module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Algebra.Group.Subgroup.Basic | {
"line": 1125,
"column": 31
} | {
"line": 1125,
"column": 53
} | {
"line": 1125,
"column": 54
} | [
{
"pp": "G✝ : Type u_1\nG' : Type u_2\nG'' : Type u_3\ninst✝⁷ : Group G✝\ninst✝⁶ : Group G'\ninst✝⁵ : Group G''\nA : Type u_4\ninst✝⁴ : AddGroup A\nN : Type u_5\ninst✝³ : Group N\nM : Type u_6\ninst✝² : AddGroup M\nI : AddSubgroup M\nG : Type u_7\ninst✝¹ : Group G\ninst✝ : MulAction G M\na b : G\nha : a ∈ {σ | ... | [
"G✝ : Type u_1\nG' : Type u_2\nG'' : Type u_3\ninst✝⁷ : Group G✝\ninst✝⁶ : Group G'\ninst✝⁵ : Group G''\nA : Type u_4\ninst✝⁴ : AddGroup A\nN : Type u_5\ninst✝³ : Group N\nM : Type u_6\ninst✝² : AddGroup M\nI : AddSubgroup M\nG : Type u_7\ninst✝¹ : Group G\ninst✝ : MulAction G M\na b : G\nha : a ∈ {σ | ∀ (x : M), σ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.BigOperators.Group.List | {
"line": 33,
"column": 23
} | {
"line": 33,
"column": 51
} | {
"line": 33,
"column": 52
} | [
{
"pp": "case cons\nM : Type u_3\ninst✝³ : Monoid M\ninst✝² : Preorder M\ninst✝¹ : MulRightMono M\ninst✝ : MulLeftMono M\nl₁ l₂ : List M\na✝ b✝ : M\nl₁✝ l₂✝ : List M\nhab : a✝ ≤ b✝\nih : Forall₂ (fun x1 x2 ↦ x1 ≤ x2) l₁✝ l₂✝\nih' : l₁✝.prod ≤ l₂✝.prod\n⊢ (a✝ :: l₁✝).prod ≤ (b✝ :: l₂✝).prod",
"ppTerm": "?con... | [
"case cons\nM : Type u_3\ninst✝³ : Monoid M\ninst✝² : Preorder M\ninst✝¹ : MulRightMono M\ninst✝ : MulLeftMono M\nl₁ l₂ : List M\na✝ b✝ : M\nl₁✝ l₂✝ : List M\nhab : a✝ ≤ b✝\nih : Forall₂ (fun x1 x2 ↦ x1 ≤ x2) l₁✝ l₂✝\nih' : l₁✝.prod ≤ l₂✝.prod\n⊢ a✝ * l₁✝.prod ≤ b✝ * l₂✝.prod"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Subgroup.Basic | {
"line": 1127,
"column": 26
} | {
"line": 1127,
"column": 37
} | {
"line": 1127,
"column": 38
} | [
{
"pp": "G✝ : Type u_1\nG' : Type u_2\nG'' : Type u_3\ninst✝⁷ : Group G✝\ninst✝⁶ : Group G'\ninst✝⁵ : Group G''\nA : Type u_4\ninst✝⁴ : AddGroup A\nN : Type u_5\ninst✝³ : Group N\nM : Type u_6\ninst✝² : AddGroup M\nI : AddSubgroup M\nG : Type u_7\ninst✝¹ : Group G\ninst✝ : MulAction G M\na : G\nha : a ∈ {σ | ∀ ... | [
"G✝ : Type u_1\nG' : Type u_2\nG'' : Type u_3\ninst✝⁷ : Group G✝\ninst✝⁶ : Group G'\ninst✝⁵ : Group G''\nA : Type u_4\ninst✝⁴ : AddGroup A\nN : Type u_5\ninst✝³ : Group N\nM : Type u_6\ninst✝² : AddGroup M\nI : AddSubgroup M\nG : Type u_7\ninst✝¹ : Group G\ninst✝ : MulAction G M\na : G\nha : a ∈ {σ | ∀ (x : M), σ •... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.BigOperators.Group.List | {
"line": 94,
"column": 2
} | {
"line": 94,
"column": 56
} | {
"line": 94,
"column": 57
} | [
{
"pp": "M : Type u_3\ninst✝³ : Monoid M\ninst✝² : Preorder M\ninst✝¹ : MulRightMono M\ninst✝ : MulLeftMono M\nl : List M\nn : M\nh : ∀ (x : M), x ∈ l → x ≤ n\n⊢ l.prod ≤ n ^ l.length",
"ppTerm": "?m.21",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"M : Type u_3\ninst✝³ : Monoid M\ninst✝² : Preorder M\ninst✝¹ : MulRightMono M\ninst✝ : MulLeftMono M\nl : List M\nn : M\nh : ∀ (x : M), x ∈ l → x ≤ n\n⊢ l.prod ≤ n ^ l.length"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Embedding.Set | {
"line": 108,
"column": 8
} | {
"line": 108,
"column": 30
} | {
"line": 109,
"column": 8
} | [
{
"pp": "case inr.hx\nα : Type u_1\np q : α → Prop\ninst✝ : DecidablePred p\nh : Disjoint p q\nx : { x // q x }\n⊢ ¬p ↑((Subtype.impEmbedding q (fun x ↦ p x ∨ q x) ⋯) x)",
"ppTerm": "?inr.hx",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Subtype.impEmbedding",
... | [
"case inr.hx\nα : Type u_1\np q : α → Prop\ninst✝ : DecidablePred p\nh : Disjoint p q\nx : { x // q x }\n⊢ ¬p ↑x"
] | suffices ¬p x by simpa | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticSuffices__1 | Lean.Parser.Tactic.tacticSuffices_ |
Mathlib.Logic.Embedding.Set | {
"line": 110,
"column": 8
} | {
"line": 110,
"column": 19
} | {
"line": 110,
"column": 20
} | [
{
"pp": "case inr.hx\nα : Type u_1\np q : α → Prop\ninst✝ : DecidablePred p\nh : Disjoint p q\nx : { x // q x }\nhp : p ↑x\n⊢ False",
"ppTerm": "?inr.hx",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case inr.hx\nα : Type u_1\np q : α → Prop\ninst✝ : DecidablePred p\nh : Disjoint p q\nx : { x // q x }\nhp : p ↑x\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Embedding.Set | {
"line": 134,
"column": 6
} | {
"line": 134,
"column": 17
} | {
"line": 134,
"column": 18
} | [
{
"pp": "case inl.inr\nα : Type u_1\nι : Type u_2\ns t r : Set α\nh : Disjoint s t\na : α\nha : a ∈ s\nb : α\nhb : b ∈ t\n⊢ Sum.elim Subtype.val Subtype.val (Sum.inl ⟨a, ha⟩) = Sum.elim Subtype.val Subtype.val (Sum.inr ⟨b, hb⟩) →\n Sum.inl ⟨a, ha⟩ = Sum.inr ⟨b, hb⟩",
"ppTerm": "?inl.inr",
"assigned":... | [
"case inl.inr\nα : Type u_1\nι : Type u_2\ns t r : Set α\nh : Disjoint s t\na : α\nha : a ∈ s\nb : α\nhb : b ∈ t\n⊢ ¬a = b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Embedding.Set | {
"line": 135,
"column": 6
} | {
"line": 135,
"column": 17
} | {
"line": 135,
"column": 18
} | [
{
"pp": "case inr.inl\nα : Type u_1\nι : Type u_2\ns t r : Set α\nh : Disjoint s t\na : α\nha : a ∈ t\nb : α\nhb : b ∈ s\n⊢ Sum.elim Subtype.val Subtype.val (Sum.inr ⟨a, ha⟩) = Sum.elim Subtype.val Subtype.val (Sum.inl ⟨b, hb⟩) →\n Sum.inr ⟨a, ha⟩ = Sum.inl ⟨b, hb⟩",
"ppTerm": "?inr.inl",
"assigned":... | [
"case inr.inl\nα : Type u_1\nι : Type u_2\ns t r : Set α\nh : Disjoint s t\na : α\nha : a ∈ t\nb : α\nhb : b ∈ s\n⊢ ¬a = b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.BigOperators.Group.List | {
"line": 218,
"column": 11
} | {
"line": 218,
"column": 22
} | {
"line": 218,
"column": 23
} | [
{
"pp": "case nil\nM : Type u_3\nN : Type u_4\ninst✝² : AddZeroClass M\ninst✝¹ : Zero N\ninst✝ : LinearOrder N\nf : M → N\nh0 : f 0 ≤ 0\nhadd : ∀ (x y : M), f (x + y) ≤ max (f x) (f y)\n⊢ f [].sum ≤ foldr max 0 (map f [])",
"ppTerm": "?nil",
"assigned": true,
"usedConstants": [
"Lattice.toSemi... | [
"case nil\nM : Type u_3\nN : Type u_4\ninst✝² : AddZeroClass M\ninst✝¹ : Zero N\ninst✝ : LinearOrder N\nf : M → N\nh0 : f 0 ≤ 0\nhadd : ∀ (x y : M), f (x + y) ≤ max (f x) (f y)\n⊢ f 0 ≤ 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.BigOperators.Group.List | {
"line": 227,
"column": 20
} | {
"line": 227,
"column": 31
} | {
"line": 227,
"column": 32
} | [
{
"pp": "M : Type u_3\ninst✝² : CommMonoid M\ninst✝¹ : Preorder M\ninst✝ : IsOrderedMonoid M\nb : M\nh : ∀ (x : M), x ∈ [b] → 1 < x\nx✝ : [b] ≠ []\n⊢ 1 < [b].prod",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"Preorder.toLT",
"Monoid.toMu... | [
"M : Type u_3\ninst✝² : CommMonoid M\ninst✝¹ : Preorder M\ninst✝ : IsOrderedMonoid M\nb : M\nh : ∀ (x : M), x ∈ [b] → 1 < x\nx✝ : [b] ≠ []\n⊢ 1 < b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.BigOperators.Group.List | {
"line": 242,
"column": 22
} | {
"line": 242,
"column": 37
} | {
"line": 242,
"column": 37
} | [
{
"pp": "case cons\nM : Type u_3\ninst✝² : CommMonoid M\ninst✝¹ : Preorder M\ninst✝ : IsOrderedMonoid M\nhead✝ : M\ntail✝ : List M\ntail_ih✝ : (∀ (x : M), x ∈ tail✝ → 1 ≤ x) → ∀ (x : M), x ∈ tail✝ → x ≤ tail✝.prod\nhl₁ : ∀ (x : M), x ∈ head✝ :: tail✝ → 1 ≤ x\n⊢ ∀ (x : M), x ∈ head✝ :: tail✝ → x ≤ head✝ * tail✝.... | [
"case cons\nM : Type u_3\ninst✝² : CommMonoid M\ninst✝¹ : Preorder M\ninst✝ : IsOrderedMonoid M\nhead✝ : M\ntail✝ : List M\ntail_ih✝ : (∀ (x : M), x ∈ tail✝ → 1 ≤ x) → ∀ (x : M), x ∈ tail✝ → x ≤ tail✝.prod\nhl₁ : 1 ≤ head✝ ∧ ∀ (x : M), x ∈ tail✝ → 1 ≤ x\n⊢ head✝ ≤ head✝ * tail✝.prod ∧ ∀ (x : M), x ∈ tail✝ → x ≤ hea... | forall_mem_cons | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Algebra.Group.Submonoid.Membership | {
