module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Order.Interval.Set.Basic | {
"line": 765,
"column": 47
} | {
"line": 765,
"column": 52
} | {
"line": 766,
"column": 0
} | [
{
"pp": "⊢ Iic True = univ",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Set.ext",
"congrArg",
"Set.mem_univ._simp_1",
"Set.univ",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Set.mem_Iic._simp_2",
"Membership.mem",
"LE.le",
"if... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Interval.Set.Basic | {
"line": 766,
"column": 49
} | {
"line": 766,
"column": 54
} | {
"line": 767,
"column": 0
} | [
{
"pp": "⊢ Ici False = univ",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Set.ext",
"False",
"Set.Ici",
"congrArg",
"Set.mem_univ._simp_1",
"Set.univ",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"LE.le",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.Interval.Set.Basic | {
"line": 766,
"column": 49
} | {
"line": 766,
"column": 54
} | {
"line": 767,
"column": 0
} | [
{
"pp": "⊢ Ici False = univ",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Set.ext",
"False",
"Set.Ici",
"congrArg",
"Set.mem_univ._simp_1",
"Set.univ",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"LE.le",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Interval.Set.Basic | {
"line": 766,
"column": 49
} | {
"line": 766,
"column": 54
} | {
"line": 767,
"column": 0
} | [
{
"pp": "⊢ Ici False = univ",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Set.ext",
"False",
"Set.Ici",
"congrArg",
"Set.mem_univ._simp_1",
"Set.univ",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"LE.le",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Interval.Set.Basic | {
"line": 767,
"column": 49
} | {
"line": 767,
"column": 54
} | {
"line": 768,
"column": 0
} | [
{
"pp": "⊢ Ici True = {True}",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Set.ext",
"Set.Ici",
"congrArg",
"PartialOrder.toPreorder",
"instInhabitedTrue",
"iff_true",
"eq_iff_iff._simp_1",
"Preorder.toLE",
"Membership.mem",
"Se... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.Interval.Set.Basic | {
"line": 767,
"column": 49
} | {
"line": 767,
"column": 54
} | {
"line": 768,
"column": 0
} | [
{
"pp": "⊢ Ici True = {True}",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Set.ext",
"Set.Ici",
"congrArg",
"PartialOrder.toPreorder",
"instInhabitedTrue",
"iff_true",
"eq_iff_iff._simp_1",
"Preorder.toLE",
"Membership.mem",
"Se... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Interval.Set.Basic | {
"line": 767,
"column": 49
} | {
"line": 767,
"column": 54
} | {
"line": 768,
"column": 0
} | [
{
"pp": "⊢ Ici True = {True}",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Set.ext",
"Set.Ici",
"congrArg",
"PartialOrder.toPreorder",
"instInhabitedTrue",
"iff_true",
"eq_iff_iff._simp_1",
"Preorder.toLE",
"Membership.mem",
"Se... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Interval.Set.Basic | {
"line": 768,
"column": 38
} | {
"line": 768,
"column": 43
} | {
"line": 769,
"column": 0
} | [
{
"pp": "⊢ Iio False = ∅",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"False",
"isMin_iff_eq_bot._simp_1",
"congrArg",
"IsMin.Iio_eq",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Prop.instHeytingAlgebra",
"Preorder.toLE",
"Bot.bot",... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.Interval.Set.Basic | {
"line": 768,
"column": 38
} | {
"line": 768,
"column": 43
} | {
"line": 769,
"column": 0
} | [
{
"pp": "⊢ Iio False = ∅",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"False",
"isMin_iff_eq_bot._simp_1",
"congrArg",
"IsMin.Iio_eq",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Prop.instHeytingAlgebra",
"Preorder.toLE",
"Bot.bot",... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Interval.Set.Basic | {
"line": 768,
"column": 38
} | {
"line": 768,
"column": 43
} | {
"line": 769,
"column": 0
} | [
{
"pp": "⊢ Iio False = ∅",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"False",
"isMin_iff_eq_bot._simp_1",
"congrArg",
"IsMin.Iio_eq",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Prop.instHeytingAlgebra",
"Preorder.toLE",
"Bot.bot",... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Interval.Set.Basic | {
"line": 771,
"column": 36
} | {
"line": 771,
"column": 41
} | {
"line": 773,
"column": 0
} | [
{
"pp": "⊢ Ioi True = ∅",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Set.Ioi",
"congrArg",
"IsMax.Ioi_eq",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CoheytingAlgebra.toOrderTop",
"isMax_iff_eq_top._simp_2",
"BiheytingAlgebra.toCoheyting... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.Interval.Set.Basic | {
"line": 771,
"column": 36
} | {
"line": 771,
"column": 41
} | {
"line": 773,
"column": 0
} | [
{
"pp": "⊢ Ioi True = ∅",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Set.Ioi",
"congrArg",
"IsMax.Ioi_eq",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CoheytingAlgebra.toOrderTop",
"isMax_iff_eq_top._simp_2",
"BiheytingAlgebra.toCoheyting... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Interval.Set.Basic | {
"line": 771,
"column": 36
} | {
"line": 771,
"column": 41
} | {
"line": 773,
"column": 0
} | [
{
"pp": "⊢ Ioi True = ∅",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Set.Ioi",
"congrArg",
"IsMax.Ioi_eq",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CoheytingAlgebra.toOrderTop",
"isMax_iff_eq_top._simp_2",
"BiheytingAlgebra.toCoheyting... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Bounds.Basic | {
"line": 195,
"column": 6
} | {
"line": 195,
"column": 11
} | {
"line": 196,
"column": 4
} | [
{
"pp": "case inl.inl\nα : Type u_1\ninst✝ : Preorder α\nt : Set α\nhn : (∅ ∪ t).Nonempty\nh✝ : DirectedOn (fun x1 x2 ↦ x1 ≤ x2) (∅ ∪ t)\nh : DirectedOn (fun x1 x2 ↦ x1 ≤ x2) ∅\n⊢ DirectedOn (fun x1 x2 ↦ x1 ≤ x2) ∅ ∧ ∅.Nonempty ∨ DirectedOn (fun x1 x2 ↦ x1 ≤ x2) t ∧ t.Nonempty",
"ppTerm": "?inl.inl",
"a... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.Bounds.Basic | {
"line": 195,
"column": 6
} | {
"line": 195,
"column": 11
} | {
"line": 196,
"column": 4
} | [
{
