module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.CategoryTheory.Limits.Types.Coproducts | {
"line": 160,
"column": 29
} | {
"line": 160,
"column": 40
} | {
"line": 160,
"column": 41
} | [
{
"pp": "C✝ : Type u\nF✝ : C✝ → Type v\nC : Type u\nF : C → Type v\nc : Cofan F\ni j : C\nf : { as := i } ⟶ { as := j }\n⊢ i = j",
"ppTerm": "?m.54",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"C✝ : Type u\nF✝ : C✝ → Type v\nC : Type u\nF : C → Type v\nc : Cofan F\ni j : C\nf : { as := i } ⟶ { as := j }\n⊢ i = j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Presheaf | {
"line": 836,
"column": 2
} | {
"line": 836,
"column": 13
} | {
"line": 836,
"column": 14
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\ninst✝¹ : LocallySmall.{w, v₁, u₁} C\nF : C ⥤ Type w\ninst✝ : HasColimitsOfShape F.Elementsᵒᵖ (Type w)\nu : F.Elements\nthis :\n (coconeπOpCompShrinkYonedaObj F u.fst).ι.app (op u) ≫\n (shrinkYonedaCompWhiskeringLeftObjπCompColimIso F).inv.app u.fst =\n ... | [
"C : Type u₁\ninst✝² : Category.{v₁, u₁} C\ninst✝¹ : LocallySmall.{w, v₁, u₁} C\nF : C ⥤ Type w\ninst✝ : HasColimitsOfShape F.Elementsᵒᵖ (Type w)\nu : F.Elements\nthis :\n (coconeπOpCompShrinkYonedaObj F u.fst).ι.app (op u) ≫\n (shrinkYonedaCompWhiskeringLeftObjπCompColimIso F).inv.app u.fst =\n colimit.ι ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Types.Coproducts | {
"line": 285,
"column": 8
} | {
"line": 286,
"column": 94
} | {
"line": 286,
"column": 94
} | [
{
"pp": "case mp\nX Y : Type u\nc : BinaryCofan X Y\nh : IsColimit c\n⊢ Injective\n ⇑(ConcreteCategory.hom\n ((binaryCoproductCocone X Y).ι.app { as := left } ≫\n (h.coconePointUniqueUpToIso (binaryCoproductColimit X Y)).inv)) ∧\n Injective ⇑(ConcreteCategory.hom c.inr) ∧\n IsCo... | [
"case mp\nX Y : Type u\nc : BinaryCofan X Y\nh : IsColimit c\n⊢ Injective\n ⇑(ConcreteCategory.hom\n ((binaryCoproductCocone X Y).ι.app { as := left } ≫\n (h.coconePointUniqueUpToIso (binaryCoproductColimit X Y)).inv)) ∧\n Injective\n ⇑(ConcreteCategory.hom\n ((binaryCo... | ← show _ = c.inr from
h.comp_coconePointUniqueUpToIso_inv (binaryCoproductColimit X Y) ⟨WalkingPair.right⟩ | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Limits.Types.Coproducts | {
"line": 283,
"column": 6
} | {
"line": 286,
"column": 95
} | {
"line": 287,
"column": 6
} | [
{
"pp": "case mp\nX Y : Type u\nc : BinaryCofan X Y\nh : IsColimit c\n⊢ Injective ⇑(ConcreteCategory.hom c.inl) ∧\n Injective ⇑(ConcreteCategory.hom c.inr) ∧\n IsCompl (Set.range ⇑(ConcreteCategory.hom c.inl)) (Set.range ⇑(ConcreteCategory.hom c.inr))",
"ppTerm": "?mp",
"assigned": true,
"us... | [
"case mp\nX Y : Type u\nc : BinaryCofan X Y\nh : IsColimit c\n⊢ Injective\n ⇑(ConcreteCategory.hom\n ((binaryCoproductCocone X Y).ι.app { as := left } ≫\n (h.coconePointUniqueUpToIso (binaryCoproductColimit X Y)).inv)) ∧\n Injective\n ⇑(ConcreteCategory.hom\n ((binaryCo... | rw [← show _ = c.inl from
h.comp_coconePointUniqueUpToIso_inv (binaryCoproductColimit X Y) ⟨WalkingPair.left⟩,
← show _ = c.inr from
h.comp_coconePointUniqueUpToIso_inv (binaryCoproductColimit X Y) ⟨WalkingPair.right⟩] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Category.ModuleCat.Injective | {
"line": 28,
"column": 34
} | {
"line": 28,
"column": 45
} | {
"line": 28,
"column": 46
} | [
{
"pp": "R : Type u\nM : Type v\ninst✝² : Ring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\ninj : Injective R M\nX✝ Y✝ : ModuleCat R\ng : X✝ ⟶ ModuleCat.of R M\nf : X✝ ⟶ Y✝\nm : Mono f\nl : ↑Y✝ →ₗ[R] M\nh : ∀ (x : ↑X✝), l ((ModuleCat.Hom.hom f) x) = (ModuleCat.Hom.hom g) x\nx : ↑X✝\n⊢ (ModuleCat.Hom.hom (f ≫... | [
"R : Type u\nM : Type v\ninst✝² : Ring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\ninj : Injective R M\nX✝ Y✝ : ModuleCat R\ng : X✝ ⟶ ModuleCat.of R M\nf : X✝ ⟶ Y✝\nm : Mono f\nl : ↑Y✝ →ₗ[R] M\nh : ∀ (x : ↑X✝), l ((ModuleCat.Hom.hom f) x) = (ModuleCat.Hom.hom g) x\nx : ↑X✝\n⊢ l ((ModuleCat.Hom.hom f) x) = (Modu... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.NegOnePow | {
"line": 110,
"column": 2
} | {
"line": 110,
"column": 41
} | {
"line": 110,
"column": 42
} | [
{
"pp": "n : ℤ\n⊢ (n * n).negOnePow = n.negOnePow",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"HSub.hSub",
