
} | {
"line": 149,
"column": 14
} | [
{
"pp": "case inr.inr\nR : Type u_1\nn : Type u_2\ninst✝² : NonUnitalNonAssocSemiring R\ninst✝¹ : Fintype n\ninst✝ : DecidableEq n\nc : RingCon R\ni j : n\nx y : R\nh : c x y\n⊢ c (Matrix.single i j x i j) (Matrix.single i j y i j)",
"ppTerm": "?inr.inr",
"assigned": true,
"usedConstants": [
"... | [
"case inr.inr\nR : Type u_1\nn : Type u_2\ninst✝² : NonUnitalNonAssocSemiring R\ninst✝¹ : Fintype n\ninst✝ : DecidableEq n\nc : RingCon R\ni j : n\nx y : R\nh : c x y\n⊢ c x y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.Ideal | {
"line": 157,
"column": 4
} | {
"line": 157,
"column": 15
} | {
"line": 157,
"column": 16
} | [
{
"pp": "R : Type u_1\nn : Type u_2\ninst✝² : NonUnitalNonAssocSemiring R\ninst✝¹ : Fintype n\ninst✝ : Nonempty n\nI J : RingCon R\neq : matrix n I = matrix n J\nr s : R\nthis :\n (matrix n I) (Matrix.of fun x x_1 ↦ r) (Matrix.of fun x x_1 ↦ s) =\n (matrix n J) (Matrix.of fun x x_1 ↦ r) (Matrix.of fun x x_1... | [
"R : Type u_1\nn : Type u_2\ninst✝² : NonUnitalNonAssocSemiring R\ninst✝¹ : Fintype n\ninst✝ : Nonempty n\nI J : RingCon R\neq : matrix n I = matrix n J\nr s : R\nthis :\n (matrix n I) (Matrix.of fun x x_1 ↦ r) (Matrix.of fun x x_1 ↦ s) =\n (matrix n J) (Matrix.of fun x x_1 ↦ r) (Matrix.of fun x x_1 ↦ s)\n⊢ I r... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.Ideal | {
"line": 182,
"column": 29
} | {
"line": 182,
"column": 40
} | {
"line": 182,
"column": 41
} | [
{
"pp": "R : Type u_1\nn : Type u_2\ninst✝² : NonUnitalNonAssocSemiring R\ninst✝¹ : Fintype n\ninst✝ : DecidableEq n\nc : RingCon (Matrix n n R)\nw✝ x✝ y✝ z✝ : R\nh₁ : ∀ (i j : n), c (single i j w✝) (single i j x✝)\nh₂ : ∀ (i j : n), c (single i j y✝) (single i j z✝)\ni j : n\n⊢ c (single i j (w✝ * y✝)) (single... | [
"R : Type u_1\nn : Type u_2\ninst✝² : NonUnitalNonAssocSemiring R\ninst✝¹ : Fintype n\ninst✝ : DecidableEq n\nc : RingCon (Matrix n n R)\nw✝ x✝ y✝ z✝ : R\nh₁ : ∀ (i j : n), c (single i j w✝) (single i j x✝)\nh₂ : ∀ (i j : n), c (single i j y✝) (single i j z✝)\ni j : n\n⊢ c (single i j (w✝ * y✝)) (single i j (x✝ * z... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.Ideal | {
"line": 181,
"column": 29
} | {
"line": 181,
"column": 53
} | {
"line": 181,
"column": 54
} | [
{
"pp": "R : Type u_1\nn : Type u_2\ninst✝² : NonUnitalNonAssocSemiring R\ninst✝¹ : Fintype n\ninst✝ : DecidableEq n\nc : RingCon (Matrix n n R)\nw✝ x✝² y✝ z✝ : R\nh₁ : ∀ (i j : n), c (single i j w✝) (single i j x✝²)\nh₂ : ∀ (i j : n), c (single i j y✝) (single i j z✝)\nx✝¹ x✝ : n\n⊢ c (single x✝¹ x✝ (w✝ + y✝))... | [
"R : Type u_1\nn : Type u_2\ninst✝² : NonUnitalNonAssocSemiring R\ninst✝¹ : Fintype n\ninst✝ : DecidableEq n\nc : RingCon (Matrix n n R)\nw✝ x✝² y✝ z✝ : R\nh₁ : ∀ (i j : n), c (single i j w✝) (single i j x✝²)\nh₂ : ∀ (i j : n), c (single i j y✝) (single i j z✝)\nx✝¹ x✝ : n\n⊢ c (single x✝¹ x✝ w✝ + single x✝¹ x✝ y✝)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.Ideal | {
"line": 196,
"column": 4