"pp": "case inl.inl\nα : Type u_1\ninst✝ : Preorder α\nt : Set α\nhn : (∅ ∪ t).Nonempty\nh✝ : DirectedOn (fun x1 x2 ↦ x1 ≤ x2) (∅ ∪ t)\nh : DirectedOn (fun x1 x2 ↦ x1 ≤ x2) ∅\n⊢ DirectedOn (fun x1 x2 ↦ x1 ≤ x2) ∅ ∧ ∅.Nonempty ∨ DirectedOn (fun x1 x2 ↦ x1 ≤ x2) t ∧ t.Nonempty",
"ppTerm": "?inl.inl",
"a... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Bounds.Basic | {
"line": 195,
"column": 6
} | {
"line": 195,
"column": 11
} | {
"line": 196,
"column": 4
} | [
{
"pp": "case inl.inl\nα : Type u_1\ninst✝ : Preorder α\nt : Set α\nhn : (∅ ∪ t).Nonempty\nh✝ : DirectedOn (fun x1 x2 ↦ x1 ≤ x2) (∅ ∪ t)\nh : DirectedOn (fun x1 x2 ↦ x1 ≤ x2) ∅\n⊢ DirectedOn (fun x1 x2 ↦ x1 ≤ x2) ∅ ∧ ∅.Nonempty ∨ DirectedOn (fun x1 x2 ↦ x1 ≤ x2) t ∧ t.Nonempty",
"ppTerm": "?inl.inl",
"a... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Bounds.Basic | {
"line": 198,
"column": 6
} | {
"line": 198,
"column": 11
} | {
"line": 199,
"column": 4
} | [
{
"pp": "case inr.inl\nα : Type u_1\ninst✝ : Preorder α\ns : Set α\nhn : (s ∪ ∅).Nonempty\nh✝ : DirectedOn (fun x1 x2 ↦ x1 ≤ x2) (s ∪ ∅)\nh : DirectedOn (fun x1 x2 ↦ x1 ≤ x2) ∅\n⊢ DirectedOn (fun x1 x2 ↦ x1 ≤ x2) s ∧ s.Nonempty ∨ DirectedOn (fun x1 x2 ↦ x1 ≤ x2) ∅ ∧ ∅.Nonempty",
"ppTerm": "?inr.inl",
"a... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.Bounds.Basic | {
"line": 198,
"column": 6
} | {
"line": 198,
"column": 11
} | {
"line": 199,
"column": 4
} | [
{
"pp": "case inr.inl\nα : Type u_1\ninst✝ : Preorder α\ns : Set α\nhn : (s ∪ ∅).Nonempty\nh✝ : DirectedOn (fun x1 x2 ↦ x1 ≤ x2) (s ∪ ∅)\nh : DirectedOn (fun x1 x2 ↦ x1 ≤ x2) ∅\n⊢ DirectedOn (fun x1 x2 ↦ x1 ≤ x2) s ∧ s.Nonempty ∨ DirectedOn (fun x1 x2 ↦ x1 ≤ x2) ∅ ∧ ∅.Nonempty",
"ppTerm": "?inr.inl",
"a... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Bounds.Basic | {
"line": 198,
"column": 6
} | {
"line": 198,
"column": 11
} | {
"line": 199,
"column": 4
} | [
{
"pp": "case inr.inl\nα : Type u_1\ninst✝ : Preorder α\ns : Set α\nhn : (s ∪ ∅).Nonempty\nh✝ : DirectedOn (fun x1 x2 ↦ x1 ≤ x2) (s ∪ ∅)\nh : DirectedOn (fun x1 x2 ↦ x1 ≤ x2) ∅\n⊢ DirectedOn (fun x1 x2 ↦ x1 ≤ x2) s ∧ s.Nonempty ∨ DirectedOn (fun x1 x2 ↦ x1 ≤ x2) ∅ ∧ ∅.Nonempty",
"ppTerm": "?inr.inl",
"a... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Hom.Set | {
"line": 44,
"column": 21
} | {
"line": 44,
"column": 26
} | {
"line": 46,
"column": 0
} | [
{
"pp": "case inl\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : α → γ\ng : β → γ\ns : Set α × Set β\nt : Set γ\nhf : MapsTo f s.1 t\nhg : MapsTo g s.2 t\na : α\n⊢ Sum.inl a ∈ sumEquiv.symm s → Sum.elim f g (Sum.inl a) ∈ t",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Set.sumEquiv"... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.Hom.Set | {
"line": 44,
"column": 21
} | {
"line": 44,
"column": 26
} | {
"line": 46,
"column": 0
} | [
{
"pp": "case inr\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : α → γ\ng : β → γ\ns : Set α × Set β\nt : Set γ\nhf : MapsTo f s.1 t\nhg : MapsTo g s.2 t\nb : β\n⊢ Sum.inr b ∈ sumEquiv.symm s → Sum.elim f g (Sum.inr b) ∈ t",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"Set.sumEquiv"... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.Hom.Set | {
"line": 49,
"column": 43
} | {
"line": 49,
"column": 48
} | {
"line": 51,
"column": 0
} | [
{
"pp": "case inl.inl\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : α → γ\ng : β → γ\ns : Set α × Set β\nhf : InjOn f s.1\nhg : InjOn g s.2\nhfg : ∀ (a : α), a ∈ s.1 → ∀ (b : β), b ∈ s.2 → f a ≠ g b\na₁ : α\nh₁ : Sum.inl a₁ ∈ sumEquiv.symm s\na₂ : α\nh₂ : Sum.inl a₂ ∈ sumEquiv.symm s\nheq : Sum.elim f g (Sum.i... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.Hom.Set | {
"line": 49,
"column": 43
} | {
"line": 49,
"column": 48
} | {
"line": 51,
"column": 0
} | [
{
"pp": "case inl.inr\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : α → γ\ng : β → γ\ns : Set α × Set β\nhf : InjOn f s.1\nhg : InjOn g s.2\nhfg : ∀ (a : α), a ∈ s.1 → ∀ (b : β), b ∈ s.2 → f a ≠ g b\na₁ : α\nh₁ : Sum.inl a₁ ∈ sumEquiv.symm s\nb₂ : β\nh₂ : Sum.inr b₂ ∈ sumEquiv.symm s\nheq : Sum.elim f g (Sum.i... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.Hom.Set | {
"line": 49,
"column": 43
} | {
"line": 49,
"column": 48
} | {
"line": 51,
"column": 0
} | [
{
"pp": "case inr.inl\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : α → γ\ng : β → γ\ns : Set α × Set β\nhf : InjOn f s.1\nhg : InjOn g s.2\nhfg : ∀ (a : α), a ∈ s.1 → ∀ (b : β), b ∈ s.2 → f a ≠ g b\nb₁ : β\nh₁ : Sum.inr b₁ ∈ sumEquiv.symm s\na₂ : α\nh₂ : Sum.inl a₂ ∈ sumEquiv.symm s\nheq : Sum.elim f g (Sum.i... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.Hom.Set | {
"line": 49,
"column": 43
} | {
"line": 49,
"column": 48
} | {
"line": 51,
"column": 0
} | [
{
"pp": "case inr.inr\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : α → γ\ng : β → γ\ns : Set α × Set β\nhf : InjOn f s.1\nhg : InjOn g s.2\nhfg : ∀ (a : α), a ∈ s.1 → ∀ (b : β), b ∈ s.2 → f a ≠ g b\nb₁ : β\nh₁ : Sum.inr b₁ ∈ sumEquiv.symm s\nb₂ : β\nh₂ : Sum.inr b₂ ∈ sumEquiv.symm s\nheq : Sum.elim f g (Sum.i... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Order.Field.Basic | {
"line": 70,
"column": 2
} | {
"line": 70,
"column": 28
} | {
"line": 72,
"column": 0
} | [
{
"pp": "α : Type u_2\ninst✝² : Semifield α\ninst✝¹ : PartialOrder α\ninst✝ : PosMulReflectLT α\na b : α\nha : 0 < a\nh : a ≤ b\n⊢ 1 / b ≤ 1 / a",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"NonAssocSemiring.toAddCommMonoidWi... | [] | simpa using inv_anti₀ ha h | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Algebra.Order.Field.Basic | {
"line": 70,
"column": 2
} | {
"line": 70,
"column": 28
} | {
"line": 72,
"column": 0
} | [
{
"pp": "α : Type u_2\ninst✝² : Semifield α\ninst✝¹ : PartialOrder α\ninst✝ : PosMulReflectLT α\na b : α\nha : 0 < a\nh : a ≤ b\n⊢ 1 / b ≤ 1 / a",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"NonAssocSemiring.toAddCommMonoidWi... | [] | simpa using inv_anti₀ ha h | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Field.Basic | {
"line": 70,
"column": 2
} | {
"line": 70,
"column": 28
} | {
"line": 72,
"column": 0
} | [
{
