module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Order.SuccPred.Basic | {
"line": 753,
"column": 6
} | {
"line": 753,
"column": 38
} | {
"line": 754,
"column": 4
} | [
{
"pp": "case pos\nα : Type u_1\nβ : Type u_2\ninst✝² : PartialOrder α\ninst✝¹ : SuccOrder α\ninst✝ : (a : α) → Decidable (succ a = a)\na✝ : α\nha' : succ a✝ = a✝\nha : ⊤ ≤ ↑a✝\n⊢ IsMax ↑a✝",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"WithTop.instPreorder",
"False.elim",
... | [] | exact (not_top_le_coe _ ha).elim | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.SuccPred | {
"line": 194,
"column": 2
} | {
"line": 194,
"column": 13
} | {
"line": 194,
"column": 14
} | [
{
"pp": "α : Type u_1\nx : α\ninst✝³ : PartialOrder α\ninst✝² : AddMonoidWithOne α\ninst✝¹ : SuccAddOrder α\ninst✝ : IsBotZeroClass α\nhx : IsSuccLimit x\n⊢ ∀ (n : ℕ), ↑n < x",
"ppTerm": "?m.10",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nx : α\ninst✝³ : PartialOrder α\ninst✝² : AddMonoidWithOne α\ninst✝¹ : SuccAddOrder α\ninst✝ : IsBotZeroClass α\nhx : IsSuccLimit x\n⊢ ∀ (n : ℕ), ↑n < x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.SuccPred.Basic | {
"line": 876,
"column": 8
} | {
"line": 876,
"column": 25
} | {
"line": 877,
"column": 8
} | [
{
"pp": "case neg.inl\nα✝ : Type u_1\nβ : Type u_2\nα : Type u_3\ninst✝² : PartialOrder α\ns : Set α\ninst✝¹ : s.OrdConnected\ninst✝ : PredOrder α\nx✝ : ↑s\nx : α\nhx : x ∈ s\nh' : pred x ∉ s\nh✝¹ : ⟨x, hx⟩ ≤ ⟨x, hx⟩\ny : α\nhy : y ∈ s\nh✝ : ⟨y, hy⟩ ≤ ⟨x, hx⟩\nh : y < x\n⊢ ⟨x, hx⟩ ≤ ⟨y, hy⟩",
"ppTerm": "?ne... | [
"case neg.inl\nα✝ : Type u_1\nβ : Type u_2\nα : Type u_3\ninst✝² : PartialOrder α\ns : Set α\ninst✝¹ : s.OrdConnected\ninst✝ : PredOrder α\nx✝ : ↑s\nx : α\nhx : x ∈ s\nh' : pred x ∉ s\nh✝¹ : ⟨x, hx⟩ ≤ ⟨x, hx⟩\ny : α\nhy : y ∈ s\nh✝ : ⟨y, hy⟩ ≤ ⟨x, hx⟩\nh : y < x\nthis : y ≤ pred x\n⊢ ⟨x, hx⟩ ≤ ⟨y, hy⟩"
] | have := h.le_pred | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Algebra.Order.SuccPred | {
"line": 218,
"column": 4
} | {
"line": 218,
"column": 19
} | {
"line": 218,
"column": 20
} | [
{
"pp": "case coe\nα : Type u_1\ninst✝⁶ : PartialOrder α\ninst✝⁵ : AddZeroClass α\ninst✝⁴ : OrderBot α\ninst✝³ : IsBotZeroClass α\ninst✝² : One α\ninst✝¹ : NoMaxOrder α\ninst✝ : SuccAddOrder α\na : α\nh : a + 1 = 0\n⊢ False",
"ppTerm": "?coe",
"assigned": false,
"usedConstants": [],
"usedFVars":... | [
"case coe\nα : Type u_1\ninst✝⁶ : PartialOrder α\ninst✝⁵ : AddZeroClass α\ninst✝⁴ : OrderBot α\ninst✝³ : IsBotZeroClass α\ninst✝² : One α\ninst✝¹ : NoMaxOrder α\ninst✝ : SuccAddOrder α\na : α\nh : a + 1 = 0\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.SuccPred | {
"line": 259,
"column": 2
} | {
"line": 259,
"column": 13
} | {
"line": 259,
"column": 14
} | [
{
"pp": "α : Type u_1\nx : α\ninst✝⁴ : LinearOrder α\ninst✝³ : AddMonoidWithOne α\ninst✝² : SuccAddOrder α\ninst✝¹ : IsBotZeroClass α\ninst✝ : NeZero 1\n⊢ x < 1 ↔ x = 0",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nx : α\ninst✝⁴ : LinearOrder α\ninst✝³ : AddMonoidWithOne α\ninst✝² : SuccAddOrder α\ninst✝¹ : IsBotZeroClass α\ninst✝ : NeZero 1\n⊢ x < 1 ↔ x = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.SuccPred | {
"line": 317,
"column": 2
} | {
"line": 317,
"column": 37
} | {
"line": 317,
"column": 38
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Add α\ninst✝² : One α\ninst✝¹ : SuccAddOrder α\ninst✝ : IsSuccArchimedean α\ns : Set α\nf : α → β\nhs : s.OrdConnected\n⊢ (∀ (a : α), ¬IsMax a → a ∈ s → a + 1 ∈ s → f a ≤ f (a + 1)) → MonotoneOn f s",
"ppTerm": "?m.3... | [
"α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Add α\ninst✝² : One α\ninst✝¹ : SuccAddOrder α\ninst✝ : IsSuccArchimedean α\ns : Set α\nf : α → β\nhs : s.OrdConnected\n⊢ (∀ (a x : α), a < x → a ∈ s → a + 1 ∈ s → f a ≤ f (a + 1)) → MonotoneOn f s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.ENat.Basic | {
"line": 244,
"column": 4
} | {
"line": 244,
"column": 15
} | {
"line": 244,
"column": 16
} | [
{
"pp": "case top\nm : ℕ\ninst✝ : NeZero m\n⊢ ⊤.toNat = m ↔ ⊤ = ↑m",
"ppTerm": "?top",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"iff_false",
"ENat.instNatCast",
"instTopENat",
"congrArg",
"id",
"instOfNatNat",
"Nat.cast",
"If... | [
"case top\nm : ℕ\ninst✝ : NeZero m\n⊢ ¬0 = m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.SuccPred | {
"line": 321,
"column": 2
} | {
"line": 321,
"column": 37
} | {
"line": 321,
"column": 38
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Add α\ninst✝² : One α\ninst✝¹ : SuccAddOrder α\ninst✝ : IsSuccArchimedean α\ns : Set α\nf : α → β\nhs : s.OrdConnected\n⊢ (∀ (a : α), ¬IsMax a → a ∈ s → a + 1 ∈ s → f (a + 1) ≤ f a) → AntitoneOn f s",
"ppTerm": "?m.3... | [
"α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Add α\ninst✝² : One α\ninst✝¹ : SuccAddOrder α\ninst✝ : IsSuccArchimedean α\ns : Set α\nf : α → β\nhs : s.OrdConnected\n⊢ (∀ (a x : α), a < x → a ∈ s → a + 1 ∈ s → f (a + 1) ≤ f a) → AntitoneOn f s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.SuccPred | {
"line": 325,
"column": 2
} | {
"line": 325,
"column": 37
} | {
"line": 325,
"column": 38
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Add α\ninst✝² : One α\ninst✝¹ : SuccAddOrder α\ninst✝ : IsSuccArchimedean α\ns : Set α\nf : α → β\nhs : s.OrdConnected\n⊢ (∀ (a : α), ¬IsMax a → a ∈ s → a + 1 ∈ s → f a < f (a + 1)) → StrictMonoOn f s",
"ppTerm": "?m... | [
"α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Add α\ninst✝² : One α\ninst✝¹ : SuccAddOrder α\ninst✝ : IsSuccArchimedean α\ns : Set α\nf : α → β\nhs : s.OrdConnected\n⊢ (∀ (a x : α), a < x → a ∈ s → a + 1 ∈ s → f a < f (a + 1)) → StrictMonoOn f s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.ENat.Basic | {
"line": 259,
"column": 19
} | {
"line": 259,
"column": 29
} | {
"line": 259,
"column": 30
} | [
{
"pp": "case coe\nn a✝ : ℕ\n⊢ (↑(a✝ - n)).toNat = (↑a✝).toNat - (↑n).toNat",
"ppTerm": "?coe",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"ENat.instNatCast",
"congrArg",
"HSub.hSub",
"id",
"instSubNat",
"Nat.cast",
"instHSub",
"Nat",
"... | [
"case coe\nn a✝ : ℕ\n⊢ a✝ - n = (↑a✝).toNat - (↑n).toNat"
] | toNat_coe, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.ENat.Basic | {
"line": 259,
"column": 30
} | {
"line": 259,
"column": 40
} | {
"line": 259,
"column": 41
} | [
{
"pp": "case coe\nn a✝ : ℕ\n⊢ a✝ - n = (↑a✝).toNat - (↑n).toNat",
"ppTerm": "?coe",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"ENat.instNatCast",
"congrArg",
"HSub.hSub",
"id",
"instSubNat",
"Nat.cast",
"instHSub",
"Nat",
"ENat",
... | [
"case coe\nn a✝ : ℕ\n⊢ a✝ - n = a✝ - (↑n).toNat"
] | toNat_coe, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.SuccPred | {
"line": 329,
"column": 2
} | {
"line": 329,
"column": 37
} | {
"line": 329,
"column": 38
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Add α\ninst✝² : One α\ninst✝¹ : SuccAddOrder α\ninst✝ : IsSuccArchimedean α\ns : Set α\nf : α → β\nhs : s.OrdConnected\n⊢ (∀ (a : α), ¬IsMax a → a ∈ s → a + 1 ∈ s → f (a + 1) < f a) → StrictAntiOn f s",
"ppTerm": "?m... | [
"α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Add α\ninst✝² : One α\ninst✝¹ : SuccAddOrder α\ninst✝ : IsSuccArchimedean α\ns : Set α\nf : α → β\nhs : s.OrdConnected\n⊢ (∀ (a x : α), a < x → a ∈ s → a + 1 ∈ s → f (a + 1) < f a) → StrictAntiOn f s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.SuccPred | {