} | {
"line": 196,
"column": 15
} | {
"line": 196,
"column": 16
} | [
{
"pp": "case mp\nR : Type u_1\nn : Type u_2\ninst✝³ : NonUnitalNonAssocSemiring R\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : Nonempty n\nc : RingCon R\nx y : R\nh : (matrix n c).ofMatrix x y\ninhabited_h : Inhabited n\n⊢ c x y",
"ppTerm": "?mp",
"assigned": false,
"usedConstants": [],
... | [
"case mp\nR : Type u_1\nn : Type u_2\ninst✝³ : NonUnitalNonAssocSemiring R\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : Nonempty n\nc : RingCon R\nx y : R\nh : (matrix n c).ofMatrix x y\ninhabited_h : Inhabited n\n⊢ c x y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Idempotents | {
"line": 282,
"column": 14
} | {
"line": 282,
"column": 25
} | {
"line": 282,
"column": 26
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝² : Ring R\ninst✝¹ : Ring S\nf : R →+* S\nI : Type u_3\ninst✝ : Finite I\nh : ∀ x ∈ RingHom.ker f, IsNilpotent x\ne : I → S\nhe : OrthogonalIdempotents e\nhe' : ∀ (i : I), e i ∈ f.range\nval✝ : Fintype I\ne' : Fin (Fintype.card I) → R\nh₁ : OrthogonalIdempotents e'\nh₂ ... | [
"R : Type u_1\nS : Type u_2\ninst✝² : Ring R\ninst✝¹ : Ring S\nf : R →+* S\nI : Type u_3\ninst✝ : Finite I\nh : ∀ x ∈ RingHom.ker f, IsNilpotent x\ne : I → S\nhe : OrthogonalIdempotents e\nhe' : ∀ (i : I), e i ∈ f.range\nval✝ : Fintype I\ne' : Fin (Fintype.card I) → R\nh₁ : OrthogonalIdempotents e'\nh₂ : ⇑f ∘ e' = ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.Ideal | {
"line": 219,
"column": 4
} | {
"line": 219,
"column": 15
} | {
"line": 219,
"column": 16
} | [
{
"pp": "case mpr\nR : Type u_1\nn : Type u_2\ninst✝² : NonAssocSemiring R\ninst✝¹ : Fintype n\ninst✝ : DecidableEq n\nc : RingCon (Matrix n n R)\nx y : Matrix n n R\nh : c x y\ni' j' i j : n\n⊢ c (single i j (x i' j')) (single i j (y i' j'))",
"ppTerm": "?mpr",
"assigned": false,
"usedConstants": [... | [
"case mpr\nR : Type u_1\nn : Type u_2\ninst✝² : NonAssocSemiring R\ninst✝¹ : Fintype n\ninst✝ : DecidableEq n\nc : RingCon (Matrix n n R)\nx y : Matrix n n R\nh : c x y\ni' j' i j : n\n⊢ c (single i j (x i' j')) (single i j (y i' j'))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.Ideal | {
"line": 225,
"column": 2
} | {
"line": 225,
"column": 13
} | {
"line": 225,
"column": 14
} | [
{
"pp": "R : Type u_1\nn : Type u_2\ninst✝² : NonAssocSemiring R\ninst✝¹ : Fintype n\ninst✝ : DecidableEq n\nc : RingCon (Matrix n n R)\nx y : R\ni j : n\nh : c (single i j x) (single i j y)\ni' j' : n\n⊢ c (single i' j' x) (single i' j' y)",
"ppTerm": "?m.29",
"assigned": false,
"usedConstants": []... | [
"R : Type u_1\nn : Type u_2\ninst✝² : NonAssocSemiring R\ninst✝¹ : Fintype n\ninst✝ : DecidableEq n\nc : RingCon (Matrix n n R)\nx y : R\ni j : n\nh : c (single i j x) (single i j y)\ni' j' : n\n⊢ c (single i' j' x) (single i' j' y)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.Ideal | {
"line": 235,
"column": 4
} | {
"line": 235,
"column": 15
} | {
"line": 235,
"column": 16
} | [
{