"pp": "α : Type u_2\ninst✝² : Semifield α\ninst✝¹ : PartialOrder α\ninst✝ : PosMulReflectLT α\na b : α\nha : 0 < a\nh : a ≤ b\n⊢ 1 / b ≤ 1 / a",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"NonAssocSemiring.toAddCommMonoidWi... | [] | simpa using inv_anti₀ ha h | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Tactic.NormNum.Basic | {
"line": 675,
"column": 44
} | {
"line": 675,
"column": 49
} | {
"line": 675,
"column": 49
} | [
{
"pp": "n✝¹ n✝ : ℕ\n⊢ ↑n✝¹ % ↑n✝ = ↑(n✝¹.mod n✝)",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"id",
"Nat.instMod",
"instHMod",
"AddMonoidWithOne.toNatCast",
"Nat.instAddMonoidWithOne",
"Nat.cast",
"HMod.hMod",
"Nat",
"Nat.mod",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Tactic.NormNum.Basic | {
"line": 675,
"column": 44
} | {
"line": 675,
"column": 49
} | {
"line": 675,
"column": 49
} | [
{
"pp": "n✝¹ n✝ : ℕ\n⊢ ↑n✝¹ % ↑n✝ = ↑(n✝¹.mod n✝)",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"id",
"Nat.instMod",
"instHMod",
"AddMonoidWithOne.toNatCast",
"Nat.instAddMonoidWithOne",
"Nat.cast",
"HMod.hMod",
"Nat",
"Nat.mod",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Tactic.NormNum.Basic | {
"line": 675,
"column": 44
} | {
"line": 675,
"column": 49
} | {
"line": 675,
"column": 49
} | [
{
"pp": "n✝¹ n✝ : ℕ\n⊢ ↑n✝¹ % ↑n✝ = ↑(n✝¹.mod n✝)",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"id",
"Nat.instMod",
"instHMod",
"AddMonoidWithOne.toNatCast",
"Nat.instAddMonoidWithOne",
"Nat.cast",
"HMod.hMod",
"Nat",
"Nat.mod",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Tactic.NormNum.Basic | {
"line": 694,
"column": 44
} | {
"line": 694,
"column": 49
} | {
"line": 694,
"column": 49
} | [
{
"pp": "n✝¹ n✝ : ℕ\n⊢ ↑n✝¹ / ↑n✝ = ↑(n✝¹.div n✝)",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"instHDiv",
"id",
"HDiv.hDiv",
"AddMonoidWithOne.toNatCast",
"Nat.div",
"Nat.instAddMonoidWithOne",
"Nat.cast",
"Nat",
"Nat.instDiv",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Tactic.NormNum.Basic | {
"line": 694,
"column": 44
} | {
"line": 694,
"column": 49
} | {
"line": 694,
"column": 49
} | [
{
"pp": "n✝¹ n✝ : ℕ\n⊢ ↑n✝¹ / ↑n✝ = ↑(n✝¹.div n✝)",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"instHDiv",
"id",
"HDiv.hDiv",
"AddMonoidWithOne.toNatCast",
"Nat.div",
"Nat.instAddMonoidWithOne",
"Nat.cast",
"Nat",
"Nat.instDiv",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Tactic.NormNum.Basic | {
"line": 694,
"column": 44
} | {
"line": 694,
"column": 49
} | {
"line": 694,
"column": 49
} | [
{
"pp": "n✝¹ n✝ : ℕ\n⊢ ↑n✝¹ / ↑n✝ = ↑(n✝¹.div n✝)",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"instHDiv",
"id",
"HDiv.hDiv",
"AddMonoidWithOne.toNatCast",
"Nat.div",
"Nat.instAddMonoidWithOne",
"Nat.cast",
"Nat",
"Nat.instDiv",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.TakeDrop | {
"line": 78,
"column": 11
} | {
"line": 78,
"column": 16
} | {
"line": 79,
"column": 2
} | [
{
"pp": "case nil\nα : Type u\nh : [] ≠ []\n⊢ drop ([].length - 1) [] = [[].getLast h]",
"ppTerm": "?nil",
"assigned": true,
"usedConstants": [
"List.getLast",
"Eq.mpr",
"False",
"congrArg",
"False.elim",
"HSub.hSub",
"List.ne_cons_self._simp_1",
"Eq.m... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.List.TakeDrop | {
"line": 78,
"column": 11
} | {
"line": 78,
"column": 16
} | {
"line": 79,
"column": 2
} | [
{
"pp": "case nil\nα : Type u\nh : [] ≠ []\n⊢ drop ([].length - 1) [] = [[].getLast h]",
"ppTerm": "?nil",
"assigned": true,
"usedConstants": [
"List.getLast",
"Eq.mpr",
"False",
"congrArg",
"False.elim",
"HSub.hSub",
"List.ne_cons_self._simp_1",
"Eq.m... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.List.TakeDrop | {
"line": 78,
"column": 11
} | {
"line": 78,
"column": 16
} | {
"line": 79,
"column": 2
} | [
{
"pp": "case nil\nα : Type u\nh : [] ≠ []\n⊢ drop ([].length - 1) [] = [[].getLast h]",
"ppTerm": "?nil",
"assigned": true,
"usedConstants": [
"List.getLast",
"Eq.mpr",
"False",
"congrArg",
"False.elim",
"HSub.hSub",
"List.ne_cons_self._simp_1",
"Eq.m... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Field.Basic | {
"line": 674,
"column": 54
} | {
"line": 674,
"column": 75
} | {
"line": 676,
"column": 0
} | [
{
"pp": "α : Type u_2\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na : α\n⊢ |1 / a| = 1 / |a|",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHDiv",
"AddGroupWithOne.toAddGroup",
"abs",
"congrArg",
"AddGroupWit... | [] | rw [abs_div, abs_one] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Order.Field.Basic | {
"line": 674,
"column": 54
} | {
"line": 674,
"column": 75
} | {
"line": 676,
"column": 0
} | [
{
"pp": "α : Type u_2\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na : α\n⊢ |1 / a| = 1 / |a|",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHDiv",
"AddGroupWithOne.toAddGroup",
"abs",
"congrArg",
"AddGroupWit... | [] | rw [abs_div, abs_one] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Field.Basic | {
"line": 674,
"column": 54
} | {
"line": 674,
"column": 75
} | {
"line": 676,
"column": 0
} | [
{
"pp": "α : Type u_2\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na : α\n⊢ |1 / a| = 1 / |a|",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHDiv",
"AddGroupWithOne.toAddGroup",
"abs",
"congrArg",
"AddGroupWit... | [] | rw [abs_div, abs_one] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Field.Basic | {
"line": 686,
"column": 2
} | {
"line": 686,
"column": 47
} | {
"line": 687,
"column": 2
} | [
{
"pp": "α : Type u_2\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nε : α\nhε : 0 < ε\nn : ℕ\nB : α\nB_pos : 0 < B\npos : 0 < 1 + ↑n * (B + 1) ^ (n - 1)\nq r : α\nhr : |r| ≤ B\nhqr : |q - r| ≤ 1 ∧ |q - r| + |q - r| * ↑n * (B + 1) ^ (n - 1) ≤ ε\n⊢ |q - r| * ↑n * max |q| |r| ^ (n - 1) ... | [
"case inl\nα : Type u_2\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nε : α\nhε : 0 < ε\nn : ℕ\nB : α\nB_pos : 0 < B\npos : 0 < 1 + ↑n * (B + 1) ^ (n - 1)\nq r : α\nhr : |r| ≤ B\nhqr : |q - r| ≤ 1 ∧ |q - r| + |q - r| * ↑n * (B + 1) ^ (n - 1) ≤ ε\nh : 0 = |q - r|\n⊢ |q - r| * ↑n * max |q|... | obtain h | h := (abs_nonneg (q - r)).eq_or_lt | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Tactic.FieldSimp.Lemmas | {
"line": 366,
"column": 2
} | {
"line": 366,
"column": 37
} | {
"line": 368,
"column": 0