"line": 332,
"column": 2
} | {
"line": 332,
"column": 37
} | {
"line": 332,
"column": 38
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Add α\ninst✝² : One α\ninst✝¹ : SuccAddOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\n⊢ (∀ (a : α), ¬IsMax a → f a ≤ f (a + 1)) → Monotone f",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"... | [
"α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Add α\ninst✝² : One α\ninst✝¹ : SuccAddOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\n⊢ (∀ (a x : α), a < x → f a ≤ f (a + 1)) → Monotone f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.SuccPred | {
"line": 335,
"column": 2
} | {
"line": 335,
"column": 37
} | {
"line": 335,
"column": 38
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Add α\ninst✝² : One α\ninst✝¹ : SuccAddOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\n⊢ (∀ (a : α), ¬IsMax a → f (a + 1) ≤ f a) → Antitone f",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"... | [
"α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Add α\ninst✝² : One α\ninst✝¹ : SuccAddOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\n⊢ (∀ (a x : α), a < x → f (a + 1) ≤ f a) → Antitone f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.SuccPred | {
"line": 338,
"column": 2
} | {
"line": 338,
"column": 37
} | {
"line": 338,
"column": 38
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Add α\ninst✝² : One α\ninst✝¹ : SuccAddOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\n⊢ (∀ (a : α), ¬IsMax a → f a < f (a + 1)) → StrictMono f",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
... | [
"α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Add α\ninst✝² : One α\ninst✝¹ : SuccAddOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\n⊢ (∀ (a x : α), a < x → f a < f (a + 1)) → StrictMono f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.SuccPred | {
"line": 341,
"column": 2
} | {
"line": 341,
"column": 37
} | {
"line": 341,
"column": 38
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Add α\ninst✝² : One α\ninst✝¹ : SuccAddOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\n⊢ (∀ (a : α), ¬IsMax a → f (a + 1) < f a) → StrictAnti f",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
... | [
"α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Add α\ninst✝² : One α\ninst✝¹ : SuccAddOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\n⊢ (∀ (a x : α), a < x → f (a + 1) < f a) → StrictAnti f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.SuccPred | {
"line": 350,
"column": 2
} | {
"line": 350,
"column": 37
} | {
"line": 350,
"column": 38
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Sub α\ninst✝² : One α\ninst✝¹ : PredSubOrder α\ninst✝ : IsPredArchimedean α\ns : Set α\nf : α → β\nhs : s.OrdConnected\n⊢ (∀ (a : α), ¬IsMin a → a ∈ s → a - 1 ∈ s → f (a - 1) ≤ f a) → MonotoneOn f s",
"ppTerm": "?m.3... | [
"α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Sub α\ninst✝² : One α\ninst✝¹ : PredSubOrder α\ninst✝ : IsPredArchimedean α\ns : Set α\nf : α → β\nhs : s.OrdConnected\n⊢ (∀ (a x : α), x < a → a ∈ s → a - 1 ∈ s → f (a - 1) ≤ f a) → MonotoneOn f s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.SuccPred | {
"line": 354,
"column": 2
} | {
"line": 354,
"column": 37
} | {
"line": 354,
"column": 38
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Sub α\ninst✝² : One α\ninst✝¹ : PredSubOrder α\ninst✝ : IsPredArchimedean α\ns : Set α\nf : α → β\nhs : s.OrdConnected\n⊢ (∀ (a : α), ¬IsMin a → a ∈ s → a - 1 ∈ s → f a ≤ f (a - 1)) → AntitoneOn f s",
"ppTerm": "?m.3... | [
"α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Sub α\ninst✝² : One α\ninst✝¹ : PredSubOrder α\ninst✝ : IsPredArchimedean α\ns : Set α\nf : α → β\nhs : s.OrdConnected\n⊢ (∀ (a x : α), x < a → a ∈ s → a - 1 ∈ s → f a ≤ f (a - 1)) → AntitoneOn f s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.SuccPred | {
"line": 358,
"column": 2
} | {
"line": 358,
"column": 37
} | {
"line": 358,
"column": 38
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Sub α\ninst✝² : One α\ninst✝¹ : PredSubOrder α\ninst✝ : IsPredArchimedean α\ns : Set α\nf : α → β\nhs : s.OrdConnected\n⊢ (∀ (a : α), ¬IsMin a → a ∈ s → a - 1 ∈ s → f (a - 1) < f a) → StrictMonoOn f s",
"ppTerm": "?m... | [
"α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Sub α\ninst✝² : One α\ninst✝¹ : PredSubOrder α\ninst✝ : IsPredArchimedean α\ns : Set α\nf : α → β\nhs : s.OrdConnected\n⊢ (∀ (a x : α), x < a → a ∈ s → a - 1 ∈ s → f (a - 1) < f a) → StrictMonoOn f s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.ENat.Basic | {
"line": 273,
"column": 2
} | {
"line": 273,
"column": 13
} | {
"line": 273,
"column": 14
} | [
{
"pp": "n m : ℕ\nh : ↑m ≤ ↑n\n⊢ (↑m).toNat ≤ n",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"ENat.instNatCast",
"id",
"LE.le",
"instLENat",
"Nat.cast",
"Nat",
"ENat",
"ENat.toNat"
],
"usedFVars": [
"m",
"n"
],
... | [
"n m : ℕ\nh : ↑m ≤ ↑n\n⊢ m ≤ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.SuccPred | {
"line": 362,
"column": 2
} | {
"line": 362,
"column": 37
} | {
"line": 362,
"column": 38
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Sub α\ninst✝² : One α\ninst✝¹ : PredSubOrder α\ninst✝ : IsPredArchimedean α\ns : Set α\nf : α → β\nhs : s.OrdConnected\n⊢ (∀ (a : α), ¬IsMin a → a ∈ s → a - 1 ∈ s → f a < f (a - 1)) → StrictAntiOn f s",
"ppTerm": "?m... | [
"α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Sub α\ninst✝² : One α\ninst✝¹ : PredSubOrder α\ninst✝ : IsPredArchimedean α\ns : Set α\nf : α → β\nhs : s.OrdConnected\n⊢ (∀ (a x : α), x < a → a ∈ s → a - 1 ∈ s → f a < f (a - 1)) → StrictAntiOn f s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.SuccPred | {
"line": 365,
"column": 2
} | {
"line": 365,
"column": 37
} | {
"line": 365,
"column": 38
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Sub α\ninst✝² : One α\ninst✝¹ : PredSubOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\n⊢ (∀ (a : α), ¬IsMin a → f (a - 1) ≤ f a) → Monotone f",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"... | [
"α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Sub α\ninst✝² : One α\ninst✝¹ : PredSubOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\n⊢ (∀ (a x : α), x < a → f (a - 1) ≤ f a) → Monotone f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.SuccPred | {
"line": 368,
"column": 2
} | {
"line": 368,
"column": 37
} | {
"line": 368,
"column": 38
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Sub α\ninst✝² : One α\ninst✝¹ : PredSubOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\n⊢ (∀ (a : α), ¬IsMin a → f a ≤ f (a - 1)) → Antitone f",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"... | [
"α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Sub α\ninst✝² : One α\ninst✝¹ : PredSubOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\n⊢ (∀ (a x : α), x < a → f a ≤ f (a - 1)) → Antitone f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.SuccPred.Limit | {
"line": 240,
"column": 2
} | {
"line": 240,
"column": 76
} | {
"line": 240,
"column": 77
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\nx : α\nh : IsSuccLimit x\n⊢ IsSuccLimit ↑x",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"Preorder.toLT",