"pp": "case mpr\nR : Type u_1\nn : Type u_2\ninst✝² : NonAssocSemiring R\ninst✝¹ : Fintype n\ninst✝ : DecidableEq n\nc : RingCon (Matrix n n R)\ni j : n\nX Y : Matrix n n R\nh : c X Y\ni' j' : n\n⊢ c (single i' j' ((fun x ↦ x i j) X)) (single i' j' ((fun x ↦ x i j) Y))",
"ppTerm": "?mpr",
"assigned": ... | [
"case mpr\nR : Type u_1\nn : Type u_2\ninst✝² : NonAssocSemiring R\ninst✝¹ : Fintype n\ninst✝ : DecidableEq n\nc : RingCon (Matrix n n R)\ni j : n\nX Y : Matrix n n R\nh : c X Y\ni' j' : n\n⊢ c (single i' j' (X i j)) (single i' j' (Y i j))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Idempotents | {
"line": 315,
"column": 4
} | {
"line": 315,
"column": 15
} | {
"line": 315,
"column": 16
} | [
{
"pp": "case inr.inr.zero\nR : Type u_1\nS : Type u_2\ninst✝¹ : Ring R\ninst✝ : Ring S\nf : R →+* S\nh : ∀ x ∈ RingHom.ker f, IsNilpotent x\nh✝¹ : Nontrivial R\nh✝ : Nontrivial S\ne : Fin 0 → S\nhe : CompleteOrthogonalIdempotents e\nhe' : ∀ (i : Fin 0), e i ∈ f.range\n⊢ ∃ e', CompleteOrthogonalIdempotents e' ∧... | [
"case inr.inr.zero\nR : Type u_1\nS : Type u_2\ninst✝¹ : Ring R\ninst✝ : Ring S\nf : R →+* S\nh : ∀ x ∈ RingHom.ker f, IsNilpotent x\nh✝¹ : Nontrivial R\nh✝ : Nontrivial S\ne : Fin 0 → S\nhe : CompleteOrthogonalIdempotents e\nhe' : ∀ (i : Fin 0), e i ∈ f.range\n⊢ CompleteOrthogonalIdempotents ![] ∧ ⇑f ∘ ![] = e"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.Ideal | {
"line": 316,
"column": 6
} | {
"line": 316,
"column": 17
} | {
"line": 316,
"column": 18
} | [
{
"pp": "case mp\nR : Type u_1\nn : Type u_2\ninst✝³ : NonAssocRing R\ninst✝² : Fintype n\ninst✝¹ : Nonempty n\ninst✝ : DecidableEq n\nI J : TwoSidedIdeal R\nx : R\nle : (of fun x_1 x_2 ↦ x) ∈ matrix n J\nxI : x ∈ I\n⊢ x ∈ J",
"ppTerm": "?mp",
"assigned": false,
"usedConstants": [],
"usedFVars":... | [
"case mp\nR : Type u_1\nn : Type u_2\ninst✝³ : NonAssocRing R\ninst✝² : Fintype n\ninst✝¹ : Nonempty n\ninst✝ : DecidableEq n\nI J : TwoSidedIdeal R\nx : R\nle : (of fun x_1 x_2 ↦ x) ∈ matrix n J\nxI : x ∈ I\n⊢ x ∈ J"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.Ideal | {
"line": 314,
"column": 6
} | {
"line": 316,
"column": 20
} | {
"line": 317,
"column": 4
} | [
{
"pp": "case mp\nR : Type u_1\nn : Type u_2\ninst✝³ : NonAssocRing R\ninst✝² : Fintype n\ninst✝¹ : Nonempty n\ninst✝ : DecidableEq n\nI J : TwoSidedIdeal R\n⊢ matrix n I ≤ matrix n J → I ≤ J",
"ppTerm": "?mp",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"TwoSidedIdeal",
... | [] | intro le x xI
specialize @le (of fun _ _ => x) (by simp [xI])
simpa using le | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Matrix.Ideal | {
"line": 314,
"column": 6
} | {
"line": 316,
"column": 20
} | {
"line": 317,
"column": 4
} | [
{
"pp": "case mp\nR : Type u_1\nn : Type u_2\ninst✝³ : NonAssocRing R\ninst✝² : Fintype n\ninst✝¹ : Nonempty n\ninst✝ : DecidableEq n\nI J : TwoSidedIdeal R\n⊢ matrix n I ≤ matrix n J → I ≤ J",
"ppTerm": "?mp",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"TwoSidedIdeal",