} | [
{
"pp": "M : Type u_1\ninst✝ : CommGroupWithZero M\nr : ℤ\nhr : r = 0\nx : M\nhx : x ≠ 0\nl : NF M\n⊢ ((r, x) ::ᵣ l).eval = l.eval",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"GroupWithZero.toMonoidWithZero",
"GroupWithZero.toDivisionMonoid",
"InvOneClass.toOne",
... | [] | simp [hr, zpow'_zero_of_ne_zero hx] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Tactic.FieldSimp.Lemmas | {
"line": 366,
"column": 2
} | {
"line": 366,
"column": 37
} | {
"line": 368,
"column": 0
} | [
{
"pp": "M : Type u_1\ninst✝ : CommGroupWithZero M\nr : ℤ\nhr : r = 0\nx : M\nhx : x ≠ 0\nl : NF M\n⊢ ((r, x) ::ᵣ l).eval = l.eval",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"GroupWithZero.toMonoidWithZero",
"GroupWithZero.toDivisionMonoid",
"InvOneClass.toOne",
... | [] | simp [hr, zpow'_zero_of_ne_zero hx] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Tactic.FieldSimp.Lemmas | {
"line": 366,
"column": 2
} | {
"line": 366,
"column": 37
} | {
"line": 368,
"column": 0
} | [
{
"pp": "M : Type u_1\ninst✝ : CommGroupWithZero M\nr : ℤ\nhr : r = 0\nx : M\nhx : x ≠ 0\nl : NF M\n⊢ ((r, x) ::ᵣ l).eval = l.eval",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"GroupWithZero.toMonoidWithZero",
"GroupWithZero.toDivisionMonoid",
"InvOneClass.toOne",
... | [] | simp [hr, zpow'_zero_of_ne_zero hx] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.Perm.Basic | {
"line": 201,
"column": 2
} | {
"line": 205,
"column": 56
} | {
"line": 207,
"column": 0
} | [
{
"pp": "α : Type u_1\no₁ o₂ : Option α\n⊢ o₁.toList ~ o₂.toList ↔ o₁ = o₂",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"False",
"congrArg",
"Option.toList",
"HEq.refl",
"False.elim",
"Option.casesOn",
"Option.mem_toList",
"noConfusion_of_N... | [] | refine ⟨fun p => ?_, fun e => e ▸ Perm.refl _⟩
rcases o₁ with - | a <;> rcases o₂ with - | b; · rfl
· cases p.length_eq
· cases p.length_eq
· exact Option.mem_toList.1 (p.symm.subset <| by simp) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.List.Perm.Basic | {
"line": 201,
"column": 2
} | {
"line": 205,
"column": 56
} | {
"line": 207,
"column": 0
} | [
{
"pp": "α : Type u_1\no₁ o₂ : Option α\n⊢ o₁.toList ~ o₂.toList ↔ o₁ = o₂",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"False",
"congrArg",
"Option.toList",
"HEq.refl",
"False.elim",
"Option.casesOn",
"Option.mem_toList",
"noConfusion_of_N... | [] | refine ⟨fun p => ?_, fun e => e ▸ Perm.refl _⟩
rcases o₁ with - | a <;> rcases o₂ with - | b; · rfl
· cases p.length_eq
· cases p.length_eq
· exact Option.mem_toList.1 (p.symm.subset <| by simp) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.Basic | {
"line": 238,
"column": 2
} | {
"line": 239,
"column": 34
} | {
"line": 241,
"column": 0
} | [
{
"pp": "α : Type u\nn : ℕ\nh : n ≠ 0\nl : List α\n⊢ (replicate n l).flatten.head? = l.head?",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"List.head?",
"List.replicate",
"congrArg",
"Option.some",
"Exists",
"List.flatten_replicate_nil",
"Ne",
... | [] | obtain ⟨n, rfl⟩ := Nat.exists_eq_succ_of_ne_zero h
induction l <;> simp [replicate] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.List.Basic | {
"line": 238,
"column": 2
} | {
"line": 239,
"column": 34
} | {
"line": 241,
"column": 0
} | [
{
"pp": "α : Type u\nn : ℕ\nh : n ≠ 0\nl : List α\n⊢ (replicate n l).flatten.head? = l.head?",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"List.head?",
"List.replicate",
"congrArg",
"Option.some",
"Exists",
"List.flatten_replicate_nil",
"Ne",
... | [] | obtain ⟨n, rfl⟩ := Nat.exists_eq_succ_of_ne_zero h
induction l <;> simp [replicate] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.Basic | {
"line": 516,
"column": 37
} | {
"line": 516,
"column": 42
} | {
"line": 518,
"column": 0
} | [
{
"pp": "case mp.cons\nα : Type u\nl : List α\na : α\na✝ : l <+ []\n⊢ l = [] ∨ l = [a]",
"ppTerm": "?mp.cons",
"assigned": true,
"usedConstants": [
"False",
"congrArg",
"List.ne_cons_self._simp_1",
"Eq.mp",
"id",
"List.cons",
"List",
"congr",
"Tr... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.List.Basic | {
"line": 516,
"column": 37
} | {
"line": 516,
"column": 42
} | {
"line": 518,
"column": 0
} | [
{
"pp": "case mp.cons_cons\nα : Type u\na : α\nl₁✝ : List α\na✝ : l₁✝ <+ []\n⊢ a :: l₁✝ = [] ∨ a :: l₁✝ = [a]",
"ppTerm": "?mp.cons_cons",
"assigned": true,
"usedConstants": [
"False",
"congrArg",
"List.cons_ne_self._simp_1",
"Eq.mp",
"id",
"List.cons",
"Lis... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.List.Basic | {
"line": 516,
"column": 37
} | {
"line": 516,
"column": 42
} | {
"line": 518,
"column": 0
} | [
{
"pp": "case mpr.inl\nα : Type u\nl : List α\na : α\nh✝ : l = []\n⊢ l <+ [a]",
"ppTerm": "?mpr.inl",
"assigned": true,
"usedConstants": [
"List.Sublist.refl._simp_1",
"List.cons",
"List",
"List.Sublist.cons._simp_1",
"of_eq_true",
"Eq.ndrec",
"List.Sublist"... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.List.Basic | {
"line": 516,
"column": 37
} | {
"line": 516,
"column": 42
} | {
"line": 518,
"column": 0
} | [
{
"pp": "case mpr.inr\nα : Type u\nl : List α\na : α\nh✝ : l = [a]\n⊢ l <+ [a]",
"ppTerm": "?mpr.inr",
"assigned": true,
"usedConstants": [
"List.Sublist.refl._simp_1",
"List.cons",
"List",
"of_eq_true",
"Eq.ndrec",
"List.Sublist",
"Eq.symm",
"List.nil... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.List.Basic | {
"line": 803,
"column": 62
} | {
"line": 804,
"column": 43
} | {
"line": 806,
"column": 0
} | [
{
"pp": "α : Type u\nβ : Type v\nf : α → β → β\nb : β\nx : α\nxs : List α\n⊢ foldr f b (xs ++ [x]) = foldr f (f x b) xs",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"congrArg",
"List.foldr_append",
"List.cons",
"instHAppendOfAppend",
"List",
"True",
... | [] | by
simp only [List.foldr_append, List.foldr] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Rat.Defs | {
"line": 112,
"column": 2
} | {
"line": 112,
"column": 27
} | {
"line": 114,
"column": 0
} | [
{
"pp": "q : ℚ\nn : ℕ\n⊢ q ^ n = mkRat (q.num ^ n) (q.den ^ n)",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"instPowNat",
"Eq.mpr",
"Rat.num",
"congrArg",
"Rat",
"Rat.instPowNat",
"Rat.den",
"id",
"Int",
"Int.instNatPow",