"Order.IsSuccPrelimit",
"and_true",
"WithTop.instPreorder",
"congrArg",
"... | [
"α : Type u_1\ninst✝ : Preorder α\nx : α\nh : IsSuccLimit x\n⊢ ∃ x_1, x_1 < x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.SuccPred | {
"line": 371,
"column": 2
} | {
"line": 371,
"column": 37
} | {
"line": 371,
"column": 38
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Sub α\ninst✝² : One α\ninst✝¹ : PredSubOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\n⊢ (∀ (a : α), ¬IsMin a → f (a - 1) < f a) → StrictMono f",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
... | [
"α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Sub α\ninst✝² : One α\ninst✝¹ : PredSubOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\n⊢ (∀ (a x : α), x < a → f (a - 1) < f a) → StrictMono f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.SuccPred | {
"line": 374,
"column": 2
} | {
"line": 374,
"column": 37
} | {
"line": 374,
"column": 38
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Sub α\ninst✝² : One α\ninst✝¹ : PredSubOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\n⊢ (∀ (a : α), ¬IsMin a → f a < f (a - 1)) → StrictAnti f",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
... | [
"α : Type u_2\nβ : Type u_3\ninst✝⁵ : PartialOrder α\ninst✝⁴ : Preorder β\ninst✝³ : Sub α\ninst✝² : One α\ninst✝¹ : PredSubOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\n⊢ (∀ (a x : α), x < a → f a < f (a - 1)) → StrictAnti f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.SuccPred.Limit | {
"line": 256,
"column": 2
} | {
"line": 256,
"column": 75
} | {
"line": 256,
"column": 76
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\nx : α\nh : IsPredLimit x\n⊢ IsPredLimit ↑x",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"Preorder.toLT",
"WithTop.instPreorder",
"congrArg",
"true_or",
"WithTop.coe_ne_top._simp_1",
... | [
"α : Type u_1\ninst✝ : Preorder α\nx : α\nh : IsPredLimit x\n⊢ (∃ x_1, x < x_1) ∧ IsPredPrelimit x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.ENat.Basic | {
"line": 456,
"column": 17
} | {
"line": 456,
"column": 29
} | {
"line": 456,
"column": 30
} | [
{
"pp": "case inr.inr\nc a : ℕ∞\nhc : c ≠ 0\nhne : a ≠ ⊤\nh0 : a ≠ 0\n⊢ a ≤ a * c",
"ppTerm": "?inr.inr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"id",
"MulOne.toMul",
"LE.le",
... | [
"case inr.inr\nc a : ℕ∞\nhc : c ≠ 0\nhne : a ≠ ⊤\nh0 : a ≠ 0\n⊢ a * 1 ≤ a * c"
] | ← mul_one a, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Logic.Small.Defs | {
"line": 61,
"column": 2
} | {
"line": 61,
"column": 13
} | {
"line": 61,
"column": 14
} | [
{
"pp": "α : Type v\ninst✝ : Small.{w, v} α\nx y : Shrink.{w, v} α\nw : (equivShrink α).symm x = (equivShrink α).symm y\n⊢ x = y",
"ppTerm": "?m.15",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type v\ninst✝ : Small.{w, v} α\nx y : Shrink.{w, v} α\nw : (equivShrink α).symm x = (equivShrink α).symm y\n⊢ x = y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Small.Defs | {
"line": 119,
"column": 52
} | {
"line": 119,
"column": 63
} | {
"line": 119,
"column": 64
} | [
{
"pp": "α : Type u_2\nβ : α → Type u_1\ninst✝¹ : Small.{w, u_2} α\ninst✝ : ∀ (a : α), Small.{w, u_1} (β a)\na : α\n⊢ β a ≃ Shrink.{w, u_1} (β ((equivShrink α).symm ((equivShrink α) a)))",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Equiv.instEquivLike",
"con... | [
"α : Type u_2\nβ : α → Type u_1\ninst✝¹ : Small.{w, u_2} α\ninst✝ : ∀ (a : α), Small.{w, u_1} (β a)\na : α\n⊢ β a ≃ Shrink.{w, u_1} (β a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Small.Defs | {
"line": 126,
"column": 6
} | {
"line": 126,
"column": 17
} | {
"line": 126,
"column": 18
} | [
{
"pp": "S : Type u\ne : Type (max u v) ≃ S\na b : Set ((α : S) × e.symm α)\nh₁ : e (Set ((α : S) × e.symm α)) = e (Set ((α : S) × e.symm α))\nh₂ : cast ⋯ a = cast ⋯ b\n⊢ a = b",
"ppTerm": "?m.67",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"S : Type u\ne : Type (max u v) ≃ S\na b : Set ((α : S) × e.symm α)\nh₁ : e (Set ((α : S) × e.symm α)) = e (Set ((α : S) × e.symm α))\nh₂ : cast ⋯ a = cast ⋯ b\n⊢ a = b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Small.Basic | {
"line": 62,
"column": 49
} | {
"line": 62,
"column": 60
} | {
"line": 62,
"column": 61
} | [
{
"pp": "α : Type u_2\nβ : α → Type u_1\ninst✝¹ : Small.{w, u_2} α\ninst✝ : ∀ (a : α), Small.{w, u_1} (β a)\na : α\n⊢ β a ≃ Shrink.{w, u_1} (β ((equivShrink α).symm ((equivShrink α) a)))",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Equiv.instEquivLike",
"con... | [
"α : Type u_2\nβ : α → Type u_1\ninst✝¹ : Small.{w, u_2} α\ninst✝ : ∀ (a : α), Small.{w, u_1} (β a)\na : α\n⊢ β a ≃ Shrink.{w, u_1} (β a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.ENat.Basic | {
"line": 614,
"column": 45
} | {
"line": 614,
"column": 82
} | {
"line": 614,
"column": 83
} | [
{
"pp": "a b c d m n : ℕ∞\nα : Type u_1\nS : Type u_2\ninst✝² : MulZeroOneClass S\ninst✝¹ : DecidableEq S\ninst✝ : Nontrivial S\nf : ℕ →*₀ S\nhf : Injective ⇑f\nthis : ∀ (z : ℕ∞), map (⇑f) z = 0 ↔ z = 0\nx : ℕ\nhx : ↑x ≠ 0\nhy : ⊤ ≠ 0\n⊢ ↑(f x) ≠ 0",
"ppTerm": "?m.147",
"assigned": true,
"usedConsta... | [
"a b c d m n : ℕ∞\nα : Type u_1\nS : Type u_2\ninst✝² : MulZeroOneClass S\ninst✝¹ : DecidableEq S\ninst✝ : Nontrivial S\nf : ℕ →*₀ S\nhf : Injective ⇑f\nthis : ∀ (z : ℕ∞), map (⇑f) z = 0 ↔ z = 0\nx : ℕ\nhx : ↑x ≠ 0\nhy : ⊤ ≠ 0\n⊢ ¬x = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.SuccPred.Archimedean | {
"line": 384,
"column": 12
} | {
"line": 384,
"column": 23
} | {
"line": 384,
"column": 24
} | [
{
"pp": "case succ.zero\nα : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\ns : Set α\nf : α → β\nhs : s.OrdConnected\nhf : ∀ (a : α), ¬IsMax a → a ∈ s → succ a ∈ s → f a < f (succ a)\na : α\nha : a ∈ s\nhab : ¬IsMax a\nhb : succ^[0 + 1] ... | [
"case succ.zero\nα : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\ns : Set α\nf : α → β\nhs : s.OrdConnected\nhf : ∀ (a : α), ¬IsMax a → a ∈ s → succ a ∈ s → f a < f (succ a)\na : α\nha : a ∈ s\nhab : ¬IsMax a\nhb : succ^[0 + 1] a ∈ s\n⊢ f a... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.ENat.Basic | {
"line": 657,
"column": 2
} | {
"line": 657,
"column": 12
} | {
"line": 658,
"column": 4
} | [
{
"pp": "case coe\nm : ℕ\nn : ℕ∞\n⊢ ↑n + 1 ≤ ↑m ↔ ↑n < ↑m",
"ppTerm": "?coe",
"assigned": true,
"usedConstants": [
"WithBot.addMonoidWithOne",
"WithBot.instPreorder",
"Eq.mpr",
"ENat.coe_ne_top._simp_1",
"False",
"WithBot.some",
"WithBot",
"Preorder.to... | [] | | coe n => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.Order.SuccPred.Archimedean | {
"line": 398,
"column": 2
} | {
"line": 398,
"column": 13
} | {
"line": 398,
"column": 14
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f a ≤ f (succ a)\n⊢ Monotone f",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals"... | [
"α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f a ≤ f (succ a)\n⊢ Monotone f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.SuccPred.Archimedean | {
"line": 398,
"column": 62
} | {
"line": 398,
"column": 73
} | {
"line": 398,
"column": 74
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f a ≤ f (succ a)\n⊢ ∀ (a : α), ¬IsMax a → a ∈ Set.univ → succ a ∈ Set.univ → f a ≤ f (succ a)",
