module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Data.List.Intervals | {
"line": 69,
"column": 59
} | {
"line": 69,
"column": 75
} | {
"line": 69,
"column": 75
} | [
{
"pp": "n m k : ℕ\n⊢ range' (k + n) (m - n) = range' (n + k) (m - n)",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"List.range'",
"HSub.hSub",
"id",
"instSubNat",
"instOfNatNat",
"List",
"instHAdd",
"instH... | [
"n m k : ℕ\n⊢ range' (k + n) (m - n) = range' (k + n) (m - n)"
] | Nat.add_comm n k | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.List.Intervals | {
"line": 189,
"column": 4
} | {
"line": 189,
"column": 15
} | {
"line": 189,
"column": 16
} | [
{
"pp": "n m : ℕ\nhnm : n < m\nx✝¹ : ℕ\nx✝ : x✝¹ ∈ Ico n m\n⊢ decide (x✝¹ ≤ n) = decide (x✝¹ < n + 1)",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"id",
"instOfNatNat",
"LE.le",
"instLENat",
"instHAdd",
"Iff",
"HAdd.hAdd",
... | [
"n m : ℕ\nhnm : n < m\nx✝¹ : ℕ\nx✝ : x✝¹ ∈ Ico n m\n⊢ x✝¹ ≤ n ↔ x✝¹ < n + 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.TakeWhile | {
"line": 110,
"column": 8
} | {
"line": 110,
"column": 19
} | {
"line": 110,
"column": 20
} | [
{
"pp": "case false\nα : Type u_1\np : α → Bool\nl : List α\nhead : α\ntail : List α\nhi : find? p tail = (dropWhile (fun x ↦ !p x) tail).head?\nphh : false = p head\nphh' : ¬p head = true\n⊢ (!p head) = true",
"ppTerm": "?false✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Bool.not... | [
"case false\nα : Type u_1\np : α → Bool\nl : List α\nhead : α\ntail : List α\nhi : find? p tail = (dropWhile (fun x ↦ !p x) tail).head?\nphh : false = p head\nphh' : ¬p head = true\n⊢ p head = false"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.TakeWhile | {
"line": 113,
"column": 8
} | {
"line": 113,
"column": 19
} | {
"line": 113,
"column": 20
} | [
{
"pp": "case true\nα : Type u_1\np : α → Bool\nl : List α\nhead : α\ntail : List α\nhi : find? p tail = (dropWhile (fun x ↦ !p x) tail).head?\nphh : true = p head\n⊢ ¬(!p head) = true",
"ppTerm": "?true✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Bool.not",
"Bool.not_eq_fal... | [
"case true\nα : Type u_1\np : α → Bool\nl : List α\nhead : α\ntail : List α\nhi : find? p tail = (dropWhile (fun x ↦ !p x) tail).head?\nphh : true = p head\n⊢ p head = true"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.TakeWhile | {
"line": 123,
"column": 62
} | {
"line": 123,
"column": 73
} | {
"line": 123,
"column": 74
} | [
{
"pp": "α : Type u_1\np : α → Bool\nl : List α\nh : ∃ x, x ∈ l ∧ p x = true\n⊢ dropWhile (fun x ↦ !p x) l ≠ []",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"List.dropWhile_eq_nil_iff._simp_1",
"Bool.not",
"Bool.not_eq_false",
"congrArg",
"M... | [
"α : Type u_1\np : α → Bool\nl : List α\nh : ∃ x, x ∈ l ∧ p x = true\n⊢ ∃ x, x ∈ l ∧ p x = true"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Lemmas | {
"line": 42,
"column": 8
} | {
"line": 42,
"column": 42
} | {
"line": 42,
"column": 43
} | [
{
"pp": "case cons.succ.succ.refine_1\nα : Type u_1\nx hd : α\ntl : List α\nIH :\n ¬x ∈ tl →\n ∀ ⦃n : ℕ⦄,\n n ∈ {n | n ≤ tl.length} →\n ∀ ⦃m : ℕ⦄, m ∈ {n | n ≤ tl.length} → (fun k ↦ tl.insertIdx k x) n = (fun k ↦ tl.insertIdx k x) m → n = m\nhx : ¬x = hd ∧ ¬x ∈ tl\nn✝¹ : ℕ\nhn : n✝¹ + 1 ≤ tl.len... | [
"case cons.succ.succ.refine_1\nα : Type u_1\nx hd : α\ntl : List α\nIH :\n ¬x ∈ tl →\n ∀ ⦃n : ℕ⦄,\n n ∈ {n | n ≤ tl.length} →\n ∀ ⦃m : ℕ⦄, m ∈ {n | n ≤ tl.length} → (fun k ↦ tl.insertIdx k x) n = (fun k ↦ tl.insertIdx k x) m → n = m\nhx : ¬x = hd ∧ ¬x ∈ tl\nn✝¹ : ℕ\nhn : n✝¹ + 1 ≤ tl.length + 1\nn✝ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.TakeWhile | {
"line": 127,
"column": 62
} | {
"line": 127,
"column": 73
} | {
"line": 127,
"column": 74
} | [
{
"pp": "α : Type u_1\np : α → Bool\nl : List α\nh : ∃ x, x ∈ l ∧ ¬p x = true\n⊢ dropWhile p l ≠ []",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"List.dropWhile_eq_nil_iff._simp_1",
"congrArg",
"Membership.mem",
"Exists",
"id",
"Ne",
... | [
"α : Type u_1\np : α → Bool\nl : List α\nh : ∃ x, x ∈ l ∧ ¬p x = true\n⊢ ∃ x, x ∈ l ∧ p x = false"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Lemmas | {
"line": 43,
"column": 8
} | {
"line": 43,
"column": 42
} | {
"line": 43,
"column": 43
} | [
{
"pp": "case cons.succ.succ.refine_2\nα : Type u_1\nx hd : α\ntl : List α\nIH :\n ¬x ∈ tl →\n ∀ ⦃n : ℕ⦄,\n n ∈ {n | n ≤ tl.length} →\n ∀ ⦃m : ℕ⦄, m ∈ {n | n ≤ tl.length} → (fun k ↦ tl.insertIdx k x) n = (fun k ↦ tl.insertIdx k x) m → n = m\nhx : ¬x = hd ∧ ¬x ∈ tl\nn✝¹ : ℕ\nhn : n✝¹ + 1 ≤ tl.len... | [
"case cons.succ.succ.refine_2\nα : Type u_1\nx hd : α\ntl : List α\nIH :\n ¬x ∈ tl →\n ∀ ⦃n : ℕ⦄,\n n ∈ {n | n ≤ tl.length} →\n ∀ ⦃m : ℕ⦄, m ∈ {n | n ≤ tl.length} → (fun k ↦ tl.insertIdx k x) n = (fun k ↦ tl.insertIdx k x) m → n = m\nhx : ¬x = hd ∧ ¬x ∈ tl\nn✝¹ : ℕ\nhn : n✝¹ + 1 ≤ tl.length + 1\nn✝ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.TakeWhile | {
"line": 130,
"column": 4
} | {
"line": 130,
"column": 15
} | {
"line": 130,
"column": 16
} | [
{
"pp": "case convert_2\nα : Type u_1\np : α → Bool\nl : List α\nh : ∃ x, x ∈ l ∧ ¬p x = true\n⊢ ∃ x, x ∈ l ∧ (!p x) = true",
"ppTerm": "?convert_2",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Bool.not",
"congrArg",
"Membership.mem",
"Exists",
"id",
"Bo... | [
"case convert_2\nα : Type u_1\np : α → Bool\nl : List α\nh : ∃ x, x ∈ l ∧ ¬p x = true\n⊢ ∃ x, x ∈ l ∧ p x = false"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.ModifyLast | {
"line": 43,
"column": 30
} | {
"line": 43,
"column": 52
} | {
"line": 43,
"column": 53
} | [
{
"pp": "case cons\nα : Type u_1\nf : α → α\na head✝ : α\ntl : List α\n⊢ (#[].push head✝).toListAppend (modifyLast.go f (tl ++ [a]) #[]) = head✝ :: (tl ++ [f a])",
"ppTerm": "?cons",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Array.toListAppend_eq",
"Array.push",
"congrA... | [
"case cons\nα : Type u_1\nf : α → α\na head✝ : α\ntl : List α\n⊢ (#[].push head✝).toList ++ modifyLast.go f (tl ++ [a]) #[] = head✝ :: (tl ++ [f a])"
] | Array.toListAppend_eq, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.List.Palindrome | {
"line": 66,
"column": 69
} | {
"line": 68,
"column": 38
} | {
"line": 70,
"column": 0
} | [
{
"pp": "α : Type u_1\nl : List α\n⊢ (l ++ l.reverse).Palindrome",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"List.Palindrome.of_reverse_eq",
"Eq.mpr",
"congrArg",
"id",
"instHAppendOfAppend",
"List",
"List.reverse_reverse",
"List.reverse"... | [] | by
apply of_reverse_eq
rw [reverse_append, reverse_reverse] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.List.SplitLengths | {
"line": 53,
"column": 46
} | {
"line": 53,
"column": 57
} | {
"line": 53,
"column": 58
} | [
{
"pp": "α : Type u_1\nl : List α\nsz : List ℕ\ni : ℕ\nhi : i < (sz.splitLengths l).length\n⊢ i < sz.length",
"ppTerm": "?m.22",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nl : List α\nsz : List ℕ\ni : ℕ\nhi : i < (sz.splitLengths l).length\n⊢ i < sz.length"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.SplitLengths | {
"line": 68,
"column": 4
} | {
"line": 68,
"column": 26
} | {
"line": 68,
"column": 27
} | [
{
"pp": "case h\nα : Type u_1\nhead : ℕ\ntail : List ℕ\nih : ∀ (l : List α), l.length ≤ tail.sum → (tail.splitLengths l).flatten = l\nl : List α\nh : l.length ≤ (head :: tail).sum\n⊢ (drop head l).length ≤ tail.sum",
"ppTerm": "?h",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrAr... | [