"line": 61,
"column": 4
} | {
"line": 61,
"column": 55
} | {
"line": 61,
"column": 56
} | [
{
"pp": "M : Type u_1\ninst✝¹ : MulOneClass M\nι : Sort u_4\ninst✝ : Nonempty ι\nS : ι → Submonoid M\nhS : Directed (fun x1 x2 ↦ x1 ≤ x2) S\nx : M\nthis : x ∈ closure (⋃ i, ↑(S i)) → ∃ i, x ∈ S i\n⊢ x ∈ ⨆ i, S i → ∃ i, x ∈ S i",
"ppTerm": "?m.58",
"assigned": false,
"usedConstants": [],
"usedFVa... | [
"M : Type u_1\ninst✝¹ : MulOneClass M\nι : Sort u_4\ninst✝ : Nonempty ι\nS : ι → Submonoid M\nhS : Directed (fun x1 x2 ↦ x1 ≤ x2) S\nx : M\nthis : x ∈ closure (⋃ i, ↑(S i)) → ∃ i, x ∈ S i\n⊢ x ∈ ⨆ i, S i → ∃ i, x ∈ S i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Submonoid.Membership | {
"line": 63,
"column": 2
} | {
"line": 63,
"column": 32
} | {
"line": 64,
"column": 2
} | [
{
"pp": "M : Type u_1\ninst✝¹ : MulOneClass M\nι : Sort u_4\ninst✝ : Nonempty ι\nS : ι → Submonoid M\nhS : Directed (fun x1 x2 ↦ x1 ≤ x2) S\nx : M\nhx : x ∈ closure (⋃ i, ↑(S i))\n⊢ ∀ (x y : M),\n x ∈ closure (⋃ i, ↑(S i)) → y ∈ closure (⋃ i, ↑(S i)) → (∃ i, x ∈ S i) → (∃ i, y ∈ S i) → ∃ i, x * y ∈ S i",
... | [
"M : Type u_1\ninst✝¹ : MulOneClass M\nι : Sort u_4\ninst✝ : Nonempty ι\nS : ι → Submonoid M\nhS : Directed (fun x1 x2 ↦ x1 ≤ x2) S\nx✝ : M\nhx : x✝ ∈ closure (⋃ i, ↑(S i))\nx y : M\nhx✝ : x ∈ closure (⋃ i, ↑(S i))\nhy✝ : y ∈ closure (⋃ i, ↑(S i))\ni : ι\nhi : x ∈ S i\nj : ι\nhj : y ∈ S j\n⊢ ∃ i, x * y ∈ S i"
] | rintro x y _ _ ⟨i, hi⟩ ⟨j, hj⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro | Lean.Parser.Tactic.rintro |
Mathlib.Algebra.Group.Submonoid.Membership | {
"line": 234,
"column": 6
} | {
"line": 234,
"column": 35
} | {
"line": 234,
"column": 36
} | [
{
"pp": "M : Type u_1\ninst✝¹ : Monoid M\nS : Submonoid M\ninst✝ : Fintype ↥S\nh : card ↥S ≤ 1\nx : M\nhx : x ∈ S\n⊢ x = 1",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"M : Type u_1\ninst✝¹ : Monoid M\nS : Submonoid M\ninst✝ : Fintype ↥S\nh : card ↥S ≤ 1\nx : M\nhx : x ∈ S\n⊢ x = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Submonoid.Membership | {
"line": 349,
"column": 6
} | {
"line": 349,
"column": 36
} | {
"line": 350,
"column": 6
} | [
{
"pp": "case inr.inl\nM : Type u_1\ninst✝ : Monoid M\na✝ : M\nha : IsIdempotentElem a✝\n⊢ a✝ * 1 ∈ {1, a✝}",
"ppTerm": "?inr.inl",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"Membership.mem",
... | [
"case inr.inr\nM : Type u_1\ninst✝ : Monoid M\nb✝ : M\nha : IsIdempotentElem b✝\n⊢ b✝ * b✝ ∈ {1, b✝}"
] | · rw [mul_one]; exact .inr rfl | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Logic.Denumerable | {
"line": 59,
"column": 2
} | {
"line": 59,
"column": 13
} | {
"line": 59,
"column": 14
} | [
{
"pp": "α : Type u_1\ninst✝ : Denumerable α\nn : ℕ\nb : α\nh : decode n = some b\n⊢ ofNat α n = b",
"ppTerm": "?m.8",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝ : Denumerable α\nn : ℕ\nb : α\nh : decode n = some b\n⊢ ofNat α n = b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Denumerable | {
"line": 237,
"column": 15
} | {
"line": 252,
"column": 86
} | {
"line": 253,
"column": 2
} | [
{
"pp": "s : Set ℕ\ninst✝¹ : Infinite ↑s\ninst✝ : DecidablePred fun x ↦ x ∈ s\nx : ℕ\nhx : x ∈ s\n⊢ ∃ a, ofNat s a = ⟨x, hx⟩",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"List.maximum",
"Iff.mpr",
"Eq.mpr",
"WithBot.some",
"WithBot",
"Preorder.toLT",
... | [] | by
set t : List s :=
((List.range x).filter fun y => y ∈ s).pmap
(fun (y : ℕ) (hy : y ∈ s) => ⟨y, hy⟩)
(by intro a ha; simpa using! (List.mem_filter.mp ha).2) with ht
have hmt : ∀ {y : s}, y ∈ t ↔ y < ⟨x, hx⟩ := by
simp [List.mem_filter, Subtype.ext_iff, ht]
cases hmax : List.max... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.List.MinMax | {
"line": 130,
"column": 22
} | {
"line": 130,
"column": 50
} | {
"line": 130,
"column": 51
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : Preorder β\ninst✝ : DecidableLT β\nf : α → β\nhd : α\ntl : List α\nm : α\n⊢ m ∈ argmax f (hd :: tl) → m ∈ hd :: tl",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Option.instMembership",
"Opti... | [
"α : Type u_1\nβ : Type u_2\ninst✝¹ : Preorder β\ninst✝ : DecidableLT β\nf : α → β\nhd : α\ntl : List α\nm : α\n⊢ foldl (argAux fun b c ↦ f c < f b) (some hd) tl = some m → m = hd ∨ m ∈ tl"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Sum | {
"line": 131,
"column": 61
} | {
"line": 131,
"column": 75
} | {
"line": 133,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nu : Finset (α ⊕ β)\nb : β\n⊢ b ∈ u.toRight ↔ inr b ∈ u",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"False",
"Finset.toRight._proof_2",
"Sum.exists._simp_1",
"Option.ctorIdx",
"congrArg",
"Finset",
"False.eli... | [] | simp [toRight] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Finset.Sum | {
"line": 131,
"column": 61
} | {
"line": 131,
"column": 75
} | {
"line": 133,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nu : Finset (α ⊕ β)\nb : β\n⊢ b ∈ u.toRight ↔ inr b ∈ u",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"False",
"Finset.toRight._proof_2",
"Sum.exists._simp_1",
"Option.ctorIdx",
"congrArg",
"Finset",
"False.eli... | [] | simp [toRight] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Finset.Sum | {
"line": 131,
"column": 61
} | {
"line": 131,
"column": 75
} | {
"line": 133,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nu : Finset (α ⊕ β)\nb : β\n⊢ b ∈ u.toRight ↔ inr b ∈ u",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"False",
"Finset.toRight._proof_2",
"Sum.exists._simp_1",
"Option.ctorIdx",
"congrArg",
"Finset",
"False.eli... | [] | simp [toRight] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Finset.Sum | {
"line": 135,
"column": 16
} | {
"line": 135,
"column": 45
} | {
"line": 135,
"column": 46
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nu v : Finset (α ⊕ β)\nh : u ⊆ v\nx✝ : α\n⊢ x✝ ∈ u.toLeft → x✝ ∈ v.toLeft",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.toLeft",
"Finset",
"Membership.mem",
"Finset.mem_toLeft._simp_1",
"Sum",
... | [
"α : Type u_1\nβ : Type u_2\nu v : Finset (α ⊕ β)\nh : u ⊆ v\nx✝ : α\n⊢ inl x✝ ∈ u → inl x✝ ∈ v"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Sum | {
"line": 139,
"column": 16
} | {
"line": 139,
"column": 46
} | {
"line": 139,
"column": 47
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nu v : Finset (α ⊕ β)\nh : u ⊆ v\nx✝ : β\n⊢ x✝ ∈ u.toRight → x✝ ∈ v.toRight",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset",
"Membership.mem",
"Sum",
"id",
"Finset.mem_toRight._simp_1",
"Finset... | [
"α : Type u_1\nβ : Type u_2\nu v : Finset (α ⊕ β)\nh : u ⊆ v\nx✝ : β\n⊢ inr x✝ ∈ u → inr x✝ ∈ v"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Sum | {
"line": 244,
"column": 10
} | {
"line": 245,
"column": 17
} | {
"line": 245,
"column": 18
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\ns : Finset α\nt : Finset β\ns₁ s₂ : Finset α\nt₁ t₂ : Finset β\na✝ : α\nb✝ : β\nx : α ⊕ β\nu v : Finset (α ⊕ β)\na : α\nb : β\nf : α ⊕ β ↪ γ\n⊢ Disjoint (map (Embedding.inl.trans f) s) (map (Embedding.inr.trans f) t)",
"ppTerm": "?m.22",
"assigned": tru... | [
"α : Type u_1\nβ : Type u_2\nγ : Type u_3\ns : Finset α\nt : Finset β\ns₁ s₂ : Finset α\nt₁ t₂ : Finset β\na✝ : α\nb✝ : β\nx : α ⊕ β\nu v : Finset (α ⊕ β)\na : α\nb : β\nf : α ⊕ β ↪ γ\n⊢ Disjoint (map f (map Embedding.inl s)) (map f (map Embedding.inr t))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.MinMax | {
"line": 476,
"column": 6
} | {
"line": 476,
"column": 17
} | {
"line": 478,
"column": 0