... | [] | rw [pow_def, mk_eq_mkRat] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Rat.Defs | {
"line": 112,
"column": 2
} | {
"line": 112,
"column": 27
} | {
"line": 114,
"column": 0
} | [
{
"pp": "q : ℚ\nn : ℕ\n⊢ q ^ n = mkRat (q.num ^ n) (q.den ^ n)",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"instPowNat",
"Eq.mpr",
"Rat.num",
"congrArg",
"Rat",
"Rat.instPowNat",
"Rat.den",
"id",
"Int",
"Int.instNatPow",
... | [] | rw [pow_def, mk_eq_mkRat] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Rat.Defs | {
"line": 112,
"column": 2
} | {
"line": 112,
"column": 27
} | {
"line": 114,
"column": 0
} | [
{
"pp": "q : ℚ\nn : ℕ\n⊢ q ^ n = mkRat (q.num ^ n) (q.den ^ n)",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"instPowNat",
"Eq.mpr",
"Rat.num",
"congrArg",
"Rat",
"Rat.instPowNat",
"Rat.den",
"id",
"Int",
"Int.instNatPow",
... | [] | rw [pow_def, mk_eq_mkRat] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Ring.Unbundled.Rat | {
"line": 41,
"column": 4
} | {
"line": 42,
"column": 47
} | {
"line": 43,
"column": 2
} | [
{
"pp": "case false\nm e : ℕ\n⊢ 0 ≤ if false = true then normalize (↑m) (10 ^ e) ⋯ else ↑(m * 10 ^ e)",
"ppTerm": "?false",
"assigned": true,
"usedConstants": [
"instPowNat",
"Rat.instOfNat",
"Eq.mpr",
"instDecidableNot",
"Rat.num",
"HMul.hMul",
"of_decide_e... | [] | rw [if_neg (by decide)]
exact num_nonneg.mp <| Int.natCast_nonneg _ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Ring.Unbundled.Rat | {
"line": 41,
"column": 4
} | {
"line": 42,
"column": 47
} | {
"line": 43,
"column": 2
} | [
{
"pp": "case false\nm e : ℕ\n⊢ 0 ≤ if false = true then normalize (↑m) (10 ^ e) ⋯ else ↑(m * 10 ^ e)",
"ppTerm": "?false",
"assigned": true,
"usedConstants": [
"instPowNat",
"Rat.instOfNat",
"Eq.mpr",
"instDecidableNot",
"Rat.num",
"HMul.hMul",
"of_decide_e... | [] | rw [if_neg (by decide)]
exact num_nonneg.mp <| Int.natCast_nonneg _ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.GroupWithZero.Divisibility | {
"line": 172,
"column": 4
} | {
"line": 172,
"column": 27
} | {
"line": 173,
"column": 2
} | [
{
"pp": "case mp\nα : Type u_1\ninst✝¹ : CommMonoidWithZero α\ninst✝ : IsCancelMulZero α\na : α\nm n : ℕ\nha₀ : a ≠ 0\nha : ¬IsUnit a\nh : a ^ n ∣ a ^ m\nhmn : m < n\nthis : a ^ m * a ∣ a ^ m * 1\n⊢ a ^ m ≠ 0",
"ppTerm": "?mp✝",
"assigned": true,
"usedConstants": [
"MulZeroClass.toMul",
... | [] | apply pow_ne_zero m ha₀ | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Data.Rat.Cast.Defs | {
"line": 159,
"column": 41
} | {
"line": 159,
"column": 62
} | {
"line": 159,
"column": 63
} | [
{
"pp": "α : Type u_3\ninst✝ : DivisionRing α\na b : ℤ\nb0 : ↑b ≠ 0\nb0' : b ≠ 0\nn : ℤ\nd : ℕ\nh : d ≠ 0\nc : n.natAbs.Coprime d\ne : a /. b = n /. ↑d\nd0 : ↑d ≠ 0\nthis : ↑a * ↑d = ↑n * ↑b\n⊢ ↑a * (↑b)⁻¹ =\n ↑{ num := n, den := d, den_nz := h, reduced := c }.num / ↑{ num := n, den := d, den_nz := h, reduce... | [
"α : Type u_3\ninst✝ : DivisionRing α\na b : ℤ\nb0 : ↑b ≠ 0\nb0' : b ≠ 0\nn : ℤ\nd : ℕ\nh : d ≠ 0\nc : n.natAbs.Coprime d\ne : a /. b = n /. ↑d\nd0 : ↑d ≠ 0\nthis : ↑a * ↑d = ↑n * ↑b\n⊢ ↑a * (↑b)⁻¹ * ↑d = ↑{ num := n, den := d, den_nz := h, reduced := c }.num"
] | eq_div_iff_mul_eq d0, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Tactic.NormNum.Pow | {
"line": 235,
"column": 34
} | {
"line": 235,
"column": 43
} | {
"line": 235,
"column": 44
} | [
{
"pp": "α : Type u_1\ninst✝ : DivisionSemiring α\na : α\nb : ℤ\nnb ne : ℕ\npb : IsInt b (Int.negOfNat nb)\npe' : IsNat (a ^ nb)⁻¹ ne\n⊢ IsNat (a ^ (-↑nb)) ne",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
... | [
"α : Type u_1\ninst✝ : DivisionSemiring α\na : α\nb : ℤ\nnb ne : ℕ\npb : IsInt b (Int.negOfNat nb)\npe' : IsNat (a ^ nb)⁻¹ ne\n⊢ IsNat (a ^ ↑nb)⁻¹ ne"
] | zpow_neg, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Tactic.NormNum.Pow | {
"line": 245,
"column": 34
} | {
"line": 245,
"column": 43
} | {
"line": 245,
"column": 44
} | [
{
"pp": "α : Type u_1\ninst✝ : DivisionRing α\na : α\nb : ℤ\nnb ne : ℕ\npb : IsInt b (Int.negOfNat nb)\npe' : IsInt (a ^ nb)⁻¹ (Int.negOfNat ne)\n⊢ IsInt (a ^ (-↑nb)) (Int.negOfNat ne)",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
... | [
"α : Type u_1\ninst✝ : DivisionRing α\na : α\nb : ℤ\nnb ne : ℕ\npb : IsInt b (Int.negOfNat nb)\npe' : IsInt (a ^ nb)⁻¹ (Int.negOfNat ne)\n⊢ IsInt (a ^ ↑nb)⁻¹ (Int.negOfNat ne)"
] | zpow_neg, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Tactic.NormNum.Pow | {
"line": 257,
"column": 34
} | {
"line": 257,
"column": 43
} | {
"line": 257,
"column": 44
} | [
{
"pp": "α : Type u_1\ninst✝ : DivisionSemiring α\na : α\nb : ℤ\nnb num den : ℕ\npb : IsInt b (Int.negOfNat nb)\npe' : IsNNRat (a ^ nb)⁻¹ num den\n⊢ IsNNRat (a ^ (-↑nb)) num den",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Neg... | [
"α : Type u_1\ninst✝ : DivisionSemiring α\na : α\nb : ℤ\nnb num den : ℕ\npb : IsInt b (Int.negOfNat nb)\npe' : IsNNRat (a ^ nb)⁻¹ num den\n⊢ IsNNRat (a ^ ↑nb)⁻¹ num den"
] | zpow_neg, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Tactic.NormNum.Pow | {
"line": 269,
"column": 34
} | {
"line": 269,
"column": 43
} | {
"line": 269,
"column": 44
} | [
{
"pp": "α : Type u_1\ninst✝ : DivisionRing α\na : α\nb : ℤ\nnb : ℕ\nnum : ℤ\nden : ℕ\npb : IsInt b (Int.negOfNat nb)\npe' : IsRat (a ^ nb)⁻¹ num den\n⊢ IsRat (a ^ (-↑nb)) num den",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"N... | [
"α : Type u_1\ninst✝ : DivisionRing α\na : α\nb : ℤ\nnb : ℕ\nnum : ℤ\nden : ℕ\npb : IsInt b (Int.negOfNat nb)\npe' : IsRat (a ^ nb)⁻¹ num den\n⊢ IsRat (a ^ ↑nb)⁻¹ num den"
] | zpow_neg, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Tactic.CancelDenoms.Core | {
"line": 78,
"column": 4
} | {
"line": 78,
"column": 28
} | {
"line": 80,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na b ad bd a' b' gcd : α\nha : ad * a = a'\nhb : bd * b = b'\nhad : 0 < ad\nhbd : 0 < bd\nhgcd : 0 < gcd\n⊢ 0 < 1 / gcd",
"ppTerm": "?m.69",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Gro... | [] | exact one_div_pos.2 hgcd | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Tactic.CancelDenoms.Core | {
"line": 78,
"column": 4
} | {
"line": 78,
"column": 28