"case h\nα : Type u_1\nhead : ℕ\ntail : List ℕ\nih : ∀ (l : List α), l.length ≤ tail.sum → (tail.splitLengths l).flatten = l\nl : List α\nh : l.length ≤ (head :: tail).sum\n⊢ l.length ≤ head + tail.sum"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.SplitLengths | {
"line": 93,
"column": 46
} | {
"line": 93,
"column": 57
} | {
"line": 93,
"column": 58
} | [
{
"pp": "α✝ : Type u_1\nl✝ : List α✝\nsz✝ : List ℕ\nα : Type u_2\nl : List α\nsz : List ℕ\nh : sz.sum ≤ l.length\ni : ℕ\nhi : i < (sz.splitLengths l).length\n⊢ i < sz.length",
"ppTerm": "?m.27",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α✝ : Type u_1\nl✝ : List α✝\nsz✝ : List ℕ\nα : Type u_2\nl : List α\nsz : List ℕ\nh : sz.sum ≤ l.length\ni : ℕ\nhi : i < (sz.splitLengths l).length\n⊢ i < sz.length"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.SplitLengths | {
"line": 97,
"column": 4
} | {
"line": 97,
"column": 15
} | {
"line": 97,
"column": 16
} | [
{
"pp": "α : Type u_2\nl : List α\nsz : List ℕ\nh : sz.sum ≤ l.length\ni : ℕ\nhi : i < (sz.splitLengths l).length\nthis : map length (sz.splitLengths l) = sz\n⊢ i < (map length (sz.splitLengths l)).length",
"ppTerm": "?m.47",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
... | [
"α : Type u_2\nl : List α\nsz : List ℕ\nh : sz.sum ≤ l.length\ni : ℕ\nhi : i < (sz.splitLengths l).length\nthis : map length (sz.splitLengths l) = sz\n⊢ i < sz.length"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.SplitLengths | {
"line": 104,
"column": 23
} | {
"line": 104,
"column": 34
} | {
"line": 104,
"column": 35
} | [
{
"pp": "α : Type u_2\nl : List α\nsz : List ℕ\nb : ℕ\nh : ∀ (n : ℕ), n ∈ sz → n ≤ b\ni : ℕ\nhi : i < (sz.splitLengths l).length\nthis : (sz.splitLengths l)[i].length ≤ sz[i]\n⊢ i < sz.length",
"ppTerm": "?m.35",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\nl : List α\nsz : List ℕ\nb : ℕ\nh : ∀ (n : ℕ), n ∈ sz → n ≤ b\ni : ℕ\nhi : i < (sz.splitLengths l).length\nthis : (sz.splitLengths l)[i].length ≤ sz[i]\n⊢ i < sz.length"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.SplitBy | {
"line": 61,
"column": 2
} | {
"line": 61,
"column": 29
} | {
"line": 62,
"column": 2
} | [
{
"pp": "α : Type u_1\nr : α → α → Bool\nl : List α\n⊢ splitBy r l = [] ↔ l = []",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"List.splitBy",
"List",
"List.flatten_splitBy",
"Eq",
"List.flatten"
],
"usedFVars": [
"α",
"r",
"l"
]... | [
"α : Type u_1\nr : α → α → Bool\nl : List α\nthis : (splitBy r l).flatten = l\n⊢ splitBy r l = [] ↔ l = []"
] | have := flatten_splitBy r l | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Data.List.SplitBy | {
"line": 76,
"column": 6
} | {
"line": 76,
"column": 17
} | {
"line": 76,
"column": 18
} | [
{
"pp": "case h_2\nα : Type u_1\nr : α → α → Bool\nb : α\nl : List α\nIH : ∀ {a : α} {g : List α}, ¬[] ∈ splitBy.loop r l a g []\na : α\ng : List α\nx✝ : Bool\nheq✝ : r a b = false\n⊢ ¬([] ∈ [(a :: g).reverse].reverse ∨ [] ∈ splitBy.loop r l b [] [])",
"ppTerm": "?h_2",
"assigned": true,
"usedConsta... | [
"case h_2\nα : Type u_1\nr : α → α → Bool\nb : α\nl : List α\nIH : ∀ {a : α} {g : List α}, ¬[] ∈ splitBy.loop r l a g []\na : α\ng : List α\nx✝ : Bool\nheq✝ : r a b = false\n⊢ ¬[] ∈ splitBy.loop r l b [] []"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.SplitBy | {
"line": 134,
"column": 4
} | {
"line": 134,
"column": 15
} | {
"line": 134,
"column": 16
} | [
{
"pp": "case nil\nα : Type u_1\nr : α → α → Bool\na : α\ng : List α\ngs : List (List α)\nhgs' : ¬[] ∈ gs\nhgs : IsChain (fun b a ↦ ∃ ha hb, r (a.getLast ha) (b.head hb) = false) gs\nhga : ∀ (m : List α), m ∈ gs.head? → ∃ ha hb, r (m.getLast ha) ((g.reverse ++ [a]).head hb) = false\n⊢ IsChain (fun b a ↦ ∃ ha hb... | [
"case nil\nα : Type u_1\nr : α → α → Bool\na : α\ng : List α\ngs : List (List α)\nhgs' : ¬[] ∈ gs\nhgs : IsChain (fun b a ↦ ∃ ha hb, r (a.getLast ha) (b.head hb) = false) gs\nhga : ∀ (m : List α), m ∈ gs.head? → ∃ ha hb, r (m.getLast ha) ((g.reverse ++ [a]).head hb) = false\n⊢ IsChain (fun b a ↦ ∃ h hb, r (a.getLas... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.Bilinear | {
"line": 148,
"column": 4
} | {
"line": 148,
"column": 15
} | {
"line": 148,
"column": 16
} | [
{
"pp": "case mp\nl : Type u_1\nm : Type u_2\nn : Type u_3\nR : Type u_5\nA : Type u_6\ninst✝⁵ : Fintype m\ninst✝⁴ : Semiring R\ninst✝³ : Semiring A\ninst✝² : Module R A\ninst✝¹ : SMulCommClass R A A\ninst✝ : Nonempty n\na : Matrix l m A\ninhabited_h : Inhabited n\ni : l\nj : m\nh : (mulLeftLinearMap n R a) (Ma... | [
"case mp\nl : Type u_1\nm : Type u_2\nn : Type u_3\nR : Type u_5\nA : Type u_6\ninst✝⁵ : Fintype m\ninst✝⁴ : Semiring R\ninst✝³ : Semiring A\ninst✝² : Module R A\ninst✝¹ : SMulCommClass R A A\ninst✝ : Nonempty n\na : Matrix l m A\ninhabited_h : Inhabited n\ni : l\nj : m\nh : (mulLeftLinearMap n R a) (Matrix.single ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.Bilinear | {
"line": 159,
"column": 50
} | {
"line": 159,
"column": 73
} | {
"line": 159,
"column": 74
} | [
{
"pp": "m : Type u_2\nn✝ : Type u_3\nR : Type u_5\nA : Type u_6\ninst✝⁵ : Fintype m\ninst✝⁴ : DecidableEq m\ninst✝³ : Semiring R\ninst✝² : Semiring A\ninst✝¹ : Module R A\ninst✝ : SMulCommClass R A A\na : Matrix m m A\nk n : ℕ\n⊢ mulLeftLinearMap n✝ R a ^ n * mulLeftLinearMap n✝ R a = mulLeftLinearMap n✝ R (a ... | [
"m : Type u_2\nn✝ : Type u_3\nR : Type u_5\nA : Type u_6\ninst✝⁵ : Fintype m\ninst✝⁴ : DecidableEq m\ninst✝³ : Semiring R\ninst✝² : Semiring A\ninst✝¹ : Module R A\ninst✝ : SMulCommClass R A A\na : Matrix m m A\nk n : ℕ\n⊢ (mulLeftLinearMap n✝ R a ^ n) ∘ₗ mulLeftLinearMap n✝ R a = mulLeftLinearMap n✝ R (a ^ n) ∘ₗ m... | Module.End.mul_eq_comp, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.LinearAlgebra.Matrix.Bilinear | {
"line": 181,
"column": 4
} | {
"line": 181,
"column": 15
} | {
"line": 181,
"column": 16
} | [
{
"pp": "case mp\nl : Type u_1\nm : Type u_2\nn : Type u_3\nR : Type u_5\nA : Type u_6\ninst✝⁵ : Fintype m\ninst✝⁴ : Semiring R\ninst✝³ : Semiring A\ninst✝² : Module R A\ninst✝¹ : IsScalarTower R A A\na : Matrix m n A\ninst✝ : Nonempty l\ninhabited_h : Inhabited l\ni : m\nj : n\nh : (mulRightLinearMap l R a) (M... | [
"case mp\nl : Type u_1\nm : Type u_2\nn : Type u_3\nR : Type u_5\nA : Type u_6\ninst✝⁵ : Fintype m\ninst✝⁴ : Semiring R\ninst✝³ : Semiring A\ninst✝² : Module R A\ninst✝¹ : IsScalarTower R A A\na : Matrix m n A\ninst✝ : Nonempty l\ninhabited_h : Inhabited l\ni : m\nj : n\nh : (mulRightLinearMap l R a) (Matrix.single... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.Bilinear | {
"line": 192,
"column": 52
} | {
"line": 192,
"column": 75
} | {
"line": 192,
"column": 76
} | [
{
"pp": "l : Type u_1\nm : Type u_2\nR : Type u_5\nA : Type u_6\ninst✝⁵ : Fintype m\ninst✝⁴ : DecidableEq m\ninst✝³ : Semiring R\ninst✝² : Semiring A\ninst✝¹ : Module R A\ninst✝ : IsScalarTower R A A\na : Matrix m m A\nk n : ℕ\n⊢ mulRightLinearMap l R a ^ n * mulRightLinearMap l R a = mulRightLinearMap l R (a ^... | [
"l : Type u_1\nm : Type u_2\nR : Type u_5\nA : Type u_6\ninst✝⁵ : Fintype m\ninst✝⁴ : DecidableEq m\ninst✝³ : Semiring R\ninst✝² : Semiring A\ninst✝¹ : Module R A\ninst✝ : IsScalarTower R A A\na : Matrix m m A\nk n : ℕ\n⊢ (mulRightLinearMap l R a ^ n) ∘ₗ mulRightLinearMap l R a = mulRightLinearMap l R (a ^ n) ∘ₗ mu... | Module.End.mul_eq_comp, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.List.SplitBy | {
"line": 143,
"column": 8
} | {
"line": 143,
"column": 19