"ppTerm": "?m.28",
"assigned": true,... | [
"α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f a ≤ f (succ a)\n⊢ ∀ (a x : α), a < x → f a ≤ f (succ a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.SuccPred.Archimedean | {
"line": 401,
"column": 2
} | {
"line": 401,
"column": 13
} | {
"line": 401,
"column": 14
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f (succ a) ≤ f a\n⊢ Antitone f",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals"... | [
"α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f (succ a) ≤ f a\n⊢ Antitone f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.SuccPred.Archimedean | {
"line": 401,
"column": 62
} | {
"line": 401,
"column": 73
} | {
"line": 401,
"column": 74
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f (succ a) ≤ f a\n⊢ ∀ (a : α), ¬IsMax a → a ∈ Set.univ → succ a ∈ Set.univ → f (succ a) ≤ f a",
"ppTerm": "?m.28",
"assigned": true,... | [
"α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f (succ a) ≤ f a\n⊢ ∀ (a x : α), a < x → f (succ a) ≤ f a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.SuccPred.Archimedean | {
"line": 404,
"column": 2
} | {
"line": 404,
"column": 13
} | {
"line": 404,
"column": 14
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f a < f (succ a)\n⊢ StrictMono f",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoal... | [
"α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f a < f (succ a)\n⊢ StrictMono f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.SuccPred.Archimedean | {
"line": 404,
"column": 64
} | {
"line": 404,
"column": 75
} | {
"line": 404,
"column": 76
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f a < f (succ a)\n⊢ ∀ (a : α), ¬IsMax a → a ∈ Set.univ → succ a ∈ Set.univ → f a < f (succ a)",
"ppTerm": "?m.28",
"assigned": true,... | [
"α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f a < f (succ a)\n⊢ ∀ (a x : α), a < x → f a < f (succ a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.SuccPred.Archimedean | {
"line": 407,
"column": 2
} | {
"line": 407,
"column": 13
} | {
"line": 407,
"column": 14
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f (succ a) < f a\n⊢ StrictAnti f",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoal... | [
"α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f (succ a) < f a\n⊢ StrictAnti f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.SuccPred.Archimedean | {
"line": 407,
"column": 64
} | {
"line": 407,
"column": 75
} | {
"line": 407,
"column": 76
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f (succ a) < f a\n⊢ ∀ (a : α), ¬IsMax a → a ∈ Set.univ → succ a ∈ Set.univ → f (succ a) < f a",
"ppTerm": "?m.28",
"assigned": true,... | [
"α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMax a → f (succ a) < f a\n⊢ ∀ (a x : α), a < x → f (succ a) < f a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.SuccPred.Archimedean | {
"line": 441,
"column": 12
} | {
"line": 441,
"column": 23
} | {
"line": 441,
"column": 24
} | [
{
"pp": "case succ.zero\nα : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\ns : Set α\nf : α → β\nhs : s.OrdConnected\nhf : ∀ (a : α), ¬IsMin a → a ∈ s → pred a ∈ s → f (pred a) < f a\nb : α\nhb : b ∈ s\nhab : ¬IsMin b\nha : pred^[0 + 1] ... | [
"case succ.zero\nα : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\ns : Set α\nf : α → β\nhs : s.OrdConnected\nhf : ∀ (a : α), ¬IsMin a → a ∈ s → pred a ∈ s → f (pred a) < f a\nb : α\nhb : b ∈ s\nhab : ¬IsMin b\nha : pred^[0 + 1] b ∈ s\n⊢ f (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.SuccPred.Archimedean | {
"line": 455,
"column": 2
} | {
"line": 455,
"column": 13
} | {
"line": 455,
"column": 14
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f (pred a) ≤ f a\n⊢ Monotone f",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals"... | [
"α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f (pred a) ≤ f a\n⊢ Monotone f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.SuccPred.Archimedean | {
"line": 455,
"column": 62
} | {
"line": 455,
"column": 73
} | {
"line": 455,
"column": 74
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f (pred a) ≤ f a\n⊢ ∀ (a : α), ¬IsMin a → a ∈ Set.univ → pred a ∈ Set.univ → f (pred a) ≤ f a",
"ppTerm": "?m.28",
"assigned": true,... | [
"α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f (pred a) ≤ f a\n⊢ ∀ (a x : α), x < a → f (pred a) ≤ f a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.SuccPred.Archimedean | {
"line": 458,
"column": 2
} | {
"line": 458,
"column": 13
} | {
"line": 458,
"column": 14
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f a ≤ f (pred a)\n⊢ Antitone f",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals"... | [
"α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f a ≤ f (pred a)\n⊢ Antitone f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.SuccPred.Archimedean | {
"line": 458,
"column": 62
} | {
"line": 458,
"column": 73
} | {
"line": 458,
"column": 74
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f a ≤ f (pred a)\n⊢ ∀ (a : α), ¬IsMin a → a ∈ Set.univ → pred a ∈ Set.univ → f a ≤ f (pred a)",
"ppTerm": "?m.28",
"assigned": true,... | [
"α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f a ≤ f (pred a)\n⊢ ∀ (a x : α), x < a → f a ≤ f (pred a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Piecewise | {
"line": 77,
"column": 92
} | {
"line": 78,
"column": 59
} | {
"line": 80,
"column": 0
} | [
{
"pp": "ι : Type u_1\nπ : ι → Sort u_2\nf g : (i : ι) → π i\ninst✝ : DecidableEq ι\ni : ι\n⊢ {i}.piecewise f g = update g i (f i)",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Finset.piecewise_insert",
"Eq.mpr",
"Function.update",
"congrArg",
"Finset",
... | [] | by
rw [← insert_empty_eq, piecewise_insert, piecewise_empty] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.SuccPred.Archimedean | {
"line": 461,
"column": 2
} | {
"line": 461,
"column": 13
} | {
"line": 461,
"column": 14
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f (pred a) < f a\n⊢ StrictMono f",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoal... | [
"α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f (pred a) < f a\n⊢ StrictMono f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.SuccPred.Archimedean | {
"line": 461,
"column": 64
} | {
"line": 461,
"column": 75
} | {
"line": 461,
"column": 76
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f (pred a) < f a\n⊢ ∀ (a : α), ¬IsMin a → a ∈ Set.univ → pred a ∈ Set.univ → f (pred a) < f a",
"ppTerm": "?m.28",
"assigned": true,... | [
"α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f (pred a) < f a\n⊢ ∀ (a x : α), x < a → f (pred a) < f a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.SuccPred.Archimedean | {
"line": 464,
"column": 2
} | {
"line": 464,
"column": 13
} | {
"line": 464,
"column": 14
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f a < f (pred a)\n⊢ StrictAnti f",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoal... | [
"α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f a < f (pred a)\n⊢ StrictAnti f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.SuccPred.Archimedean | {
"line": 464,
"column": 64
} | {
"line": 464,
"column": 75
} | {
"line": 464,
"column": 76
} | [
{
