module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
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.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.ConditionallyCompleteLattice.Indexed | {
"line": 364,
"column": 4
} | {
"line": 364,
"column": 30
} | {
"line": 364,
"column": 31
} | [
{
"pp": "α : Type u_1\ninst✝ : ConditionallyCompleteLattice α\nι : Type u_5\nι' : Type u_6\ns : Set ι\nf : ι → ι'\ng : ι' → α\nhf : BddAbove (range fun i ↦ g (f ↑i))\nhg' : sSup ∅ ≤ ⨆ i, g (f ↑i)\nhs : s.Nonempty\n⊢ BddAbove (range fun i ↦ g ↑i)",
"ppTerm": "?m.86",
"assigned": true,
"usedConstants"... | [
"α : Type u_1\ninst✝ : ConditionallyCompleteLattice α\nι : Type u_5\nι' : Type u_6\ns : Set ι\nf : ι → ι'\ng : ι' → α\nhf : BddAbove (range fun i ↦ g (f ↑i))\nhg' : sSup ∅ ≤ ⨆ i, g (f ↑i)\nhs : s.Nonempty\n⊢ ∃ x, ∀ a ∈ s, g (f a) ≤ x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.ConditionallyCompleteLattice.Indexed | {
"line": 375,
"column": 4
} | {
"line": 375,
"column": 30
} | {
"line": 375,
"column": 31
} | [
{
"pp": "α : Type u_1\ninst✝ : ConditionallyCompleteLattice α\nι : Type u_5\nι' : Type u_6\ns : Set ι\nf : ι → ι'\ng : ι' → α\nhf : BddAbove (range fun i ↦ g (f ↑i))\nhg' : sSup ∅ ≤ ⨆ i, g (f ↑i)\nhs : s.Nonempty\nhg : BddAbove (range fun i ↦ g ↑i)\nthis : Nonempty ↑s\ni : ι\nh : i ∈ s\nt : ↑(f '' s)\nht : g ↑t... | [
"α : Type u_1\ninst✝ : ConditionallyCompleteLattice α\nι : Type u_5\nι' : Type u_6\ns : Set ι\nf : ι → ι'\ng : ι' → α\nhf : BddAbove (range fun i ↦ g (f ↑i))\nhg' : sSup ∅ ≤ ⨆ i, g (f ↑i)\nhs : s.Nonempty\nhg : BddAbove (range fun i ↦ g ↑i)\nthis : Nonempty ↑s\ni : ι\nh : i ∈ s\nt : ↑(f '' s)\nht : g ↑t = g (f ↑⟨i,... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.ConditionallyCompleteLattice.Indexed | {
"line": 387,
"column": 4
} | {
"line": 390,
"column": 7
} | {
"line": 391,
"column": 2
} | [
{
"pp": "case pos\nα : Type u_1\nι : Sort u_4\ninst✝ : ConditionallyCompleteLattice α\np : ι → Prop\nf : Exists p → α\nh : Exists p\n⊢ ⨆ (ih : Exists p), f ih ≤ ⨆ i, ⨆ (h : p i), f ⋯",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"le_ciSup₂",
"le_refl",
"iSup",
"Pa... | [] | have : Nonempty <| Exists p := ⟨h⟩
refine ciSup_le fun ⟨i, hi⟩ ↦ le_ciSup₂ (f := fun _ _ ↦ _) ⟨f ⟨i, hi⟩, ?_⟩ i hi
rintro _ ⟨_, ⟨j, rfl⟩, ⟨hj, rfl⟩⟩
rfl | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.ConditionallyCompleteLattice.Indexed | {
"line": 387,
"column": 4
} | {
"line": 390,
"column": 7
} | {
"line": 391,
"column": 2
} | [
{
"pp": "case pos\nα : Type u_1\nι : Sort u_4\ninst✝ : ConditionallyCompleteLattice α\np : ι → Prop\nf : Exists p → α\nh : Exists p\n⊢ ⨆ (ih : Exists p), f ih ≤ ⨆ i, ⨆ (h : p i), f ⋯",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"le_ciSup₂",
"le_refl",
"iSup",
"Pa... | [] | have : Nonempty <| Exists p := ⟨h⟩
refine ciSup_le fun ⟨i, hi⟩ ↦ le_ciSup₂ (f := fun _ _ ↦ _) ⟨f ⟨i, hi⟩, ?_⟩ i hi
rintro _ ⟨_, ⟨j, rfl⟩, ⟨hj, rfl⟩⟩
rfl | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Finset.Sigma | {
"line": 77,
"column": 2
} | {
"line": 81,
"column": 42
} | {
"line": 83,
"column": 0
} | [
{
"pp": "ι : Type u_1\nα : ι → Type u_2\ns : Finset ι\nt : (i : ι) → Finset (α i)\n⊢ (↑s).PairwiseDisjoint fun i ↦ map (Embedding.sigmaMk i) (t i)",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"Function.Embedding.sigmaMk_apply",
"Function.onFun"... | [] | intro i _ j _ hij
rw [Function.onFun, disjoint_left]
simp_rw [mem_map, Function.Embedding.sigmaMk_apply]
rintro _ ⟨y, _, rfl⟩ ⟨z, _, hz'⟩
exact hij (congr_arg Sigma.fst hz'.symm) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Finset.Sigma | {
"line": 77,
"column": 2
} | {
"line": 81,
"column": 42
} | {
"line": 83,
"column": 0
} | [
{
"pp": "ι : Type u_1\nα : ι → Type u_2\ns : Finset ι\nt : (i : ι) → Finset (α i)\n⊢ (↑s).PairwiseDisjoint fun i ↦ map (Embedding.sigmaMk i) (t i)",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"Function.Embedding.sigmaMk_apply",
"Function.onFun"... | [] | intro i _ j _ hij
rw [Function.onFun, disjoint_left]
simp_rw [mem_map, Function.Embedding.sigmaMk_apply]
rintro _ ⟨y, _, rfl⟩ ⟨z, _, hz'⟩
exact hij (congr_arg Sigma.fst hz'.symm) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Finset.Preimage | {
"line": 119,
"column": 25
} | {
"line": 119,
"column": 36
} | {
"line": 119,
"column": 37
} | [
{
"pp": "α : Type u\nβ : Type v\ninst✝ : DecidableEq β\nf : α → β\ns : Finset β\nhf : BijOn f (f ⁻¹' ↑s) ↑s\n⊢ ↑(image f (s.preimage f ⋯)) = ↑s",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Finset",
"Finset.coe_image",
"id",
"Set... | [
"α : Type u\nβ : Type v\ninst✝ : DecidableEq β\nf : α → β\ns : Finset β\nhf : BijOn f (f ⁻¹' ↑s) ↑s\n⊢ f '' f ⁻¹' ↑s = ↑s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.ConditionallyCompleteLattice.Indexed | {
"line": 510,
"column": 6
} | {
"line": 510,
"column": 21
} | {
"line": 510,
"column": 22
} | [
{
"pp": "α : Type u_1\nι : Sort u_4\ninst✝¹ : ConditionallyCompleteLinearOrderBot α\ninst✝ : IsEmpty ι\nf : ι → α\n⊢ ⨆ i, f i = ⊥",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"congrArg",
"iSup",
"OrderBot.toBot",
"... | [
"α : Type u_1\nι : Sort u_4\ninst✝¹ : ConditionallyCompleteLinearOrderBot α\ninst✝ : IsEmpty ι\nf : ι → α\n⊢ sSup ∅ = ⊥"
] | iSup_of_empty', | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.ConditionallyCompleteLattice.Indexed | {
"line": 510,
"column": 2
} | {
"line": 510,
"column": 34
} | {
"line": 512,
"column": 0
} | [
{
"pp": "α : Type u_1\nι : Sort u_4\ninst✝¹ : ConditionallyCompleteLinearOrderBot α\ninst✝ : IsEmpty ι\nf : ι → α\n⊢ ⨆ i, f i = ⊥",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"congrArg",
"iSup",
"OrderBot.toBot",
"... | [] | rw [iSup_of_empty', csSup_empty] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Order.ConditionallyCompleteLattice.Indexed | {
"line": 510,
"column": 2
} | {
"line": 510,
"column": 34
} | {
"line": 512,
"column": 0
} | [
{
"pp": "α : Type u_1\nι : Sort u_4\ninst✝¹ : ConditionallyCompleteLinearOrderBot α\ninst✝ : IsEmpty ι\nf : ι → α\n⊢ ⨆ i, f i = ⊥",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"congrArg",
"iSup",
"OrderBot.toBot",
"... | [] | rw [iSup_of_empty', csSup_empty] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.ConditionallyCompleteLattice.Indexed | {
"line": 510,
"column": 2
} | {
"line": 510,
"column": 34
} | {
"line": 512,
"column": 0
} | [
{
"pp": "α : Type u_1\nι : Sort u_4\ninst✝¹ : ConditionallyCompleteLinearOrderBot α\ninst✝ : IsEmpty ι\nf : ι → α\n⊢ ⨆ i, f i = ⊥",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"congrArg",
"iSup",
"OrderBot.toBot",
"... | [] | rw [iSup_of_empty', csSup_empty] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.ConditionallyCompleteLattice.Indexed | {
"line": 540,
"column": 2
} | {
"line": 540,
"column": 39
} | {
"line": 540,
"column": 40
} | [
{
"pp": "α : Type u_1\nι : Sort u_4\ninst✝ : ConditionallyCompleteLinearOrderBot α\na : α\nf : ι → α\nh : BddAbove (range f)\n⊢ a < iSup f ↔ ∃ i, a < f i",
"ppTerm": "?m.14",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nι : Sort u_4\ninst✝ : ConditionallyCompleteLinearOrderBot α\na : α\nf : ι → α\nh : BddAbove (range f)\n⊢ a < iSup f ↔ ∃ i, a < f i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Preimage | {
"line": 164,
"column": 14
} | {
"line": 164,
"column": 25
} | {
"line": 164,
"column": 26
} | [
{
"pp": "α : Type u\ninst✝¹ : Lattice α\ninst✝ : OrderBot α\nP : α → Prop\nPsup : ∀ ⦃s t : α⦄, P s → P t → P (s ⊔ t)\nPbot : P ⊥\nt : Finset α\nht : ∀ x ∈ t, P x\nthis : OrderBot (Subtype P) := Subtype.orderBot Pbot\nx : α\nhx : x ∈ ↑t\n⊢ x ∈ Subtype.val '' Subtype.val ⁻¹' ↑t",