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : OrderBot α\nl : List α\nhd : α\ntl : List α\nIH : tl ≠ [] → ↑(foldr max ⊥ tl) = tl.maximum\nh✝ : hd :: tl ≠ []\nh : ¬tl = []\n⊢ max ↑hd ↑(foldr max ⊥ tl) = max (↑hd) tl.maximum",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
... | [] | simp [IH h] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.List.MinMax | {
"line": 476,
"column": 6
} | {
"line": 476,
"column": 17
} | {
"line": 478,
"column": 0
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : OrderBot α\nl : List α\nhd : α\ntl : List α\nIH : tl ≠ [] → ↑(foldr max ⊥ tl) = tl.maximum\nh✝ : hd :: tl ≠ []\nh : ¬tl = []\n⊢ max ↑hd ↑(foldr max ⊥ tl) = max (↑hd) tl.maximum",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
... | [] | simp [IH h] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.List.MinMax | {
"line": 476,
"column": 6
} | {
"line": 476,
"column": 17
} | {
"line": 478,
"column": 0
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : OrderBot α\nl : List α\nhd : α\ntl : List α\nIH : tl ≠ [] → ↑(foldr max ⊥ tl) = tl.maximum\nh✝ : hd :: tl ≠ []\nh : ¬tl = []\n⊢ max ↑hd ↑(foldr max ⊥ tl) = max (↑hd) tl.maximum",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
... | [] | simp [IH h] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.MinMax | {
"line": 481,
"column": 19
} | {
"line": 481,
"column": 50
} | {
"line": 481,
"column": 51
} | [
{
"pp": "case cons\nα : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : OrderBot α\na y : α\nl : List α\nIH : (∀ (x : α), x ∈ l → x ≤ a) → foldr max ⊥ l ≤ a\nh : ∀ (x : α), x ∈ y :: l → x ≤ a\n⊢ foldr max ⊥ (y :: l) ≤ a",
"ppTerm": "?cons",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Latti... | [
"case cons\nα : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : OrderBot α\na y : α\nl : List α\nIH : (∀ (x : α), x ∈ l → x ≤ a) → foldr max ⊥ l ≤ a\nh : ∀ (x : α), x ∈ y :: l → x ≤ a\n⊢ foldr max ⊥ l ≤ a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Sublists | {
"line": 55,
"column": 2
} | {
"line": 55,
"column": 13
} | {
"line": 55,
"column": 14
} | [
{
"pp": "α : Type u\na : α\nr₁ r₂ : List (List α)\nthis : foldl (fun r l ↦ r ++ [a :: l]) r₂.toArray.toList r₁ = (foldl (fun r l ↦ r.push (a :: l)) r₂.toArray r₁).toList\n⊢ Array.foldl (fun r l ↦ r ++ [a :: l]) r₂ { toList := r₁ } =\n (Array.foldl (fun r l ↦ r.push (a :: l)) r₂.toArray r₁.toArray).toList",
... | [
"α : Type u\na : α\nr₁ r₂ : List (List α)\nthis : foldl (fun r l ↦ r ++ [a :: l]) r₂.toArray.toList r₁ = (foldl (fun r l ↦ r.push (a :: l)) r₂.toArray r₁).toList\n⊢ (map (fun x2 ↦ [a :: x2]) r₁).flatten = map (cons a) r₁"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Sublists | {
"line": 65,
"column": 75
} | {
"line": 67,
"column": 23
} | {
"line": 69,
"column": 0
} | [
{
"pp": "α : Type u\na : α\nr₁✝ r₁ : List (List α)\nl : List α\nih : ∀ (r₂ : List (List α)), sublists'Aux a r₁ r₂ = r₂ ++ map (cons a) r₁\nr₂ : List (List α)\n⊢ sublists'Aux a (r₁ ++ [l]) r₂ = r₂ ++ map (cons a) (r₁ ++ [l])",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [] | by
rw [map_append, map_singleton, ← append_assoc, ← ih, sublists'Aux, foldl_append, foldl]
simp [sublists'Aux] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.List.Sublists | {
"line": 81,
"column": 2
} | {
"line": 81,
"column": 53
} | {
"line": 82,
"column": 2
} | [
{
"pp": "case cons\nα : Type u\na : α\nt : List α\nIH : ∀ {s : List α}, s ∈ t.sublists' ↔ s <+ t\ns : List α\n⊢ s ∈ (a :: t).sublists' ↔ s <+ a :: t",
"ppTerm": "?cons",
"assigned": true,
"usedConstants": [
"List.sublists'",
"Eq.mpr",
"_private.Mathlib.Data.List.Sublists.0.List.mem... | [
"case cons\nα : Type u\na : α\nt : List α\nIH : ∀ {s : List α}, s ∈ t.sublists' ↔ s <+ t\ns : List α\n⊢ (s <+ t ∨ ∃ a_1, a_1 <+ t ∧ a :: a_1 = s) ↔ s <+ a :: t"
] | simp only [sublists'_cons, mem_append, IH, mem_map] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Finset.Max | {
"line": 431,
"column": 48
} | {
"line": 431,
"column": 59
} | {
"line": 431,
"column": 60
} | [
{
"pp": "α : Type u_2\ninst✝ : LinearOrder α\ns t : Finset α\nh : ∀ x ∈ s, ∀ y ∈ s, x < y → ∃ z ∈ t, x < z ∧ z < y\nf : α → WithTop α := fun x ↦ {y ∈ t | x < y}.min\nx : α\nhx : x ∈ ↑s\ny : α\nhy : y ∈ ↑s\nhxy : x < y\na : α\nhat : a ∈ t\nhxa : x < a\nhay : a < y\nb : α\nhb : b ∈ {y_1 ∈ t | y < y_1}\n⊢ y < b",
... | [
"α : Type u_2\ninst✝ : LinearOrder α\ns t : Finset α\nh : ∀ x ∈ s, ∀ y ∈ s, x < y → ∃ z ∈ t, x < z ∧ z < y\nf : α → WithTop α := fun x ↦ {y ∈ t | x < y}.min\nx : α\nhx : x ∈ ↑s\ny : α\nhy : y ∈ ↑s\nhxy : x < y\na : α\nhat : a ∈ t\nhxa : x < a\nhay : a < y\nb : α\nhb : b ∈ {y_1 ∈ t | y < y_1}\n⊢ y < b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Sublists | {
"line": 117,
"column": 2
} | {
"line": 117,
"column": 13
} | {
"line": 117,
"column": 14
} | [
{
"pp": "α : Type u\na : α\nr : List (List α)\nthis : foldl (fun r l ↦ r ++ [l, a :: l]) #[].toList r = (foldl (fun r l ↦ (r.push l).push (a :: l)) #[] r).toList\n⊢ foldl (fun r l ↦ r ++ [l, a :: l]) [] r = (Array.foldl (fun r l ↦ (r.push l).push (a :: l)) #[] r.toArray).toList",
"ppTerm": "?m.60",
"ass... | [
"α : Type u\na : α\nr : List (List α)\nthis : foldl (fun r l ↦ r ++ [l, a :: l]) #[].toList r = (foldl (fun r l ↦ (r.push l).push (a :: l)) #[] r).toList\n⊢ (map (fun x2 ↦ [x2, a :: x2]) r).flatten = (foldl (fun r l ↦ (r.push l).push (a :: l)) #[] r).toList"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Choose.Basic | {
"line": 329,
"column": 2
} | {
"line": 329,
"column": 11
} | {
"line": 329,
"column": 12
} | [
{
"pp": "case self\nn r : ℕ\n⊢ n.choose (n / 2) ≤ n.choose (n / 2)",
"ppTerm": "?self",
"assigned": true,
"usedConstants": [
"le_refl",
"Nat.choose",
"instHDiv",
"HDiv.hDiv",
"instOfNatNat",
"Nat.instPreorder",
"Nat",
"Nat.instDiv",
"OfNat.ofNat"... | [] | | self => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.Data.Multiset.Powerset | {
"line": 123,
"column": 4
} | {
"line": 123,
"column": 15
} | {
"line": 123,
"column": 16
} | [
{
"pp": "α : Type u_1\ns : Multiset α\npowerset : s.powerset = {0}\n⊢ s = 0",
"ppTerm": "?m.14",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ns : Multiset α\npowerset : s.powerset = {0}\n⊢ s = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.Powerset | {
"line": 147,
"column": 15
} | {
"line": 147,
"column": 35
} | {
"line": 147,
"column": 35
} | [
{
"pp": "α : Type u_2\ninst✝ : DecidableEq α\nl : List α\nl' : List (Multiset α)\nH : ∀ ⦃x : Multiset α × Multiset α⦄, x ∈ l'.revzip → x.1 + x.2 = ↑l\ns t : Multiset α\nh : (s, t) ∈ l'.revzip\n⊢ (s, t) = (s, (s, t).1 + (s, t).2 - s)",
"ppTerm": "?m.77",
"assigned": true,
"usedConstants": [
"Eq... | [
"α : Type u_2\ninst✝ : DecidableEq α\nl : List α\nl' : List (Multiset α)\nH : ∀ ⦃x : Multiset α × Multiset α⦄, x ∈ l'.revzip → x.1 + x.2 = ↑l\ns t : Multiset α\nh : (s, t) ∈ l'.revzip\n⊢ (s, t) = (s, (s, t).2)"
] | add_tsub_cancel_left | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Multiset.Powerset | {
"line": 149,
"column": 2
} | {
"line": 149,
"column": 13
} | {
"line": 149,
"column": 14
} | [
{
"pp": "α : Type u_2\ninst✝ : DecidableEq α\nl : List α\nl' : List (Multiset α)\nH : ∀ ⦃x : Multiset α × Multiset α⦄, x ∈ l'.revzip → x.1 + x.2 = ↑l\nthis : Forall₂ (fun p s ↦ p = (s, ↑l - s)) l'.revzip (List.map Prod.fst l'.revzip)\n⊢ Forall₂ (fun a c ↦ a = (c, ↑l - c)) l'.revzip l'",
"ppTerm": "?m.96",
... | [