... | [] | intro le x xI
specialize @le (of fun _ _ => x) (by simp [xI])
simpa using le | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.Idempotents | {
"line": 332,
"column": 14
} | {
"line": 332,
"column": 25
} | {
"line": 332,
"column": 26
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝² : Ring R\ninst✝¹ : Ring S\nf : R →+* S\nI : Type u_3\ninst✝ : Fintype I\nh : ∀ x ∈ RingHom.ker f, IsNilpotent x\ne : I → S\nhe : CompleteOrthogonalIdempotents e\nhe' : ∀ (i : I), e i ∈ f.range\ne' : Fin (Fintype.card I) → R\nh₁ : CompleteOrthogonalIdempotents e'\nh₂ :... | [
"R : Type u_1\nS : Type u_2\ninst✝² : Ring R\ninst✝¹ : Ring S\nf : R →+* S\nI : Type u_3\ninst✝ : Fintype I\nh : ∀ x ∈ RingHom.ker f, IsNilpotent x\ne : I → S\nhe : CompleteOrthogonalIdempotents e\nhe' : ∀ (i : I), e i ∈ f.range\ne' : Fin (Fintype.card I) → R\nh₁ : CompleteOrthogonalIdempotents e'\nh₂ : ⇑f ∘ e' = e... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Idempotents | {
"line": 359,
"column": 4
} | {
"line": 359,
"column": 46
} | {
"line": 359,
"column": 47
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝² : Ring R\ninst✝¹ : Ring S\nf : R →+* S\nI : Type u_3\ne : I → R\ninst✝ : Fintype I\nh : ∀ x ∈ RingHom.ker f, IsNilpotent x\nhe : ∀ (i : I), IsIdempotentElem (e i)\nhe' : ∀ (i : I), IsMulCentral (e i)\nhe'' : CompleteOrthogonalIdempotents (⇑f ∘ e)\ne' : I → R\nh₁ : Com... | [
"R : Type u_1\nS : Type u_2\ninst✝² : Ring R\ninst✝¹ : Ring S\nf : R →+* S\nI : Type u_3\ne : I → R\ninst✝ : Fintype I\nh : ∀ x ∈ RingHom.ker f, IsNilpotent x\nhe : ∀ (i : I), IsIdempotentElem (e i)\nhe' : ∀ (i : I), IsMulCentral (e i)\nhe'' : CompleteOrthogonalIdempotents (⇑f ∘ e)\ne' : I → R\nh₁ : CompleteOrthogo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Eigenspace.Basic | {
"line": 81,
"column": 40
} | {
"line": 81,
"column": 51
} | {
"line": 81,
"column": 52
} | [
{
"pp": "R : Type v\nM : Type w\ninst✝² : CommRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nf : End R M\nμ : R\nk : ℕ∞\nx : M\nthis : Nonempty { l // ↑l ≤ k }\nm n : { i // ↑i ≤ k }\nh : m ≤ n\n⊢ ((f - μ • 1) ^ ↑m).ker ≤ ((f - μ • 1) ^ ↑n).ker",
"ppTerm": "?m.164",
"assigned": false,
"usedCon... | [
"R : Type v\nM : Type w\ninst✝² : CommRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nf : End R M\nμ : R\nk : ℕ∞\nx : M\nthis : Nonempty { l // ↑l ≤ k }\nm n : { i // ↑i ≤ k }\nh : m ≤ n\n⊢ ((f - μ • 1) ^ ↑m).ker ≤ ((f - μ • 1) ^ ↑n).ker"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Eigenspace.Basic | {
"line": 87,
"column": 70
} | {
"line": 87,
"column": 81
} | {
"line": 87,
"column": 82
} | [
{
"pp": "R : Type v\nM : Type w\ninst✝² : CommRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nf : End R M\nμ : R\nk : ℕ∞\nx y : { l // ↑l ≤ k }\nh : x ≤ y\n⊢ (fun x ↦ ↑↑x) x ≤ (fun x ↦ ↑↑x) y",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instCompleteLinearOrde... | [