} | {
"line": 80,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na b ad bd a' b' gcd : α\nha : ad * a = a'\nhb : bd * b = b'\nhad : 0 < ad\nhbd : 0 < bd\nhgcd : 0 < gcd\n⊢ 0 < 1 / gcd",
"ppTerm": "?m.69",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Gro... | [] | exact one_div_pos.2 hgcd | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Tactic.CancelDenoms.Core | {
"line": 78,
"column": 4
} | {
"line": 78,
"column": 28
} | {
"line": 80,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na b ad bd a' b' gcd : α\nha : ad * a = a'\nhb : bd * b = b'\nhad : 0 < ad\nhbd : 0 < bd\nhgcd : 0 < gcd\n⊢ 0 < 1 / gcd",
"ppTerm": "?m.69",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Gro... | [] | exact one_div_pos.2 hgcd | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Tactic.CancelDenoms.Core | {
"line": 87,
"column": 4
} | {
"line": 87,
"column": 28
} | {
"line": 89,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na b ad bd a' b' gcd : α\nha : ad * a = a'\nhb : bd * b = b'\nhad : 0 < ad\nhbd : 0 < bd\nhgcd : 0 < gcd\n⊢ 0 < 1 / gcd",
"ppTerm": "?m.69",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Gro... | [] | exact one_div_pos.2 hgcd | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Tactic.CancelDenoms.Core | {
"line": 87,
"column": 4
} | {
"line": 87,
"column": 28
} | {
"line": 89,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na b ad bd a' b' gcd : α\nha : ad * a = a'\nhb : bd * b = b'\nhad : 0 < ad\nhbd : 0 < bd\nhgcd : 0 < gcd\n⊢ 0 < 1 / gcd",
"ppTerm": "?m.69",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Gro... | [] | exact one_div_pos.2 hgcd | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Tactic.CancelDenoms.Core | {
"line": 87,
"column": 4
} | {
"line": 87,
"column": 28
} | {
"line": 89,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na b ad bd a' b' gcd : α\nha : ad * a = a'\nhb : bd * b = b'\nhad : 0 < ad\nhbd : 0 < bd\nhgcd : 0 < gcd\n⊢ 0 < 1 / gcd",
"ppTerm": "?m.69",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Gro... | [] | exact one_div_pos.2 hgcd | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Interval.Set.Image | {
"line": 29,
"column": 15
} | {
"line": 29,
"column": 20
} | {
"line": 31,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\ninst✝¹ : Preorder α\ninst✝ : Preorder β\na : α\nh : MonotoneOn f (Ici a)\nx✝¹ : α\nx✝ : x✝¹ ∈ Ici a\n⊢ f x✝¹ ∈ Ici (f a)",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ici",
"instReflLe",
"Preorder.toLE... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.Interval.Set.Image | {
"line": 29,
"column": 15
} | {
"line": 29,
"column": 20
} | {
"line": 31,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\ninst✝¹ : Preorder α\ninst✝ : Preorder β\na : α\nh : MonotoneOn f (Ici a)\nx✝¹ : α\nx✝ : x✝¹ ∈ Ici a\n⊢ f x✝¹ ∈ Ici (f a)",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ici",
"instReflLe",
"Preorder.toLE... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Interval.Set.Image | {
"line": 29,
"column": 15
} | {
"line": 29,
"column": 20
} | {
"line": 31,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\ninst✝¹ : Preorder α\ninst✝ : Preorder β\na : α\nh : MonotoneOn f (Ici a)\nx✝¹ : α\nx✝ : x✝¹ ∈ Ici a\n⊢ f x✝¹ ∈ Ici (f a)",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ici",
"instReflLe",
"Preorder.toLE... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Interval.Set.Image | {
"line": 32,
"column": 15
} | {
"line": 32,
"column": 20
} | {
"line": 34,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\ninst✝¹ : Preorder α\ninst✝ : Preorder β\nb : α\nh : MonotoneOn f (Iic b)\nx✝¹ : α\nx✝ : x✝¹ ∈ Iic b\n⊢ f x✝¹ ∈ Iic (f b)",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instReflLe",
"Preorder.toLE",
"Std.le_... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.Interval.Set.Image | {
"line": 32,
"column": 15
} | {
"line": 32,
"column": 20
} | {
"line": 34,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\ninst✝¹ : Preorder α\ninst✝ : Preorder β\nb : α\nh : MonotoneOn f (Iic b)\nx✝¹ : α\nx✝ : x✝¹ ∈ Iic b\n⊢ f x✝¹ ∈ Iic (f b)",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instReflLe",
"Preorder.toLE",
"Std.le_... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Interval.Set.Image | {
"line": 32,
"column": 15
} | {
"line": 32,
"column": 20
} | {
"line": 34,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\ninst✝¹ : Preorder α\ninst✝ : Preorder β\nb : α\nh : MonotoneOn f (Iic b)\nx✝¹ : α\nx✝ : x✝¹ ∈ Iic b\n⊢ f x✝¹ ∈ Iic (f b)",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instReflLe",
"Preorder.toLE",
"Std.le_... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Interval.Set.Image | {
"line": 39,
"column": 15
} | {
"line": 39,
"column": 20
} | {
"line": 41,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\ninst✝¹ : Preorder α\ninst✝ : Preorder β\na : α\nh : AntitoneOn f (Ici a)\nx✝¹ : α\nx✝ : x✝¹ ∈ Ici a\n⊢ f x✝¹ ∈ Iic (f a)",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ici",
"instReflLe",
"Preorder.toLE... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.Interval.Set.Image | {
"line": 39,
"column": 15
} | {
"line": 39,
"column": 20
} | {
"line": 41,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\ninst✝¹ : Preorder α\ninst✝ : Preorder β\na : α\nh : AntitoneOn f (Ici a)\nx✝¹ : α\nx✝ : x✝¹ ∈ Ici a\n⊢ f x✝¹ ∈ Iic (f a)",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ici",
"instReflLe",
"Preorder.toLE... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Interval.Set.Image | {
"line": 39,
"column": 15
} | {
"line": 39,
"column": 20
} | {
"line": 41,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\ninst✝¹ : Preorder α\ninst✝ : Preorder β\na : α\nh : AntitoneOn f (Ici a)\nx✝¹ : α\nx✝ : x✝¹ ∈ Ici a\n⊢ f x✝¹ ∈ Iic (f a)",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ici",
"instReflLe",
"Preorder.toLE... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Interval.Set.Image | {
"line": 42,
"column": 15
} | {
"line": 42,
"column": 20
} | {
"line": 44,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\ninst✝¹ : Preorder α\ninst✝ : Preorder β\nb : α\nh : AntitoneOn f (Iic b)\nx✝¹ : α\nx✝ : x✝¹ ∈ Iic b\n⊢ f x✝¹ ∈ Ici (f b)",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ici",