"α : Type u_2\ninst✝ : DecidableEq α\nl : List α\nl' : List (Multiset α)\nH : ∀ ⦃x : Multiset α × Multiset α⦄, x ∈ l'.revzip → x.1 + x.2 = ↑l\nthis : Forall₂ (fun p s ↦ p = (s, ↑l - s)) l'.revzip (List.map Prod.fst l'.revzip)\n⊢ Forall₂ (fun a c ↦ a = (c, ↑l - c)) l'.revzip l'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Sublists | {
"line": 259,
"column": 24
} | {
"line": 259,
"column": 64
} | {
"line": 259,
"column": 65
} | [
{
"pp": "case succ.cons_cons\nα : Type u\nn : ℕ\nIHn : ∀ {l₁ l₂ : List α}, l₁ <+ l₂ → sublistsLen n l₁ <+ sublistsLen n l₂\nl₁ l₂ l₁✝ l₂✝ : List α\na : α\ns : l₁✝ <+ l₂✝\nIH : sublistsLen (n + 1) l₁✝ <+ sublistsLen (n + 1) l₂✝\n⊢ sublistsLen (n + 1) (a :: l₁✝) <+ sublistsLen (n + 1) (a :: l₂✝)",
"ppTerm": "... | [
"case succ.cons_cons\nα : Type u\nn : ℕ\nIHn : ∀ {l₁ l₂ : List α}, l₁ <+ l₂ → sublistsLen n l₁ <+ sublistsLen n l₂\nl₁ l₂ l₁✝ l₂✝ : List α\na : α\ns : l₁✝ <+ l₂✝\nIH : sublistsLen (n + 1) l₁✝ <+ sublistsLen (n + 1) l₂✝\n⊢ sublistsLen (n + 1) l₁✝ ++ map (cons a) (sublistsLen n l₁✝) <+\n sublistsLen (n + 1) l₂✝ ++... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Sublists | {
"line": 322,
"column": 49
} | {
"line": 322,
"column": 60
} | {
"line": 322,
"column": 61
} | [
{
"pp": "α : Type u\nl : List α\nh✝ : l.Nodup\nl₁ l₂ : List α\nh : ((Lex fun x1 x2 ↦ x1 ≠ x2) on reverse) l₁ l₂\n⊢ l₁ ≠ l₂",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"id",
"Ne",
"List"
],
"usedFVars": [
"α",
"l₁",
"l₂"
],
"usedGoals"... | [
"α : Type u\nl : List α\nh✝ : l.Nodup\nl₁ l₂ : List α\nh : ((Lex fun x1 x2 ↦ x1 ≠ x2) on reverse) l₁ l₂\n⊢ ¬l₁ = l₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Lattice.Fold | {
"line": 122,
"column": 61
} | {
"line": 122,
"column": 72
} | {
"line": 122,
"column": 73
} | [
{
"pp": "α : Type u_2\ninst✝¹ : SemilatticeSup α\ninst✝ : OrderBot α\ns : Finset α\n⊢ IsLUB (↑s) (s.sup id)",
"ppTerm": "?m.10",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝¹ : SemilatticeSup α\ninst✝ : OrderBot α\ns : Finset α\n⊢ IsLUB (↑s) (s.sup id)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Lattice.Fold | {
"line": 157,
"column": 34
} | {
"line": 157,
"column": 45
} | {
"line": 157,
"column": 46
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\nγ : Type u_4\ninst✝¹ : SemilatticeSup α\ninst✝ : OrderBot α\ns : Finset β\nt : Finset γ\nf : β → γ → α\na : α\n⊢ (s.sup fun b ↦ t.sup (f b)) ≤ a ↔ (t.sup fun c ↦ s.sup fun b ↦ f b c) ≤ a",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"α : Type u_2\nβ : Type u_3\nγ : Type u_4\ninst✝¹ : SemilatticeSup α\ninst✝ : OrderBot α\ns : Finset β\nt : Finset γ\nf : β → γ → α\na : α\n⊢ (∀ b ∈ s, ∀ b_1 ∈ t, f b b_1 ≤ a) ↔ ∀ b ∈ t, ∀ b_1 ∈ s, f b_1 b ≤ a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Sublists | {
"line": 390,
"column": 35
} | {
"line": 390,
"column": 46
} | {
"line": 390,
"column": 47
} | [
{
"pp": "α : Type u\nl₁ l₂ : List α\nh : (l₁, l₂) ∈ [].sublists.zip [].sublists.reverse\n⊢ l₁ = [] ∧ l₂ = []",
"ppTerm": "?m.36",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\nl₁ l₂ : List α\nh : (l₁, l₂) ∈ [].sublists.zip [].sublists.reverse\n⊢ l₁ = [] ∧ l₂ = []"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Powerset | {
"line": 108,
"column": 2
} | {
"line": 109,
"column": 25
} | {
"line": 111,
"column": 0
} | [
{
"pp": "α : Type u_1\ns t : Finset α\na : α\nht : t ∈ s.powerset\nh : a ∉ s\n⊢ a ∉ t",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Finset",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"mt",
"LE.le",
"Finset.mem_powerset",
... | [] | apply mt _ h
apply mem_powerset.1 ht | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Finset.Powerset | {
"line": 108,
"column": 2
} | {
"line": 109,
"column": 25
} | {
"line": 111,
"column": 0
} | [
{
"pp": "α : Type u_1\ns t : Finset α\na : α\nht : t ∈ s.powerset\nh : a ∉ s\n⊢ a ∉ t",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Finset",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"mt",
"LE.le",
"Finset.mem_powerset",
... | [] | apply mt _ h
apply mem_powerset.1 ht | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Set.Finite.Powerset | {
"line": 51,
"column": 2
} | {
"line": 52,
"column": 37
} | {
"line": 52,
"column": 38
} | [
{
"pp": "α : Type u\na : Set α\nh : a.Finite\ns : Set α\n⊢ s ∈ {b | b ⊆ a} ↔ s ∈ ↑(Finset.map Finset.coeEmb.toEmbedding h.toFinset.powerset)",
"ppTerm": "?m.77",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"and_true",
"Finset.coe_powerset",
"congrArg",
"Finset",
... | [
"α : Type u\na : Set α\nh : a.Finite\ns : Set α\n⊢ s ⊆ a → s.Finite"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Finite.Range | {
"line": 95,
"column": 2
} | {
"line": 95,
"column": 21
} | {
"line": 95,
"column": 22
} | [
{
"pp": "α : Type u\nβ : Type v\ns : Set α\nhs : s.Finite\nF : (i : α) → i ∈ s → β\nthis : Finite ↑s\n⊢ {y | ∃ x, ∃ (hx : x ∈ s), F x hx = y}.Finite",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\nβ : Type v\ns : Set α\nhs : s.Finite\nF : (i : α) → i ∈ s → β\nthis : Finite ↑s\n⊢ {y | ∃ x, ∃ (hx : x ∈ s), F x hx = y}.Finite"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Finite.Range | {
"line": 102,
"column": 2
} | {
"line": 105,
"column": 65
} | {
"line": 107,
"column": 0
} | [
{
"pp": "α : Type u\nβ : Type v\nf : α → β\ns : Set α\nu : Set β\nhu : u.Finite\nhsu : u ⊆ f '' s\n⊢ ∃ t ⊆ s, ∃ (_ : t.Finite), f '' t = u",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Set.ext",
"Iff.of_eq",
"congrArg",
"Finite",
"Set.mem_i... | [] | have : Finite u := Finite.to_subtype hu
choose g hg hg' using hsu
let g' (x : u) : α := g x.property
exact ⟨range g', fun a ha ↦ by aesop, finite_range _, by aesop⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Set.Finite.Range | {
"line": 102,
"column": 2
} | {
"line": 105,
"column": 65
} | {
"line": 107,
"column": 0
} | [
{
"pp": "α : Type u\nβ : Type v\nf : α → β\ns : Set α\nu : Set β\nhu : u.Finite\nhsu : u ⊆ f '' s\n⊢ ∃ t ⊆ s, ∃ (_ : t.Finite), f '' t = u",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Set.ext",
"Iff.of_eq",
"congrArg",
"Finite",
"Set.mem_i... | [] | have : Finite u := Finite.to_subtype hu
choose g hg hg' using hsu
let g' (x : u) : α := g x.property
exact ⟨range g', fun a ha ↦ by aesop, finite_range _, by aesop⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Set.Pairwise.Lattice | {
"line": 200,
"column": 4
} | {
"line": 200,
"column": 46
} | {
"line": 200,
"column": 47
} | [
{
"pp": "case ex\nα : Type u_1\nι : Type u_2\nf : ι → Set α\ns : Set ι\ny : α\nh_disjoint : s.PairwiseDisjoint f\nhy : y ∈ ⋃ i ∈ s, f i\n⊢ ∃ x ∈ s, y ∈ f x",
"ppTerm": "?ex",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case ex\nα : Type u_1\nι : Type u_2\nf : ι → Set α\ns : Set ι\ny : α\nh_disjoint : s.PairwiseDisjoint f\nhy : y ∈ ⋃ i ∈ s, f i\n⊢ ∃ x ∈ s, y ∈ f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Powerset | {
"line": 318,
"column": 2
} | {
"line": 318,
"column": 42
} | {
"line": 318,
"column": 43
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq (Finset α)\ns : Finset α\n⊢ s.powerset = (range (#s + 1)).biUnion fun i ↦ powersetCard i s",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝ : DecidableEq (Finset α)\ns : Finset α\n⊢ s.powerset = (range (#s + 1)).biUnion fun i ↦ powersetCard i s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Powerset | {
"line": 348,
"column": 2
} | {
"line": 348,
"column": 52
} | {
"line": 348,
"column": 53
} | [
{
"pp": "α : Type u_1\na b : Finset α\nr : ℕ\nhab : #a = #b\nhr₀ : r ≠ 0\nhra : r ≤ #a\nh : powersetCard r a = powersetCard r b\n⊢ a = b",