} | {
"line": 143,
"column": 20
} | [
{
"pp": "case h_2.hgs'\nα : Type u_1\nr : α → α → Bool\nb : α\nl : List α\nIH :\n ∀ {a : α} {g : List α} {gs : List (List α)},\n ¬[] ∈ gs →\n IsChain (fun b a ↦ ∃ ha hb, r (a.getLast ha) (b.head hb) = false) gs →\n (∀ (m : List α), m ∈ gs.head? → ∃ ha hb, r (m.getLast ha) ((g.reverse ++ [a]).hea... | [
"case h_2.hgs'\nα : Type u_1\nr : α → α → Bool\nb : α\nl : List α\nIH :\n ∀ {a : α} {g : List α} {gs : List (List α)},\n ¬[] ∈ gs →\n IsChain (fun b a ↦ ∃ ha hb, r (a.getLast ha) (b.head hb) = false) gs →\n (∀ (m : List α), m ∈ gs.head? → ∃ ha hb, r (m.getLast ha) ((g.reverse ++ [a]).head hb) = fals... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.DershowitzManna | {
"line": 60,
"column": 4
} | {
"line": 60,
"column": 38
} | {
"line": 60,
"column": 39
} | [
{
"pp": "case refine_1\nα : Type u_1\ninst✝ : Preorder α\nX₁ Y₁ Z₁ : Multiset α\nhYZ₁ : ∀ (y : α), y ∈ Y₁ → ∃ z, z ∈ Z₁ ∧ y < z\nX₂ Y₂ Z₂ : Multiset α\nhZ₂ : Z₂ ≠ ∅\nhXZXY : Z₁ + X₁ = Y₂ + X₂\nhYZ₂ : ∀ (y : α), y ∈ Y₂ → ∃ z, z ∈ Z₂ ∧ y < z\n⊢ Z₂ + (Z₁ - Y₂) ≠ ∅",
"ppTerm": "?refine_1",
"assigned": true,... | [
"case refine_1\nα : Type u_1\ninst✝ : Preorder α\nX₁ Y₁ Z₁ : Multiset α\nhYZ₁ : ∀ (y : α), y ∈ Y₁ → ∃ z, z ∈ Z₁ ∧ y < z\nX₂ Y₂ Z₂ : Multiset α\nhZ₂ : Z₂ ≠ ∅\nhXZXY : Z₁ + X₁ = Y₂ + X₂\nhYZ₂ : ∀ (y : α), y ∈ Y₂ → ∃ z, z ∈ Z₂ ∧ y < z\n⊢ ¬Z₂ = 0 ∨ ¬Z₁ - Y₂ = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.DershowitzManna | {
"line": 93,
"column": 4
} | {
"line": 93,
"column": 56
} | {
"line": 93,
"column": 57
} | [
{
"pp": "case inl\nα : Type u_1\ninst✝ : Preorder α\nM : Multiset α\na : α\nX Y : Multiset α\nh0 : a ::ₘ M = X + {a}\nh2 : ∀ (y : α), y ∈ Y → y < a\n⊢ X + Y = M + Y",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"PartialOrder.toPreorder",
"instIsRightCancelAddOf... | [
"case inl\nα : Type u_1\ninst✝ : Preorder α\nM : Multiset α\na : α\nX Y : Multiset α\nh0 : a ::ₘ M = X + {a}\nh2 : ∀ (y : α), y ∈ Y → y < a\n⊢ M = X"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.DershowitzManna | {
"line": 99,
"column": 4
} | {
"line": 99,
"column": 21
} | {
"line": 99,
"column": 22
} | [
{
"pp": "case inr.refine_1\nα : Type u_1\ninst✝ : Preorder α\nM : Multiset α\na : α\nX Y : Multiset α\nb : α\nh0 : M + {a} = X + {b}\nh2 : ∀ (y : α), y ∈ Y → y < b\nhab : a ≠ b\nthis : a ∈ X + {b}\n⊢ {a} ≤ X",
"ppTerm": "?inr.refine_1",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Par... | [
"case inr.refine_1\nα : Type u_1\ninst✝ : Preorder α\nM : Multiset α\na : α\nX Y : Multiset α\nb : α\nh0 : M + {a} = X + {b}\nh2 : ∀ (y : α), y ∈ Y → y < b\nhab : a ≠ b\nthis : a ∈ X + {b}\n⊢ a ∈ X"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.DershowitzManna | {
"line": 102,
"column": 4
} | {
"line": 102,
"column": 26
} | {
"line": 102,
"column": 27
} | [
{
"pp": "case inr.refine_2\nα : Type u_1\ninst✝ : Preorder α\nM : Multiset α\na : α\nX Y : Multiset α\nb : α\nh0 : a ::ₘ M = X + {b}\nh2 : ∀ (y : α), y ∈ Y → y < b\nhab : a ≠ b\nthis : b ∈ a ::ₘ M\n⊢ {b} ≤ M",
"ppTerm": "?inr.refine_2",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Par... | [
"case inr.refine_2\nα : Type u_1\ninst✝ : Preorder α\nM : Multiset α\na : α\nX Y : Multiset α\nb : α\nh0 : a ::ₘ M = X + {b}\nh2 : ∀ (y : α), y ∈ Y → y < b\nhab : a ≠ b\nthis : b ∈ a ::ₘ M\n⊢ b ∈ M"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.DershowitzManna | {
"line": 115,
"column": 4
} | {
"line": 115,
"column": 15
} | {
"line": 115,
"column": 16
} | [
{
"pp": "case intro.intro.inr.empty\nα : Type u_1\ninst✝ : Preorder α\na✝ a : α\nh✝ : ∀ (y : α), y < a → Acc LT.lt y\nha : ∀ (y : α), y < a → ∀ {M : Multiset α}, Acc OneStep M → Acc OneStep (y ::ₘ M)\nM✝ M : Multiset α\nhM : ∀ (y : Multiset α), y.OneStep M → Acc OneStep y\nihM : ∀ (y : Multiset α), y.OneStep M ... | [
"case intro.intro.inr.empty\nα : Type u_1\ninst✝ : Preorder α\na✝ a : α\nh✝ : ∀ (y : α), y < a → Acc LT.lt y\nha : ∀ (y : α), y < a → ∀ {M : Multiset α}, Acc OneStep M → Acc OneStep (y ::ₘ M)\nM✝ M : Multiset α\nhM : ∀ (y : Multiset α), y.OneStep M → Acc OneStep y\nihM : ∀ (y : Multiset α), y.OneStep M → Acc OneSte... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.DershowitzManna | {
"line": 145,
"column": 39
} | {
"line": 145,
"column": 50
} | {
"line": 145,
"column": 51
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\nz : α\nM N X Y : Multiset α\nhM : M = X + Y\nih :\n ∀ {M N : Multiset α} (X Y : Multiset α),\n 0 ≠ ∅ → M = X + Y → N = X + 0 → (∀ (y : α), y ∈ Y → ∃ z, z ∈ 0 ∧ y < z) → TransGen OneStep M N\nhZ : z ::ₘ 0 ≠ ∅\nhN : N = X + z ::ₘ 0\nhYZ : ∀ (y : α), y ∈ Y → ∃ z_1, z_... | [
"α : Type u_1\ninst✝ : Preorder α\nz : α\nM N X Y : Multiset α\nhM : M = X + Y\nih :\n ∀ {M N : Multiset α} (X Y : Multiset α),\n 0 ≠ ∅ → M = X + Y → N = X + 0 → (∀ (y : α), y ∈ Y → ∃ z, z ∈ 0 ∧ y < z) → TransGen OneStep M N\nhZ : z ::ₘ 0 ≠ ∅\nhN : N = X + z ::ₘ 0\nhYZ : ∀ (y : α), y ∈ Y → ∃ z_1, z_1 ∈ z ::ₘ 0 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.DershowitzManna | {
"line": 146,
"column": 2
} | {
"line": 146,
"column": 41
} | {
"line": 147,
"column": 2
} | [
{
"pp": "case cons.inr\nα : Type u_1\ninst✝ : Preorder α\nz : α\nZ : Multiset α\nih :\n ∀ {M N : Multiset α} (X Y : Multiset α),\n Z ≠ ∅ → M = X + Y → N = X + Z → (∀ (y : α), y ∈ Y → ∃ z, z ∈ Z ∧ y < z) → TransGen OneStep M N\nM N X Y : Multiset α\nhZ✝ : z ::ₘ Z ≠ ∅\nhM : M = X + Y\nhN : N = X + z ::ₘ Z\nhY... | [
"case cons.inr\nα : Type u_1\ninst✝ : Preorder α\nz : α\nZ : Multiset α\nih :\n ∀ {M N : Multiset α} (X Y : Multiset α),\n Z ≠ ∅ → M = X + Y → N = X + Z → (∀ (y : α), y ∈ Y → ∃ z, z ∈ Z ∧ y < z) → TransGen OneStep M N\nM N X Y : Multiset α\nhZ✝ : z ::ₘ Z ≠ ∅\nhM : M = X + Y\nhN : N = X + z ::ₘ Z\nhYZ : ∀ (y : α... | let Y' : Multiset α := Y.filter (· < z) | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLet___1 | Lean.Parser.Tactic.tacticLet__ |
Mathlib.Data.Multiset.DershowitzManna | {
"line": 151,
"column": 4
} | {
"line": 151,
"column": 22
} | {
"line": 151,
"column": 23
} | [
{
"pp": "case cons.inr.refine_2\nα : Type u_1\ninst✝ : Preorder α\nz : α\nZ : Multiset α\nih :\n ∀ {M N : Multiset α} (X Y : Multiset α),\n Z ≠ ∅ → M = X + Y → N = X + Z → (∀ (y : α), y ∈ Y → ∃ z, z ∈ Z ∧ y < z) → TransGen OneStep M N\nM N X Y : Multiset α\nhZ✝ : z ::ₘ Z ≠ ∅\nhM : M = X + Y\nhN : N = X + z ... | [
"case cons.inr.refine_2\nα : Type u_1\ninst✝ : Preorder α\nz : α\nZ : Multiset α\nih :\n ∀ {M N : Multiset α} (X Y : Multiset α),\n Z ≠ ∅ → M = X + Y → N = X + Z → (∀ (y : α), y ∈ Y → ∃ z, z ∈ Z ∧ y < z) → TransGen OneStep M N\nM N X Y : Multiset α\nhZ✝ : z ::ₘ Z ≠ ∅\nhM : M = X + Y\nhN : N = X + z ::ₘ Z\nhYZ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.NNRat.Floor | {
"line": 36,
"column": 23
} | {
"line": 36,
"column": 34
} | {
"line": 36,
"column": 35
} | [
{
"pp": "a✝ : ℚ≥0\nh : a✝ < 0\n⊢ ⌊↑a✝⌋₊ = 0",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Rat.instOfNat",
"Eq.mpr",
"Nat.floor_eq_zero._simp_1",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Preorder.toLT",
"FloorRing.toFloorSemiring",
"NNRat.inst... | [
"a✝ : ℚ≥0\nh : a✝ < 0\n⊢ a✝ < 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.ChineseRemainder | {
"line": 128,
"column": 16
} | {
"line": 128,
"column": 55
} | {
"line": 128,
"column": 56
} | [
{
"pp": "ι : Type u_1\na s : ι → ℕ\nl l' : List ι\nhl : l.Perm l'\nhs : ∀ i ∈ l, s i ≠ 0\nco : List.Pairwise (Coprime on s) l\nz : { k // ∀ i ∈ l', k ≡ a i [MOD s i] } := chineseRemainderOfList a s l' ⋯\nhlp : (List.map s l).prod = (List.map s l').prod\n⊢ ∀ i ∈ l', s i ≠ 0",