"pp": "α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f a < f (pred a)\n⊢ ∀ (a : α), ¬IsMin a → a ∈ Set.univ → pred a ∈ Set.univ → f a < f (pred a)",
"ppTerm": "?m.28",
"assigned": true,... | [
"α : Type u_3\nβ : Type u_4\ninst✝³ : PartialOrder α\ninst✝² : Preorder β\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\nf : α → β\nhf : ∀ (a : α), ¬IsMin a → f a < f (pred a)\n⊢ ∀ (a x : α), x < a → f a < f (pred a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fintype.Sum | {
"line": 98,
"column": 67
} | {
"line": 98,
"column": 83
} | {
"line": 98,
"column": 83
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : Fintype α\ninst✝ : DecidableEq β\nt : Finset β\nhαt : Fintype.card α = #t\nf : α → β\nhfst : image f ∅ ⊆ t\nhfs : Set.InjOn f ↑∅\n⊢ Fintype.card α = Fintype.card ↥t",
"ppTerm": "?m.44",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg... | [
"α : Type u_1\nβ : Type u_2\ninst✝¹ : Fintype α\ninst✝ : DecidableEq β\nt : Finset β\nhαt : Fintype.card α = #t\nf : α → β\nhfst : image f ∅ ⊆ t\nhfs : Set.InjOn f ↑∅\n⊢ Fintype.card α = #t"
] | Fintype.card_coe | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.BigOperators.Group.Finset.Piecewise | {
"line": 31,
"column": 43
} | {
"line": 31,
"column": 54
} | {
"line": 31,
"column": 55
} | [
{
"pp": "ι : Type u_1\nκ : Type u_2\nM : Type u_3\nβ : Type u_4\nγ : Type u_5\ns : Finset ι\ninst✝² : CommMonoid M\np : ι → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred fun x ↦ ¬p x\nf : (x : ι) → p x → γ\ng : (x : ι) → ¬p x → γ\nh : γ → M\nx : ↥({x ∈ s | p x})\n⊢ p ↑x",
"ppTerm": "?m.45",
"ass... | [
"ι : Type u_1\nκ : Type u_2\nM : Type u_3\nβ : Type u_4\nγ : Type u_5\ns : Finset ι\ninst✝² : CommMonoid M\np : ι → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred fun x ↦ ¬p x\nf : (x : ι) → p x → γ\ng : (x : ι) → ¬p x → γ\nh : γ → M\nx : ↥({x ∈ s | p x})\n⊢ p ↑x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.BigOperators.Group.Finset.Piecewise | {
"line": 32,
"column": 45
} | {
"line": 32,
"column": 56
} | {
"line": 32,
"column": 57
} | [
{
"pp": "ι : Type u_1\nκ : Type u_2\nM : Type u_3\nβ : Type u_4\nγ : Type u_5\ns : Finset ι\ninst✝² : CommMonoid M\np : ι → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred fun x ↦ ¬p x\nf : (x : ι) → p x → γ\ng : (x : ι) → ¬p x → γ\nh : γ → M\nx : ↥({x ∈ s | ¬p x})\n⊢ ¬p ↑x",
"ppTerm": "?m.62",
"a... | [
"ι : Type u_1\nκ : Type u_2\nM : Type u_3\nβ : Type u_4\nγ : Type u_5\ns : Finset ι\ninst✝² : CommMonoid M\np : ι → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred fun x ↦ ¬p x\nf : (x : ι) → p x → γ\ng : (x : ι) → ¬p x → γ\nh : γ → M\nx : ↥({x ∈ s | ¬p x})\n⊢ ¬p ↑x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.BigOperators.Group.Finset.Piecewise | {
"line": 41,
"column": 45
} | {
"line": 41,
"column": 56
} | {
"line": 41,
"column": 57
} | [
{
"pp": "ι : Type u_1\nM : Type u_3\nγ : Type u_5\ns : Finset ι\ninst✝² : CommMonoid M\np : ι → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred fun x ↦ ¬p x\nf : (x : ι) → p x → γ\ng : (x : ι) → ¬p x → γ\nh : γ → M\nx : ↥({x ∈ s | p x})\n⊢ p ↑x",
"ppTerm": "?m.216",
"assigned": false,
"usedCon... | [
"ι : Type u_1\nM : Type u_3\nγ : Type u_5\ns : Finset ι\ninst✝² : CommMonoid M\np : ι → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred fun x ↦ ¬p x\nf : (x : ι) → p x → γ\ng : (x : ι) → ¬p x → γ\nh : γ → M\nx : ↥({x ∈ s | p x})\n⊢ p ↑x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.BigOperators.Group.Finset.Piecewise | {
"line": 42,
"column": 47
} | {
"line": 42,
"column": 58
} | {
"line": 42,
"column": 59
} | [
{
"pp": "ι : Type u_1\nM : Type u_3\nγ : Type u_5\ns : Finset ι\ninst✝² : CommMonoid M\np : ι → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred fun x ↦ ¬p x\nf : (x : ι) → p x → γ\ng : (x : ι) → ¬p x → γ\nh : γ → M\nx : ↥({x ∈ s | ¬p x})\n⊢ ¬p ↑x",
"ppTerm": "?m.229",
"assigned": false,
"usedC... | [
"ι : Type u_1\nM : Type u_3\nγ : Type u_5\ns : Finset ι\ninst✝² : CommMonoid M\np : ι → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred fun x ↦ ¬p x\nf : (x : ι) → p x → γ\ng : (x : ι) → ¬p x → γ\nh : γ → M\nx : ↥({x ∈ s | ¬p x})\n⊢ ¬p ↑x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.BigOperators.Group.Finset.Piecewise | {
"line": 44,
"column": 35
} | {
"line": 44,
"column": 46
} | {
"line": 44,
"column": 47
} | [
{
"pp": "ι : Type u_1\nM : Type u_3\nγ : Type u_5\ns : Finset ι\ninst✝² : CommMonoid M\np : ι → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred fun x ↦ ¬p x\nf : (x : ι) → p x → γ\ng : (x : ι) → ¬p x → γ\nh : γ → M\nx : ↥({x ∈ s | p x})\n_hx : x ∈ univ\n⊢ p ↑x",
"ppTerm": "?m.261",
"assigned": fal... | [
"ι : Type u_1\nM : Type u_3\nγ : Type u_5\ns : Finset ι\ninst✝² : CommMonoid M\np : ι → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred fun x ↦ ¬p x\nf : (x : ι) → p x → γ\ng : (x : ι) → ¬p x → γ\nh : γ → M\nx : ↥({x ∈ s | p x})\n_hx : x ∈ univ\n⊢ p ↑x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.BigOperators.Group.Finset.Piecewise | {
"line": 45,
"column": 64
} | {
"line": 45,
"column": 75
} | {
"line": 45,
"column": 76
} | [
{
"pp": "ι : Type u_1\nM : Type u_3\nγ : Type u_5\ns : Finset ι\ninst✝² : CommMonoid M\np : ι → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred fun x ↦ ¬p x\nf : (x : ι) → p x → γ\ng : (x : ι) → ¬p x → γ\nh : γ → M\nx : ↥({x ∈ s | ¬p x})\n_hx : x ∈ univ\n⊢ ¬p ↑x",
"ppTerm": "?m.283",
"assigned": f... | [
"ι : Type u_1\nM : Type u_3\nγ : Type u_5\ns : Finset ι\ninst✝² : CommMonoid M\np : ι → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred fun x ↦ ¬p x\nf : (x : ι) → p x → γ\ng : (x : ι) → ¬p x → γ\nh : γ → M\nx : ↥({x ∈ s | ¬p x})\n_hx : x ∈ univ\n⊢ ¬p ↑x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.BigOperators.Group.Finset.Piecewise | {
"line": 58,
"column": 38
} | {
"line": 58,
"column": 49
} | {
"line": 58,
"column": 50
} | [
{
"pp": "ι : Type u_1\nκ : Type u_2\nM : Type u_3\nβ : Type u_4\nγ : Type u_5\ns✝ : Finset ι\ninst✝¹ : CommMonoid M\ns : Finset ι\np : ι → Prop\ninst✝ : DecidablePred p\nf : (x : ι) → p x → M\ng : (x : ι) → ¬p x → M\nx : ↥({x ∈ s | p x})\n⊢ p ↑x",
"ppTerm": "?m.44",
"assigned": false,
"usedConstants... | [
"ι : Type u_1\nκ : Type u_2\nM : Type u_3\nβ : Type u_4\nγ : Type u_5\ns✝ : Finset ι\ninst✝¹ : CommMonoid M\ns : Finset ι\np : ι → Prop\ninst✝ : DecidablePred p\nf : (x : ι) → p x → M\ng : (x : ι) → ¬p x → M\nx : ↥({x ∈ s | p x})\n⊢ p ↑x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.BigOperators.Group.Finset.Piecewise | {
"line": 59,
"column": 40
} | {
"line": 59,
"column": 51
} | {
"line": 59,
"column": 52
} | [
{
"pp": "ι : Type u_1\nκ : Type u_2\nM : Type u_3\nβ : Type u_4\nγ : Type u_5\ns✝ : Finset ι\ninst✝¹ : CommMonoid M\ns : Finset ι\np : ι → Prop\ninst✝ : DecidablePred p\nf : (x : ι) → p x → M\ng : (x : ι) → ¬p x → M\nx : ↥({x ∈ s | ¬p x})\n⊢ ¬p ↑x",
"ppTerm": "?m.61",
"assigned": false,
"usedConstan... | [
"ι : Type u_1\nκ : Type u_2\nM : Type u_3\nβ : Type u_4\nγ : Type u_5\ns✝ : Finset ι\ninst✝¹ : CommMonoid M\ns : Finset ι\np : ι → Prop\ninst✝ : DecidablePred p\nf : (x : ι) → p x → M\ng : (x : ι) → ¬p x → M\nx : ↥({x ∈ s | ¬p x})\n⊢ ¬p ↑x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.BigOperators.Group.Finset.Piecewise | {
"line": 82,
"column": 2
} | {
"line": 82,
"column": 79