"instReflLe",
"Preorder.toLE... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.Interval.Set.Image | {
"line": 42,
"column": 15
} | {
"line": 42,
"column": 20
} | {
"line": 44,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\ninst✝¹ : Preorder α\ninst✝ : Preorder β\nb : α\nh : AntitoneOn f (Iic b)\nx✝¹ : α\nx✝ : x✝¹ ∈ Iic b\n⊢ f x✝¹ ∈ Ici (f b)",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ici",
"instReflLe",
"Preorder.toLE... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Interval.Set.Image | {
"line": 42,
"column": 15
} | {
"line": 42,
"column": 20
} | {
"line": 44,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\ninst✝¹ : Preorder α\ninst✝ : Preorder β\nb : α\nh : AntitoneOn f (Iic b)\nx✝¹ : α\nx✝ : x✝¹ ∈ Iic b\n⊢ f x✝¹ ∈ Ici (f b)",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ici",
"instReflLe",
"Preorder.toLE... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Set.Lattice | {
"line": 1407,
"column": 54
} | {
"line": 1409,
"column": 5
} | {
"line": 1411,
"column": 0
} | [
{
"pp": "α : Type u_12\nβ : Type u_13\nt : α → Set β\nh : Pairwise (Disjoint on t)\nx : ↑(⋃ i, t i)\n⊢ ↑((unionEqSigmaOfDisjoint h) x).snd = ↑x",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Equiv.instEquivLike",
"congrArg",
"Equiv.symm_apply_apply",
... | [] | by
conv => right; rw [← unionEqSigmaOfDisjoint h |>.symm_apply_apply x]
rfl | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.ConditionallyCompleteLattice.Basic | {
"line": 654,
"column": 4
} | {
"line": 661,
"column": 34
} | {
"line": 662,
"column": 4
} | [
{
"pp": "case pos\nβ : Type u_5\ninst✝ : ConditionallyCompleteLattice β\ns : Set (WithTop β)\nhs : s.Nonempty\nh₁ : ⊤ ∉ s\nh₂ : BddAbove ((fun a ↦ ↑a) ⁻¹' s)\n⊢ ↑(sSup ((fun a ↦ ↑a) ⁻¹' s)) ∈ lowerBounds (upperBounds s)",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Iff.mpr",
... | [
"case neg\nβ : Type u_5\ninst✝ : ConditionallyCompleteLattice β\ns : Set (WithTop β)\nhs : s.Nonempty\nh₁ : ⊤ ∉ s\nh₂ : ¬BddAbove ((fun a ↦ ↑a) ⁻¹' s)\n⊢ ⊤ ∈ lowerBounds (upperBounds s)"
] | · rintro (⟨⟩ | b) hb
· exact le_top
refine coe_le_coe.2 (csSup_le ?_ ?_)
· rcases hs with ⟨⟨⟩ | b, hb⟩
· exact absurd hb h₁
· exact ⟨b, hb⟩
· intro a ha
exact coe_le_coe.1 (hb ha) | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Order.Antichain | {
"line": 78,
"column": 2
} | {
"line": 78,
"column": 49
} | {
"line": 79,
"column": 2
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\ns : Set α\ninst✝ : Std.Trichotomous r\nh : IsAntichain r s\na : α\nha : a ∈ s\nb : α\nhb : b ∈ s\n⊢ a = b",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Or.casesOn",
"Or",
"trichotomous_of",
"Eq"
],
"usedFVars": [
... | [
"case inl\nα : Type u_1\nr : α → α → Prop\ns : Set α\ninst✝ : Std.Trichotomous r\nh : IsAntichain r s\na : α\nha : a ∈ s\nb : α\nhb : b ∈ s\nhab : r a b\n⊢ a = b",
"case inr.inl\nα : Type u_1\nr : α → α → Prop\ns : Set α\ninst✝ : Std.Trichotomous r\nh : IsAntichain r s\na : α\nha : a ∈ s\nb : α\nhb : b ∈ s\nhab :... | obtain hab | hab | hab := trichotomous_of r a b | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Order.Preorder.Chain | {
"line": 220,
"column": 6
} | {
"line": 221,
"column": 27
} | {
"line": 221,
"column": 27
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nr : α → α → Prop\ninst✝ : Std.Refl r\nf : β → α\nc : Set β\nh : IsChain (f ⁻¹'o r) c\nx✝¹ x✝ : { a // a ∈ c }\na : β\nha : a ∈ c\nb : β\nhb : b ∈ c\nhab : a = b\n⊢ ∃ z, r ((fun x ↦ f ↑x) ⟨a, ha⟩) ((fun x ↦ f ↑x) z) ∧ r ((fun x ↦ f ↑x) ⟨b, hb⟩) ((fun x ↦ f ↑x) z)",
"ppTer... | [] | simp only [hab, exists_prop, and_self_iff, Subtype.exists]
exact ⟨b, hb, refl _⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Preorder.Chain | {
"line": 220,
"column": 6
} | {
"line": 221,
"column": 27
} | {
"line": 221,
"column": 27
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nr : α → α → Prop\ninst✝ : Std.Refl r\nf : β → α\nc : Set β\nh : IsChain (f ⁻¹'o r) c\nx✝¹ x✝ : { a // a ∈ c }\na : β\nha : a ∈ c\nb : β\nhb : b ∈ c\nhab : a = b\n⊢ ∃ z, r ((fun x ↦ f ↑x) ⟨a, ha⟩) ((fun x ↦ f ↑x) z) ∧ r ((fun x ↦ f ↑x) ⟨b, hb⟩) ((fun x ↦ f ↑x) z)",
"ppTer... | [] | simp only [hab, exists_prop, and_self_iff, Subtype.exists]
exact ⟨b, hb, refl _⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Group.PosPart | {
"line": 276,
"column": 29
} | {
"line": 276,
"column": 36
} | {
"line": 276,
"column": 36
} | [
{
"pp": "α : Type u_1\ninst✝³ : LinearOrder α\ninst✝² : Group α\na b : α\ninst✝¹ : MulLeftMono α\ninst✝ : MulRightMono α\n⊢ a⁻¹ < b ∧ 1 < b ↔ b⁻¹ < a ∧ 1 < b",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"instIsRightCancelMulOfMulRightReflectLE",
"inv_lt'",
"Eq.mpr",
... | [
"α : Type u_1\ninst✝³ : LinearOrder α\ninst✝² : Group α\na b : α\ninst✝¹ : MulLeftMono α\ninst✝ : MulRightMono α\n⊢ b⁻¹ < a ∧ 1 < b ↔ b⁻¹ < a ∧ 1 < b"
] | inv_lt' | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Nat.Factorial.Basic | {
"line": 443,
"column": 4
} | {
"line": 443,
"column": 55
} | {
"line": 444,
"column": 4
} | [
{
"pp": "n k : ℕ\nh : k + 1 + 2 ≤ n\n⊢ (n - (k + 1 + 1)) ^ (k + 1 + 2) < n.descFactorial (k + 1 + 2)",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"instPowNat",
"Eq.mpr",
"HMul.hMul",
"congrArg",
"HSub.hSub",
"Nat.pow_succ",
"id",
"instSubN... | [
"n k : ℕ\nh : k + 1 + 2 ≤ n\n⊢ (n - (k + 1 + 1)) * (n - (k + 1 + 1)) ^ (k + 2) < (n - (k + 2)) * n.descFactorial (k + 2)"
] | rw [descFactorial_succ, Nat.pow_succ, Nat.mul_comm] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Rat.Cast.Lemmas | {
"line": 77,
"column": 13
} | {
"line": 77,
"column": 22
} | {
"line": 77,
"column": 23
} | [
{
"pp": "case inr\nK : Type u_1\ninst✝ : DivisionSemiring K\nq : ℚ≥0\nhq : ↑q.num ≠ 0\nn : ℕ\n⊢ ↑(q ^ (-↑n)) = ↑q ^ (-↑n)",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toDivisionMonoid",
"GroupWithZero.toDivInvMonoid",
"DivisionCommMonoid.t... | [
"case inr\nK : Type u_1\ninst✝ : DivisionSemiring K\nq : ℚ≥0\nhq : ↑q.num ≠ 0\nn : ℕ\n⊢ ↑(q ^ ↑n)⁻¹ = (↑q ^ ↑n)⁻¹"
] | zpow_neg, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Algebra.Order.Round | {