"ppTerm": "?m.95",
"assig... | [
"α : Type u\ninst✝¹ : Lattice α\ninst✝ : OrderBot α\nP : α → Prop\nPsup : ∀ ⦃s t : α⦄, P s → P t → P (s ⊔ t)\nPbot : P ⊥\nt : Finset α\nht : ∀ x ∈ t, P x\nthis : OrderBot (Subtype P) := Subtype.orderBot Pbot\nx : α\nhx : x ∈ ↑t\n⊢ x ∈ t ∧ P x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.ConditionallyCompleteLattice.Indexed | {
"line": 652,
"column": 6
} | {
"line": 652,
"column": 76
} | {
"line": 652,
"column": 77
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nι : Sort u_4\ninst✝¹ : ConditionallyCompleteLinearOrderBot α\ninst✝ : ConditionallyCompleteLinearOrderBot β\ne : α ≃o β\nf : ι → α\nh✝ : Nonempty ι\nhf : ¬BddAbove (range f)\n⊢ ¬BddAbove (range fun i ↦ e (f i))",
"ppTerm": "?m.75",
"assigned": true,
"usedConstant... | [
"α : Type u_1\nβ : Type u_2\nι : Sort u_4\ninst✝¹ : ConditionallyCompleteLinearOrderBot α\ninst✝ : ConditionallyCompleteLinearOrderBot β\ne : α ≃o β\nf : ι → α\nh✝ : Nonempty ι\nhf : ¬BddAbove (range f)\n⊢ ∀ (x : α), ∃ x_1, x < f x_1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.ConditionallyCompleteLattice.Indexed | {
"line": 669,
"column": 17
} | {
"line": 669,
"column": 61
} | {
"line": 669,
"column": 62
} | [
{
"pp": "α : Type u_1\nι : Sort u_4\ninst✝ : ConditionallyCompleteLinearOrderBot α\nf : ι → α\nhf : ∀ (x : α), ∃ y ∈ range f, x < y\na : WithTop α\nha : a < ⊤\ni : ι\nhi : a.untop ⋯ < f i\n⊢ a < ↑(f i)",
"ppTerm": "?m.98",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals":... | [
"α : Type u_1\nι : Sort u_4\ninst✝ : ConditionallyCompleteLinearOrderBot α\nf : ι → α\nhf : ∀ (x : α), ∃ y ∈ range f, x < y\na : WithTop α\nha : a < ⊤\ni : ι\nhi : a.untop ⋯ < f i\n⊢ a < ↑(f i)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Cover | {
"line": 495,
"column": 68
} | {
"line": 500,
"column": 65
} | {
"line": 502,
"column": 0
} | [
{
"pp": "α : Type u_1\nx : α\ns : Set α\n⊢ s ⩿ insert x s",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Eq.mpr",
"wcovBy_of_eq_or_eq",
"congrArg",
"PartialOrder.toPreorder",
"Classical.propDecidable",
"Preorder.toLE",
"Membership... | [] | by
refine wcovBy_of_eq_or_eq (subset_insert x s) fun t hst h2t => ?_
by_cases h : x ∈ t
· exact Or.inr (subset_antisymm h2t <| insert_subset_iff.mpr ⟨h, hst⟩)
· refine Or.inl (subset_antisymm ?_ hst)
rwa [← sdiff_singleton_eq_self h, sdiff_singleton_subset_iff] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.Cover | {
"line": 643,
"column": 46
} | {
"line": 643,
"column": 80
} | {
"line": 643,
"column": 81
} | [
{
"pp": "ι : Type u_3\nα : ι → Type u_4\ninst✝ : (i : ι) → Preorder (α i)\na b : (i : ι) → α i\nh : a ⩿ b\ni : ι\nci : α i\nh₁ : a i < ci\nh₂ : ci < b i\n⊢ Function.update a i ci ≤ b",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Order.Cover.0.WCovBy.eval._simp_1_1... | [
"ι : Type u_3\nα : ι → Type u_4\ninst✝ : (i : ι) → Preorder (α i)\na b : (i : ι) → α i\nh : a ⩿ b\ni : ι\nci : α i\nh₁ : a i < ci\nh₂ : ci < b i\n⊢ ∀ (j : ι), ¬j = i → a j ≤ b j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Cover | {
"line": 654,
"column": 24
} | {
"line": 654,
"column": 54
} | {
"line": 654,
"column": 55
} | [
{
"pp": "ι : Type u_3\nα : ι → Type u_4\ninst✝ : (i : ι) → Preorder (α i)\na b : (i : ι) → α i\nh : ∀ ⦃c : (i : ι) → α i⦄, a ≤ c → ∀ (x : ι), a x < c x → c ≤ b → ∀ (x : ι), ¬c x < b x\nhab : a ≤ b\ni : ι\nhi : a i < b i\nj : ι\nhj : j ≠ i\nc : (i : ι) → α i := Function.update a i (b i)\n⊢ c ≤ b",
"ppTerm": ... | [
"ι : Type u_3\nα : ι → Type u_4\ninst✝ : (i : ι) → Preorder (α i)\na b : (i : ι) → α i\nh : ∀ ⦃c : (i : ι) → α i⦄, a ≤ c → ∀ (x : ι), a x < c x → c ≤ b → ∀ (x : ι), ¬c x < b x\nhab : a ≤ b\ni : ι\nhi : a i < b i\nj : ι\nhj : j ≠ i\nc : (i : ι) → α i := Function.update a i (b i)\n⊢ ∀ (j : ι), ¬j = i → a j ≤ b j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Cover | {
"line": 656,
"column": 19
} | {
"line": 656,
"column": 63
} | {
"line": 656,
"column": 64
} | [
{
"pp": "ι : Type u_3\nα : ι → Type u_4\ninst✝ : (i : ι) → Preorder (α i)\na b : (i : ι) → α i\nh : ∀ ⦃c : (i : ι) → α i⦄, a ≤ c → ∀ (x : ι), a x < c x → c ≤ b → ∀ (x : ι), ¬c x < b x\nhab : a ≤ b\ni : ι\nhi : a i < b i\nj : ι\nhj : j ≠ i\nc : (i : ι) → α i := Function.update a i (b i)\nh₁ : c ≤ b\nh₂ : ¬c j < ... | [
"ι : Type u_3\nα : ι → Type u_4\ninst✝ : (i : ι) → Preorder (α i)\na b : (i : ι) → α i\nh : ∀ ⦃c : (i : ι) → α i⦄, a ≤ c → ∀ (x : ι), a x < c x → c ≤ b → ∀ (x : ι), ¬c x < b x\nhab : a ≤ b\ni : ι\nhi : a i < b i\nj : ι\nhj : j ≠ i\nc : (i : ι) → α i := Function.update a i (b i)\nh₁ : c ≤ b\nh₂ : ¬c j < b j\n⊢ b j ≤... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Cover | {
"line": 731,
"column": 26
} | {
"line": 731,
"column": 71
} | {
"line": 731,
"column": 72
} | [
{
"pp": "ι : Type u_3\nα : ι → Type u_4\ninst✝² : (i : ι) → PartialOrder (α i)\na b : (i : ι) → α i\ninst✝¹ : Nonempty ι\ninst✝ : DecidableEq ι\ni : ι\nhi : a i ⩿ b i\nh : ∀ (j : ι), j ≠ i → a j = b j\n⊢ b = Function.update a i (b i)",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"E... | [
"ι : Type u_3\nα : ι → Type u_4\ninst✝² : (i : ι) → PartialOrder (α i)\na b : (i : ι) → α i\ninst✝¹ : Nonempty ι\ninst✝ : DecidableEq ι\ni : ι\nhi : a i ⩿ b i\nh : ∀ (j : ι), j ≠ i → a j = b j\n⊢ ∀ (x : ι), ¬i = x → a x = b x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Preorder.Finite | {
"line": 37,
"column": 41
} | {
"line": 37,
"column": 58
} | {
"line": 37,
"column": 59
} | [
{
"pp": "ι : Type u_1\nα : Type u_2\ninst✝¹ : LE α\ninst✝ : IsTrans α LE.le\nf : ι → α\ns✝ : Finset ι\ni : ι\ns : Finset ι\nhi : i ∉ s\nhs : s.Nonempty\nj : ι\nhj : MaximalFor (fun x ↦ x ∈ s) f j\nhji : ¬f j ≤ f i\n⊢ ∀ ⦃j_1 : ι⦄, (fun x ↦ x ∈ cons i s hi) j_1 → f j ≤ f j_1 → f j_1 ≤ f j",
"ppTerm": "?m.90",... | [
"ι : Type u_1\nα : Type u_2\ninst✝¹ : LE α\ninst✝ : IsTrans α LE.le\nf : ι → α\ns✝ : Finset ι\ni : ι\ns : Finset ι\nhi : i ∉ s\nhs : s.Nonempty\nj : ι\nhj : MaximalFor (fun x ↦ x ∈ s) f j\nhji : ¬f j ≤ f i\n⊢ ∀ a ∈ s, f j ≤ f a → f a ≤ f j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Preorder.Finite | {
"line": 51,
"column": 4
} | {
"line": 51,
"column": 36
} | {
"line": 51,
"column": 37
} | [
{
"pp": "α : Type u_2\ninst✝ : Preorder α\na : α\ns : Finset α\nha : a ∈ s\n⊢ ∃ b ∈ s, a ≤ b ∧ ?m.24 b",
"ppTerm": "?m.26",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝ : Preorder α\na : α\ns : Finset α\nha : a ∈ s\n⊢ ∃ b ∈ s, a ≤ b ∧ ?m.24 b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Preorder.Finite | {
"line": 63,
"column": 35
} | {
"line": 64,
"column": 60
} | {
"line": 66,
"column": 0
} | [
{
"pp": "ι : Type u_1\nα : Type u_2\ninst✝¹ : LE α\ninst✝ : IsTrans α LE.le\nf : ι → α\ns : Set ι\nh : s.Finite\nhs : s.Nonempty\n⊢ ∃ i, MaximalFor (fun x ↦ x ∈ s) f i",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"MaximalFor",
"Finset",
"Set.Finite",
"Membership.... | [] | by
lift s to Finset ι using h; exact s.exists_maximalFor f hs | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.Cover | {
"line": 740,
"column": 26
} | {
"line": 740,
"column": 71
} | {
"line": 740,
"column": 72
} | [
{
"pp": "ι : Type u_3\nα : ι → Type u_4\ninst✝¹ : (i : ι) → PartialOrder (α i)\na b : (i : ι) → α i\ninst✝ : DecidableEq ι\ni : ι\nhi : a i ⋖ b i\nh : ∀ (j : ι), j ≠ i → a j = b j\n⊢ b = Function.update a i (b i)",
"ppTerm": "?m.47",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Functi... | [