"ppTerm": "?m.15",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\na b : Finset α\nr : ℕ\nhab : #a = #b\nhr₀ : r ≠ 0\nhra : r ≤ #a\nh : powersetCard r a = powersetCard r b\n⊢ a = b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Lattice.Fold | {
"line": 476,
"column": 6
} | {
"line": 476,
"column": 73
} | {
"line": 476,
"column": 74
} | [
{
"pp": "α : Type u_2\nι : Type u_5\ninst✝¹ : LinearOrder α\ninst✝ : OrderBot α\ns : Finset ι\nf : ι → α\na : α\nha : ⊥ < a\nc : ι\nt : Finset ι\nhc : c ∉ t\n⊢ ((∀ b ∈ t, f b < a) → t.sup f < a) → (∀ b ∈ cons c t hc, f b < a) → (cons c t hc).sup f < a",
"ppTerm": "?m.43",
"assigned": true,
"usedCons... | [
"α : Type u_2\nι : Type u_5\ninst✝¹ : LinearOrder α\ninst✝ : OrderBot α\ns : Finset ι\nf : ι → α\na : α\nha : ⊥ < a\nc : ι\nt : Finset ι\nhc : c ∉ t\n⊢ ((∀ b ∈ t, f b < a) → t.sup f < a) → (f c < a ∧ ∀ b ∈ t, f b < a) → f c < a ∧ t.sup f < a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Lattice.Fold | {
"line": 487,
"column": 4
} | {
"line": 487,
"column": 15
} | {
"line": 488,
"column": 6
} | [
{
"pp": "case insert.inr\nα : Type u_2\nι : Type u_5\ninst✝¹ : LinearOrder α\ninst✝ : OrderBot α\ns✝ : Finset ι\nf : ι → α\na : ι\ns : Finset ι\na✝ : a ∉ s\nh : s.Nonempty → s.sup f ∈ f '' ↑s\nhs✝ : (insert a s).Nonempty\nhs : s.Nonempty\n⊢ max (f a) (s.sup f) ∈ f '' ↑(insert a s)",
"ppTerm": "?insert.inr",... | [] | | inr hs => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | null |
Mathlib.Data.Finset.Lattice.Fold | {
"line": 576,
"column": 34
} | {
"line": 576,
"column": 45
} | {
"line": 576,
"column": 46
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\nγ : Type u_4\ninst✝ : SemilatticeSup α\ns : Finset β\nt : Finset γ\nhs : s.Nonempty\nht : t.Nonempty\nf : β → γ → α\na : α\n⊢ (s.sup' hs fun b ↦ t.sup' ht (f b)) ≤ a ↔ (t.sup' ht fun c ↦ s.sup' hs fun b ↦ f b c) ≤ a",
"ppTerm": "?m.27",
"assigned": true,
"usedCon... | [
"α : Type u_2\nβ : Type u_3\nγ : Type u_4\ninst✝ : SemilatticeSup α\ns : Finset β\nt : Finset γ\nhs : s.Nonempty\nht : t.Nonempty\nf : β → γ → α\na : α\n⊢ (∀ b ∈ s, ∀ b_1 ∈ t, f b b_1 ≤ a) ↔ ∀ b ∈ t, ∀ b_1 ∈ s, f b_1 b ≤ a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.ConditionallyCompletePartialOrder.Indexed | {
"line": 73,
"column": 8
} | {
"line": 73,
"column": 23
} | {
"line": 73,
"column": 24
} | [
{
"pp": "case inl\nα : Type u_1\nι : Sort u_4\ninst✝ : ConditionallyCompletePartialOrderSup α\nf g : ι → α\nhdf : Directed (fun x1 x2 ↦ x1 ≤ x2) f\nhdg : Directed (fun x1 x2 ↦ x1 ≤ x2) g\nB : BddAbove (range g)\nH : ∀ (x : ι), f x ≤ g x\nh✝ : IsEmpty ι\n⊢ iSup f ≤ iSup g",
"ppTerm": "?inl",
"assigned": ... | [
"case inl\nα : Type u_1\nι : Sort u_4\ninst✝ : ConditionallyCompletePartialOrderSup α\nf g : ι → α\nhdf : Directed (fun x1 x2 ↦ x1 ≤ x2) f\nhdg : Directed (fun x1 x2 ↦ x1 ≤ x2) g\nB : BddAbove (range g)\nH : ∀ (x : ι), f x ≤ g x\nh✝ : IsEmpty ι\n⊢ sSup ∅ ≤ iSup g"
] | iSup_of_empty', | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.ConditionallyCompletePartialOrder.Indexed | {
"line": 116,
"column": 2
} | {
"line": 116,
"column": 23
} | {
"line": 117,
"column": 2
} | [
{
"pp": "α : Type u_1\nι : Sort u_4\ninst✝ : ConditionallyCompletePartialOrderSup α\np : ι → Prop\nf : Subtype p → α\nhp : ∀ (i : ι), p i\n⊢ (range fun i ↦ f ⟨i, ⋯⟩) = range f",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Set.Subset.antisymm",
"Iff.mpr",
"Inhabited.def... | [
"case h₁\nα : Type u_1\nι : Sort u_4\ninst✝ : ConditionallyCompletePartialOrderSup α\np : ι → Prop\nf : Subtype p → α\nhp : ∀ (i : ι), p i\n⊢ (range fun i ↦ f ⟨i, ⋯⟩) ⊆ range f",
"case h₂\nα : Type u_1\nι : Sort u_4\ninst✝ : ConditionallyCompletePartialOrderSup α\np : ι → Prop\nf : Subtype p → α\nhp : ∀ (i : ι), ... | apply Subset.antisymm | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Order.ConditionallyCompletePartialOrder.Indexed | {
"line": 171,
"column": 2
} | {
"line": 171,
"column": 13
} | {
"line": 171,
"column": 14
} | [
{
"pp": "α : Type u_1\nι : Sort u_4\ninst✝¹ : ConditionallyCompletePartialOrderSup α\ninst✝ : Nonempty ι\nf : ι → α\nhd : Directed (fun x1 x2 ↦ x1 ≤ x2) f\nhf : BddAbove (range f)\nx✝ : α\n⊢ x✝ ∈ Ici (⨆ i, f i) ↔ x✝ ∈ ⋂ i, Ici (f i)",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Eq... | [
"α : Type u_1\nι : Sort u_4\ninst✝¹ : ConditionallyCompletePartialOrderSup α\ninst✝ : Nonempty ι\nf : ι → α\nhd : Directed (fun x1 x2 ↦ x1 ≤ x2) f\nhf : BddAbove (range f)\nx✝ : α\n⊢ ⨆ i, f i ≤ x✝ ↔ ∀ (i : ι), f i ≤ x✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.ConditionallyCompletePartialOrder.Indexed | {
"line": 206,
"column": 2
} | {
"line": 207,
"column": 9
} | {
"line": 207,
"column": 10
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : ConditionallyCompletePartialOrderSup α\ninst✝ : ConditionallyCompletePartialOrderSup β\nl : α → β\nu : β → α\ngc : GaloisConnection l u\ns : Set α\nhd : DirectedOn (fun x1 x2 ↦ x1 ≤ x2) s\nhne : s.Nonempty\nhbdd : BddAbove s\n⊢ l (sSup s) = ⨆ x, l ↑x",
"ppTerm":... | [
"α : Type u_1\nβ : Type u_2\ninst✝¹ : ConditionallyCompletePartialOrderSup α\ninst✝ : ConditionallyCompletePartialOrderSup β\nl : α → β\nu : β → α\ngc : GaloisConnection l u\ns : Set α\nhd : DirectedOn (fun x1 x2 ↦ x1 ≤ x2) s\nhne : s.Nonempty\nhbdd : BddAbove s\n⊢ l (sSup s) = sSup (l '' s)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.ConditionallyCompleteLattice.Finset | {
"line": 115,
"column": 2
} | {
"line": 115,
"column": 13
} | {
"line": 115,
"column": 14
} | [
{
"pp": "ι : Type u_1\nα : Type u_2\ninst✝ : ConditionallyCompleteLinearOrder α\nf : ι → α\ns : Finset ι\nh : ∃ x ∈ s, sSup ∅ ≤ f x\n⊢ ⨆ i ∈ ↑s, f i ∈ f '' ↑s",
"ppTerm": "?m.55",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SetLike.mem_coe._simp_1",
"Iff.of_eq",
"congrArg... | [
"ι : Type u_1\nα : Type u_2\ninst✝ : ConditionallyCompleteLinearOrder α\nf : ι → α\ns : Finset ι\nh : ∃ x ∈ s, sSup ∅ ≤ f x\n⊢ ∃ x ∈ s, f x = ⨆ i ∈ s, f i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.ConditionallyCompleteLattice.Finset | {
"line": 121,
"column": 2
} | {
"line": 121,
"column": 13
} | {
"line": 121,
"column": 14
} | [
{
"pp": "ι : Type u_1\nα : Type u_2\ninst✝ : ConditionallyCompleteLinearOrder α\nf : ι → α\ns : Finset ι\nh : ∃ x ∈ s, f x ≤ sInf ∅\n⊢ ⨅ i ∈ ↑s, f i ∈ f '' ↑s",
"ppTerm": "?m.55",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SetLike.mem_coe._simp_1",
"iInf",
"Iff.of_eq",
... | [
"ι : Type u_1\nα : Type u_2\ninst✝ : ConditionallyCompleteLinearOrder α\nf : ι → α\ns : Finset ι\nh : ∃ x ∈ s, f x ≤ sInf ∅\n⊢ ∃ x ∈ s, f x = ⨅ i ∈ s, f i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.ConditionallyCompleteLattice.Finset | {
"line": 169,
"column": 2
} | {
"line": 169,
"column": 13
} | {
"line": 169,
"column": 14
} | [
{
"pp": "ι : Type u_1\nα : Type u_2\ninst✝ : ConditionallyCompleteLinearOrder α\nl : List ι\nf : ι → α\nh : ∃ x ∈ l, sSup ∅ ≤ f x\n⊢ ⨆ x ∈ l, f x ∈ map f l",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"iSup",
"List.map",
"Membership.mem",
"Exists"... | [
"ι : Type u_1\nα : Type u_2\ninst✝ : ConditionallyCompleteLinearOrder α\nl : List ι\nf : ι → α\nh : ∃ x ∈ l, sSup ∅ ≤ f x\n⊢ ∃ a ∈ l, f a = ⨆ x ∈ l, f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.ConditionallyCompleteLattice.Finset | {
"line": 169,
"column": 47
} | {
"line": 169,
"column": 58
} | {
"line": 169,
"column": 59
} | [
{
"pp": "ι : Type u_1\nα : Type u_2\ninst✝ : ConditionallyCompleteLinearOrder α\nl : List ι\nf : ι → α\nh : ∃ x ∈ l, sSup ∅ ≤ f x\n⊢ ∃ x ∈ l.toFinset, sSup ∅ ≤ f x",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Finset",
"PartialOrder.toPreord... | [