"line": 141,
"column": 16
} | {
"line": 141,
"column": 34
} | {
"line": 141,
"column": 35
} | [
{
"pp": "α : Type u_2\ninst✝³ : Ring α\ninst✝² : LinearOrder α\ninst✝¹ : IsStrictOrderedRing α\ninst✝ : FloorRing α\nx : α\ny : ℕ\n⊢ round (x + ↑y) = ↑y + round x",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"round_add_natCast",
"congrArg",
"AddGroupWit... | [
"α : Type u_2\ninst✝³ : Ring α\ninst✝² : LinearOrder α\ninst✝¹ : IsStrictOrderedRing α\ninst✝ : FloorRing α\nx : α\ny : ℕ\n⊢ round x + ↑y = ↑y + round x"
] | round_add_natCast, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.PNat.Basic | {
"line": 358,
"column": 6
} | {
"line": 358,
"column": 11
} | {
"line": 358,
"column": 11
} | [
{
"pp": "n : ℕ+\na : ℕ\nh : a ∣ ↑n\nhzero : a = 0\n⊢ False",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"PNat.val",
"Nat.instMulZeroClass",
"Dvd.dvd",
"congrArg",
"Eq.mp",
"Nat.instDvd",
"Nat",
"Zero.toOfNat0",
"OfNat.ofNat",
"... | [
"n : ℕ+\na : ℕ\nh : 0 ∣ ↑n\nhzero : a = 0\n⊢ False"
] | hzero | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Floor.Ring | {
"line": 253,
"column": 2
} | {
"line": 253,
"column": 7
} | {
"line": 255,
"column": 0
} | [
{
"pp": "R : Type u_2\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : FloorRing R\ninst✝ : IsOrderedRing R\na : R\n⊢ ↑⌊a⌋ = a ↔ a ∈ range Int.cast",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Int.cast",
"Eq.mpr",
"Int.floor",
"Int.floor_intCast",
"congr... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Order.Floor.Ring | {
"line": 253,
"column": 2
} | {
"line": 253,
"column": 7
} | {
"line": 255,
"column": 0
} | [
{
"pp": "R : Type u_2\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : FloorRing R\ninst✝ : IsOrderedRing R\na : R\n⊢ ↑⌊a⌋ = a ↔ a ∈ range Int.cast",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Int.cast",
"Eq.mpr",
"Int.floor",
"Int.floor_intCast",
"congr... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Floor.Ring | {
"line": 253,
"column": 2
} | {
"line": 253,
"column": 7
} | {
"line": 255,
"column": 0
} | [
{
"pp": "R : Type u_2\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : FloorRing R\ninst✝ : IsOrderedRing R\na : R\n⊢ ↑⌊a⌋ = a ↔ a ∈ range Int.cast",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Int.cast",
"Eq.mpr",
"Int.floor",
"Int.floor_intCast",
"congr... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Floor.Ring | {
"line": 271,
"column": 2
} | {
"line": 271,
"column": 41
} | {
"line": 272,
"column": 2
} | [
{
"pp": "R : Type u_4\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : IsStrictOrderedRing R\ninst✝ : FloorRing R\nx k : R\nhk : 1 < k\n⊢ k * fract x = 1 ↔ ∃ n, k * x = k * ↑n + 1",
"ppTerm": "?m.40",
"assigned": true,
"usedConstants": [
"Int.cast",
"Eq.mpr",
"HMul.hMul",
"... | [
"R : Type u_4\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : IsStrictOrderedRing R\ninst✝ : FloorRing R\nx k : R\nhk : 1 < k\n⊢ k * x = k * ↑⌊x⌋ + 1 ↔ ∃ n, k * x = k * ↑n + 1"
] | rw [fract, mul_sub, sub_eq_iff_eq_add'] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Rat.Floor | {
"line": 345,
"column": 96
} | {
"line": 346,
"column": 50
} | {
"line": 348,
"column": 0
} | [
{
"pp": "n : ℤ\nd : ℕ\n⊢ n % ↑d = n - ↑d * ⌊↑n / ↑d⌋",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Int.cast",
"Eq.mpr",
"Int.instDiv",
"instHDiv",
"HMul.hMul",
"Int.floor",
"congrArg",
"Rat",
"Rat.instFloorRing",
"HSub.hSub",
... | [] | by
rw [Int.emod_def, Rat.floor_intCast_div_natCast] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Order.Archimedean.Basic | {
"line": 248,
"column": 21
} | {
"line": 248,
"column": 30
} | {
"line": 248,
"column": 31
} | [
{
"pp": "K : Type u_4\ninst✝⁴ : Semifield K\ninst✝³ : LinearOrder K\ninst✝² : IsStrictOrderedRing K\ninst✝¹ : Archimedean K\nx y : K\ninst✝ : ExistsAddOfLE K\nhx : 0 < x\nhy : 1 < y\nm : ℤ\nhle : y ^ m ≤ x⁻¹\nhlt : x⁻¹ < y ^ (m + 1)\nhyp : 0 < y\n⊢ y ^ (-(m + 1)) < x",
"ppTerm": "?m.85",
"assigned": tru... | [
"K : Type u_4\ninst✝⁴ : Semifield K\ninst✝³ : LinearOrder K\ninst✝² : IsStrictOrderedRing K\ninst✝¹ : Archimedean K\nx y : K\ninst✝ : ExistsAddOfLE K\nhx : 0 < x\nhy : 1 < y\nm : ℤ\nhle : y ^ m ≤ x⁻¹\nhlt : x⁻¹ < y ^ (m + 1)\nhyp : 0 < y\n⊢ (y ^ (m + 1))⁻¹ < x"
] | zpow_neg, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Archimedean.Basic | {
"line": 249,
"column": 40
} | {
"line": 249,
"column": 49
} | {
"line": 249,
"column": 50
} | [
{
"pp": "K : Type u_4\ninst✝⁴ : Semifield K\ninst✝³ : LinearOrder K\ninst✝² : IsStrictOrderedRing K\ninst✝¹ : Archimedean K\nx y : K\ninst✝ : ExistsAddOfLE K\nhx : 0 < x\nhy : 1 < y\nm : ℤ\nhle : y ^ m ≤ x⁻¹\nhlt : x⁻¹ < y ^ (m + 1)\nhyp : 0 < y\n⊢ x ≤ y ^ (-m)",
"ppTerm": "?m.138",
"assigned": true,
... | [
"K : Type u_4\ninst✝⁴ : Semifield K\ninst✝³ : LinearOrder K\ninst✝² : IsStrictOrderedRing K\ninst✝¹ : Archimedean K\nx y : K\ninst✝ : ExistsAddOfLE K\nhx : 0 < x\nhy : 1 < y\nm : ℤ\nhle : y ^ m ≤ x⁻¹\nhlt : x⁻¹ < y ^ (m + 1)\nhyp : 0 < y\n⊢ x ≤ (y ^ m)⁻¹"
] | zpow_neg, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.AddConstMap.Basic | {
"line": 280,
"column": 6
} | {
"line": 282,
"column": 53
} | {
"line": 283,
"column": 6
} | [
{
"pp": "F : Type u_1\nG : Type u_2\nH : Type u_3\ninst✝⁷ : FunLike F G H\na : G\nb : H\ninst✝⁶ : AddCommGroup G\ninst✝⁵ : LinearOrder G\ninst✝⁴ : IsOrderedAddMonoid G\ninst✝³ : Archimedean G\ninst✝² : AddGroup H\ninst✝¹ : AddConstMapClass F G H a b\nf : F\nR : H → H → Prop\ninst✝ : IsTrans H R\nha : 0 < a\nl :... | [
"F : Type u_1\nG : Type u_2\nH : Type u_3\ninst✝⁷ : FunLike F G H\na : G\nb : H\ninst✝⁶ : AddCommGroup G\ninst✝⁵ : LinearOrder G\ninst✝⁴ : IsOrderedAddMonoid G\ninst✝³ : Archimedean G\ninst✝² : AddGroup H\ninst✝¹ : AddConstMapClass F G H a b\nf : F\nR : H → H → Prop\ninst✝ : IsTrans H R\nha : 0 < a\nl : G\nhf : ∀ x... | · refine Int.rel_of_forall_rel_succ_of_lt R (f := (f <| l + · • a)) (fun k ↦ ?_) hn
simp_rw [add_comm k 1, add_zsmul, ← add_assoc, one_zsmul, map_add_zsmul]
refine hR (k • b) (hf _ ?_ _ ?_ ?_) <;> simpa | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
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