"ppTerm": "?m.90",
"assigned... | [
"ι : Type u_1\na s : ι → ℕ\nl l' : List ι\nhl : l.Perm l'\nhs : ∀ i ∈ l, s i ≠ 0\nco : List.Pairwise (Coprime on s) l\nz : { k // ∀ i ∈ l', k ≡ a i [MOD s i] } := chineseRemainderOfList a s l' ⋯\nhlp : (List.map s l).prod = (List.map s l').prod\n⊢ ∀ i ∈ l, ¬s i = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.ChineseRemainder | {
"line": 142,
"column": 39
} | {
"line": 142,
"column": 73
} | {
"line": 142,
"column": 74
} | [
{
"pp": "ι : Type u_1\na s : ι → ℕ\nm : Multiset ι\nl l' : List ι\npp : l.Perm l'\nnod' : l'.Nodup\nnod : l.Nodup\nhs' : ∀ i ∈ l', s i ≠ 0\n⊢ ∀ i ∈ l, s i ≠ 0",
"ppTerm": "?m.170",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Membership.mem",
"id",
"Ne",
"instOfNatNa... | [
"ι : Type u_1\na s : ι → ℕ\nm : Multiset ι\nl l' : List ι\npp : l.Perm l'\nnod' : l'.Nodup\nnod : l.Nodup\nhs' : ∀ i ∈ l', s i ≠ 0\n⊢ ∀ i ∈ l', ¬s i = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.ChineseRemainder | {
"line": 144,
"column": 62
} | {
"line": 144,
"column": 96
} | {
"line": 144,
"column": 97
} | [
{
"pp": "ι : Type u_1\na s : ι → ℕ\nm : Multiset ι\nl l' : List ι\npp : l.Perm l'\nnod' : l'.Nodup\nnod : l.Nodup\nhs' : ∀ i ∈ l', s i ≠ 0\nhs : ∀ i ∈ l, s i ≠ 0\nco' : {x | x ∈ l'}.Pairwise (Coprime on s)\n⊢ {x | x ∈ l}.Pairwise (Coprime on s)",
"ppTerm": "?m.178",
"assigned": true,
"usedConstants"... | [
"ι : Type u_1\na s : ι → ℕ\nm : Multiset ι\nl l' : List ι\npp : l.Perm l'\nnod' : l'.Nodup\nnod : l.Nodup\nhs' : ∀ i ∈ l', s i ≠ 0\nhs : ∀ i ∈ l, s i ≠ 0\nco' : {x | x ∈ l'}.Pairwise (Coprime on s)\n⊢ {x | x ∈ l'}.Pairwise (Coprime on s)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.ChineseRemainder | {
"line": 151,
"column": 50
} | {
"line": 152,
"column": 33
} | {
"line": 153,
"column": 6
} | [
{
"pp": "ι : Type u_1\na s : ι → ℕ\nm : Multiset ι\nl l' : List ι\npp : l.Perm l'\nnod' : l'.Nodup\nnod : l.Nodup\nhs' : ∀ i ∈ l', s i ≠ 0\nhs : ∀ i ∈ l, s i ≠ 0\nco' : {x | x ∈ l'}.Pairwise (Coprime on s)\nco : {x | x ∈ l}.Pairwise (Coprime on s)\nlco : List.Pairwise (Coprime on s) l\n⊢ ∀ {m' : Multiset ι} {e ... | [] | by
rintro _ rfl _ _ _; rfl | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Nat.ChineseRemainder | {
"line": 168,
"column": 2
} | {
"line": 168,
"column": 13
} | {
"line": 168,
"column": 14
} | [
{
"pp": "ι : Type u_1\na s : ι → ℕ\nt : Finset ι\nhs : ∀ i ∈ t, s i ≠ 0\npp : (↑t).Pairwise (Coprime on s)\n⊢ { k // ∀ i ∈ t, k ≡ a i [MOD s i] }",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"ι : Type u_1\na s : ι → ℕ\nt : Finset ι\nhs : ∀ i ∈ t, s i ≠ 0\npp : (↑t).Pairwise (Coprime on s)\n⊢ { k // ∀ i ∈ t, k ≡ a i [MOD s i] }"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.ChineseRemainder | {
"line": 168,
"column": 57
} | {
"line": 168,
"column": 68
} | {
"line": 168,
"column": 69
} | [
{
"pp": "ι : Type u_1\na s : ι → ℕ\nt : Finset ι\nhs : ∀ i ∈ t, s i ≠ 0\npp : (↑t).Pairwise (Coprime on s)\n⊢ ∀ i ∈ t.val, s i ≠ 0",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Membership.mem",
"Multiset",
"id",
"Ne",
"instOfNatNat",
"Finset.val",
... | [
"ι : Type u_1\na s : ι → ℕ\nt : Finset ι\nhs : ∀ i ∈ t, s i ≠ 0\npp : (↑t).Pairwise (Coprime on s)\n⊢ ∀ i ∈ t, ¬s i = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.ChineseRemainder | {
"line": 168,
"column": 77
} | {
"line": 168,
"column": 88
} | {
"line": 168,
"column": 89
} | [
{
"pp": "ι : Type u_1\na s : ι → ℕ\nt : Finset ι\nhs : ∀ i ∈ t, s i ≠ 0\npp : (↑t).Pairwise (Coprime on s)\n⊢ {x | x ∈ t.val}.Pairwise (Coprime on s)",
"ppTerm": "?m.39",
"assigned": true,
"usedConstants": [
"Nat.Coprime",
"Function.onFun",
"setOf",
"Membership.mem",
"M... | [
"ι : Type u_1\na s : ι → ℕ\nt : Finset ι\nhs : ∀ i ∈ t, s i ≠ 0\npp : (↑t).Pairwise (Coprime on s)\n⊢ (↑t).Pairwise (Coprime on s)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.ChineseRemainder | {
"line": 173,
"column": 2
} | {
"line": 173,
"column": 40
} | {
"line": 174,
"column": 4
} | [
{
"pp": "ι : Type u_1\na s : ι → ℕ\nt : Finset ι\nhs : ∀ i ∈ t, s i ≠ 0\npp : (↑t).Pairwise (Coprime on s)\n⊢ ↑(chineseRemainderOfFinset a s t hs pp) < ∏ i ∈ t, s i",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Finset",
"Membership.mem",
"id",
"Finset.prod",
... | [
"ι : Type u_1\na s : ι → ℕ\nt : Finset ι\nhs : ∀ i ∈ t, s i ≠ 0\npp : (↑t).Pairwise (Coprime on s)\n⊢ ↑(chineseRemainderOfMultiset a s ⋯ ⋯ ⋯) < ∏ i ∈ t, s i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.ChineseRemainder | {
"line": 174,
"column": 55
} | {
"line": 174,
"column": 66
} | {
"line": 174,
"column": 67
} | [
{
"pp": "ι : Type u_1\na s : ι → ℕ\nt : Finset ι\nhs : ∀ i ∈ t, s i ≠ 0\npp : (↑t).Pairwise (Coprime on s)\n⊢ ∀ i ∈ t.val, s i ≠ 0",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Membership.mem",
"Multiset",
"id",
"Ne",
"instOfNatNat",
"Finset.val",
... | [
"ι : Type u_1\na s : ι → ℕ\nt : Finset ι\nhs : ∀ i ∈ t, s i ≠ 0\npp : (↑t).Pairwise (Coprime on s)\n⊢ ∀ i ∈ t, ¬s i = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.ChineseRemainder | {
"line": 174,
"column": 75
} | {
"line": 174,
"column": 86
} | {
"line": 174,
"column": 87
} | [
{
"pp": "ι : Type u_1\na s : ι → ℕ\nt : Finset ι\nhs : ∀ i ∈ t, s i ≠ 0\npp : (↑t).Pairwise (Coprime on s)\n⊢ {x | x ∈ t.val}.Pairwise (Coprime on s)",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Nat.Coprime",
"Function.onFun",
"setOf",
"Membership.mem",
"M... | [
"ι : Type u_1\na s : ι → ℕ\nt : Finset ι\nhs : ∀ i ∈ t, s i ≠ 0\npp : (↑t).Pairwise (Coprime on s)\n⊢ (↑t).Pairwise (Coprime on s)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Factorial.NatCast | {
"line": 35,
"column": 12
} | {
"line": 35,
"column": 23
} | {
"line": 35,
"column": 24
} | [
{
"pp": "case zero\nA : Type u_1\ninst✝ : Semiring A\nm : ℕ\nhn_fac : IsUnit ↑(m + 0)!\n⊢ IsUnit ↑m !",
"ppTerm": "?zero",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case zero\nA : Type u_1\ninst✝ : Semiring A\nm : ℕ\nhn_fac : IsUnit ↑(m + 0)!\n⊢ IsUnit ↑m !"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Factorial.NatCast | {
"line": 50,
"column": 4
} | {
"line": 50,
"column": 15
} | {
"line": 50,
"column": 16
} | [
{
"pp": "A : Type u_1\ninst✝³ : Semiring A\nK : Type u_2\ninst✝² : Semifield K\ninst✝¹ : CharZero K\ninst✝ : Algebra K A\nn : ℕ\nthis : IsUnit ↑n !\n⊢ IsUnit ↑n !",
"ppTerm": "?m.10",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"A : Type u_1\ninst✝³ : Semiring A\nK : Type u_2\ninst✝² : Semifield K\ninst✝¹ : CharZero K\ninst✝ : Algebra K A\nn : ℕ\nthis : IsUnit ↑n !\n⊢ IsUnit ↑n !"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Factorial.NatCast | {
"line": 83,
"column": 4
} | {
"line": 83,
"column": 20
} | {
"line": 83,
"column": 21
} | [
{
"pp": "A : Type u_1\ninst✝ : CommRing A\nn p : ℕ\nh✝ : p.Coprime n\nm : ℕ\nhm : ↑p ^ m = 0\na b : A\nh : ↑p ^ m * a + ↑n * b = 1\n⊢ ↑n * b = 1",
"ppTerm": "?m.58",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"A : Type u_1\ninst✝ : CommRing A\nn p : ℕ\nh✝ : p.Coprime n\nm : ℕ\nhm : ↑p ^ m = 0\na b : A\nh : ↑p ^ m * a + ↑n * b = 1\n⊢ ↑n * b = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Choose.Lucas | {
"line": 42,
"column": 4
} | {
"line": 42,
"column": 15
} | {
"line": 42,
"column": 16
} | [
{
"pp": "n k p : ℕ\ninst✝ : Fact (Nat.Prime p)\n⊢ (X + 1) ^ n = (X + 1) ^ (n % p) * (X ^ p + 1) ^ (n / p)",