"ι : Type u_3\nα : ι → Type u_4\ninst✝¹ : (i : ι) → PartialOrder (α i)\na b : (i : ι) → α i\ninst✝ : DecidableEq ι\ni : ι\nhi : a i ⋖ b i\nh : ∀ (j : ι), j ≠ i → a j = b j\n⊢ ∀ (x : ι), ¬i = x → a x = b x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Cover | {
"line": 749,
"column": 26
} | {
"line": 749,
"column": 71
} | {
"line": 749,
"column": 72
} | [
{
"pp": "ι : Type u_3\nα : ι → Type u_4\ninst✝² : (i : ι) → PartialOrder (α i)\na b : (i : ι) → α i\ninst✝¹ : Nonempty ι\ninst✝ : DecidableEq ι\ni : ι\nhi : a i ⩿ b i\nh : ∀ (j : ι), j ≠ i → a j = b j\n⊢ a = Function.update b i (a i)",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"E... | [
"ι : Type u_3\nα : ι → Type u_4\ninst✝² : (i : ι) → PartialOrder (α i)\na b : (i : ι) → α i\ninst✝¹ : Nonempty ι\ninst✝ : DecidableEq ι\ni : ι\nhi : a i ⩿ b i\nh : ∀ (j : ι), j ≠ i → a j = b j\n⊢ ∀ (x : ι), ¬i = x → a x = b x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Cover | {
"line": 758,
"column": 26
} | {
"line": 758,
"column": 71
} | {
"line": 758,
"column": 72
} | [
{
"pp": "ι : Type u_3\nα : ι → Type u_4\ninst✝¹ : (i : ι) → PartialOrder (α i)\na b : (i : ι) → α i\ninst✝ : DecidableEq ι\ni : ι\nhi : a i ⋖ b i\nh : ∀ (j : ι), j ≠ i → a j = b j\n⊢ a = Function.update b i (a i)",
"ppTerm": "?m.47",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Order... | [
"ι : Type u_3\nα : ι → Type u_4\ninst✝¹ : (i : ι) → PartialOrder (α i)\na b : (i : ι) → α i\ninst✝ : DecidableEq ι\ni : ι\nhi : a i ⋖ b i\nh : ∀ (j : ι), j ≠ i → a j = b j\n⊢ ∀ (x : ι), ¬i = x → a x = b x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Minimal | {
"line": 358,
"column": 2
} | {
"line": 358,
"column": 61
} | {
"line": 358,
"column": 62
} | [
{
"pp": "α : Type u_2\nP : Set α → Prop\ns : Set α\nhP : ∀ ⦃s t : Set α⦄, P t → t ⊆ s → P s\nhs : P s\nh : ¬Minimal P s\n⊢ ∃ x, x ∈ s ∧ P (s \\ {x})",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\nP : Set α → Prop\ns : Set α\nhP : ∀ ⦃s t : Set α⦄, P t → t ⊆ s → P s\nhs : P s\nh : ¬Minimal P s\n⊢ ∃ x, x ∈ s ∧ P (s \\ {x})"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Minimal | {
"line": 380,
"column": 2
} | {
"line": 380,
"column": 52
} | {
"line": 380,
"column": 53
} | [
{
"pp": "α : Type u_2\nP : Set α → Prop\ns : Set α\nhP : ∀ ⦃s t : Set α⦄, P t → s ⊆ t → P s\nhs : P s\nh : ¬Maximal P s\n⊢ ∃ x, ¬x ∈ s ∧ P (insert x s)",
"ppTerm": "?m.15",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\nP : Set α → Prop\ns : Set α\nhP : ∀ ⦃s t : Set α⦄, P t → s ⊆ t → P s\nhs : P s\nh : ¬Maximal P s\n⊢ ∃ x, ¬x ∈ s ∧ P (insert x s)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Multiset | {
"line": 252,
"column": 47
} | {
"line": 254,
"column": 5
} | {
"line": 256,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : PartialOrder α\ninst✝¹ : LocallyFiniteOrder α\na b : α\ninst✝ : DecidablePred fun x ↦ x ≤ a\nhab : a < b\n⊢ filter (fun x ↦ x ≤ a) (Ico a b) = {a}",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Finset",
"Finset... | [] | by
rw [Ico, ← Finset.filter_val, Finset.Ico_filter_le_left hab]
rfl | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.Interval.Finset.Nat | {
"line": 161,
"column": 6
} | {
"line": 161,
"column": 17
} | {
"line": 161,
"column": 18
} | [
{
"pp": "case succ.inl.inr\na n : ℕ\nih : Set.InjOn (fun x ↦ x % a) ↑(Ico n (n + a))\nl : ℕ\nha : 0 < a\nhkl : n % a = l % a\nhkn : n + a ≠ n\nhln : l ≠ n\nhl : l ∈ Ico n (n + a)\n⊢ n ∈ ↑(Ico n (n + a))",
"ppTerm": "?succ.inl.inr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.c... | [
"case succ.inl.inr\na n : ℕ\nih : Set.InjOn (fun x ↦ x % a) ↑(Ico n (n + a))\nl : ℕ\nha : 0 < a\nhkl : n % a = l % a\nhkn : n + a ≠ n\nhln : l ≠ n\nhl : l ∈ Ico n (n + a)\n⊢ 0 < a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.Nat | {
"line": 165,
"column": 6
} | {
"line": 165,
"column": 17
} | {
"line": 165,
"column": 18
} | [
{
"pp": "case succ.inr.inl\na n : ℕ\nih : Set.InjOn (fun x ↦ x % a) ↑(Ico n (n + a))\nk : ℕ\nha : 0 < a\nhkn : k ≠ n\nhk : k ∈ Ico n (n + a)\nhkl : k % a = n % a\nhln : n + a ≠ n\n⊢ n ∈ ↑(Ico n (n + a))",
"ppTerm": "?succ.inr.inl",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.c... | [
"case succ.inr.inl\na n : ℕ\nih : Set.InjOn (fun x ↦ x % a) ↑(Ico n (n + a))\nk : ℕ\nha : 0 < a\nhkn : k ≠ n\nhk : k ∈ Ico n (n + a)\nhkl : k % a = n % a\nhln : n + a ≠ n\n⊢ 0 < a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.Nat | {
"line": 184,
"column": 6
} | {
"line": 184,
"column": 33
} | {
"line": 184,
"column": 34
} | [
{
"pp": "case inr.mpr.inl.refine_1\nn a : ℕ\nha : a ≠ 0\ni : ℕ\nhia : i < a\nhn : n % a + a * (n / a) = n\nhi : i < n % a\n⊢ n % a ≤ i + a",
"ppTerm": "?inr.mpr.inl.refine_1",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case inr.mpr.inl.refine_1\nn a : ℕ\nha : a ≠ 0\ni : ℕ\nhia : i < a\nhn : n % a + a * (n / a) = n\nhi : i < n % a\n⊢ n % a ≤ i + a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.Nat | {
"line": 188,
"column": 4
} | {
"line": 191,
"column": 58
} | {
"line": 193,
"column": 0
} | [
{
"pp": "case inr.mpr.inr\nn a : ℕ\nha : a ≠ 0\ni : ℕ\nhia : i < a\nhn : n % a + a * (n / a) = n\nhi : n % a ≤ i\n⊢ ∃ a_1, (n ≤ a_1 ∧ a_1 < n + a) ∧ a_1 % a = i",
"ppTerm": "?inr.mpr.inr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"instHDiv",
"HMul.hMul"... | [] | refine ⟨i + a * (n / a), ⟨?_, ?_⟩, ?_⟩
· lia
· lia
· rw [Nat.add_mul_mod_self_left, Nat.mod_eq_of_lt hia] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Interval.Finset.Nat | {
"line": 188,
"column": 4
} | {
"line": 191,
"column": 58
} | {
"line": 193,
"column": 0
} | [
{
"pp": "case inr.mpr.inr\nn a : ℕ\nha : a ≠ 0\ni : ℕ\nhia : i < a\nhn : n % a + a * (n / a) = n\nhi : n % a ≤ i\n⊢ ∃ a_1, (n ≤ a_1 ∧ a_1 < n + a) ∧ a_1 % a = i",
"ppTerm": "?inr.mpr.inr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"instHDiv",
"HMul.hMul"... | [] | refine ⟨i + a * (n / a), ⟨?_, ?_⟩, ?_⟩
· lia
· lia
· rw [Nat.add_mul_mod_self_left, Nat.mod_eq_of_lt hia] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.WellQuasiOrder | {
"line": 121,
"column": 23
} | {
"line": 121,
"column": 56
} | {
"line": 121,
"column": 57
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\nr : α → α → Prop\ns : β → β → Prop\nh : WellQuasiOrdered r\nf : r →r s\nhf : Function.Surjective ⇑f\nseq : ℕ → β\nw✝¹ w✝ : ℕ\nhle : w✝¹ < w✝\nhr : r ((Function.surjInv hf ∘ seq) w✝¹) ((Function.surjInv hf ∘ seq) w✝)\n⊢ s (seq w✝¹) (seq w✝)",
"ppTerm": "?m.65",
"assig... | [
"α : Type u_3\nβ : Type u_4\nr : α → α → Prop\ns : β → β → Prop\nh : WellQuasiOrdered r\nf : r →r s\nhf : Function.Surjective ⇑f\nseq : ℕ → β\nw✝¹ w✝ : ℕ\nhle : w✝¹ < w✝\nhr : r ((Function.surjInv hf ∘ seq) w✝¹) ((Function.surjInv hf ∘ seq) w✝)\n⊢ s (seq w✝¹) (seq w✝)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.WellQuasiOrder | {
"line": 135,
"column": 2
} | {
"line": 135,
"column": 38
} | {
"line": 135,
"column": 39
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝¹ : LE α\ninst✝ : LE β\nf : α ≃o β\n⊢ WellQuasiOrderedLE α ↔ WellQuasiOrderedLE β",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"_private.Mathlib.Order.WellQuasiOrder.0.OrderIso.wellQuasiOrderedLE_iff._simp_... | [
"α : Type u_3\nβ : Type u_4\ninst✝¹ : LE α\ninst✝ : LE β\nf : α ≃o β\n⊢ (WellQuasiOrdered fun x1 x2 ↦ x1 ≤ x2) ↔ WellQuasiOrdered fun x1 x2 ↦ x1 ≤ x2"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.Basic | {
"line": 147,
"column": 2
} | {
"line": 147,
"column": 28
} | {
"line": 147,
"column": 29
} | [