} | {
"line": 84,
"column": 0
} | [
{
"pp": "ι : Type u_1\nM : Type u_3\ns : Finset ι\ninst✝¹ : CommMonoid M\np : ι → Prop\ninst✝ : DecidablePred p\nh : ∀ i ∈ s, p i\nf : (i : ι) → p i → M\ng : (i : ι) → ¬p i → M\n⊢ (∏ i ∈ s, if hi : p i then f i hi else g i hi) = ∏ i, f ↑i ⋯",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
... | [] | refine prod_bij' (fun x hx => ⟨x, hx⟩) (fun x _ ↦ x) ?_ ?_ ?_ ?_ ?_ <;> grind | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Algebra.BigOperators.Group.Finset.Piecewise | {
"line": 82,
"column": 2
} | {
"line": 82,
"column": 79
} | {
"line": 84,
"column": 0
} | [
{
"pp": "ι : Type u_1\nM : Type u_3\ns : Finset ι\ninst✝¹ : CommMonoid M\np : ι → Prop\ninst✝ : DecidablePred p\nh : ∀ i ∈ s, p i\nf : (i : ι) → p i → M\ng : (i : ι) → ¬p i → M\n⊢ (∏ i ∈ s, if hi : p i then f i hi else g i hi) = ∏ i, f ↑i ⋯",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
... | [] | refine prod_bij' (fun x hx => ⟨x, hx⟩) (fun x _ ↦ x) ?_ ?_ ?_ ?_ ?_ <;> grind | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.BigOperators.Group.Finset.Piecewise | {
"line": 82,
"column": 2
} | {
"line": 82,
"column": 79
} | {
"line": 84,
"column": 0
} | [
{
"pp": "ι : Type u_1\nM : Type u_3\ns : Finset ι\ninst✝¹ : CommMonoid M\np : ι → Prop\ninst✝ : DecidablePred p\nh : ∀ i ∈ s, p i\nf : (i : ι) → p i → M\ng : (i : ι) → ¬p i → M\n⊢ (∏ i ∈ s, if hi : p i then f i hi else g i hi) = ∏ i, f ↑i ⋯",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
... | [] | refine prod_bij' (fun x hx => ⟨x, hx⟩) (fun x _ ↦ x) ?_ ?_ ?_ ?_ ?_ <;> grind | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.BigOperators.Group.Finset.Piecewise | {
"line": 291,
"column": 32
} | {
"line": 291,
"column": 43
} | {
"line": 291,
"column": 44
} | [
{
"pp": "ι : Type u_1\nM : Type u_3\ninst✝² : CommMonoid M\ninst✝¹ : Fintype ι\np : ι → Prop\ninst✝ : DecidablePred p\nh : ∀ (i j : ι), p i → p j → i = j\na : M\n⊢ ∀ i ∈ univ, ∀ j ∈ univ, p i → p j → i = j",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.univ",... | [
"ι : Type u_1\nM : Type u_3\ninst✝² : CommMonoid M\ninst✝¹ : Fintype ι\np : ι → Prop\ninst✝ : DecidablePred p\nh : ∀ (i j : ι), p i → p j → i = j\na : M\n⊢ ∀ (i j : ι), p i → p j → i = j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Vector.Basic | {
"line": 353,
"column": 4
} | {
"line": 353,
"column": 42
} | {
"line": 354,
"column": 2
} | [
{
"pp": "case zero\nα : Type u_1\nβ : Type u_6\nf : β → α → β\nb : β\nv : Vector α 0\nthis : v = nil\n⊢ (scanl f b v).head = b",
"ppTerm": "?zero",
"assigned": true,
"usedConstants": [
"List.Vector.scanl_nil",
"congrArg",
"List.Vector.head",
"List.Vector",
"List.Vector.... | [] | simp only [this, scanl_nil, head_cons] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Fintype.BigOperators | {
"line": 108,
"column": 2
} | {
"line": 109,
"column": 31
} | {
"line": 111,
"column": 0
} | [
{
"pp": "α : Type u_1\nM : Type u_4\ninst✝² : Fintype α\ninst✝¹ : CommMonoid M\ninst✝ : DecidableEq α\nf : α → M\na : α\n⊢ ∏ i, f i = f a * ∏ i, f ↑i",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Fintype.prod_option",
"Eq.mpr",
"instDecidableNot",
"Equiv.instEqui... | [] | simp_rw [← (Equiv.optionSubtypeNe a).prod_comp, prod_option, Equiv.optionSubtypeNe_none,
Equiv.optionSubtypeNe_some] | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | Mathlib.Tactic.tacticSimp_rw___ |
Mathlib.Data.Fintype.BigOperators | {
"line": 108,
"column": 2
} | {
"line": 109,
"column": 31
} | {
"line": 111,
"column": 0
} | [
{
"pp": "α : Type u_1\nM : Type u_4\ninst✝² : Fintype α\ninst✝¹ : CommMonoid M\ninst✝ : DecidableEq α\nf : α → M\na : α\n⊢ ∏ i, f i = f a * ∏ i, f ↑i",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Fintype.prod_option",
"Eq.mpr",
"instDecidableNot",
"Equiv.instEqui... | [] | simp_rw [← (Equiv.optionSubtypeNe a).prod_comp, prod_option, Equiv.optionSubtypeNe_none,
Equiv.optionSubtypeNe_some] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Fintype.BigOperators | {
"line": 108,
"column": 2
} | {
"line": 109,
"column": 31
} | {
"line": 111,
"column": 0
} | [
{
"pp": "α : Type u_1\nM : Type u_4\ninst✝² : Fintype α\ninst✝¹ : CommMonoid M\ninst✝ : DecidableEq α\nf : α → M\na : α\n⊢ ∏ i, f i = f a * ∏ i, f ↑i",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Fintype.prod_option",
"Eq.mpr",
"instDecidableNot",
"Equiv.instEqui... | [] | simp_rw [← (Equiv.optionSubtypeNe a).prod_comp, prod_option, Equiv.optionSubtypeNe_none,
Equiv.optionSubtypeNe_some] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Vector.Basic | {
"line": 565,
"column": 8
} | {
"line": 565,
"column": 37
} | {
"line": 565,
"column": 38
} | [
{
"pp": "case pos.a\nα : Type u_1\nn : ℕ\na : α\nv : Vector α (n + 1)\ni : ℕ\nhi : i < n + 1\nj : ℕ\nhj : j.succ < n + 2\nhij : i < j.succ\n⊢ ↑⟨i, ⋯⟩ ≤ j",
"ppTerm": "?pos.a✝",
"assigned": true,
"usedConstants": [
"Fin.mk",
"id",
"instOfNatNat",
"LE.le",
"instLENat",
... | [
"case pos.a\nα : Type u_1\nn : ℕ\na : α\nv : Vector α (n + 1)\ni : ℕ\nhi : i < n + 1\nj : ℕ\nhj : j.succ < n + 2\nhij : i < j.succ\n⊢ i ≤ j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Vector.Basic | {
"line": 570,
"column": 8
} | {
"line": 570,
"column": 28
} | {
"line": 570,
"column": 29
} | [
{
"pp": "case neg.a\nα : Type u_1\nn : ℕ\na : α\nv : Vector α (n + 1)\ni : ℕ\nhi : i < n + 1\nj : ℕ\nhj : j < n + 2\nhij : ¬i < j\n⊢ j ≤ i",
"ppTerm": "?neg.a✝",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case neg.a\nα : Type u_1\nn : ℕ\na : α\nv : Vector α (n + 1)\ni : ℕ\nhi : i < n + 1\nj : ℕ\nhj : j < n + 2\nhij : ¬i < j\n⊢ j ≤ i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Countable | {
"line": 228,
"column": 25
} | {
"line": 228,
"column": 46
} | {
"line": 228,
"column": 47
} | [
{
"pp": "α : Type u\nβ : Type v\ns : Set α\nt : (a : α) → a ∈ s → Set β\nhs : s.Countable\nthis : Countable ↑s\n⊢ (⋃ x, t ↑x ⋯).Countable ↔ ∀ (a : α) (ha : a ∈ s), (t a ha).Countable",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Membership.mem",
... | [
"α : Type u\nβ : Type v\ns : Set α\nt : (a : α) → a ∈ s → Set β\nhs : s.Countable\nthis : Countable ↑s\n⊢ (∀ (i : ↑s), (t ↑i ⋯).Countable) ↔ ∀ (a : α) (ha : a ∈ s), (t a ha).Countable"
] | countable_iUnion_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Vector.Basic | {
"line": 605,
"column": 4
} | {
"line": 605,
"column": 15
} | {
"line": 605,
"column": 16
} | [
{
"pp": "case mk.mk.mk.h\nα : Type u_1\nn : ℕ\na : α\nval✝² : List α\nproperty✝ : val✝².length = n\nval✝¹ : ℕ\nisLt✝¹ : val✝¹ < n\nval✝ : ℕ\nisLt✝ : val✝ < n\nh : ⟨val✝¹, isLt✝¹⟩ ≠ ⟨val✝, isLt✝⟩\n⊢ val✝¹ ≠ val✝",
"ppTerm": "?mk.mk.mk.h",
"assigned": true,
"usedConstants": [
"id",
"Ne",
... | [
"case mk.mk.mk.h\nα : Type u_1\nn : ℕ\na : α\nval✝² : List α\nproperty✝ : val✝².length = n\nval✝¹ : ℕ\nisLt✝¹ : val✝¹ < n\nval✝ : ℕ\nisLt✝ : val✝ < n\nh : ⟨val✝¹, isLt✝¹⟩ ≠ ⟨val✝, isLt✝⟩\n⊢ ¬val✝¹ = val✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Countable | {
"line": 284,
"column": 2
} | {
"line": 284,
"column": 13
} | {
"line": 284,
"column": 14
} | [
{
"pp": "α : Type u\ninst✝ : Countable α\n⊢ {s | s.Finite}.Countable",
"ppTerm": "?m.4",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\ninst✝ : Countable α\n⊢ {s | s.Finite}.Countable"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Hom.Lex | {