"ppTerm": "?m.84",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"n k p : ℕ\ninst✝ : Fact (Nat.Prime p)\n⊢ (X + 1) ^ n = (X + 1) ^ (n % p) * (X ^ p + 1) ^ (n / p)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Fib.Zeckendorf | {
"line": 69,
"column": 22
} | {
"line": 69,
"column": 70
} | {
"line": 69,
"column": 70
} | [
{
"pp": "n a : ℕ\nl : List ℕ\nhn : ∀ a_1 ∈ (a :: l ++ [0]).head?, a_1 < n\nthis : ∀ b ∈ (l ++ [0]).head?, b < a - 1\nhl : ((∀ x ∈ l, x + 2 ≤ a) ∧ 2 ≤ a) ∧ IsChain (fun a b ↦ b + 2 ≤ a) (l ++ [0])\n⊢ fib (a - 1) + fib a ≤ fib n",
"ppTerm": "?m.179",
"assigned": true,
"usedConstants": [
"Eq.mpr"... | [
"n a : ℕ\nl : List ℕ\nhn : ∀ a_1 ∈ (a :: l ++ [0]).head?, a_1 < n\nthis : ∀ b ∈ (l ++ [0]).head?, b < a - 1\nhl : ((∀ x ∈ l, x + 2 ≤ a) ∧ 2 ≤ a) ∧ IsChain (fun a b ↦ b + 2 ≤ a) (l ++ [0])\n⊢ fib (a + 1) ≤ fib n"
] | ← fib_add_one (hl.1.2.trans_lt' zero_lt_two).ne' | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Nat.Fib.Zeckendorf | {
"line": 101,
"column": 14
} | {
"line": 101,
"column": 25
} | {
"line": 101,
"column": 26
} | [
{
"pp": "n : ℕ\nh : n.greatestFib = 0\n⊢ n = 0",
"ppTerm": "?m.10",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"n : ℕ\nh : n.greatestFib = 0\n⊢ n = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Factorization.Root | {
"line": 69,
"column": 83
} | {
"line": 70,
"column": 69
} | {
"line": 72,
"column": 0
} | [
{
"pp": "n : ℕ\nhn : n ≠ 0\na : ℕ\n⊢ n.floorRoot (a ^ n) = a",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"instPowNat",
"Finsupp.instPosSMulReflectLE",
"Eq.mpr",
"Finsupp.smulZeroClass",
"Finsupp.instFloorDiv",
"False",
"Nat.inst... | [] | by
simp [floorRoot_def, pos_iff_ne_zero.2, hn]; split_ifs <;> simp [*] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Nat.Fib.Zeckendorf | {
"line": 113,
"column": 4
} | {
"line": 113,
"column": 52
} | {
"line": 113,
"column": 53
} | [
{
"pp": "n : ℕ\nhn : n ≠ 0\n⊢ n.greatestFib - 1 ≠ 0",
"ppTerm": "?m.39",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.instCanonicallyOrderedAdd",
"Nat.instOrderedSub",
"Preorder.toLT",
"congrArg",
"_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.greatestFib_... | [
"n : ℕ\nhn : n ≠ 0\n⊢ 1 ≤ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Factorization.Root | {
"line": 145,
"column": 40
} | {
"line": 145,
"column": 51
} | {
"line": 145,
"column": 52
} | [
{
"pp": "n a : ℕ\nh : ¬(n = 0 ∨ a = 0)\np : ℕ\nhp : p ∈ (a.factorization ⌈/⌉ n).support\n⊢ Prime p ∧ p ∣ a ∧ ¬a = 0",
"ppTerm": "?m.60",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"n a : ℕ\nh : ¬(n = 0 ∨ a = 0)\np : ℕ\nhp : p ∈ (a.factorization ⌈/⌉ n).support\n⊢ Prime p ∧ p ∣ a ∧ ¬a = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Choose.Lucas | {
"line": 148,
"column": 4
} | {
"line": 148,
"column": 25
} | {
"line": 148,
"column": 26
} | [
{
"pp": "n p : ℕ\nhp : Fact (Nat.Prime p)\nhn : 0 < n\nhn₀ : n ≠ p ^ multiplicity p n\nm : ℕ\nh : ↑m ≡ 0 [ZMOD ↑p]\nhm : n = p ^ multiplicity p n * m\n⊢ p ^ (multiplicity p n + 1) ∣ p ^ multiplicity p n * m",
"ppTerm": "?m.151",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Semigroup.t... | [
"n p : ℕ\nhp : Fact (Nat.Prime p)\nhn : 0 < n\nhn₀ : n ≠ p ^ multiplicity p n\nm : ℕ\nh : ↑m ≡ 0 [ZMOD ↑p]\nhm : n = p ^ multiplicity p n * m\n⊢ p ^ multiplicity p n * p ∣ p ^ multiplicity p n * m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Choose.Lucas | {
"line": 210,
"column": 4
} | {
"line": 210,
"column": 15
} | {
"line": 210,
"column": 16
} | [
{
"pp": "n : ℕ\nh : IsPrimePow n\nne_zero : (Icc 1 (n - 1)).gcd n.choose ≠ 0\nisPrime : Nat.Prime n.minFac\n⊢ n.minFac ^ 1 ∣ (Icc 1 (n - 1)).gcd n.choose",
"ppTerm": "?m.92",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Dvd.dvd",
"Nat.choose",
"congrArg",
"Nat.instMo... | [
"n : ℕ\nh : IsPrimePow n\nne_zero : (Icc 1 (n - 1)).gcd n.choose ≠ 0\nisPrime : Nat.Prime n.minFac\n⊢ n.minFac ∣ (Icc 1 (n - 1)).gcd n.choose"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Choose.Lucas | {
"line": 204,
"column": 47
} | {
"line": 212,
"column": 66
} | {
"line": 214,
"column": 0
} | [
{
"pp": "n : ℕ\nh : IsPrimePow n\n⊢ (Icc 1 (n - 1)).gcd n.choose = n.minFac",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Finsupp.instFunLike",
"Nat.multiplicity_eq_factorization",
"Eq.mpr",
"Inhabited.default",
"Nat.instMulZeroClass",
... | [] | by
have ne_zero : (Icc 1 (n - 1)).gcd n.choose ≠ 0 :=
gcd_ne_zero_iff.mpr ⟨1, by simp; grind [IsPrimePow.two_le h]⟩
have isPrime := minFac_prime_iff.mpr (IsPrimePow.ne_one h)
have : multiplicity n.minFac ((Icc 1 (n - 1)).gcd n.choose) = 1 := by
refine multiplicity_eq_of_dvd_of_not_dvd ?_ (minFac_sq_ndvd_g... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Nat.Nth | {
"line": 172,
"column": 2
} | {
"line": 172,
"column": 70
} | {
"line": 173,
"column": 2
} | [
{
"pp": "p : ℕ → Prop\nx : ℕ\nh : p x\n⊢ ∃ n, (∀ (hf : (setOf p).Finite), n < #hf.toFinset) ∧ nth p n = x",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Set.finite_or_infinite",
"setOf",
"Set.Finite",
"Exists",
"And",
"Set.Finite.toFinset",
"Nat"... | [
"case refine_1\np : ℕ → Prop\nx : ℕ\nh : p x\nhf : (setOf p).Finite\n⊢ ∃ n, (∀ (hf : (setOf p).Finite), n < #hf.toFinset) ∧ nth p n = x",
"case refine_2\np : ℕ → Prop\nx : ℕ\nh : p x\nhf : (setOf p).Infinite\n⊢ ∃ n, (∀ (hf : (setOf p).Finite), n < #hf.toFinset) ∧ nth p n = x"
] | refine (setOf p).finite_or_infinite.elim (fun hf => ?_) fun hf => ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Data.Ordmap.Ordnode | {
"line": 194,
"column": 6
} | {
"line": 194,
"column": 15
} | {
"line": 195,
"column": 4
} | [
{
"pp": "case nil.nil\nα : Type u_1\nl : Ordnode α\nx : α\nr : Ordnode α\n⊢ Ordnode α",
"ppTerm": "?nil.nil",
"assigned": true,
"usedConstants": [
"Ordnode.singleton"
],
"usedFVars": [
"α",
"x"
],
"usedGoals": []
}
] | [] | exact ι x | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Data.Ordmap.Ordnode | {
"line": 194,
"column": 6
} | {
"line": 194,
"column": 15
} | {
"line": 195,
"column": 4
} | [
{
"pp": "case nil.nil\nα : Type u_1\nl : Ordnode α\nx : α\nr : Ordnode α\n⊢ Ordnode α",
"ppTerm": "?nil.nil",
"assigned": true,
"usedConstants": [
"Ordnode.singleton"
],
"usedFVars": [
"α",
"x"
],
"usedGoals": []
}
] | [] | exact ι x | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Ordmap.Ordnode | {
"line": 194,
"column": 6
} | {
"line": 194,
"column": 15
} | {
"line": 195,
"column": 4
} | [
{
"pp": "case nil.nil\nα : Type u_1\nl : Ordnode α\nx : α\nr : Ordnode α\n⊢ Ordnode α",
"ppTerm": "?nil.nil",
"assigned": true,
"usedConstants": [
"Ordnode.singleton"
],
"usedFVars": [
"α",
"x"
],
"usedGoals": []
}
] | [] | exact ι x | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Nat.Nth | {
"line": 501,
"column": 18
} | {
"line": 501,
"column": 29
} | {
"line": 501,
"column": 30
} | [
{
"pp": "p : ℕ → Prop\nn n' : ℕ\nhn' : n' ∈ setOf p\nhp : n' ∉ ↑(range n)\n⊢ n' ≥ n",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GE.ge",
"id",
"LE.le",
"instLENat",
"ge_iff_le._simp_1",
"Nat",
"Eq"
],
"usedFVars": [
... | [
"p : ℕ → Prop\nn n' : ℕ\nhn' : n' ∈ setOf p\nhp : n' ∉ ↑(range n)\n⊢ n ≤ n'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Ordmap.Ordnode | {
"line": 228,
"column": 6
} | {
"line": 228,
"column": 15
} | {
"line": 229,
"column": 4
} | [
{
"pp": "case nil.nil\nα : Type u_1\nl : Ordnode α\nx : α\nr : Ordnode α\n⊢ Ordnode α",
"ppTerm": "?nil.nil",