{
"pp": "α : Type u_2\na₁ a₂ b₁ b₂ : α\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrder α\nha : a₂ ≤ a₁\nhb : b₁ ≤ b₂\n⊢ Icc a₁ b₁ ⊆ Icc a₂ b₂",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Finset",
"PartialOrder.toPreorder",
"Finset.co... | [
"α : Type u_2\na₁ a₂ b₁ b₂ : α\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrder α\nha : a₂ ≤ a₁\nhb : b₁ ≤ b₂\n⊢ Set.Icc a₁ b₁ ⊆ Set.Icc a₂ b₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.Basic | {
"line": 151,
"column": 2
} | {
"line": 151,
"column": 28
} | {
"line": 151,
"column": 29
} | [
{
"pp": "α : Type u_2\na₁ a₂ b₁ b₂ : α\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrder α\nha : a₂ ≤ a₁\nhb : b₁ ≤ b₂\n⊢ Ico a₁ b₁ ⊆ Ico a₂ b₂",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.coe_Ico",
"congrArg",
"Finset",
"PartialOrder.toPre... | [
"α : Type u_2\na₁ a₂ b₁ b₂ : α\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrder α\nha : a₂ ≤ a₁\nhb : b₁ ≤ b₂\n⊢ Set.Ico a₁ b₁ ⊆ Set.Ico a₂ b₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.Basic | {
"line": 155,
"column": 2
} | {
"line": 155,
"column": 28
} | {
"line": 155,
"column": 29
} | [
{
"pp": "α : Type u_2\na₁ a₂ b₁ b₂ : α\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrder α\nha : a₂ ≤ a₁\nhb : b₁ ≤ b₂\n⊢ Ioc a₁ b₁ ⊆ Ioc a₂ b₂",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ioc",
"congrArg",
"Finset",
"PartialOrder.toPreorder",... | [
"α : Type u_2\na₁ a₂ b₁ b₂ : α\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrder α\nha : a₂ ≤ a₁\nhb : b₁ ≤ b₂\n⊢ Set.Ioc a₁ b₁ ⊆ Set.Ioc a₂ b₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.Basic | {
"line": 159,
"column": 2
} | {
"line": 159,
"column": 28
} | {
"line": 159,
"column": 29
} | [
{
"pp": "α : Type u_2\na₁ a₂ b₁ b₂ : α\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrder α\nha : a₂ ≤ a₁\nhb : b₁ ≤ b₂\n⊢ Ioo a₁ b₁ ⊆ Ioo a₂ b₂",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Finset",
"PartialOrder.toPreorder",
"Preorder.... | [
"α : Type u_2\na₁ a₂ b₁ b₂ : α\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrder α\nha : a₂ ≤ a₁\nhb : b₁ ≤ b₂\n⊢ Set.Ioo a₁ b₁ ⊆ Set.Ioo a₂ b₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.Basic | {
"line": 364,
"column": 2
} | {
"line": 364,
"column": 28
} | {
"line": 364,
"column": 29
} | [
{
"pp": "α : Type u_2\na b : α\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrderTop α\nh : a ≤ b\n⊢ Ioi b ⊆ Ioi a",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ioi",
"Finset.Ioi",
"congrArg",
"Finset",
"PartialOrder.toPreorder",
"Pr... | [
"α : Type u_2\na b : α\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrderTop α\nh : a ≤ b\n⊢ Set.Ioi b ⊆ Set.Ioi a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.Basic | {
"line": 368,
"column": 2
} | {
"line": 368,
"column": 29
} | {
"line": 368,
"column": 30
} | [
{
"pp": "α : Type u_2\na b : α\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrderTop α\nh : a < b\n⊢ Ioi b ⊂ Ioi a",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ioi",
"Preorder.toLT",
"Finset.Ioi",
"congrArg",
"Finset",
"PartialOrder... | [
"α : Type u_2\na b : α\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrderTop α\nh : a < b\n⊢ Set.Ioi b ⊂ Set.Ioi a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.Basic | {
"line": 373,
"column": 2
} | {
"line": 373,
"column": 28
} | {
"line": 373,
"column": 29
} | [
{
"pp": "α : Type u_2\na b : α\ninst✝² : Preorder α\ninst✝¹ : LocallyFiniteOrderTop α\ninst✝ : LocallyFiniteOrder α\n⊢ Icc a b ⊆ Ici a",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ici",
"congrArg",
"Finset",
"PartialOrder.toPreorder",
"... | [
"α : Type u_2\na b : α\ninst✝² : Preorder α\ninst✝¹ : LocallyFiniteOrderTop α\ninst✝ : LocallyFiniteOrder α\n⊢ Set.Icc a b ⊆ Set.Ici a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.Basic | {
"line": 376,
"column": 2
} | {
"line": 376,
"column": 28
} | {
"line": 376,
"column": 29
} | [
{
"pp": "α : Type u_2\na b : α\ninst✝² : Preorder α\ninst✝¹ : LocallyFiniteOrderTop α\ninst✝ : LocallyFiniteOrder α\n⊢ Ico a b ⊆ Ici a",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.coe_Ico",
"Set.Ici",
"congrArg",
"Finset",
"PartialOr... | [
"α : Type u_2\na b : α\ninst✝² : Preorder α\ninst✝¹ : LocallyFiniteOrderTop α\ninst✝ : LocallyFiniteOrder α\n⊢ Set.Ico a b ⊆ Set.Ici a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.Basic | {
"line": 379,
"column": 2
} | {
"line": 379,
"column": 28
} | {
"line": 379,
"column": 29
} | [
{
"pp": "α : Type u_2\na b : α\ninst✝² : Preorder α\ninst✝¹ : LocallyFiniteOrderTop α\ninst✝ : LocallyFiniteOrder α\n⊢ Ioc a b ⊆ Ioi a",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ioc",
"Set.Ioi",
"Finset.Ioi",
"congrArg",
"Finset",
... | [
"α : Type u_2\na b : α\ninst✝² : Preorder α\ninst✝¹ : LocallyFiniteOrderTop α\ninst✝ : LocallyFiniteOrder α\n⊢ Set.Ioc a b ⊆ Set.Ioi a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.Basic | {
"line": 382,
"column": 2
} | {
"line": 382,
"column": 28
} | {
"line": 382,
"column": 29
} | [
{
"pp": "α : Type u_2\na b : α\ninst✝² : Preorder α\ninst✝¹ : LocallyFiniteOrderTop α\ninst✝ : LocallyFiniteOrder α\n⊢ Ioo a b ⊆ Ioi a",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ioi",
"Finset.Ioi",
"congrArg",
"Finset",
"PartialOrder.... | [
"α : Type u_2\na b : α\ninst✝² : Preorder α\ninst✝¹ : LocallyFiniteOrderTop α\ninst✝ : LocallyFiniteOrder α\n⊢ Set.Ioo a b ⊆ Set.Ioi a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.Basic | {
"line": 427,
"column": 2
} | {
"line": 427,
"column": 28
} | {
"line": 427,
"column": 29
} | [
{
"pp": "α : Type u_2\na b : α\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrderBot α\nh : a ≤ b\n⊢ Iio a ⊆ Iio b",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Finset",
"PartialOrder.toPreorder",
"Finset.Iio",
"Preorder.toLE",
... | [
"α : Type u_2\na b : α\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrderBot α\nh : a ≤ b\n⊢ Set.Iio a ⊆ Set.Iio b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.Basic | {
"line": 431,
"column": 2
} | {
"line": 431,
"column": 29
} | {
"line": 431,
"column": 30
} | [
{
"pp": "α : Type u_2\na b : α\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrderBot α\nh : a < b\n⊢ Iio a ⊂ Iio b",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"congrArg",
"Finset",
"PartialOrder.toPreorder",
"Finset.Iio",
... | [
"α : Type u_2\na b : α\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrderBot α\nh : a < b\n⊢ Set.Iio a ⊂ Set.Iio b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.Basic | {
"line": 435,
"column": 54
} | {
"line": 435,
"column": 65
} | {
"line": 435,
"column": 66
} | [
{
"pp": "α : Type u_2\na : α\ninst✝³ : Preorder α\ninst✝² : LocallyFiniteOrderBot α\nβ : Type u_3\ninst✝¹ : SemilatticeSup β\ninst✝ : OrderBot β\nf : α → β\nhf : Monotone f\nx✝ : α\nh : x✝ ∈ Iic a\n⊢ x✝ ≤ a",
"ppTerm": "?m.32",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGo... | [
"α : Type u_2\na : α\ninst✝³ : Preorder α\ninst✝² : LocallyFiniteOrderBot α\nβ : Type u_3\ninst✝¹ : SemilatticeSup β\ninst✝ : OrderBot β\nf : α → β\nhf : Monotone f\nx✝ : α\nh : x✝ ∈ Iic a\n⊢ x✝ ≤ a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.Basic | {
"line": 440,
"column": 2
} | {
"line": 440,
"column": 28
} | {
"line": 440,
"column": 29
} | [
{
"pp": "α : Type u_2\na b : α\ninst✝² : Preorder α\ninst✝¹ : LocallyFiniteOrderBot α\ninst✝ : LocallyFiniteOrder α\n⊢ Icc a b ⊆ Iic b",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.coe_Iic",