"line": 44,
"column": 6
} | {
"line": 44,
"column": 17
} | {
"line": 44,
"column": 18
} | [
{
"pp": "case inl.inr\nα : Type u_1\nr : α → α → Prop\nx y : α\ninst✝² : IsTrans α r\ninst✝¹ : Std.Trichotomous r\ninst✝ : DecidableRel r\na : α\nha : r a x\nb : α\nhb : ¬r b x\n⊢ r ((Equiv.sumCompl fun x_1 ↦ r x_1 x) (Sum.inl ⟨a, ha⟩)) ((Equiv.sumCompl fun x_1 ↦ r x_1 x) (Sum.inr ⟨b, hb⟩)) ↔\n Sum.Lex (Subr... | [
"case inl.inr\nα : Type u_1\nr : α → α → Prop\nx y : α\ninst✝² : IsTrans α r\ninst✝¹ : Std.Trichotomous r\ninst✝ : DecidableRel r\na : α\nha : r a x\nb : α\nhb : ¬r b x\n⊢ r a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Hom.Lex | {
"line": 45,
"column": 6
} | {
"line": 45,
"column": 17
} | {
"line": 45,
"column": 18
} | [
{
"pp": "case inr.inl\nα : Type u_1\nr : α → α → Prop\nx y : α\ninst✝² : IsTrans α r\ninst✝¹ : Std.Trichotomous r\ninst✝ : DecidableRel r\na : α\nha : ¬r a x\nb : α\nhb : r b x\n⊢ r ((Equiv.sumCompl fun x_1 ↦ r x_1 x) (Sum.inr ⟨a, ha⟩)) ((Equiv.sumCompl fun x_1 ↦ r x_1 x) (Sum.inl ⟨b, hb⟩)) ↔\n Sum.Lex (Subr... | [
"case inr.inl\nα : Type u_1\nr : α → α → Prop\nx y : α\ninst✝² : IsTrans α r\ninst✝¹ : Std.Trichotomous r\ninst✝ : DecidableRel r\na : α\nha : ¬r a x\nb : α\nhb : r b x\n⊢ ¬r a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Hom.Lex | {
"line": 64,
"column": 6
} | {
"line": 64,
"column": 17
} | {
"line": 64,
"column": 18
} | [
{
"pp": "case inl.inr\nα : Type u_1\nr : α → α → Prop\nx y : α\ninst✝² : IsTrans α r\ninst✝¹ : Std.Trichotomous r\ninst✝ : DecidableRel r\na : α\nha : ¬r x a\nb : α\nhb : r x b\n⊢ r (((Equiv.sumComm { x_1 // ¬r x x_1 } (Subtype (r x))).trans (Equiv.sumCompl (r x))) (Sum.inl ⟨a, ha⟩))\n (((Equiv.sumComm { x... | [
"case inl.inr\nα : Type u_1\nr : α → α → Prop\nx y : α\ninst✝² : IsTrans α r\ninst✝¹ : Std.Trichotomous r\ninst✝ : DecidableRel r\na : α\nha : ¬r x a\nb : α\nhb : r x b\n⊢ r a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Hom.Lex | {
"line": 65,
"column": 6
} | {
"line": 65,
"column": 17
} | {
"line": 65,
"column": 18
} | [
{
"pp": "case inr.inl\nα : Type u_1\nr : α → α → Prop\nx y : α\ninst✝² : IsTrans α r\ninst✝¹ : Std.Trichotomous r\ninst✝ : DecidableRel r\na : α\nha : r x a\nb : α\nhb : ¬r x b\n⊢ r (((Equiv.sumComm { x_1 // ¬r x x_1 } (Subtype (r x))).trans (Equiv.sumCompl (r x))) (Sum.inr ⟨a, ha⟩))\n (((Equiv.sumComm { x... | [
"case inr.inl\nα : Type u_1\nr : α → α → Prop\nx y : α\ninst✝² : IsTrans α r\ninst✝¹ : Std.Trichotomous r\ninst✝ : DecidableRel r\na : α\nha : r x a\nb : α\nhb : ¬r x b\n⊢ ¬r a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Hom.Lex | {
"line": 157,
"column": 38
} | {
"line": 157,
"column": 49
} | {
"line": 157,
"column": 50
} | [
{
"pp": "α✝ : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝² : PartialOrder α\ninst✝¹ : Preorder β\ninst✝ : Unique β\nx : Lex (α × β)\nx✝ : α × β\na : α\nb : β\n⊢ (fun x ↦ toLex (x, default)) ((fun x ↦ (ofLex x).1) (toLex (a, b))) = toLex (a, b)",
"ppTerm": "?m.59",
"assigned": true,
"usedConstants": ... | [
"α✝ : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝² : PartialOrder α\ninst✝¹ : Preorder β\ninst✝ : Unique β\nx : Lex (α × β)\nx✝ : α × β\na : α\nb : β\n⊢ default = b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Hom.Lex | {
"line": 160,
"column": 4
} | {
"line": 160,
"column": 41
} | {
"line": 160,
"column": 42
} | [
{
"pp": "α✝ : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝² : PartialOrder α\ninst✝¹ : Preorder β\ninst✝ : Unique β\na✝ b✝ : Lex (α × β)\na b : α × β\n⊢ { toFun := fun x ↦ (ofLex x).1, invFun := fun x ↦ toLex (x, default), left_inv := ⋯, right_inv := ⋯ } (toLex a) ≤\n { toFun := fun x ↦ (ofLex x).1, invFun ... | [
"α✝ : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝² : PartialOrder α\ninst✝¹ : Preorder β\ninst✝ : Unique β\na✝ b✝ : Lex (α × β)\na b : α × β\n⊢ a.1 ≤ b.1 ↔ a.1 < b.1 ∨ a.1 = b.1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Hom.Lex | {
"line": 171,
"column": 38
} | {
"line": 171,
"column": 49
} | {
"line": 171,
"column": 50
} | [
{
"pp": "α✝ : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝² : Preorder α\ninst✝¹ : Unique α\ninst✝ : LE β\nx : Lex (α × β)\nx✝ : α × β\na : α\nb : β\n⊢ (fun x ↦ toLex (default, x)) ((fun x ↦ (ofLex x).2) (toLex (a, b))) = toLex (a, b)",
"ppTerm": "?m.59",
"assigned": true,
"usedConstants": [
"E... | [
"α✝ : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝² : Preorder α\ninst✝¹ : Unique α\ninst✝ : LE β\nx : Lex (α × β)\nx✝ : α × β\na : α\nb : β\n⊢ default = a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.SuccPred.CompleteLinearOrder | {
"line": 131,
"column": 2
} | {
"line": 131,
"column": 17
} | {
"line": 131,
"column": 18
} | [
{
"pp": "α : Type u_2\ninst✝ : ConditionallyCompleteLinearOrderBot α\nx : α\nh : sSup (Iio x) = x\nhx : ¬IsSuccPrelimit (sSup (Iio x))\n⊢ False",
"ppTerm": "?m.24",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝ : ConditionallyCompleteLinearOrderBot α\nx : α\nh : sSup (Iio x) = x\nhx : ¬IsSuccPrelimit (sSup (Iio x))\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Cardinal.Defs | {
"line": 466,
"column": 2
} | {
"line": 466,
"column": 27
} | {
"line": 466,
"column": 28
} | [
{
"pp": "ι : Type u\na : Cardinal.{max u v}\nf : ι → Cardinal.{max u v}\n⊢ a ^ sum f = prod fun i ↦ a ^ f i",
"ppTerm": "?m.13",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"ι : Type u\na : Cardinal.{max u v}\nf : ι → Cardinal.{max u v}\n⊢ a ^ sum f = prod fun i ↦ a ^ f i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.FixedPoints.Defs | {
"line": 44,
"column": 22
} | {
"line": 44,
"column": 33
} | {
"line": 44,
"column": 34
} | [
{
"pp": "α : Type u_1\nx✝ : α\n⊢ x✝ ∈ fixedPoints id ↔ x✝ ∈ Set.univ",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Set.mem_univ._simp_1",
"Set.univ",
"Function.fixedPoints",
"iff_true",
"Membership.mem",
"id",
"F... | [
"α : Type u_1\nx✝ : α\n⊢ IsFixedPt id x✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.FixedPoints.Basic | {
"line": 130,
"column": 2
} | {
"line": 130,
"column": 30
} | {
"line": 130,
"column": 31
} | [
{
"pp": "α : Type u_1\nf g : α → α\nh : Function.Commute f g\n⊢ Set.InvOn f g (fixedPoints (f ∘ g)) (fixedPoints (f ∘ g))",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Set.InvOn",
"Eq.mpr",
"Function.Semiconj.comp_eq",
"congrArg",
"Function.fixedPoints",
... | [
"α : Type u_1\nf g : α → α\nh : Function.Commute f g\n⊢ Set.InvOn f g (fixedPoints (g ∘ f)) (fixedPoints (g ∘ f))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.FixedPoints.Basic | {
"line": 136,
"column": 2
} | {
"line": 136,
"column": 30
} | {
"line": 136,
"column": 31
} | [
{
"pp": "α : Type u_1\nf g : α → α\nh : Function.Commute f g\n⊢ Set.BijOn f (fixedPoints (f ∘ g)) (fixedPoints (f ∘ g))",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Function.Semiconj.comp_eq",
"congrArg",
"Function.fixedPoints",
"Function.comp",
... | [
"α : Type u_1\nf g : α → α\nh : Function.Commute f g\n⊢ Set.BijOn f (fixedPoints (g ∘ f)) (fixedPoints (g ∘ f))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.FixedPoints.Basic | {
"line": 142,
"column": 2
} | {
"line": 142,
"column": 30
} | {
"line": 142,
"column": 31
} | [
{