"R : Type v\nM : Type w\ninst✝² : CommRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nf : End R M\nμ : R\nk : ℕ∞\nx y : { l // ↑l ≤ k }\nh : x ≤ y\n⊢ x ≤ y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Idempotents | {
"line": 451,
"column": 40
} | {
"line": 451,
"column": 51
} | {
"line": 451,
"column": 52
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nI : Type u_3\ninst✝ : Fintype I\ne : I → R\nhe : ∀ (i : I), IsIdempotentElem (e i)\nhe₁ : ∀ (i j : I), i ≠ j → (1 - e i) * (1 - e j) = 0\nhe₂ : ∏ i, e i = 0\n⊢ ∏ i, (1 - (1 - e i)) = 0",
"ppTerm": "?m.68",
"assigned": true,
"usedConstants": [
"Eq.mpr... | [
"R : Type u_1\ninst✝¹ : CommRing R\nI : Type u_3\ninst✝ : Fintype I\ne : I → R\nhe : ∀ (i : I), IsIdempotentElem (e i)\nhe₁ : ∀ (i j : I), i ≠ j → (1 - e i) * (1 - e j) = 0\nhe₂ : ∏ i, e i = 0\n⊢ ∏ x, e x = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Eigenspace.Basic | {
"line": 209,
"column": 15
} | {
"line": 209,
"column": 50
} | {
"line": 209,
"column": 51
} | [
{
"pp": "R : Type v\nM : Type w\ninst✝² : CommRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nf : End R M\nμ : R\nh : f.HasUnifEigenvalue μ 1\nn : ℕ\nm : M\nhm : f.HasUnifEigenvector μ 1 m\n⊢ m ∈ ((f ^ n).genEigenspace (μ ^ n)) 1",
"ppTerm": "?m.69",
"assigned": true,
"usedConstants": [
"... | [
"R : Type v\nM : Type w\ninst✝² : CommRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nf : End R M\nμ : R\nh : f.HasUnifEigenvalue μ 1\nn : ℕ\nm : M\nhm : f.HasUnifEigenvector μ 1 m\n⊢ (f ^ n) m = μ ^ n • m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Eigenspace.Basic | {
"line": 219,
"column": 15
} | {
"line": 219,
"column": 61
} | {
"line": 219,
"column": 62
} | [
{
"pp": "R : Type v\nM : Type w\ninst✝⁴ : CommRing R\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : IsDomain R\ninst✝ : IsTorsionFree R M\nf : End R M\nμ : R\nhf : f.HasUnifEigenvalue μ 1\nm : M\nhm : f.HasUnifEigenvector μ 1 m\nn : ℕ\nhn : f ^ n = 0\n⊢ μ ^ n = 0",
"ppTerm": "?m.61",
"assigned"... | [
"R : Type v\nM : Type w\ninst✝⁴ : CommRing R\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : IsDomain R\ninst✝ : IsTorsionFree R M\nf : End R M\nμ : R\nhf : f.HasUnifEigenvalue μ 1\nm : M\nhm : f.HasUnifEigenvector μ 1 m\nn : ℕ\nhn : f ^ n = 0\n⊢ μ = 0 ∧ ¬n = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Eigenspace.Basic | {
"line": 223,
"column": 2
} | {
"line": 223,
"column": 45
} | {
"line": 224,
"column": 2
} | [
{
"pp": "R : Type v\nM : Type w\ninst✝² : CommRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nf : End R M\nμ : R\nhμ : f.HasUnifEigenvalue μ 1\n⊢ μ ∈ spectrum R f",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Module.End.instRing",
"Iff.mpr",
"instSMulOfMul",
... | [
"R : Type v\nM : Type w\ninst✝² : CommRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nf : End R M\nμ : R\nhμ : f.HasUnifEigenvalue μ 1\nh_unit : IsUnit ((algebraMap R (End R M)) μ - f)\n⊢ False"
] | refine spectrum.mem_iff.mpr fun h_unit ↦ ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.RingTheory.Idempotents | {
"line": 499,
"column": 68
} | {
"line": 499,