"congrArg",
"Finset",
"PartialOrder.toPreorder",
... | [
"α : Type u_2\na b : α\ninst✝² : Preorder α\ninst✝¹ : LocallyFiniteOrderBot α\ninst✝ : LocallyFiniteOrder α\n⊢ Set.Icc a b ⊆ Set.Iic b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.Basic | {
"line": 443,
"column": 2
} | {
"line": 443,
"column": 28
} | {
"line": 443,
"column": 29
} | [
{
"pp": "α : Type u_2\na b : α\ninst✝² : Preorder α\ninst✝¹ : LocallyFiniteOrderBot α\ninst✝ : LocallyFiniteOrder α\n⊢ Ioc a b ⊆ Iic b",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ioc",
"Finset.coe_Iic",
"congrArg",
"Finset",
"PartialOr... | [
"α : Type u_2\na b : α\ninst✝² : Preorder α\ninst✝¹ : LocallyFiniteOrderBot α\ninst✝ : LocallyFiniteOrder α\n⊢ Set.Ioc a b ⊆ Set.Iic b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.Basic | {
"line": 446,
"column": 2
} | {
"line": 446,
"column": 28
} | {
"line": 446,
"column": 29
} | [
{
"pp": "α : Type u_2\na b : α\ninst✝² : Preorder α\ninst✝¹ : LocallyFiniteOrderBot α\ninst✝ : LocallyFiniteOrder α\n⊢ Ico a b ⊆ Iio b",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.coe_Ico",
"congrArg",
"Finset",
"PartialOrder.toPreorder",
... | [
"α : Type u_2\na b : α\ninst✝² : Preorder α\ninst✝¹ : LocallyFiniteOrderBot α\ninst✝ : LocallyFiniteOrder α\n⊢ Set.Ico a b ⊆ Set.Iio b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.Basic | {
"line": 445,
"column": 49
} | {
"line": 446,
"column": 52
} | {
"line": 448,
"column": 0
} | [
{
"pp": "α : Type u_2\na b : α\ninst✝² : Preorder α\ninst✝¹ : LocallyFiniteOrderBot α\ninst✝ : LocallyFiniteOrder α\n⊢ Ico a b ⊆ Iio b",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.coe_Ico",
"Set.Ico_subset_Iio_self",
"congrArg",
"Finset",
... | [] | by
simpa [← coe_subset] using Set.Ico_subset_Iio_self | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.Interval.Finset.Basic | {
"line": 449,
"column": 2
} | {
"line": 449,
"column": 28
} | {
"line": 449,
"column": 29
} | [
{
"pp": "α : Type u_2\na b : α\ninst✝² : Preorder α\ninst✝¹ : LocallyFiniteOrderBot α\ninst✝ : LocallyFiniteOrder α\n⊢ Ioo a b ⊆ Iio b",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Finset",
"PartialOrder.toPreorder",
"Finset.Iio",
... | [
"α : Type u_2\na b : α\ninst✝² : Preorder α\ninst✝¹ : LocallyFiniteOrderBot α\ninst✝ : LocallyFiniteOrder α\n⊢ Set.Ioo a b ⊆ Set.Iio b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.Basic | {
"line": 472,
"column": 2
} | {
"line": 472,
"column": 28
} | {
"line": 472,
"column": 29
} | [
{
"pp": "α : Type u_2\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrderTop α\na : α\n⊢ Ioi a ⊆ Ici a",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ioi",
"Set.Ici",
"Finset.Ioi",
"congrArg",
"Finset",
"PartialOrder.toPreorder",
... | [
"α : Type u_2\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrderTop α\na : α\n⊢ Set.Ioi a ⊆ Set.Ici a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.Basic | {
"line": 493,
"column": 2
} | {
"line": 493,
"column": 28
} | {
"line": 493,
"column": 29
} | [
{
"pp": "α : Type u_2\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrderBot α\na : α\n⊢ Iio a ⊆ Iic a",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.coe_Iic",
"congrArg",
"Finset",
"PartialOrder.toPreorder",
"Finset.Iio",
"Preorder... | [
"α : Type u_2\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrderBot α\na : α\n⊢ Set.Iio a ⊆ Set.Iic a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.WellFoundedSet | {
"line": 89,
"column": 4
} | {
"line": 89,
"column": 59
} | {
"line": 90,
"column": 2
} | [
{
"pp": "case pos\nα : Type u_2\nr : α → α → Prop\ns : Set α\nf : (Subrel r fun x ↦ x ∈ s) ↪r fun a b ↦ r a b ∧ a ∈ s ∧ b ∈ s\nh : s.WellFoundedOn r\nt : Set α\nht : t.Nonempty\nhst : (Subtype.val ⁻¹' t).Nonempty\nm : α\nms : m ∈ s\nmt : ⟨m, ms⟩ ∈ Subtype.val ⁻¹' t\nhm : ∀ x ∈ Subtype.val ⁻¹' t, ¬Subrel r (fun ... | [] | exact ⟨m, mt, fun x xt ⟨xm, xs, _⟩ => hm ⟨x, xs⟩ xt xm⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Order.Interval.Finset.Defs | {
"line": 1138,
"column": 20
} | {
"line": 1139,
"column": 65
} | {
"line": 1140,
"column": 2
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝⁶ : Preorder α\np : α → Prop\ninst✝⁵ : DecidablePred p\ny : α\nF : Type u_3\nM : Type u_4\nN : Type u_5\ninst✝⁴ : Preorder M\ninst✝³ : Preorder N\ninst✝² : EquivLike F M N\ninst✝¹ : OrderIsoClass F M N\nf : F\ninst✝ : LocallyFiniteOrder N\n⊢ ∀ (a b x : M), x ∈ map { toF... | [] | by
simp [finset_mem_Ioc, EquivLike.inv_apply_eq, map_lt_map_iff] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.WellFoundedSet | {
"line": 176,
"column": 4
} | {
"line": 176,
"column": 34
} | {
"line": 176,
"column": 35
} | [
{
"pp": "case mp\nα : Type u_2\nr : α → α → Prop\ninst✝ : IsStrictOrder α r\ns : Set α\nf : ℕ ↪ α\nhf : ∀ {a b : ℕ}, r (f a) (f b) ∧ f a ∈ s ∧ f b ∈ s ↔ a > b\nH : ∀ (n : ℕ), f n ∈ s\n⊢ ∀ {a b : ℕ}, r (f a) (f b) ↔ a > b",
"ppTerm": "?mp",
"assigned": false,
"usedConstants": [],
"usedFVars": [],... | [
"case mp\nα : Type u_2\nr : α → α → Prop\ninst✝ : IsStrictOrder α r\ns : Set α\nf : ℕ ↪ α\nhf : ∀ {a b : ℕ}, r (f a) (f b) ∧ f a ∈ s ∧ f b ∈ s ↔ a > b\nH : ∀ (n : ℕ), f n ∈ s\n⊢ ∀ {a b : ℕ}, r (f a) (f b) ↔ a > b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.WellFoundedSet | {
"line": 179,
"column": 4
} | {
"line": 179,
"column": 36
} | {
"line": 179,
"column": 37
} | [
{
"pp": "case mpr\nα : Type u_2\nr : α → α → Prop\ninst✝ : IsStrictOrder α r\ns : Set α\nf : ℕ ↪ α\nhf : ∀ {a b : ℕ}, r (f a) (f b) ↔ a > b\nhfs : ∀ (n : ℕ), f n ∈ s\n⊢ ∀ {a b : ℕ}, r (f a) (f b) ∧ f a ∈ s ∧ f b ∈ s ↔ a > b",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"case mpr\nα : Type u_2\nr : α → α → Prop\ninst✝ : IsStrictOrder α r\ns : Set α\nf : ℕ ↪ α\nhf : ∀ {a b : ℕ}, r (f a) (f b) ↔ a > b\nhfs : ∀ (n : ℕ), f n ∈ s\n⊢ ∀ {a b : ℕ}, r (f a) (f b) ↔ a > b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.Basic | {
"line": 1021,
"column": 2
} | {
"line": 1021,
"column": 30
} | {
"line": 1021,
"column": 31
} | [
{
"pp": "α : Type u_2\ninst✝¹ : DistribLattice α\ninst✝ : LocallyFiniteOrder α\na : α\n⊢ Injective (uIcc a)",
"ppTerm": "?m.7",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝¹ : DistribLattice α\ninst✝ : LocallyFiniteOrder α\na : α\n⊢ Injective (uIcc a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.Defs | {
"line": 380,
"column": 2
} | {
"line": 380,
"column": 31
} | {
"line": 380,
"column": 32
} | [
{
"pp": "G : Type u_1\nα : Type u_2\ninst✝¹ : Group G\ninst✝ : MulAction G α\nx y : Quotient G α\nh : (orbitRel G α) (Quotient.out x) (Quotient.out y)\n⊢ x = y",
"ppTerm": "?m.29",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"G : Type u_1\nα : Type u_2\ninst✝¹ : Group G\ninst✝ : MulAction G α\nx y : Quotient G α\nh : (orbitRel G α) (Quotient.out x) (Quotient.out y)\n⊢ x = y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.Basic | {
"line": 1146,
"column": 2
} | {
"line": 1146,
"column": 32
} | {
"line": 1146,
"column": 33
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝² : Preorder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : Preorder β\nf : α → β\nh : ∀ (a b : α), a ⩿ b → f a ≤ f b\na b : α\nhab : a ≤ b\n⊢ f a ≤ f b",
"ppTerm": "?m.27",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\nβ : Type u_3\ninst✝² : Preorder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : Preorder β\nf : α → β\nh : ∀ (a b : α), a ⩿ b → f a ≤ f b\na b : α\nhab : a ≤ b\n⊢ f a ≤ f b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.Basic | {