"ι : Type u_1\nα : Type u_2\ninst✝ : ConditionallyCompleteLinearOrder α\nl : List ι\nf : ι → α\nh : ∃ x ∈ l, sSup ∅ ≤ f x\n⊢ ∃ x ∈ l, sSup ∅ ≤ f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.ConditionallyCompleteLattice.Finset | {
"line": 175,
"column": 2
} | {
"line": 175,
"column": 13
} | {
"line": 175,
"column": 14
} | [
{
"pp": "ι : Type u_1\nα : Type u_2\ninst✝ : ConditionallyCompleteLinearOrder α\nl : List ι\nf : ι → α\nh : ∃ x ∈ l, f x ≤ sInf ∅\n⊢ ⨅ x ∈ l, f x ∈ map f l",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"iInf",
"List.map",
"Membership.mem",
"Exists"... | [
"ι : Type u_1\nα : Type u_2\ninst✝ : ConditionallyCompleteLinearOrder α\nl : List ι\nf : ι → α\nh : ∃ x ∈ l, f x ≤ sInf ∅\n⊢ ∃ a ∈ l, f a = ⨅ x ∈ l, f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.ConditionallyCompleteLattice.Finset | {
"line": 175,
"column": 47
} | {
"line": 175,
"column": 58
} | {
"line": 175,
"column": 59
} | [
{
"pp": "ι : Type u_1\nα : Type u_2\ninst✝ : ConditionallyCompleteLinearOrder α\nl : List ι\nf : ι → α\nh : ∃ x ∈ l, f x ≤ sInf ∅\n⊢ ∃ x ∈ l.toFinset, f x ≤ sInf ∅",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Finset",
"PartialOrder.toPreord... | [
"ι : Type u_1\nα : Type u_2\ninst✝ : ConditionallyCompleteLinearOrder α\nl : List ι\nf : ι → α\nh : ∃ x ∈ l, f x ≤ sInf ∅\n⊢ ∃ x ∈ l, f x ≤ sInf ∅"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.ConditionallyCompleteLattice.Finset | {
"line": 181,
"column": 2
} | {
"line": 181,
"column": 13
} | {
"line": 181,
"column": 14
} | [
{
"pp": "ι : Type u_1\nα : Type u_2\ninst✝ : ConditionallyCompleteLinearOrder α\ns : Multiset ι\nf : ι → α\nh : ∃ x ∈ s, sSup ∅ ≤ f x\n⊢ ⨆ x ∈ s, f x ∈ map f s",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Multiset.map",
"iSup",
"Multiset.mem_map._simp_... | [
"ι : Type u_1\nα : Type u_2\ninst✝ : ConditionallyCompleteLinearOrder α\ns : Multiset ι\nf : ι → α\nh : ∃ x ∈ s, sSup ∅ ≤ f x\n⊢ ∃ a ∈ s, f a = ⨆ x ∈ s, f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.ConditionallyCompleteLattice.Finset | {
"line": 181,
"column": 47
} | {
"line": 181,
"column": 58
} | {
"line": 181,
"column": 59
} | [
{
"pp": "ι : Type u_1\nα : Type u_2\ninst✝ : ConditionallyCompleteLinearOrder α\ns : Multiset ι\nf : ι → α\nh : ∃ x ∈ s, sSup ∅ ≤ f x\n⊢ ∃ x ∈ s.toFinset, sSup ∅ ≤ f x",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"Multiset.toFinset",
"Eq.mpr",
"congrArg",
"Finset... | [
"ι : Type u_1\nα : Type u_2\ninst✝ : ConditionallyCompleteLinearOrder α\ns : Multiset ι\nf : ι → α\nh : ∃ x ∈ s, sSup ∅ ≤ f x\n⊢ ∃ x ∈ s, sSup ∅ ≤ f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.ConditionallyCompleteLattice.Finset | {
"line": 187,
"column": 2
} | {
"line": 187,
"column": 13
} | {
"line": 187,
"column": 14
} | [
{
"pp": "ι : Type u_1\nα : Type u_2\ninst✝ : ConditionallyCompleteLinearOrder α\ns : Multiset ι\nf : ι → α\nh : ∃ x ∈ s, f x ≤ sInf ∅\n⊢ ⨅ x ∈ s, f x ∈ map f s",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"iInf",
"Multiset.map",
"Multiset.mem_map._simp_... | [
"ι : Type u_1\nα : Type u_2\ninst✝ : ConditionallyCompleteLinearOrder α\ns : Multiset ι\nf : ι → α\nh : ∃ x ∈ s, f x ≤ sInf ∅\n⊢ ∃ a ∈ s, f a = ⨅ x ∈ s, f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.ConditionallyCompleteLattice.Finset | {
"line": 187,
"column": 47
} | {
"line": 187,
"column": 58
} | {
"line": 187,
"column": 59
} | [
{
"pp": "ι : Type u_1\nα : Type u_2\ninst✝ : ConditionallyCompleteLinearOrder α\ns : Multiset ι\nf : ι → α\nh : ∃ x ∈ s, f x ≤ sInf ∅\n⊢ ∃ x ∈ s.toFinset, f x ≤ sInf ∅",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"Multiset.toFinset",
"Eq.mpr",
"congrArg",
"Finset... | [
"ι : Type u_1\nα : Type u_2\ninst✝ : ConditionallyCompleteLinearOrder α\ns : Multiset ι\nf : ι → α\nh : ∃ x ∈ s, f x ≤ sInf ∅\n⊢ ∃ x ∈ s, f x ≤ sInf ∅"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.ConditionallyCompleteLattice.Finset | {
"line": 186,
"column": 2
} | {
"line": 187,
"column": 61
} | {
"line": 189,
"column": 0
} | [
{
"pp": "ι : Type u_1\nα : Type u_2\ninst✝ : ConditionallyCompleteLinearOrder α\ns : Multiset ι\nf : ι → α\nh : ∃ x ∈ s, f x ≤ sInf ∅\n⊢ ⨅ x ∈ s, f x ∈ map f s",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Multiset.toFinset",
"Eq.mpr",
"iInf",
"LinearOrder.toDeci... | [] | classical
simpa using s.toFinset.ciInf_mem_image f (by simpa using h) | Lean.Elab.Tactic.evalClassical | Lean.Parser.Tactic.classical |
Mathlib.Order.ConditionallyCompleteLattice.Finset | {
"line": 186,
"column": 2
} | {
"line": 187,
"column": 61
} | {
"line": 189,
"column": 0
} | [
{
"pp": "ι : Type u_1\nα : Type u_2\ninst✝ : ConditionallyCompleteLinearOrder α\ns : Multiset ι\nf : ι → α\nh : ∃ x ∈ s, f x ≤ sInf ∅\n⊢ ⨅ x ∈ s, f x ∈ map f s",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Multiset.toFinset",
"Eq.mpr",
"iInf",
"LinearOrder.toDeci... | [] | classical
simpa using s.toFinset.ciInf_mem_image f (by simpa using h) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.ConditionallyCompleteLattice.Finset | {
"line": 186,
"column": 2
} | {
"line": 187,
"column": 61
} | {
"line": 189,
"column": 0
} | [
{
"pp": "ι : Type u_1\nα : Type u_2\ninst✝ : ConditionallyCompleteLinearOrder α\ns : Multiset ι\nf : ι → α\nh : ∃ x ∈ s, f x ≤ sInf ∅\n⊢ ⨅ x ∈ s, f x ∈ map f s",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Multiset.toFinset",
"Eq.mpr",
"iInf",
"LinearOrder.toDeci... | [] | classical
simpa using s.toFinset.ciInf_mem_image f (by simpa using h) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.ConditionallyCompleteLattice.Finset | {
"line": 318,
"column": 47
} | {
"line": 318,
"column": 58
} | {
"line": 318,
"column": 59
} | [
{
"pp": "ι : Type u_1\nα : Type u_2\ninst✝ : ConditionallyCompleteLinearOrderBot α\nl : List ι\nf : ι → α\nh : l ≠ []\n⊢ ∃ x ∈ l, sSup ∅ ≤ f x",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"and_true",
"congrArg",
"OrderB... | [
"ι : Type u_1\nα : Type u_2\ninst✝ : ConditionallyCompleteLinearOrderBot α\nl : List ι\nf : ι → α\nh : l ≠ []\n⊢ ∃ x, x ∈ l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.ConditionallyCompleteLattice.Finset | {
"line": 322,
"column": 47
} | {
"line": 322,
"column": 58
} | {
"line": 322,
"column": 59
} | [
{
"pp": "ι : Type u_1\nα : Type u_2\ninst✝ : ConditionallyCompleteLinearOrderBot α\ns : Multiset ι\nf : ι → α\nh : s ≠ 0\n⊢ ∃ x ∈ s, sSup ∅ ≤ f x",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"and_true",
"congrArg",
"Ord... | [
"ι : Type u_1\nα : Type u_2\ninst✝ : ConditionallyCompleteLinearOrderBot α\ns : Multiset ι\nf : ι → α\nh : s ≠ 0\n⊢ ∃ x, x ∈ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Finite.Lattice | {
"line": 156,
"column": 2
} | {
"line": 156,
"column": 38
} | {
"line": 156,
"column": 39
} | [
{
"pp": "α : Type u\ns : Set (Set α)\nhs : s.Finite\nH : ∀ t ∈ s, t.Finite\n⊢ (⋃₀ s).Finite",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Set.sUnion",
"Set.Finite",
"Membership.mem",
"id",
"Set.sUnion_eq_biUnion",
"Eq"... | [
"α : Type u\ns : Set (Set α)\nhs : s.Finite\nH : ∀ t ∈ s, t.Finite\n⊢ (⋃ i ∈ s, i).Finite"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.ConditionallyCompleteLattice.Indexed | {
"line": 69,
"column": 4
} | {
"line": 69,
"column": 33
} | {
"line": 69,
"column": 34
} | [
{
"pp": "case pos\nι : Type u_5\ns : Set ι\nα : Type u_6\ninst✝ : CompleteLattice α\nf : ι → α\nj : ι\nhj : j ∈ s\nthis : Nonempty ι\ni : ι\nh : i ∈ s\n⊢ ↑(⨆ (_ : i ∈ s), f i) ≤ ⨆ i ∈ s, ↑(f i)",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"WithBot.instSupSet",
"Eq.mpr",
... | [