"pp": "α : Type u_1\nf g : α → α\nh : Function.Commute f g\n⊢ Set.BijOn g (fixedPoints (f ∘ g)) (fixedPoints (f ∘ g))",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Function.Semiconj.comp_eq",
"congrArg",
"Function.fixedPoints",
"Function.comp",
... | [
"α : Type u_1\nf g : α → α\nh : Function.Commute f g\n⊢ Set.BijOn g (fixedPoints (g ∘ f)) (fixedPoints (g ∘ f))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.InitialSeg | {
"line": 201,
"column": 4
} | {
"line": 201,
"column": 58
} | {
"line": 202,
"column": 4
} | [
{
"pp": "case inl\nα : Type u_1\nβ : Type u_2\nr : α → α → Prop\ns : β → β → Prop\ninst✝ : IsWellOrder β s\nf : r ≼i s\nb : β\nh : ∀ (b : β), ∃ x, x ∈ Set.range ⇑f ∧ ¬s x b ∨ x ∉ Set.range ⇑f ∧ s x b\nx : β\nIH : ∀ (y : β), s y x → ∃ a, f a = y\ny : β\nhy : y ∈ Set.range ⇑f\nhs : ¬s y x\n⊢ ∃ a, f a = x",
"p... | [
"case inl.inl\nα : Type u_1\nβ : Type u_2\nr : α → α → Prop\ns : β → β → Prop\ninst✝ : IsWellOrder β s\nf : r ≼i s\nb : β\nh : ∀ (b : β), ∃ x, x ∈ Set.range ⇑f ∧ ¬s x b ∨ x ∉ Set.range ⇑f ∧ s x b\ny : β\nhy : y ∈ Set.range ⇑f\nIH : ∀ (y_1 : β), s y_1 y → ∃ a, f a = y_1\nhs : ¬s y y\n⊢ ∃ a, f a = y",
"case inl.inr... | obtain (rfl | h) := (trichotomous y x).resolve_left hs | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Order.InitialSeg | {
"line": 306,
"column": 2
} | {
"line": 306,
"column": 13
} | {
"line": 306,
"column": 14
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nr : α → α → Prop\ns : β → β → Prop\nf : r ≺i s\nb : β\nh : b ∈ {b | s b f.top}\n⊢ b ∈ ⇑f.toRelEmbedding '' Set.univ",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.image_univ",
"congrArg",
"Set.univ",
"Princi... | [
"α : Type u_1\nβ : Type u_2\nr : α → α → Prop\ns : β → β → Prop\nf : r ≺i s\nb : β\nh : b ∈ {b | s b f.top}\n⊢ ∃ y, f.toRelEmbedding y = b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.UpperLower.Basic | {
"line": 113,
"column": 17
} | {
"line": 113,
"column": 28
} | {
"line": 113,
"column": 29
} | [
{
"pp": "α : Type u_1\ninst✝ : LE α\ns : Set α\na : α\nhs : IsUpperSet s\nhas : ∀ b ∈ s, b ≤ a → b = a\n⊢ ∀ b ∈ s, ∀ c ∈ {a}, b ≤ c → b ∈ {a}",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Membership.mem",
"Set.instSingletonSet",
"id",
"LE.le",
... | [
"α : Type u_1\ninst✝ : LE α\ns : Set α\na : α\nhs : IsUpperSet s\nhas : ∀ b ∈ s, b ≤ a → b = a\n⊢ ∀ b ∈ s, b ≤ a → b = a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.UpperLower.Basic | {
"line": 257,
"column": 2
} | {
"line": 257,
"column": 13
} | {
"line": 257,
"column": 14
} | [
{
"pp": "α : Type u_1\ninst✝¹ : LinearOrder α\ns : Set α\ninst✝ : WellFoundedLT α\nh : IsLowerSet s\n⊢ sᶜ = univᶜ ∨ ∃ a, sᶜ = (Iio a)ᶜ",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ici",
"congrArg",
"Compl.compl",
"Set.univ",
"PartialOrd... | [
"α : Type u_1\ninst✝¹ : LinearOrder α\ns : Set α\ninst✝ : WellFoundedLT α\nh : IsLowerSet s\n⊢ s = univ ∨ ∃ a, sᶜ = Ici a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Part | {
"line": 43,
"column": 2
} | {
"line": 43,
"column": 39
} | {
"line": 43,
"column": 40
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝ : Preorder α\nf : β → γ\ng : α → Part β\nhg : Monotone g\n⊢ Monotone fun x ↦ map f (g x)",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Part",
"Eq.mpr",
"congrArg",
"Part.bind",
"Part.some",
"Par... | [
"α : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝ : Preorder α\nf : β → γ\ng : α → Part β\nhg : Monotone g\n⊢ Monotone fun x ↦ (g x).bind fun y ↦ Part.some (f y)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Part | {
"line": 46,
"column": 2
} | {
"line": 46,
"column": 39
} | {
"line": 46,
"column": 40
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝ : Preorder α\nf : β → γ\ng : α → Part β\nhg : Antitone g\n⊢ Antitone fun x ↦ map f (g x)",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Part",
"Eq.mpr",
"congrArg",
"Part.bind",
"Part.some",
"_pr... | [
"α : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝ : Preorder α\nf : β → γ\ng : α → Part β\nhg : Antitone g\n⊢ Antitone fun x ↦ (g x).bind fun y ↦ Part.some (f y)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Part | {
"line": 269,
"column": 4
} | {
"line": 269,
"column": 19
} | {
"line": 269,
"column": 20
} | [
{
"pp": "case pos\nα : Type u_1\no : Part α\ninst✝ : Decidable o.Dom\na : α\nh : o.Dom\n⊢ (a ∈ if h : o.Dom then Option.some (o.get h) else Option.none) ↔ a ∈ o",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"dite_cond_eq_true",
"Part",
"Eq.mpr",
"congrArg",
... | [
"case pos\nα : Type u_1\no : Part α\ninst✝ : Decidable o.Dom\na : α\nh : o.Dom\n⊢ o.get ⋯ = a ↔ a ∈ o"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Part | {
"line": 670,
"column": 23
} | {
"line": 670,
"column": 47
} | {
"line": 672,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : Div α\na b : Part α\nma mb : α\nha : ma ∈ a\nhb : mb ∈ b\n⊢ ma / mb ∈ a / b",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Part",
"Eq.mpr",
"instHDiv",
"congrArg",
"Part.bind",
"Part.mem_bind_iff._simp_1",
"Membersh... | [] | by simp [div_def]; aesop | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.CompleteLattice.Chain | {
"line": 43,
"column": 2
} | {
"line": 43,
"column": 13
} | {
"line": 43,
"column": 14
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\nthis : ChainClosure r (⋃₀ ∅)\n⊢ ChainClosure r ∅",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nr : α → α → Prop\nthis : ChainClosure r (⋃₀ ∅)\n⊢ ChainClosure r ∅"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Zorn | {
"line": 192,
"column": 2
} | {
"line": 192,
"column": 37
} | {
"line": 192,
"column": 38
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\na b : α\nhab : a ≤ b\n⊢ ∃ s, a ∈ s ∧ b ∈ s",
"ppTerm": "?m.12",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝ : Preorder α\na b : α\nhab : a ≤ b\n⊢ ∃ s, a ∈ s ∧ b ∈ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.FixedPoints | {
"line": 146,
"column": 2
} | {
"line": 146,
"column": 27
} | {
"line": 147,
"column": 2
} | [
{
"pp": "α : Type u\ninst✝ : CompleteLattice α\nh : α →o α →o α\n⊢ lfp (lfp.comp h) = lfp h.onDiag",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"ChainCompletePartialOrder.instOfCompleteLattice",
"PartialOrder.toPreorder",
"OrderHom.instPreorder",
"OrderHom.comp",... | [
"α : Type u\ninst✝ : CompleteLattice α\nh : α →o α →o α\na : α := lfp (lfp.comp h)\n⊢ lfp (lfp.comp h) = lfp h.onDiag"
] | let a := (lfp.comp h).lfp | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLet___1 | Lean.Parser.Tactic.tacticLet__ |
Mathlib.Order.OmegaCompletePartialOrder | {
"line": 275,
"column": 2
} | {
"line": 276,
"column": 9
} | {
"line": 276,
"column": 10
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝¹ : OmegaCompletePartialOrder α\ninst✝ : OmegaCompletePartialOrder β\nf : α → β\nc : Chain α\nhf : ωScottContinuous f\n⊢ IsLUB (Set.range ⇑(c.map { toFun := f, monotone' := ⋯ })) (f (ωSup c))",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"S... | [
"α : Type u_2\nβ : Type u_3\ninst✝¹ : OmegaCompletePartialOrder α\ninst✝ : OmegaCompletePartialOrder β\nf : α → β\nc : Chain α\nhf : ωScottContinuous f\n⊢ IsLUB (f '' Set.range ⇑c) (f (ωSup c))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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