"line": 1153,
"column": 2
} | {
"line": 1153,
"column": 36
} | {
"line": 1153,
"column": 37
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝² : PartialOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : Preorder β\nf : α → β\nh : ∀ (a b : α), a ⋖ b → f a ≤ f b\na b : α\nhab : a ≤ b\n⊢ f a ≤ f b",
"ppTerm": "?m.27",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
... | [
"α : Type u_2\nβ : Type u_3\ninst✝² : PartialOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : Preorder β\nf : α → β\nh : ∀ (a b : α), a ⋖ b → f a ≤ f b\na b : α\nhab : a ≤ b\n⊢ f a ≤ f b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.Defs | {
"line": 533,
"column": 2
} | {
"line": 533,
"column": 63
} | {
"line": 533,
"column": 64
} | [
{
"pp": "G : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝⁴ : Group G\ninst✝³ : MulAction G α\ninst✝² : MulAction G β\ninst✝¹ : SMul α β\ninst✝ : IsScalarTower G α β\na✝ : α\nb : β\nh : Injective fun x ↦ x • b\na : G\nha : a ∈ stabilizer G (a✝ • b)\n⊢ a ∈ stabilizer G a✝",
"ppTerm": "?m.41",
"assigned": t... | [
"G : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝⁴ : Group G\ninst✝³ : MulAction G α\ninst✝² : MulAction G β\ninst✝¹ : SMul α β\ninst✝ : IsScalarTower G α β\na✝ : α\nb : β\nh : Injective fun x ↦ x • b\na : G\nha : a ∈ stabilizer G (a✝ • b)\n⊢ a • a✝ = a✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Submonoid.Center | {
"line": 55,
"column": 4
} | {
"line": 55,
"column": 42
} | {
"line": 56,
"column": 4
} | [
{
"pp": "M✝ : Type u_1\ninst✝² : MulOneClass M✝\nM : Type u_2\nα : Type u_3\ninst✝¹ : Monoid M\ninst✝ : MulAction M α\nc : ↥(center M)\nr : M\nv : α\n⊢ c • r • v = r • c • v",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Semigroup.toMul",
"HMul.hMul",
"Monoid.toMulOneCl... | [
"M✝ : Type u_1\ninst✝² : MulOneClass M✝\nM : Type u_2\nα : Type u_3\ninst✝¹ : Monoid M\ninst✝ : MulAction M α\nc : ↥(center M)\nr : M\nv : α\nthis : ∀ (g : M), g * ↑c = ↑c * g\n⊢ c • r • v = r • c • v"
] | have := Semigroup.mem_center_iff.1 c.2 | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.GroupTheory.Submonoid.Center | {
"line": 169,
"column": 7
} | {
"line": 169,
"column": 18
} | {
"line": 169,
"column": 19
} | [
{
"pp": "M : Type u_3\nN : Type u_1\nF : Type u_2\ninst✝³ : EquivLike F M N\ninst✝² : Mul M\ninst✝¹ : Mul N\ninst✝ : MulEquivClass F M N\ne : F\nx : M\nx✝ : e x ∈ Set.center N\n⊢ x ∈ Set.center M",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"M : Type u_3\nN : Type u_1\nF : Type u_2\ninst✝³ : EquivLike F M N\ninst✝² : Mul M\ninst✝¹ : Mul N\ninst✝ : MulEquivClass F M N\ne : F\nx : M\nx✝ : e x ∈ Set.center N\n⊢ x ∈ Set.center M"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.WellFoundedSet | {
"line": 851,
"column": 4
} | {
"line": 853,
"column": 71
} | {
"line": 854,
"column": 2
} | [
{
"pp": "case inr.refine_1\nα : Type u_2\nr : α → α → Prop\ninst✝ : IsPreorder α r\ns : Set α\nh : s.PartiallyWellOrderedOn r\nh✝ : Nonempty α\ninhabited_h : Inhabited α\nf : ℕ → List α\nhf1 : IsBadSeq (List.SublistForall₂ r) {l | ∀ x ∈ l, x ∈ s} f\nhf2 : ∀ (n : ℕ), IsMinBadSeq (List.SublistForall₂ r) List.leng... | [] | simp only [if_neg (lt_irrefl (g 0)), Nat.sub_self]
rw [List.length_tail, ← Nat.pred_eq_sub_one]
exact Nat.pred_lt fun con => hnil _ (List.length_eq_zero_iff.1 con) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.WellFoundedSet | {
"line": 851,
"column": 4
} | {
"line": 853,
"column": 71
} | {
"line": 854,
"column": 2
} | [
{
"pp": "case inr.refine_1\nα : Type u_2\nr : α → α → Prop\ninst✝ : IsPreorder α r\ns : Set α\nh : s.PartiallyWellOrderedOn r\nh✝ : Nonempty α\ninhabited_h : Inhabited α\nf : ℕ → List α\nhf1 : IsBadSeq (List.SublistForall₂ r) {l | ∀ x ∈ l, x ∈ s} f\nhf2 : ∀ (n : ℕ), IsMinBadSeq (List.SublistForall₂ r) List.leng... | [] | simp only [if_neg (lt_irrefl (g 0)), Nat.sub_self]
rw [List.length_tail, ← Nat.pred_eq_sub_one]
exact Nat.pred_lt fun con => hnil _ (List.length_eq_zero_iff.1 con) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Group.Center | {
"line": 182,
"column": 20
} | {
"line": 182,
"column": 31
} | {
"line": 182,
"column": 32
} | [
{
"pp": "ι : Type u_2\nA : ι → Type u_3\ninst✝ : (i : ι) → Mul (A i)\nx : (i : ι) → A i\nx✝ :\n (∀ (a : (i : ι) → A i) (x_1 : ι), x x_1 * a x_1 = a x_1 * x x_1) ∧\n (∀ (b c : (i : ι) → A i) (x_1 : ι), x x_1 * (b x_1 * c x_1) = x x_1 * b x_1 * c x_1) ∧\n ∀ (a b : (i : ι) → A i) (x_1 : ι), a x_1 * b x_1 ... | [
"ι : Type u_2\nA : ι → Type u_3\ninst✝ : (i : ι) → Mul (A i)\nx : (i : ι) → A i\nx✝ :\n (∀ (a : (i : ι) → A i) (x_1 : ι), x x_1 * a x_1 = a x_1 * x x_1) ∧\n (∀ (b c : (i : ι) → A i) (x_1 : ι), x x_1 * (b x_1 * c x_1) = x x_1 * b x_1 * c x_1) ∧\n ∀ (a b : (i : ι) → A i) (x_1 : ι), a x_1 * b x_1 * x x_1 = a ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Center | {
"line": 183,
"column": 17
} | {
"line": 183,
"column": 28
} | {
"line": 183,
"column": 29
} | [
{
"pp": "ι : Type u_2\nA : ι → Type u_3\ninst✝ : (i : ι) → Mul (A i)\nx : (i : ι) → A i\nx✝ :\n (∀ (a : (i : ι) → A i) (x_1 : ι), x x_1 * a x_1 = a x_1 * x x_1) ∧\n (∀ (b c : (i : ι) → A i) (x_1 : ι), x x_1 * (b x_1 * c x_1) = x x_1 * b x_1 * c x_1) ∧\n ∀ (a b : (i : ι) → A i) (x_1 : ι), a x_1 * b x_1 ... | [
"ι : Type u_2\nA : ι → Type u_3\ninst✝ : (i : ι) → Mul (A i)\nx : (i : ι) → A i\nx✝ :\n (∀ (a : (i : ι) → A i) (x_1 : ι), x x_1 * a x_1 = a x_1 * x x_1) ∧\n (∀ (b c : (i : ι) → A i) (x_1 : ι), x x_1 * (b x_1 * c x_1) = x x_1 * b x_1 * c x_1) ∧\n ∀ (a b : (i : ι) → A i) (x_1 : ι), a x_1 * b x_1 * x x_1 = a ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Center | {
"line": 184,
"column": 17
} | {
"line": 184,
"column": 28
} | {
"line": 184,
"column": 29
} | [
{
"pp": "ι : Type u_2\nA : ι → Type u_3\ninst✝ : (i : ι) → Mul (A i)\nx : (i : ι) → A i\nx✝ :\n (∀ (a : (i : ι) → A i) (x_1 : ι), x x_1 * a x_1 = a x_1 * x x_1) ∧\n (∀ (b c : (i : ι) → A i) (x_1 : ι), x x_1 * (b x_1 * c x_1) = x x_1 * b x_1 * c x_1) ∧\n ∀ (a b : (i : ι) → A i) (x_1 : ι), a x_1 * b x_1 ... | [
"ι : Type u_2\nA : ι → Type u_3\ninst✝ : (i : ι) → Mul (A i)\nx : (i : ι) → A i\nx✝ :\n (∀ (a : (i : ι) → A i) (x_1 : ι), x x_1 * a x_1 = a x_1 * x x_1) ∧\n (∀ (b c : (i : ι) → A i) (x_1 : ι), x x_1 * (b x_1 * c x_1) = x x_1 * b x_1 * c x_1) ∧\n ∀ (a b : (i : ι) → A i) (x_1 : ι), a x_1 * b x_1 * x x_1 = a ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Center | {
"line": 297,
"column": 2
} | {
"line": 297,
"column": 35
} | {
"line": 297,
"column": 36
} | [
{
"pp": "M : Type u_1\nS : Set M\ninst✝ : Group M\na b : M\nha : a ∈ S.centralizer\nhb : b ∈ S.centralizer\n⊢ a / b ∈ S.centralizer",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"instHDiv",
"HMul.hMul",
"Monoid.toMulOneClass",... | [
"M : Type u_1\nS : Set M\ninst✝ : Group M\na b : M\nha : a ∈ S.centralizer\nhb : b ∈ S.centralizer\n⊢ a * b⁻¹ ∈ S.centralizer"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Subgroup.Centralizer | {
"line": 90,
"column": 4
} | {
"line": 91,
"column": 11
} | {
"line": 91,
"column": 12
} | [
{
"pp": "G : Type u_1\nG' : Type u_2\ninst✝² : Group G\ninst✝¹ : Group G'\nH K : Subgroup G\ninst✝ : H.Normal\ng : G\nhg : g ∈ centralizer ↑H\ni h : G\nhh : h ∈ ↑H\n⊢ h * (i * g * i⁻¹) = i * g * i⁻¹ * h",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Semigroup.toMul"... | [
"G : Type u_1\nG' : Type u_2\ninst✝² : Group G\ninst✝¹ : Group G'\nH K : Subgroup G\ninst✝ : H.Normal\ng : G\nhg : g ∈ centralizer ↑H\ni h : G\nhh : h ∈ ↑H\n⊢ h * (i * (g * i⁻¹)) = i * (g * (i⁻¹ * h))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Subgroup.Centralizer | {