"case pos\nι : Type u_5\ns : Set ι\nα : Type u_6\ninst✝ : CompleteLattice α\nf : ι → α\nj : ι\nhj : j ∈ s\nthis : Nonempty ι\ni : ι\nh : i ∈ s\n⊢ ↑(f i) ≤ ⨆ i ∈ s, ↑(f i)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.ConditionallyCompleteLattice.Indexed | {
"line": 70,
"column": 4
} | {
"line": 70,
"column": 33
} | {
"line": 70,
"column": 34
} | [
{
"pp": "case neg\nι : Type u_5\ns : Set ι\nα : Type u_6\ninst✝ : CompleteLattice α\nf : ι → α\nj : ι\nhj : j ∈ s\nthis : Nonempty ι\ni : ι\nh : i ∉ s\n⊢ ↑(⨆ (_ : i ∈ s), f i) ≤ ⨆ i ∈ s, ↑(f i)",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"WithBot.instSupSet",
"Eq.mpr",
... | [
"case neg\nι : Type u_5\ns : Set ι\nα : Type u_6\ninst✝ : CompleteLattice α\nf : ι → α\nj : ι\nhj : j ∈ s\nthis : Nonempty ι\ni : ι\nh : i ∉ s\n⊢ ↑⊥ ≤ ⨆ i ∈ s, ↑(f i)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.ConditionallyCompleteLattice.Indexed | {
"line": 63,
"column": 2
} | {
"line": 70,
"column": 68
} | {
"line": 72,
"column": 0
} | [
{
"pp": "ι : Type u_5\ns : Set ι\nhs : s.Nonempty\nα : Type u_6\ninst✝ : CompleteLattice α\nf : ι → α\n⊢ ↑(⨆ i ∈ s, f i) = ⨆ i ∈ s, ↑(f i)",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"WithBot.instSupSet",
"Iff.mpr",
"Eq.mpr",
"instCompleteLatticeWithBot",
... | [] | rcases hs with ⟨j, hj⟩
have : Nonempty ι := Nonempty.intro j
refine le_antisymm ((WithBot.coe_iSup (OrderTop.bddAbove _)).trans_le <|
iSup_le_iff.mpr fun i ↦ ?_) <| iSup_le_iff.mpr <| fun _ ↦ iSup_le_iff.mpr <|
fun hi ↦ WithBot.coe_le_coe.mpr (le_biSup _ hi)
by_cases h : i ∈ s
· simpa only [iSup_pos h... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.ConditionallyCompleteLattice.Indexed | {
"line": 63,
"column": 2
} | {
"line": 70,
"column": 68
} | {
"line": 72,
"column": 0
} | [
{
"pp": "ι : Type u_5\ns : Set ι\nhs : s.Nonempty\nα : Type u_6\ninst✝ : CompleteLattice α\nf : ι → α\n⊢ ↑(⨆ i ∈ s, f i) = ⨆ i ∈ s, ↑(f i)",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"WithBot.instSupSet",
"Iff.mpr",
"Eq.mpr",
"instCompleteLatticeWithBot",
... | [] | rcases hs with ⟨j, hj⟩
have : Nonempty ι := Nonempty.intro j
refine le_antisymm ((WithBot.coe_iSup (OrderTop.bddAbove _)).trans_le <|
iSup_le_iff.mpr fun i ↦ ?_) <| iSup_le_iff.mpr <| fun _ ↦ iSup_le_iff.mpr <|
fun hi ↦ WithBot.coe_le_coe.mpr (le_biSup _ hi)
by_cases h : i ∈ s
· simpa only [iSup_pos h... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Set.Finite.Lattice | {
"line": 243,
"column": 52
} | {
"line": 243,
"column": 76
} | {
"line": 243,
"column": 77
} | [
{
"pp": "α : Type u\ns : Set α\nhs : s.Finite\nι : Type u_1\nt : ι → Set α\nh : s ⊆ ⋃ i, t i\nthis : Finite ↑s\n⊢ ∀ (x : ↑s), ∃ i, ↑x ∈ t i",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Subtype.forall._simp_1",
"Membership.mem",
"Exists",
"Set.Ele... | [
"α : Type u\ns : Set α\nhs : s.Finite\nι : Type u_1\nt : ι → Set α\nh : s ⊆ ⋃ i, t i\nthis : Finite ↑s\n⊢ ∀ a ∈ s, ∃ i, a ∈ t i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.ConditionallyCompleteLattice.Indexed | {
"line": 79,
"column": 25
} | {
"line": 79,
"column": 36
} | {
"line": 79,
"column": 37
} | [
{
"pp": "ι : Type u_5\ns : Set ι\nα : Type u_6\ninst✝ : CompleteLattice α\nf : ι → α\n⊢ ↑(⨅ i ∈ s, f i) ≤ ⨅ i ∈ s, ↑(f i)",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instCompleteLatticeWithBot",
"WithBot.some",
"WithBot",
"Lattice.toSemilatticeS... | [
"ι : Type u_5\ns : Set ι\nα : Type u_6\ninst✝ : CompleteLattice α\nf : ι → α\n⊢ ∀ i ∈ s, ⨅ i ∈ s, f i ≤ f i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.ConditionallyCompleteLattice.Indexed | {
"line": 82,
"column": 4
} | {
"line": 82,
"column": 33
} | {
"line": 82,
"column": 34
} | [
{
"pp": "case pos\nι : Type u_5\ns : Set ι\nα : Type u_6\ninst✝ : CompleteLattice α\nf : ι → α\ni : ι\nh : i ∈ s\n⊢ ⨅ i ∈ s, ↑(f i) ≤ ↑(⨅ (_ : i ∈ s), f i)",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instCompleteLatticeWithBot",
"WithBot.some",
"WithB... | [
"case pos\nι : Type u_5\ns : Set ι\nα : Type u_6\ninst✝ : CompleteLattice α\nf : ι → α\ni : ι\nh : i ∈ s\n⊢ ⨅ i ∈ s, ↑(f i) ≤ ↑(f i)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.ConditionallyCompleteLattice.Indexed | {
"line": 168,
"column": 8
} | {
"line": 168,
"column": 23
} | {
"line": 168,
"column": 24
} | [
{
"pp": "case inl\nα : Type u_1\nι : Sort u_4\ninst✝ : ConditionallyCompleteLattice α\nf g : ι → α\nB : BddAbove (range g)\nH : ∀ (x : ι), f x ≤ g x\nh✝ : IsEmpty ι\n⊢ iSup f ≤ iSup g",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"iSup",
"Part... | [
"case inl\nα : Type u_1\nι : Sort u_4\ninst✝ : ConditionallyCompleteLattice α\nf g : ι → α\nB : BddAbove (range g)\nH : ∀ (x : ι), f x ≤ g x\nh✝ : IsEmpty ι\n⊢ sSup ∅ ≤ iSup g"
] | iSup_of_empty', | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.ConditionallyCompleteLattice.Indexed | {
"line": 174,
"column": 4
} | {
"line": 174,
"column": 25
} | {
"line": 175,
"column": 2
} | [
{
"pp": "case inl\nα : Type u_1\nι : Sort u_4\ninst✝ : ConditionallyCompleteLattice α\nf g : ι → α\nHf : BddAbove (range f)\nHg : BddAbove (range g)\nh✝ : IsEmpty ι\n⊢ ⨆ x, f x ⊔ g x = (⨆ x, f x) ⊔ ⨆ x, g x",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Lattice.toSemilatticeSup",
... | [] | simp [iSup_of_empty'] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Order.ConditionallyCompleteLattice.Indexed | {
"line": 174,
"column": 4
} | {
"line": 174,
"column": 25
} | {
"line": 175,
"column": 2
} | [
{
"pp": "case inl\nα : Type u_1\nι : Sort u_4\ninst✝ : ConditionallyCompleteLattice α\nf g : ι → α\nHf : BddAbove (range f)\nHg : BddAbove (range g)\nh✝ : IsEmpty ι\n⊢ ⨆ x, f x ⊔ g x = (⨆ x, f x) ⊔ ⨆ x, g x",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Lattice.toSemilatticeSup",
... | [] | simp [iSup_of_empty'] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.ConditionallyCompleteLattice.Indexed | {
"line": 174,
"column": 4
} | {
"line": 174,
"column": 25
} | {
"line": 175,
"column": 2
} | [
{
"pp": "case inl\nα : Type u_1\nι : Sort u_4\ninst✝ : ConditionallyCompleteLattice α\nf g : ι → α\nHf : BddAbove (range f)\nHg : BddAbove (range g)\nh✝ : IsEmpty ι\n⊢ ⨆ x, f x ⊔ g x = (⨆ x, f x) ⊔ ⨆ x, g x",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Lattice.toSemilatticeSup",
... | [] | simp [iSup_of_empty'] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.ConditionallyCompleteLattice.Indexed | {
"line": 236,
"column": 4
} | {
"line": 236,
"column": 25
} | {
"line": 237,
"column": 2
} | [
{
"pp": "case inl\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝ : ConditionallyCompleteLattice α\nf : β × γ → α\nhf : BddAbove (range f)\nh✝ : IsEmpty β\n⊢ ⨆ p, f p = ⨆ b, ⨆ c, f (b, c)",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"congrArg",
"iSup",
"Prod.mk",
... | [] | simp [iSup_of_empty'] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Order.ConditionallyCompleteLattice.Indexed | {
"line": 236,
"column": 4
} | {
"line": 236,
"column": 25
} | {
"line": 237,
"column": 2
} | [
{
"pp": "case inl\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝ : ConditionallyCompleteLattice α\nf : β × γ → α\nhf : BddAbove (range f)\nh✝ : IsEmpty β\n⊢ ⨆ p, f p = ⨆ b, ⨆ c, f (b, c)",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"congrArg",
"iSup",
"Prod.mk",
... | [] | simp [iSup_of_empty'] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.ConditionallyCompleteLattice.Indexed | {
"line": 236,
"column": 4
} | {
"line": 236,
"column": 25
} | {
"line": 237,
"column": 2
} | [
{