"assigned": true,
"usedConstants": [
"Ordnode.singleton"
],
"usedFVars": [
"α",
"x"
],
"usedGoals": []
}
] | [] | exact ι x | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Data.Ordmap.Ordnode | {
"line": 228,
"column": 6
} | {
"line": 228,
"column": 15
} | {
"line": 229,
"column": 4
} | [
{
"pp": "case nil.nil\nα : Type u_1\nl : Ordnode α\nx : α\nr : Ordnode α\n⊢ Ordnode α",
"ppTerm": "?nil.nil",
"assigned": true,
"usedConstants": [
"Ordnode.singleton"
],
"usedFVars": [
"α",
"x"
],
"usedGoals": []
}
] | [] | exact ι x | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Ordmap.Ordnode | {
"line": 228,
"column": 6
} | {
"line": 228,
"column": 15
} | {
"line": 229,
"column": 4
} | [
{
"pp": "case nil.nil\nα : Type u_1\nl : Ordnode α\nx : α\nr : Ordnode α\n⊢ Ordnode α",
"ppTerm": "?nil.nil",
"assigned": true,
"usedConstants": [
"Ordnode.singleton"
],
"usedFVars": [
"α",
"x"
],
"usedGoals": []
}
] | [] | exact ι x | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Ordmap.Ordnode | {
"line": 262,
"column": 6
} | {
"line": 262,
"column": 15
} | {
"line": 263,
"column": 4
} | [
{
"pp": "case nil.nil\nα : Type u_1\nl : Ordnode α\nx : α\nr : Ordnode α\n⊢ Ordnode α",
"ppTerm": "?nil.nil",
"assigned": true,
"usedConstants": [
"Ordnode.singleton"
],
"usedFVars": [
"α",
"x"
],
"usedGoals": []
}
] | [] | exact ι x | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Data.Ordmap.Ordnode | {
"line": 262,
"column": 6
} | {
"line": 262,
"column": 15
} | {
"line": 263,
"column": 4
} | [
{
"pp": "case nil.nil\nα : Type u_1\nl : Ordnode α\nx : α\nr : Ordnode α\n⊢ Ordnode α",
"ppTerm": "?nil.nil",
"assigned": true,
"usedConstants": [
"Ordnode.singleton"
],
"usedFVars": [
"α",
"x"
],
"usedGoals": []
}
] | [] | exact ι x | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Ordmap.Ordnode | {
"line": 262,
"column": 6
} | {
"line": 262,
"column": 15
} | {
"line": 263,
"column": 4
} | [
{
"pp": "case nil.nil\nα : Type u_1\nl : Ordnode α\nx : α\nr : Ordnode α\n⊢ Ordnode α",
"ppTerm": "?nil.nil",
"assigned": true,
"usedConstants": [
"Ordnode.singleton"
],
"usedFVars": [
"α",
"x"
],
"usedGoals": []
}
] | [] | exact ι x | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Num.ZNum | {
"line": 125,
"column": 6
} | {
"line": 125,
"column": 17
} | {
"line": 125,
"column": 18
} | [
{
"pp": "case pos\nα : Type u_1\ninst✝ : AddGroupWithOne α\na : PosNum\ne : a.succ.pred' = Num.pos a\nthis : ↑(-↑a) = -1 + ↑(-↑a + 1)\n⊢ -↑(Num.casesOn (Num.pos a) 1 bit1) = -↑a.succ + -↑a.succ + 1",
"ppTerm": "?pos",
"assigned": true,
"usedConstants": [
"neg_add_rev",
"AddGroup.toSubtra... | [
"case pos\nα : Type u_1\ninst✝ : AddGroupWithOne α\na : PosNum\ne : a.succ.pred' = Num.pos a\nthis : ↑(-↑a) = -1 + ↑(-↑a + 1)\n⊢ -↑a = -1 + (-↑a + 1)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Num.ZNum | {
"line": 134,
"column": 2
} | {
"line": 134,
"column": 30
} | {
"line": 134,
"column": 31
} | [
{
"pp": "α : Type u_1\ninst✝ : AddGroupWithOne α\nn : ZNum\nthis : ↑(-1 + ↑n + ↑n) = ↑(↑n + ↑n + -1)\n⊢ -(↑(-n) + ↑(-n) + 1) = ↑n + ↑n - 1",
"ppTerm": "?m.56",
"assigned": true,
"usedConstants": [
"neg_add_rev",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"castZNum",
"Neg... | [
"α : Type u_1\ninst✝ : AddGroupWithOne α\nn : ZNum\nthis : ↑(-1 + ↑n + ↑n) = ↑(↑n + ↑n + -1)\n⊢ -1 + (↑n + ↑n) = ↑n + (↑n + -1)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Num.ZNum | {
"line": 171,
"column": 4
} | {
"line": 171,
"column": 32
} | {
"line": 171,
"column": 33
} | [
{
"pp": "α : Type u_1\ninst✝ : AddGroupWithOne α\na b : PosNum\nthis : ↑(↑a + -↑b + (↑a + -↑b)) = ↑a + ↑a + (-↑b + -↑b)\n⊢ ↑a - ↑b + (↑a - ↑b) = ↑a.bit0 - ↑b.bit0",
"ppTerm": "?m.160",
"assigned": true,
"usedConstants": [
"neg_add_rev",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
... | [
"α : Type u_1\ninst✝ : AddGroupWithOne α\na b : PosNum\nthis : ↑(↑a + -↑b + (↑a + -↑b)) = ↑a + ↑a + (-↑b + -↑b)\n⊢ -↑b + (↑a + -↑b) = ↑a + (-↑b + -↑b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Num.ZNum | {
"line": 176,
"column": 4
} | {
"line": 176,
"column": 32
} | {
"line": 176,
"column": 33
} | [
{
"pp": "α : Type u_1\ninst✝ : AddGroupWithOne α\na b : PosNum\nthis : ↑(-↑b + (↑a + (-↑b + -1))) = ↑(↑a + -1 + (-↑b + -↑b))\n⊢ ↑a - ↑b + (↑a - ↑b) - 1 = ↑a.bit0 - ↑b.bit1",
"ppTerm": "?m.223",
"assigned": true,
"usedConstants": [
"neg_add_rev",
"AddGroup.toSubtractionMonoid",
"Eq.... | [
"α : Type u_1\ninst✝ : AddGroupWithOne α\na b : PosNum\nthis : ↑(-↑b + (↑a + (-↑b + -1))) = ↑(↑a + -1 + (-↑b + -↑b))\n⊢ -↑b + (↑a + (-↑b + -1)) = ↑a + (-1 + (-↑b + -↑b))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Num.ZNum | {
"line": 178,
"column": 4
} | {
"line": 178,
"column": 44
} | {
"line": 179,
"column": 4
} | [
{
"pp": "α : Type u_1\ninst✝ : AddGroupWithOne α\na b : PosNum\n⊢ ↑(a.bit1.sub' b.bit0) = ↑a.bit1 - ↑b.bit0",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"castZNum",
"NegZeroClass.toNeg",
"castPosNum",
"ZNum.bi... | [
"α : Type u_1\ninst✝ : AddGroupWithOne α\na b : PosNum\n⊢ ↑a - ↑b + (↑a - ↑b) + 1 = ↑a.bit1 - ↑b.bit0"
] | rw [sub', ZNum.cast_bit1, cast_sub' a b] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Num.ZNum | {
"line": 181,
"column": 4
} | {
"line": 181,
"column": 32
} | {
"line": 181,
"column": 33
} | [
{
"pp": "α : Type u_1\ninst✝ : AddGroupWithOne α\na b : PosNum\nthis : ↑(-↑b + (↑a + (-↑b + 1))) = ↑(↑a + 1 + (-↑b + -↑b))\n⊢ ↑a - ↑b + (↑a - ↑b) + 1 = ↑a.bit1 - ↑b.bit0",
"ppTerm": "?m.282",
"assigned": true,
"usedConstants": [
"neg_add_rev",
"AddGroup.toSubtractionMonoid",
"Eq.mp... | [
"α : Type u_1\ninst✝ : AddGroupWithOne α\na b : PosNum\nthis : ↑(-↑b + (↑a + (-↑b + 1))) = ↑(↑a + 1 + (-↑b + -↑b))\n⊢ -↑b + (↑a + (-↑b + 1)) = ↑a + (1 + (-↑b + -↑b))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Num.ZNum | {
"line": 185,
"column": 4
} | {
"line": 185,
"column": 32
} | {
"line": 185,
"column": 33
} | [
{
"pp": "α : Type u_1\ninst✝ : AddGroupWithOne α\na b : PosNum\nthis : ↑(-↑b + (↑a + -↑b)) = ↑a + (-↑b + -↑b)\n⊢ ↑a - ↑b + (↑a - ↑b) = ↑a.bit1 - ↑b.bit1",
"ppTerm": "?m.329",
"assigned": true,
"usedConstants": [
"neg_add_rev",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"castPo... | [
"α : Type u_1\ninst✝ : AddGroupWithOne α\na b : PosNum\nthis : ↑(-↑b + (↑a + -↑b)) = ↑a + (-↑b + -↑b)\n⊢ -↑b + (↑a + -↑b) = ↑a + (-↑b + -↑b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Num.ZNum | {
"line": 307,
"column": 60
} | {
"line": 307,
"column": 71
} | {
"line": 307,
"column": 71
} | [
{
"pp": "α : Type u_1\ninst✝ : NonAssocRing α\nm n : ZNum\n⊢ ↑m * ↑↑n = ↑m * ↑n",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Int.cast",
"Eq.mpr",
"castZNum",
"NegZeroClass.toNeg",
"HMul.hMul",
"AddMonoid.toAddSem... | [
"α : Type u_1\ninst✝ : NonAssocRing α\nm n : ZNum\n⊢ ↑m * ↑n = ↑m * ↑n"
] | cast_to_int | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Num.ZNum | {
"line": 356,
"column": 27
} | {
"line": 357,
"column": 40
} | {
"line": 359,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : Ring α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nm n : ZNum\n⊢ ↑m ≤ ↑n ↔ m ≤ n",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"castZNum",
"NegZeroClass.toNeg",
"Preorder.toLT",
"congrArg",
"PartialO... | [] | by
rw [← not_lt]; exact not_congr cast_lt | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Ordmap.Invariants | {
"line": 64,
"column": 4
} | {
"line": 64,
"column": 27
} | {
"line": 64,