"line": 165,
"column": 4
} | {
"line": 165,
"column": 15
} | {
"line": 165,
"column": 16
} | [
{
"pp": "G : Type u_1\ninst✝ : Group G\ns : Set G\ng : G\nhg : g ∈ centralizer s\nh : G\nhh : g * h * g⁻¹ ∈ s\n⊢ h = g * h * g⁻¹",
"ppTerm": "?m.80",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"G : Type u_1\ninst✝ : Group G\ns : Set G\ng : G\nhg : g ∈ centralizer s\nh : G\nhh : g * h * g⁻¹ ∈ s\n⊢ h = g * h * g⁻¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Subgroup.Centralizer | {
"line": 182,
"column": 6
} | {
"line": 182,
"column": 17
} | {
"line": 182,
"column": 18
} | [
{
"pp": "case refine_2.refine_2\nG : Type u_1\ninst✝ : Group G\nh g : G\nhh : h ∈ centralizer {h * g * h⁻¹}\n⊢ g ∈ {h * g * h⁻¹}",
"ppTerm": "?refine_2.refine_2",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClas... | [
"case refine_2.refine_2\nG : Type u_1\ninst✝ : Group G\nh g : G\nhh : h ∈ centralizer {h * g * h⁻¹}\n⊢ g = h * g * h⁻¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Support | {
"line": 39,
"column": 4
} | {
"line": 39,
"column": 32
} | {
"line": 39,
"column": 33
} | [
{
"pp": "case succ\nα : Type u_1\nM : Type u_2\ninst✝ : Monoid M\nf : α → M\nn : ℕ\nhfn : (mulSupport fun x ↦ f x ^ n) ⊆ mulSupport f\n⊢ (mulSupport fun x ↦ f x ^ (n + 1)) ⊆ mulSupport f",
"ppTerm": "?succ",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"HMul.hMul"... | [
"case succ\nα : Type u_1\nM : Type u_2\ninst✝ : Monoid M\nf : α → M\nn : ℕ\nhfn : (mulSupport fun x ↦ f x ^ n) ⊆ mulSupport f\n⊢ (mulSupport fun x ↦ f x * f x ^ n) ⊆ mulSupport f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Commute.Hom | {
"line": 26,
"column": 39
} | {
"line": 26,
"column": 77
} | {
"line": 26,
"column": 78
} | [
{
"pp": "F : Type u_1\nM : Type u_2\nN : Type u_3\ninst✝³ : Mul M\ninst✝² : Mul N\na x y : M\ninst✝¹ : FunLike F M N\ninst✝ : MulHomClass F M N\nh : SemiconjBy a x y\nf : F\n⊢ SemiconjBy (f a) (f x) (f y)",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"SemiconjBy",
"id",
... | [
"F : Type u_1\nM : Type u_2\nN : Type u_3\ninst✝³ : Mul M\ninst✝² : Mul N\na x y : M\ninst✝¹ : FunLike F M N\ninst✝ : MulHomClass F M N\nh : SemiconjBy a x y\nf : F\n⊢ f a * f x = f y * f a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Commute.Hom | {
"line": 35,
"column": 9
} | {
"line": 35,
"column": 47
} | {
"line": 35,
"column": 48
} | [
{
"pp": "F : Type u_1\nM : Type u_2\nN : Type u_3\ninst✝³ : Mul M\ninst✝² : Mul N\na x y : M\ninst✝¹ : FunLike F M N\ninst✝ : MulHomClass F M N\nf : F\nhf : Function.Injective ⇑f\nh : SemiconjBy (f a) (f x) (f y)\n⊢ f (a * x) = f (y * a)",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
... | [
"F : Type u_1\nM : Type u_2\nN : Type u_3\ninst✝³ : Mul M\ninst✝² : Mul N\na x y : M\ninst✝¹ : FunLike F M N\ninst✝ : MulHomClass F M N\nf : F\nhf : Function.Injective ⇑f\nh : SemiconjBy (f a) (f x) (f y)\n⊢ f a * f x = f y * f a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Commute.Hom | {
"line": 40,
"column": 9
} | {
"line": 40,
"column": 35
} | {
"line": 40,
"column": 36
} | [
{
"pp": "F : Type u_1\nM : Type u_2\nN : Type u_3\ninst✝³ : Mul M\ninst✝² : Mul N\nx y : M\ninst✝¹ : FunLike F M N\ninst✝ : MulHomClass F M N\nf : F\nhf : Function.Injective ⇑f\nh : Commute (f x) (f y)\n⊢ f (x * y) = f (y * x)",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",... | [
"F : Type u_1\nM : Type u_2\nN : Type u_3\ninst✝³ : Mul M\ninst✝² : Mul N\nx y : M\ninst✝¹ : FunLike F M N\ninst✝ : MulHomClass F M N\nf : F\nhf : Function.Injective ⇑f\nh : Commute (f x) (f y)\n⊢ f x * f y = f y * f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Subgroup.Pointwise | {
"line": 144,
"column": 16
} | {
"line": 144,
"column": 42
} | {
"line": 144,
"column": 43
} | [
{
"pp": "case mul_left.inr\nG : Type u_2\ninst✝ : Group G\ns : Set G\np : (x : G) → x ∈ closure s → Prop\none : p 1 ⋯\nx✝ : G\nmul_left : ∀ (x : G) (hx : x ∈ s) (y : G) (hy : y ∈ Submonoid.closure (s ∪ s⁻¹)), p y ⋯ → p (x * y) ⋯\ninv_mul_cancel : ∀ (x : G) (hx : x ∈ s) (y : G) (hy : y ∈ Submonoid.closure (s ∪ s... | [
"case mul_left.inr\nG : Type u_2\ninst✝ : Group G\ns : Set G\np : (x : G) → x ∈ closure s → Prop\none : p 1 ⋯\nx✝ : G\nmul_left : ∀ (x : G) (hx : x ∈ s) (y : G) (hy : y ∈ Submonoid.closure (s ∪ s⁻¹)), p y ⋯ → p (x * y) ⋯\ninv_mul_cancel : ∀ (x : G) (hx : x ∈ s) (y : G) (hy : y ∈ Submonoid.closure (s ∪ s⁻¹)), p y ⋯ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.BigOperators.Group.Finset.Defs | {
"line": 771,
"column": 2
} | {
"line": 771,
"column": 43
} | {
"line": 771,
"column": 44
} | [
{
"pp": "α : Type u_6\na : Multiset α\nl : List (Multiset α)\n⊢ Disjoint a l.sum ↔ ∀ b ∈ l, Disjoint a b",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"List.sum",
"Disjoint",
"Membership.mem",
"Multiset",
"disjoint_comm",
... | [
"α : Type u_6\na : Multiset α\nl : List (Multiset α)\n⊢ Disjoint l.sum a ↔ ∀ b ∈ l, Disjoint b a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Subgroup.Pointwise | {
"line": 276,
"column": 4
} | {
"line": 277,
"column": 11
} | {
"line": 277,
"column": 12
} | [
{
"pp": "case inv_mem\nG : Type u_2\ninst✝ : Group G\nH N : Subgroup G\nhLE : H ≤ normalizer ↑N\nx✝ x : G\nhx : x ∈ ↑H\ny : G\nhy : y ∈ ↑N\n⊢ ((fun x1 x2 ↦ x1 * x2) x y)⁻¹ ∈ ↑H * ↑N",
"ppTerm": "?inv_mem",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"HMul.h... | [
"case inv_mem\nG : Type u_2\ninst✝ : Group G\nH N : Subgroup G\nhLE : H ≤ normalizer ↑N\nx✝ x : G\nhx : x ∈ ↑H\ny : G\nhy : y ∈ ↑N\n⊢ y⁻¹ * x⁻¹ ∈ ↑H * ↑N"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.BigOperators.Group.Finset.Defs | {
"line": 781,
"column": 2
} | {
"line": 781,
"column": 43
} | {
"line": 781,
"column": 44
} | [
{
"pp": "α : Type u_6\na : Multiset α\ni : Multiset (Multiset α)\n⊢ Disjoint a i.sum ↔ ∀ b ∈ i, Disjoint a b",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Multiset.sum",
"Eq.mpr",
"congrArg",
"Multiset.instAddCancelCommMonoid",
"Disjoint",
"Membership... | [
"α : Type u_6\na : Multiset α\ni : Multiset (Multiset α)\n⊢ Disjoint i.sum a ↔ ∀ b ∈ i, Disjoint b a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.BigOperators.Group.Finset.Defs | {
"line": 792,
"column": 2
} | {
"line": 792,
"column": 34
} | {
"line": 792,
"column": 35
} | [
{
"pp": "ι : Type u_1\nα : Type u_6\ni : Finset ι\nf : ι → Multiset α\na : Multiset α\n⊢ Disjoint a (i.sum f) ↔ ∀ b ∈ i, Disjoint a (f b)",
"ppTerm": "?m.14",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"ι : Type u_1\nα : Type u_6\ni : Finset ι\nf : ι → Multiset α\na : Multiset α\n⊢ Disjoint a (i.sum f) ↔ ∀ b ∈ i, Disjoint a (f b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.BigOperators.Group.Finset.Defs | {
"line": 833,
"column": 2
} | {
"line": 833,
"column": 26
} | {
"line": 835,
"column": 0
} | [
{
"pp": "M : Type u_3\ninst✝ : Monoid M\ns : List (Additive M)\n⊢ toMul s.sum = (List.map (⇑toMul) s).prod",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"Equiv.instEquivLike",
"Monoid.toMulOneClass",
"congrArg",
"Additive",
... | [] | simp [toMul, ofMul]; rfl | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.BigOperators.Group.Finset.Defs | {
"line": 833,
"column": 2
} | {
"line": 833,
"column": 26
} | {
"line": 835,
"column": 0
} | [
{
"pp": "M : Type u_3\ninst✝ : Monoid M\ns : List (Additive M)\n⊢ toMul s.sum = (List.map (⇑toMul) s).prod",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"Equiv.instEquivLike",