"column": 79
} | {
"line": 499,
"column": 80
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝² : CommRing R\ninst✝¹ : Ring S\nI : Type u_3\ninst✝ : Fintype I\nf : R →+* S\ne₀ : R\nhe₀ : IsIdempotentElem e₀\nhfe₀ : RingHom.ker f = Ideal.span {e₀}\ne : I → S\nhe : CompleteOrthogonalIdempotents e\ne' : I → R\nhe' : ∀ (i : I), f (e' i) = e i\nk : I → R\nhk : ∀ (i :... | [
"R : Type u_1\nS : Type u_2\ninst✝² : CommRing R\ninst✝¹ : Ring S\nI : Type u_3\ninst✝ : Fintype I\nf : R →+* S\ne₀ : R\nhe₀ : IsIdempotentElem e₀\nhfe₀ : RingHom.ker f = Ideal.span {e₀}\ne : I → S\nhe : CompleteOrthogonalIdempotents e\ne' : I → R\nhe' : ∀ (i : I), f (e' i) = e i\nk : I → R\nhk : ∀ (i : I), e' i * ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Idempotents | {
"line": 503,
"column": 46
} | {
"line": 503,
"column": 76
} | {
"line": 503,
"column": 77
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝² : CommRing R\ninst✝¹ : Ring S\nI : Type u_3\ninst✝ : Fintype I\nf : R →+* S\ne₀ : R\nhe₀ : IsIdempotentElem e₀\nhfe₀ : RingHom.ker f = Ideal.span {e₀}\ne : I → S\nhe : CompleteOrthogonalIdempotents e\ne' : I → R\nhe' : ∀ (i : I), f (e' i) = e i\nk : I → R\nhk : ∀ (i :... | [
"R : Type u_1\nS : Type u_2\ninst✝² : CommRing R\ninst✝¹ : Ring S\nI : Type u_3\ninst✝ : Fintype I\nf : R →+* S\ne₀ : R\nhe₀ : IsIdempotentElem e₀\nhfe₀ : RingHom.ker f = Ideal.span {e₀}\ne : I → S\nhe : CompleteOrthogonalIdempotents e\ne' : I → R\nhe' : ∀ (i : I), f (e' i) = e i\nk : I → R\nhk : ∀ (i : I), e' i * ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Eigenspace.Basic | {
"line": 302,
"column": 40
} | {
"line": 302,
"column": 51
} | {
"line": 302,
"column": 52
} | [
{
"pp": "R : Type v\nM : Type w\ninst✝³ : CommRing R\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\ninst✝ : IsNoetherian R M\nf : End R M\nμ : R\nk : ℕ\nhk : f.maxUnifEigenspaceIndex μ ≤ k\n⊢ ↑(f.maxUnifEigenspaceIndex μ) ≤ ↑k",
"ppTerm": "?m.60",
"assigned": true,
"usedConstants": [
"Eq.mpr",... | [
"R : Type v\nM : Type w\ninst✝³ : CommRing R\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\ninst✝ : IsNoetherian R M\nf : End R M\nμ : R\nk : ℕ\nhk : f.maxUnifEigenspaceIndex μ ≤ k\n⊢ f.maxUnifEigenspaceIndex μ ≤ k"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Idempotents | {
"line": 507,
"column": 26
} | {
"line": 507,
"column": 37
} | {
"line": 507,
"column": 38
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝² : CommRing R\ninst✝¹ : Ring S\nI : Type u_3\ninst✝ : Fintype I\nf : R →+* S\ne₀ : R\nhe₀ : IsIdempotentElem e₀\nhfe₀ : RingHom.ker f = Ideal.span {e₀}\ne : I → S\nhe : CompleteOrthogonalIdempotents e\ne' : I → R\nhe' : ∀ (i : I), f (e' i) = e i\nk : I → R\nhk : ∀ (i :... | [
"R : Type u_1\nS : Type u_2\ninst✝² : CommRing R\ninst✝¹ : Ring S\nI : Type u_3\ninst✝ : Fintype I\nf : R →+* S\ne₀ : R\nhe₀ : IsIdempotentElem e₀\nhfe₀ : RingHom.ker f = Ideal.span {e₀}\ne : I → S\nhe : CompleteOrthogonalIdempotents e\ne' : I → R\nhe' : ∀ (i : I), f (e' i) = e i\nk : I → R\nhk : ∀ (i : I), e' i * ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Eigenspace.Basic | {