"column": 28
} | [
{
"pp": "a b : ℕ\nh₁ : delta * a < b\nh₂ : delta * b < a\n⊢ a ≤ delta * (delta * a)",
"ppTerm": "?m.31",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"a b : ℕ\nh₁ : delta * a < b\nh₂ : delta * b < a\n⊢ a ≤ delta * (delta * a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Num.ZNum | {
"line": 559,
"column": 6
} | {
"line": 559,
"column": 17
} | {
"line": 559,
"column": 18
} | [
{
"pp": "case bit0.h₂\nd n : PosNum\nq r : Num\nIH : ↑r + ↑d * ↑q = ↑n ∧ ↑r < ↑d\n⊢ ↑r.bit0 < 2 * ↑d",
"ppTerm": "?bit0.h₂",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"castPosNum",
"Nat.instMulZeroClass",
"Preorder.toLT",
... | [
"case bit0.h₂\nd n : PosNum\nq r : Num\nIH : ↑r + ↑d * ↑q = ↑n ∧ ↑r < ↑d\n⊢ ↑r < ↑d"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Num.ZNum | {
"line": 592,
"column": 6
} | {
"line": 592,
"column": 20
} | {
"line": 594,
"column": 0
} | [
{
"pp": "case pos\na✝ : PosNum\n⊢ (pos a✝).mod 0 = pos a✝",
"ppTerm": "?pos",
"assigned": true,
"usedConstants": [
"Num",
"eq_self",
"Num.pos",
"of_eq_true",
"Eq"
],
"usedFVars": [
"a✝"
],
"usedGoals": []
}
] | [] | simp [Num.mod] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Num.ZNum | {
"line": 592,
"column": 6
} | {
"line": 592,
"column": 20
} | {
"line": 594,
"column": 0
} | [
{
"pp": "case pos\na✝ : PosNum\n⊢ (pos a✝).mod 0 = pos a✝",
"ppTerm": "?pos",
"assigned": true,
"usedConstants": [
"Num",
"eq_self",
"Num.pos",
"of_eq_true",
"Eq"
],
"usedFVars": [
"a✝"
],
"usedGoals": []
}
] | [] | simp [Num.mod] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Num.ZNum | {
"line": 592,
"column": 6
} | {
"line": 592,
"column": 20
} | {
"line": 594,
"column": 0
} | [
{
"pp": "case pos\na✝ : PosNum\n⊢ (pos a✝).mod 0 = pos a✝",
"ppTerm": "?pos",
"assigned": true,
"usedConstants": [
"Num",
"eq_self",
"Num.pos",
"of_eq_true",
"Eq"
],
"usedFVars": [
"a✝"
],
"usedGoals": []
}
] | [] | simp [Num.mod] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Num.ZNum | {
"line": 681,
"column": 10
} | {
"line": 681,
"column": 30
} | {
"line": 681,
"column": 31
} | [
{
"pp": "n : PosNum\nd : ZNum\n⊢ ↑(Num.pos n % d.abs) = ↑(pos n) % ↑d",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"castZNum",
"Nat.instMulZeroClass",
"Nat.instOne",
"congrArg",
"AddGroupWithOne.toAddMonoidWithOne",
"ZNum.abs",
"... | [
"n : PosNum\nd : ZNum\n⊢ ↑↑(Num.pos n % d.abs) = ↑(pos n) % ↑d"
] | ← Num.to_nat_to_int, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Num.ZNum | {
"line": 685,
"column": 10
} | {
"line": 685,
"column": 30
} | {
"line": 685,
"column": 31
} | [
{
"pp": "n : PosNum\nd : ZNum\n⊢ ↑d.abs - ↑(n.pred' % d.abs).succ = ↑(neg n) % ↑d",
"ppTerm": "?m.45",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"castZNum",
"Nat.instMulZeroClass",
"Nat.instOne",
"AddMonoid.toAddSemigroup",
... | [
"n : PosNum\nd : ZNum\n⊢ ↑↑d.abs - ↑(n.pred' % d.abs).succ = ↑(neg n) % ↑d"
] | ← Num.to_nat_to_int, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Num.ZNum | {
"line": 685,
"column": 41
} | {
"line": 685,
"column": 61
} | {
"line": 685,
"column": 62
} | [
{
"pp": "n : PosNum\nd : ZNum\n⊢ ↑↑d.abs - ↑(n.pred' % d.abs).succ = -↑n % ↑d",
"ppTerm": "?m.86",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"castZNum",
"castPosNum",
"Nat.instMulZeroClass",
"Nat.instOne",
"AddMonoid.toAd... | [
"n : PosNum\nd : ZNum\n⊢ ↑↑d.abs - ↑↑(n.pred' % d.abs).succ = -↑n % ↑d"
] | ← Num.to_nat_to_int, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Ordmap.Invariants | {
"line": 548,
"column": 4
} | {
"line": 551,
"column": 69
} | {
"line": 553,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : LE α\ninst✝¹ : Std.Total fun x1 x2 ↦ x1 ≤ x2\ninst✝ : DecidableLE α\nx : α\nsize✝ : ℕ\nl : Ordnode α\ny : α\nr : Ordnode α\n⊢ (Ordnode.insert x (node size✝ l y r)).dual = Ordnode.insert x (node size✝ l y r).dual",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": ... | [] | have : @cmpLE αᵒᵈ _ _ x y = cmpLE y x := rfl
rw [Ordnode.insert, dual, Ordnode.insert, this, ← cmpLE_swap x y]
cases cmpLE x y <;>
simp [Ordering.swap, dual_balanceL, dual_balanceR, dual_insert] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Ordmap.Invariants | {
"line": 548,
"column": 4
} | {
"line": 551,
"column": 69
} | {
"line": 553,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : LE α\ninst✝¹ : Std.Total fun x1 x2 ↦ x1 ≤ x2\ninst✝ : DecidableLE α\nx : α\nsize✝ : ℕ\nl : Ordnode α\ny : α\nr : Ordnode α\n⊢ (Ordnode.insert x (node size✝ l y r)).dual = Ordnode.insert x (node size✝ l y r).dual",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": ... | [] | have : @cmpLE αᵒᵈ _ _ x y = cmpLE y x := rfl
rw [Ordnode.insert, dual, Ordnode.insert, this, ← cmpLE_swap x y]
cases cmpLE x y <;>
simp [Ordering.swap, dual_balanceL, dual_balanceR, dual_insert] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.PNat.Factors | {
"line": 312,
"column": 4
} | {
"line": 312,
"column": 46
} | {
"line": 313,
"column": 4
} | [
{
"pp": "case mpr\nm n : ℕ+\nh : m ∣ n\n⊢ m.factorMultiset ≤ n.factorMultiset",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"PNat.factorMultiset_mul",
"HMul.hMul",
"instDistribLatticePrimeMultiset",
"congrArg",
"instAddCommMonoidPrimeMultiset"... | [
"case mpr\nm n : ℕ+\nh : m ∣ n\n⊢ m.factorMultiset ≤ m.factorMultiset + (n.divExact m).factorMultiset"
] | rw [← mul_div_exact h, factorMultiset_mul] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.PNat.Xgcd | {
"line": 291,
"column": 4
} | {
"line": 291,
"column": 17
} | {
"line": 292,
"column": 4
} | [
{
"pp": "case fst\nu : XgcdType\nhr✝ : u.r ≠ 0\nha : u.r + ↑u.b * u.q = ↑u.a := rq_eq u\nhr : u.r - 1 + 1 = u.r := Eq.trans (add_comm (u.r - 1) 1) (add_tsub_cancel_of_le (Nat.pos_of_ne_zero hr✝))\n⊢ (u.y * u.q + ↑u.z) * ↑u.b + u.y * (u.r - 1 + 1) = u.y * ↑u.a + ↑u.z * ↑u.b",
"ppTerm": "?fst",
"assigned"... | [
"case fst\nu : XgcdType\nhr✝ : u.r ≠ 0\nha : u.r + ↑u.b * u.q = ↑u.a := rq_eq u\nhr : u.r - 1 + 1 = u.r := Eq.trans (add_comm (u.r - 1) 1) (add_tsub_cancel_of_le (Nat.pos_of_ne_zero hr✝))\n⊢ (u.y * u.q + ↑u.z) * ↑u.b + u.y * u.r = u.y * (u.r + ↑u.b * u.q) + ↑u.z * ↑u.b"
] | rw [← ha, hr] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.PNat.Xgcd | {
"line": 294,
"column": 4
} | {
"line": 294,
"column": 17
} | {
"line": 295,
"column": 4
} | [
{
"pp": "case snd\nu : XgcdType\nhr✝ : u.r ≠ 0\nha : u.r + ↑u.b * u.q = ↑u.a := rq_eq u\nhr : u.r - 1 + 1 = u.r := Eq.trans (add_comm (u.r - 1) 1) (add_tsub_cancel_of_le (Nat.pos_of_ne_zero hr✝))\n⊢ (↑u.w * u.q + u.x) * ↑u.b + ↑u.w * (u.r - 1 + 1) = ↑u.w * ↑u.a + u.x * ↑u.b",
"ppTerm": "?snd",
"assigned... | [
"case snd\nu : XgcdType\nhr✝ : u.r ≠ 0\nha : u.r + ↑u.b * u.q = ↑u.a := rq_eq u\nhr : u.r - 1 + 1 = u.r := Eq.trans (add_comm (u.r - 1) 1) (add_tsub_cancel_of_le (Nat.pos_of_ne_zero hr✝))\n⊢ (↑u.w * u.q + u.x) * ↑u.b + ↑u.w * u.r = ↑u.w * (u.r + ↑u.b * u.q) + u.x * ↑u.b"
] | rw [← ha, hr] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.PNat.Xgcd | {
"line": 293,
"column": 2
} | {
"line": 295,
"column": 8
} | {
"line": 297,
"column": 0
} | [
{
"pp": "case snd\nu : XgcdType\nhr✝ : u.r ≠ 0\nha : u.r + ↑u.b * u.q = ↑u.a := ⋯\nhr : u.r - 1 + 1 = u.r := ⋯\n⊢ u.step.v.2 = u.v.swap.2",
"ppTerm": "?snd",
"assigned": true,
"usedConstants": [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"PNat.val",
"Eq.mpr",
"NonAssocSemiring... | [] | · change ((u.w * u.q + u.x) * u.b + u.w * (u.r - 1 + 1) : ℕ) = u.w * u.a + u.x * u.b