"pp": "case inl\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝ : ConditionallyCompleteLattice α\nf : β × γ → α\nhf : BddAbove (range f)\nh✝ : IsEmpty β\n⊢ ⨆ p, f p = ⨆ b, ⨆ c, f (b, c)",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"congrArg",
"iSup",
"Prod.mk",
... | [] | simp [iSup_of_empty'] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.ConditionallyCompleteLattice.Indexed | {
"line": 238,
"column": 4
} | {
"line": 238,
"column": 25
} | {
"line": 239,
"column": 2
} | [
{
"pp": "case inr.inl\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝ : ConditionallyCompleteLattice α\nf : β × γ → α\nhf : BddAbove (range f)\nh✝¹ : Nonempty β\nh✝ : IsEmpty γ\n⊢ ⨆ p, f p = ⨆ b, ⨆ c, f (b, c)",
"ppTerm": "?inr.inl",
"assigned": true,
"usedConstants": [
"congrArg",
"iSu... | [] | simp [iSup_of_empty'] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Order.ConditionallyCompleteLattice.Indexed | {
"line": 238,
"column": 4
} | {
"line": 238,
"column": 25
} | {
"line": 239,
"column": 2
} | [
{
"pp": "case inr.inl\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝ : ConditionallyCompleteLattice α\nf : β × γ → α\nhf : BddAbove (range f)\nh✝¹ : Nonempty β\nh✝ : IsEmpty γ\n⊢ ⨆ p, f p = ⨆ b, ⨆ c, f (b, c)",
"ppTerm": "?inr.inl",
"assigned": true,
"usedConstants": [
"congrArg",
"iSu... | [] | simp [iSup_of_empty'] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.ConditionallyCompleteLattice.Indexed | {
"line": 238,
"column": 4
} | {
"line": 238,
"column": 25
} | {
"line": 239,
"column": 2
} | [
{
"pp": "case inr.inl\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝ : ConditionallyCompleteLattice α\nf : β × γ → α\nhf : BddAbove (range f)\nh✝¹ : Nonempty β\nh✝ : IsEmpty γ\n⊢ ⨆ p, f p = ⨆ b, ⨆ c, f (b, c)",
"ppTerm": "?inr.inl",
"assigned": true,
"usedConstants": [
"congrArg",
"iSu... | [] | simp [iSup_of_empty'] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Set.Finite.Lattice | {
"line": 323,
"column": 2
} | {
"line": 323,
"column": 30
} | {
"line": 323,
"column": 31
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nα : Type u_3\ninst✝⁴ : Finite ι\ninst✝³ : Preorder ι'\ninst✝² : Nonempty ι'\ninst✝¹ : IsDirectedOrder ι'\ninst✝ : Order.Frame α\nf : ι → ι' → α\nhf : ∀ (i : ι), Monotone (f i)\n⊢ ⨆ j, ⨅ i, f i j = ⨅ i, ⨆ j, f i j",
"ppTerm": "?m.26",
"assigned": false,
"usedCons... | [
"ι : Type u_1\nι' : Type u_2\nα : Type u_3\ninst✝⁴ : Finite ι\ninst✝³ : Preorder ι'\ninst✝² : Nonempty ι'\ninst✝¹ : IsDirectedOrder ι'\ninst✝ : Order.Frame α\nf : ι → ι' → α\nhf : ∀ (i : ι), Monotone (f i)\n⊢ ⨆ j, ⨅ i, f i j = ⨅ i, ⨆ j, f i j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Finite.Lattice | {
"line": 399,
"column": 4
} | {
"line": 400,
"column": 11
} | {
"line": 400,
"column": 12
} | [
{
"pp": "α : Type u\nι : Type v\nκ : ι → Sort w\ninst✝¹ : Nonempty ((a : ι) → κ a)\ninst✝ : Order.Frame α\ns : Set ι\nhs : s.Finite\nf : (a : ι) → κ a → α\nh : ∀ {κ : ι → Type w} [Nonempty ((a : ι) → κ a)] (f : (a : ι) → κ a → α), ⨅ a ∈ s, ⨆ b, f a b = ⨆ g, ⨅ a ∈ s, f a (g a)\nthis : Nonempty ((a : ι) → PLift (... | [
"α : Type u\nι : Type v\nκ : ι → Sort w\ninst✝¹ : Nonempty ((a : ι) → κ a)\ninst✝ : Order.Frame α\ns : Set ι\nhs : s.Finite\nf : (a : ι) → κ a → α\nh : ∀ {κ : ι → Type w} [Nonempty ((a : ι) → κ a)] (f : (a : ι) → κ a → α), ⨅ a ∈ s, ⨆ b, f a b = ⨆ g, ⨅ a ∈ s, f a (g a)\nthis : Nonempty ((a : ι) → PLift (κ a))\n⊢ ⨅ a... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.ConditionallyCompleteLattice.Indexed | {
"line": 276,
"column": 2
} | {
"line": 276,
"column": 13
} | {
"line": 276,
"column": 14
} | [
{
"pp": "α : Type u_1\nι : Sort u_4\ninst✝¹ : ConditionallyCompleteLattice α\ninst✝ : Nonempty ι\nf : ι → α\nhf : BddBelow (range f)\nx✝ : α\n⊢ x✝ ∈ Iic (⨅ i, f i) ↔ x✝ ∈ ⋂ i, Iic (f i)",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"iInf",
"congrArg",
"S... | [
"α : Type u_1\nι : Sort u_4\ninst✝¹ : ConditionallyCompleteLattice α\ninst✝ : Nonempty ι\nf : ι → α\nhf : BddBelow (range f)\nx✝ : α\n⊢ x✝ ≤ ⨅ i, f i ↔ ∀ (i : ι), x✝ ≤ f i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.ConditionallyCompleteLattice.Indexed | {
"line": 286,
"column": 8
} | {
"line": 286,
"column": 23
} | {
"line": 286,
"column": 24
} | [
{
"pp": "case inl\nα : Type u_1\nι : Sort u_4\ninst✝ : ConditionallyCompleteLattice α\np : ι → Prop\nf : Subtype p → α\nhf : BddAbove (range f)\nhf' : sSup ∅ ≤ iSup f\nh✝ : IsEmpty (Subtype p)\n⊢ iSup f = ⨆ i, ⨆ (h : p i), f ⟨i, h⟩",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Eq.m... | [
"case inl\nα : Type u_1\nι : Sort u_4\ninst✝ : ConditionallyCompleteLattice α\np : ι → Prop\nf : Subtype p → α\nhf : BddAbove (range f)\nhf' : sSup ∅ ≤ iSup f\nh✝ : IsEmpty (Subtype p)\n⊢ sSup ∅ = ⨆ i, ⨆ (h : p i), f ⟨i, h⟩"
] | iSup_of_empty', | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Set.Finite.Lattice | {
"line": 454,
"column": 2
} | {
"line": 454,
"column": 52
} | {
"line": 454,
"column": 53
} | [
{
"pp": "α : Type u\ninst✝ : LinearOrder α\ns : Set α\n⊢ (s \\ ⋃ x, Ioo ↑x.1 ↑x.2).Finite",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Eq.mpr",
"Iff.of_eq",
"congrArg",
"iSup",
"iSup_subtype",
"PartialOrder.toPreorder",
"Set.Fi... | [
"α : Type u\ninst✝ : LinearOrder α\ns : Set α\n⊢ (s \\ ⨆ i ∈ s, ⨆ i_1 ∈ s, Ioo i i_1).Finite"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Finite.Lattice | {
"line": 475,
"column": 2
} | {
"line": 475,
"column": 13
} | {
"line": 475,
"column": 14
} | [
{
"pp": "α : Type u_1\nι : Type u_2\nf : ι → Set α\nc : Set ι\nhn : c.Nonempty\nhc : DirectedOn (fun i j ↦ f i ⊆ f j) c\ns : Finset α\nhs : ↑s ⊆ ⋃ x, f ↑x\nthis : Nonempty ↑c\n⊢ ∃ i ∈ c, ↑s ⊆ f i",
"ppTerm": "?m.36",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"α : Type u_1\nι : Type u_2\nf : ι → Set α\nc : Set ι\nhn : c.Nonempty\nhc : DirectedOn (fun i j ↦ f i ⊆ f j) c\ns : Finset α\nhs : ↑s ⊆ ⋃ x, f ↑x\nthis : Nonempty ↑c\n⊢ ∃ i ∈ c, ↑s ⊆ f i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.CompleteLattice.Finset | {
"line": 112,
"column": 37
} | {
"line": 112,
"column": 48
} | {
"line": 112,
"column": 49
} | [
{
"pp": "α : Type u_2\ninst✝ : DecidableEq α\nP : Finset α → Prop\ns : Finset α\nhP : ∀ ⦃s t : Finset α⦄, P t → t ⊆ s → P s\nh : Minimal P s\nx : α\nhxs : x ∈ s\nhx : P (s.erase x)\n⊢ False",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝ : DecidableEq α\nP : Finset α → Prop\ns : Finset α\nhP : ∀ ⦃s t : Finset α⦄, P t → t ⊆ s → P s\nh : Minimal P s\nx : α\nhxs : x ∈ s\nhx : P (s.erase x)\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.CompleteLattice.Finset | {
"line": 143,
"column": 2
} | {
"line": 143,
"column": 32
} | {
"line": 145,
"column": 0
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝¹ : CompleteLattice β\ninst✝ : DecidableEq α\nf : α → β\ns t : Finset α\n⊢ ⨆ x ∈ s ∪ t, f x = (⨆ x ∈ s, f x) ⊔ ⨆ x ∈ t, f x",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"Finset.instUnion",
... | [] | simpa using! _root_.iSup_union | Lean.Elab.Tactic.Simpa.evalSimpaUsingBang | Lean.Parser.Tactic.simpaUsingBang |
Mathlib.Order.CompleteLattice.Finset | {
"line": 143,
"column": 2
} | {
"line": 143,
"column": 32
} | {
"line": 145,
"column": 0
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝¹ : CompleteLattice β\ninst✝ : DecidableEq α\nf : α → β\ns t : Finset α\n⊢ ⨆ x ∈ s ∪ t, f x = (⨆ x ∈ s, f x) ⊔ ⨆ x ∈ t, f x",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"Finset.instUnion",
... | [] | simpa using! _root_.iSup_union | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
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