"line": 354,
"column": 47
} | {
"line": 354,
"column": 58
} | {
"line": 354,
"column": 59
} | [
{
"pp": "K : Type v\nV : Type w\ninst✝³ : Field K\ninst✝² : AddCommGroup V\ninst✝¹ : Module K V\ninst✝ : FiniteDimensional K V\nf : End K V\nμ : K\nk : ℕ∞\n⊢ ↑(f.maxUnifEigenspaceIndex μ) ≤ ↑(finrank K V)",
"ppTerm": "?m.97",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instCompleteLi... | [
"K : Type v\nV : Type w\ninst✝³ : Field K\ninst✝² : AddCommGroup V\ninst✝¹ : Module K V\ninst✝ : FiniteDimensional K V\nf : End K V\nμ : K\nk : ℕ∞\n⊢ f.maxUnifEigenspaceIndex μ ≤ finrank K V"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Eigenspace.Basic | {
"line": 362,
"column": 40
} | {
"line": 362,
"column": 51
} | {
"line": 362,
"column": 52
} | [
{
"pp": "K : Type v\nV : Type w\ninst✝³ : Field K\ninst✝² : AddCommGroup V\ninst✝¹ : Module K V\ninst✝ : FiniteDimensional K V\nf : End K V\nμ : K\nk : ℕ\nhk : finrank K V ≤ k\n⊢ ↑(finrank K V) ≤ ↑k",
"ppTerm": "?m.56",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instCompleteLinearOr... | [
"K : Type v\nV : Type w\ninst✝³ : Field K\ninst✝² : AddCommGroup V\ninst✝¹ : Module K V\ninst✝ : FiniteDimensional K V\nf : End K V\nμ : K\nk : ℕ\nhk : finrank K V ≤ k\n⊢ finrank K V ≤ k"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Eigenspace.Basic | {
"line": 372,
"column": 62
} | {
"line": 372,
"column": 85
} | {
"line": 373,
"column": 4
} | [
{
"pp": "case right\nR : Type v\nM : Type w\ninst✝² : CommRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nf g : End R M\nμ : R\nk : ℕ∞\nx : M\nl : ℕ\nhl : ↑l ≤ k\nhx : ((f - μ • 1) ^ l) x = 0\nh : Commute ((f - μ • 1) ^ l) g\n⊢ (g * (f - μ • 1) ^ l) x = 0",
"ppTerm": "?right",
"assigned": true,
... | [
"case right\nR : Type v\nM : Type w\ninst✝² : CommRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nf g : End R M\nμ : R\nk : ℕ∞\nx : M\nl : ℕ\nhl : ↑l ≤ k\nhx : ((f - μ • 1) ^ l) x = 0\nh : Commute ((f - μ • 1) ^ l) g\n⊢ (g ∘ₗ (f - μ • 1) ^ l) x = 0"
] | Module.End.mul_eq_comp, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.DirectSum.LinearMap | {
"line": 62,
"column": 4
} | {
"line": 62,
"column": 25
} | {
"line": 62,
"column": 26
} | [
{
"pp": "case neg\nι : Type u_1\nR : Type u_2\nM : Type u_3\ninst✝⁵ : CommRing R\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\nN : ι → Submodule R M\ninst✝² : DecidableEq ι\nκ : ι → Type u_4\ninst✝¹ : (i : ι) → Fintype (κ i)\ninst✝ : (i : ι) → DecidableEq (κ i)\ns : Finset ι\nh : IsInternal fun i ↦ N ↑i\nb : (... | [
"case neg\nι : Type u_1\nR : Type u_2\nM : Type u_3\ninst✝⁵ : CommRing R\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\nN : ι → Submodule R M\ninst✝² : DecidableEq ι\nκ : ι → Type u_4\ninst✝¹ : (i : ι) → Fintype (κ i)\ninst✝ : (i : ι) → DecidableEq (κ i)\ns : Finset ι\nh : IsInternal fun i ↦ N ↑i\nb : (i : ↥s) → Ba... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.