"Monoid.toMulOneClass",
"congrArg",
"Additive",
... | [] | simp [toMul, ofMul]; rfl | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Finset.NoncommProd | {
"line": 183,
"column": 2
} | {
"line": 183,
"column": 13
} | {
"line": 183,
"column": 14
} | [
{
"pp": "case h\nF : Type u_1\nα : Type u_3\nβ : Type u_4\ninst✝³ : Monoid α\ninst✝² : Monoid β\ninst✝¹ : FunLike F α β\ninst✝ : MonoidHomClass F α β\nf : F\na✝ : List α\ncomm : {x | x ∈ ⟦a✝⟧}.Pairwise Commute\n⊢ f (noncommProd ⟦a✝⟧ comm) = (map ⇑f ⟦a✝⟧).noncommProd ⋯",
"ppTerm": "?h",
"assigned": true,... | [
"case h\nF : Type u_1\nα : Type u_3\nβ : Type u_4\ninst✝³ : Monoid α\ninst✝² : Monoid β\ninst✝¹ : FunLike F α β\ninst✝ : MonoidHomClass F α β\nf : F\na✝ : List α\ncomm : {x | x ∈ ⟦a✝⟧}.Pairwise Commute\n⊢ f a✝.prod = (List.map (⇑f) a✝).prod"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.BigOperators.Group.Finset.Defs | {
"line": 864,
"column": 2
} | {
"line": 864,
"column": 26
} | {
"line": 866,
"column": 0
} | [
{
"pp": "M : Type u_3\ninst✝ : CommMonoid M\ns : Multiset (Additive M)\n⊢ toMul s.sum = (Multiset.map (⇑toMul) s).prod",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Multiset.sum",
"Eq.mpr",
"Equiv.instEquivLike",
"Multiset.map",
"congrArg",
"Additive"... | [] | simp [toMul, ofMul]; rfl | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.BigOperators.Group.Finset.Defs | {
"line": 864,
"column": 2
} | {
"line": 864,
"column": 26
} | {
"line": 866,
"column": 0
} | [
{
"pp": "M : Type u_3\ninst✝ : CommMonoid M\ns : Multiset (Additive M)\n⊢ toMul s.sum = (Multiset.map (⇑toMul) s).prod",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Multiset.sum",
"Eq.mpr",
"Equiv.instEquivLike",
"Multiset.map",
"congrArg",
"Additive"... | [] | simp [toMul, ofMul]; rfl | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Finset.NoncommProd | {
"line": 254,
"column": 48
} | {
"line": 254,
"column": 59
} | {
"line": 254,
"column": 60
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝ : Monoid β\ns : Finset α\nf : α → β\ncomm : (↑s).Pairwise (Commute on f)\np : β → Prop\nhom : ∀ (a b : β), p a → p b → p (a * b)\nunit : p 1\nbase : ∀ x ∈ s, p (f x)\nb : β\nhb : b ∈ Multiset.map f s.val\n⊢ ?m.28",
"ppTerm": "?m.33",
"assigned": false,
"use... | [
"α : Type u_3\nβ : Type u_4\ninst✝ : Monoid β\ns : Finset α\nf : α → β\ncomm : (↑s).Pairwise (Commute on f)\np : β → Prop\nhom : ∀ (a b : β), p a → p b → p (a * b)\nunit : p 1\nbase : ∀ x ∈ s, p (f x)\nb : β\nhb : b ∈ Multiset.map f s.val\n⊢ ?m.28"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Submonoid.BigOperators | {
"line": 190,
"column": 4
} | {
"line": 190,
"column": 64
} | {
"line": 191,
"column": 4
} | [
{
"pp": "M : Type u_1\ninst✝ : CommMonoid M\ns : Finset M\nf : M → ℕ\nt : Finset M\nhts : ↑t ⊆ ↑s\nhf : Function.support f ⊆ ↑t\n⊢ ∃ f_1, Function.support f_1 ⊆ ↑s ∧ ∏ a ∈ s, a ^ f_1 a = ∏ a ∈ t, a ^ f a",
"ppTerm": "?m.68",
"assigned": true,
"usedConstants": [
"Finset",
"AddMonoid.toAdd... | [
"M : Type u_1\ninst✝ : CommMonoid M\ns : Finset M\nf : M → ℕ\nt : Finset M\nhts : ↑t ⊆ ↑s\nhf : Function.support f ⊆ ↑t\n⊢ ∀ x ∈ s, x ∉ t → x ^ f x = 1"
] | refine ⟨f, hf.trans hts, .symm <| Finset.prod_subset hts ?_⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Data.Finset.NoncommProd | {
"line": 327,
"column": 4
} | {
"line": 327,
"column": 15
} | {
"line": 327,
"column": 16
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝ : Monoid β\ns : Finset α\nf : α → β\ncomm : (↑s).Pairwise (Commute on f)\nm : β\nh : ∀ x ∈ s, f x = m\n⊢ ∀ x ∈ Multiset.map f s.val, x = m",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Multiset.map",
"Finset",
... | [
"α : Type u_3\nβ : Type u_4\ninst✝ : Monoid β\ns : Finset α\nf : α → β\ncomm : (↑s).Pairwise (Commute on f)\nm : β\nh : ∀ x ∈ s, f x = m\n⊢ ∀ a ∈ s, f a = m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Setoid.Basic | {
"line": 120,
"column": 31
} | {
"line": 120,
"column": 56
} | {
"line": 120,
"column": 57
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nr : Setoid α\ns : Setoid β\nq : Quotient (r.prod s)\nx y : α × β\nhxy : (r.prod s) x y\n⊢ (Quotient.mk'' x.1, Quotient.mk'' x.2).1 = (Quotient.mk'' y.1, Quotient.mk'' y.2).1",
"ppTerm": "?m.72",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"α : Type u_1\nβ : Type u_2\nγ : Type u_3\nr : Setoid α\ns : Setoid β\nq : Quotient (r.prod s)\nx y : α × β\nhxy : (r.prod s) x y\n⊢ r x.1 y.1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Setoid.Basic | {
"line": 120,
"column": 68
} | {
"line": 120,
"column": 93
} | {
"line": 120,
"column": 94
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nr : Setoid α\ns : Setoid β\nq : Quotient (r.prod s)\nx y : α × β\nhxy : (r.prod s) x y\n⊢ (Quotient.mk'' x.1, Quotient.mk'' x.2).2 = (Quotient.mk'' y.1, Quotient.mk'' y.2).2",
"ppTerm": "?m.81",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"α : Type u_1\nβ : Type u_2\nγ : Type u_3\nr : Setoid α\ns : Setoid β\nq : Quotient (r.prod s)\nx y : α × β\nhxy : (r.prod s) x y\n⊢ s x.2 y.2"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Setoid.Basic | {
"line": 135,
"column": 4
} | {
"line": 135,
"column": 29
} | {
"line": 135,
"column": 30
} | [
{
"pp": "α✝ : Type u_1\nβ : Type u_2\nγ : Type u_3\nι : Sort u_4\nα : ι → Sort u_5\nr : (i : ι) → Setoid (α i)\nq : Quotient piSetoid\nx y : (i : ι) → α i\nhxy : piSetoid x y\ni : ι\n⊢ Quotient.mk'' (x i) = Quotient.mk'' (y i)",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
"Eq.mpr",... | [
"α✝ : Type u_1\nβ : Type u_2\nγ : Type u_3\nι : Sort u_4\nα : ι → Sort u_5\nr : (i : ι) → Setoid (α i)\nq : Quotient piSetoid\nx y : (i : ι) → α i\nhxy : piSetoid x y\ni : ι\n⊢ (r i) (x i) (y i)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.NoncommProd | {
"line": 419,
"column": 6
} | {
"line": 419,
"column": 17
} | {
"line": 419,
"column": 18
} | [
{
"pp": "case convert_8.h\nι : Type u_2\nM : ι → Type u_6\ninst✝² : (i : ι) → Monoid (M i)\ninst✝¹ : Fintype ι\ninst✝ : DecidableEq ι\nx : (i : ι) → M i\ni : ι\n⊢ ∀ x_1 ∈ univ.erase i, Pi.mulSingle x_1 (x x_1) i = 1",
"ppTerm": "?convert_8.h",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"case convert_8.h\nι : Type u_2\nM : ι → Type u_6\ninst✝² : (i : ι) → Monoid (M i)\ninst✝¹ : Fintype ι\ninst✝ : DecidableEq ι\nx : (i : ι) → M i\ni : ι\n⊢ ∀ (x_1 : ι), ¬x_1 = i → Pi.mulSingle x_1 (x x_1) i = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Setoid.Basic | {
"line": 540,
"column": 2
} | {
"line": 540,
"column": 94
} | {
"line": 541,
"column": 2
} | [
{
"pp": "α : Type u_1\ns : Setoid α\n⊢ Subsingleton (Quotient s) ↔ s = ⊤",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"Setoid.completeLattice",
"CompleteLattice.toLattice",
"_private.Mathlib.Data.Setoid.Basic.0.Quotient.... | [
"α : Type u_1\ns : Setoid α\n⊢ (∀ (x y : Quotient s), x = y) ↔ ∀ {x y : α}, ⊤ → s x y"
] | simp only [_root_.subsingleton_iff, eq_top_iff, Setoid.le_def, Setoid.top_def, Pi.top_apply] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Setoid.Basic | {
"line": 543,
"column": 29
} | {
"line": 543,
"column": 42
} | {
"line": 543,
"column": 43
} | [
{
"pp": "α : Type u_1\ns : Setoid α\na b : α\n⊢ Quotient.mk' a = Quotient.mk' b ↔ True → s a b",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"id",
"Iff",
"Quotient",
"Quotient.mk'",
"true_implies",
"True",
"Eq",
... | [
"α : Type u_1\ns : Setoid α\na b : α\n⊢ Quotient.mk' a = Quotient.mk' b ↔ s a b"
] | true_implies, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.