rw [← ha, hr]
ring | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Data.Ordmap.Ordset | {
"line": 324,
"column": 4
} | {
"line": 325,
"column": 86
} | {
"line": 327,
"column": 0
} | [
{
"pp": "case inr.inr\nα : Type u_2\nl r : Ordnode α\nr' : ℕ\nhr : r.size.dist r' ≤ 1\nleft✝ : l.size ≤ delta * r'\nh₂ : r' ≤ delta * l.size\n⊢ r.size ≤ 3 * (l.size + 1)",
"ppTerm": "?inr.inr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.mul_succ",
"Nat.instIsOrderedAddMono... | [] | rw [Nat.mul_succ]
exact le_trans (Nat.dist_tri_right' _ _) (add_le_add h₂ (le_trans hr (by decide))) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Ordmap.Ordset | {
"line": 324,
"column": 4
} | {
"line": 325,
"column": 86
} | {
"line": 327,
"column": 0
} | [
{
"pp": "case inr.inr\nα : Type u_2\nl r : Ordnode α\nr' : ℕ\nhr : r.size.dist r' ≤ 1\nleft✝ : l.size ≤ delta * r'\nh₂ : r' ≤ delta * l.size\n⊢ r.size ≤ 3 * (l.size + 1)",
"ppTerm": "?inr.inr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.mul_succ",
"Nat.instIsOrderedAddMono... | [] | rw [Nat.mul_succ]
exact le_trans (Nat.dist_tri_right' _ _) (add_le_add h₂ (le_trans hr (by decide))) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Ordmap.Invariants | {
"line": 685,
"column": 24
} | {
"line": 685,
"column": 33
} | {
"line": 685,
"column": 33
} | [
{
"pp": "α : Type u_1\nl : Ordnode α\nx₁ x₂ : α\nr₁ r₂ : Ordnode α\nH : Raised r₁.size r₂.size\n⊢ Raised (l.size + r₁.size + 1) (l.node' x₂ r₂).size",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Ordnode.node'",
"Eq.mpr",
"Ordnode.size_node",
"congrArg",
"id... | [
"α : Type u_1\nl : Ordnode α\nx₁ x₂ : α\nr₁ r₂ : Ordnode α\nH : Raised r₁.size r₂.size\n⊢ Raised (l.size + r₁.size + 1) (l.size + r₂.size + 1)"
] | size_node | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.QPF.Multivariate.Constructions.Cofix | {
"line": 101,
"column": 6
} | {
"line": 101,
"column": 35
} | {
"line": 101,
"column": 35
} | [
{
"pp": "n : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα β : TypeVec.{u} n\ng : α ⟹ β\n⊢ ∀ (a b : (P F).M α), Mcongr a b → Quot.mk Mcongr (g <$$> a) = Quot.mk Mcongr (g <$$> b)",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"instOfNatNat",
"And.casesOn",
"instHAd... | [
"n : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα β : TypeVec.{u} n\ng : α ⟹ β\naa₁ aa₂ : (P F).M α\nr : (P F).M α → (P F).M α → Prop\npr : IsPrecongr r\nra₁a₂ : r aa₁ aa₂\n⊢ Quot.mk Mcongr (g <$$> aa₁) = Quot.mk Mcongr (g <$$> aa₂)"
] | rintro aa₁ aa₂ ⟨r, pr, ra₁a₂⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro | Lean.Parser.Tactic.rintro |
Mathlib.Data.QPF.Multivariate.Constructions.Cofix | {
"line": 115,
"column": 64
} | {
"line": 115,
"column": 78
} | {
"line": 115,
"column": 78
} | [
{
"pp": "case h.left\nn : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα β : TypeVec.{u} n\ng : α ⟹ β\naa₁ aa₂ : (P F).M α\nr : (P F).M α → (P F).M α → Prop\npr : IsPrecongr r\nra₁a₂✝ : r aa₁ aa₂\nr' : (P F).M β → (P F).M β → Prop := fun b₁ b₂ ↦ ∃ a₁ a₂, r a₁ a₂ ∧ b₁ = g <$$> a₁ ∧ b₂ = g <$$> a₂\nb₁ b₂ : (... | [
"case h.left\nn : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα β : TypeVec.{u} n\ng : α ⟹ β\naa₁ aa₂ : (P F).M α\nr : (P F).M α → (P F).M α → Prop\npr : IsPrecongr r\nra₁a₂✝ : r aa₁ aa₂\nr' : (P F).M β → (P F).M β → Prop := fun b₁ b₂ ↦ ∃ a₁ a₂, r a₁ a₂ ∧ b₁ = g <$$> a₁ ∧ b₂ = g <$$> a₂\nb₁ b₂ : (P F).M β\na₁... | ← q.P.comp_map | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.QPF.Univariate.Basic | {
"line": 103,
"column": 4
} | {
"line": 103,
"column": 29
} | {
"line": 104,
"column": 4
} | [
{
"pp": "case mp\nF : Type u → Type v\nq : QPF F\nα : Type u\np : α → Prop\nx : F α\ny : F (Subtype p)\nhy : Subtype.val <$> y = x\na : (P F).A\nf : (P F).B a → Subtype p\nh : repr y = ⟨a, f⟩\n⊢ ∃ a f, x = abs ⟨a, f⟩ ∧ ∀ (i : (P F).B a), p (f i)",
"ppTerm": "?mp",
"assigned": true,
"usedConstants": ... | [
"case h\nF : Type u → Type v\nq : QPF F\nα : Type u\np : α → Prop\nx : F α\ny : F (Subtype p)\nhy : Subtype.val <$> y = x\na : (P F).A\nf : (P F).B a → Subtype p\nh : repr y = ⟨a, f⟩\n⊢ x = abs ⟨a, fun i ↦ ↑(f i)⟩ ∧ ∀ (i : (P F).B a), p ((fun i ↦ ↑(f i)) i)"
] | use a, fun i => (f i).val | Mathlib.Tactic._aux_Mathlib_Tactic_Use___elabRules_Mathlib_Tactic_useSyntax_1 | Mathlib.Tactic.useSyntax |
Mathlib.Data.QPF.Univariate.Basic | {
"line": 197,
"column": 2
} | {
"line": 201,
"column": 67
} | {
"line": 203,
"column": 0
} | [
{
"pp": "F : Type u → Type v\nq : QPF F\nx y : (P F).W\n⊢ Wequiv x y → Wequiv y x",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"QPF.Wequiv.trans",
"PFunctor.A",
"QPF.Wequiv.rec",
"PFunctor.B",
"PFunctor.W",
"QPF.Wequiv",
"QPF.P",
"QPF.Wequi... | [] | intro h
induction h with
| ind a f f' _ ih => exact Wequiv.ind _ _ _ ih
| abs a f a' f' h => exact Wequiv.abs _ _ _ _ h.symm
| trans x y z _ _ ih₁ ih₂ => exact QPF.Wequiv.trans _ _ _ ih₂ ih₁ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.QPF.Univariate.Basic | {
"line": 197,
"column": 2
} | {
"line": 201,
"column": 67
} | {
"line": 203,
"column": 0
} | [
{
"pp": "F : Type u → Type v\nq : QPF F\nx y : (P F).W\n⊢ Wequiv x y → Wequiv y x",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"QPF.Wequiv.trans",
"PFunctor.A",
"QPF.Wequiv.rec",
"PFunctor.B",
"PFunctor.W",
"QPF.Wequiv",
"QPF.P",
"QPF.Wequi... | [] | intro h
induction h with
| ind a f f' _ ih => exact Wequiv.ind _ _ _ ih
| abs a f a' f' h => exact Wequiv.abs _ _ _ _ h.symm
| trans x y z _ _ ih₁ ih₂ => exact QPF.Wequiv.trans _ _ _ ih₂ ih₁ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.QPF.Univariate.Basic | {
"line": 251,
"column": 4
} | {
"line": 251,
"column": 21
} | {
"line": 252,
"column": 2
} | [
{
"pp": "case mk\nF : Type u → Type u\nq : QPF F\nα : Type u\ng : F α → α\nx✝¹ : F (Fix F)\nx✝ : Fix F\nx : (P F).W\n⊢ Wequiv (Quotient.lift Wrepr ⋯ (Quot.mk (⇑Wsetoid) x)) x",
"ppTerm": "?mk",
"assigned": true,
"usedConstants": [
"QPF.Wrepr_equiv"
],
"usedFVars": [
"F",
"q... | [] | apply Wrepr_equiv | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Data.QPF.Univariate.Basic | {
"line": 269,
"column": 2
} | {
"line": 269,
"column": 19
} | {
"line": 271,
"column": 0
} | [
{
"pp": "F : Type u → Type u\nq : QPF F\na : (P F).A\nf : (P F).B a → (P F).W\nthis : mk (abs ⟨a, fun x ↦ ⟦f x⟧⟩) = ⟦Wrepr (WType.mk a f)⟧\n⊢ Wsetoid (Wrepr (WType.mk a f)) (WType.mk a f)",
"ppTerm": "?m.86",
"assigned": true,
"usedConstants": [
"PFunctor.A",
"PFunctor.B",
"QPF.Wre... | [] | apply Wrepr_equiv | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Data.QPF.Univariate.Basic | {
"line": 607,
"column": 2
} | {
"line": 611,
"column": 12
} | {
"line": 612,
"column": 2
} | [
{
"pp": "case mp\nF : Type u → Type u\nq : QPF F\nh : IsUniform\nα : Type u\nx : F α\np : α → Prop\na : (P F).A\nf : (P F).B a → α\n⊢ (∃ a_1 f_1, abs ⟨a, f⟩ = abs ⟨a_1, f_1⟩ ∧ ∀ (i : (P F).B a_1), p (f_1 i)) → ∀ u ∈ supp (abs ⟨a, f⟩), p u",
"ppTerm": "?mp",
"assigned": true,
"usedConstants": [
... | [
"case mpr\nF : Type u → Type u\nq : QPF F\nh : IsUniform\nα : Type u\nx : F α\np : α → Prop\na : (P F).A\nf : (P F).B a → α\n⊢ (∀ u ∈ supp (abs ⟨a, f⟩), p u) → ∃ a_2 f_1, abs ⟨a, f⟩ = abs ⟨a_2, f_1⟩ ∧ ∀ (i : (P F).B a_2), p (f_1 i)"
] | · rintro ⟨a', f', abseq, hf⟩ u
rw [supp_eq_of_isUniform h, h _ _ _ _ abseq]
rintro ⟨i, _, hi⟩
rw [← hi]
apply hf | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
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