"Units",
"id",
"Int",
"Int.instMonoid",
"Int.instMul",
"instHSub",
"_private.Mathlib.Algebra.Ring... | [
"n : ℤ\n⊢ Even (n * n - n)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Periodic | {
"line": 73,
"column": 4
} | {
"line": 73,
"column": 37
} | {
"line": 73,
"column": 38
} | [
{
"pp": "case cons\nα : Type u_1\nβ : Type u_2\nc : α\ninst✝¹ : Add α\ninst✝ : MulOneClass β\ng : α → β\nl : List (α → β)\nih : (∀ f ∈ l, Periodic f c) → Periodic l.prod c\nhl : Periodic g c ∧ ∀ x ∈ l, Periodic x c\n⊢ Periodic (g :: l).prod c",
"ppTerm": "?cons",
"assigned": true,
"usedConstants": [... | [
"case cons\nα : Type u_1\nβ : Type u_2\nc : α\ninst✝¹ : Add α\ninst✝ : MulOneClass β\ng : α → β\nl : List (α → β)\nih : (∀ f ∈ l, Periodic f c) → Periodic l.prod c\nhl : Periodic g c ∧ ∀ x ∈ l, Periodic x c\n⊢ Periodic (g * l.prod) c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Periodic | {
"line": 91,
"column": 2
} | {
"line": 91,
"column": 44
} | {
"line": 91,
"column": 45
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : α → β\nc : α\ninst✝² : AddMonoid α\ninst✝¹ : Group γ\ninst✝ : DistribMulAction γ α\nh : Periodic f c\na : γ\nx : α\n⊢ (fun x ↦ f (a • x)) (x + a⁻¹ • c) = (fun x ↦ f (a • x)) x",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Eq.m... | [
"α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : α → β\nc : α\ninst✝² : AddMonoid α\ninst✝¹ : Group γ\ninst✝ : DistribMulAction γ α\nh : Periodic f c\na : γ\nx : α\n⊢ f (a • x + c) = f (a • x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Periodic | {
"line": 95,
"column": 2
} | {
"line": 95,
"column": 28
} | {
"line": 95,
"column": 29
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : α → β\nc : α\ninst✝² : AddMonoid α\ninst✝¹ : Group γ\ninst✝ : DistribMulAction γ α\nh : Periodic f c\na : γ\n⊢ Periodic (fun x ↦ f (a⁻¹ • x)) (a • c)",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoal... | [
"α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : α → β\nc : α\ninst✝² : AddMonoid α\ninst✝¹ : Group γ\ninst✝ : DistribMulAction γ α\nh : Periodic f c\na : γ\n⊢ Periodic (fun x ↦ f (a⁻¹ • x)) (a • c)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Periodic | {
"line": 101,
"column": 2
} | {
"line": 101,
"column": 35
} | {
"line": 101,
"column": 36
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝ : AddGroup α\nh : Periodic f c\nx : α\n⊢ f (x - c) = f x",
"ppTerm": "?m.9",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝ : AddGroup α\nh : Periodic f c\nx : α\n⊢ f (x - c) = f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Periodic | {
"line": 104,
"column": 2
} | {
"line": 104,
"column": 35
} | {
"line": 104,
"column": 36
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\nc x : α\ninst✝ : SubtractionCommMonoid α\nh : Periodic f c\n⊢ f (c - x) = f (-x)",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"congrArg",
"AddMonoid.toAddZeroClass",
"sub_eq_neg... | [
"α : Type u_1\nβ : Type u_2\nf : α → β\nc x : α\ninst✝ : SubtractionCommMonoid α\nh : Periodic f c\n⊢ f (-x + c) = f (-x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Periodic | {
"line": 107,
"column": 2
} | {
"line": 107,
"column": 45
} | {
"line": 107,
"column": 46
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝ : AddGroup α\nh : Periodic f c\n⊢ Periodic f (-c)",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"AddMonoid.toAddSemigroup",
"id",
"SubtractionMo... | [
"α : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝ : AddGroup α\nh : Periodic f c\n⊢ ∀ (x : α), f (x + -c) = f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Periodic | {
"line": 114,
"column": 51
} | {
"line": 114,
"column": 74
} | {
"line": 114,
"column": 75
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝ : AddSemigroup α\nh : Periodic f c\na x : α\n⊢ (fun x ↦ f (a + x)) (x + c) = (fun x ↦ f (a + x)) x",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"id",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
... | [
"α : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝ : AddSemigroup α\nh : Periodic f c\na x : α\n⊢ f (a + (x + c)) = f (a + x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Periodic | {
"line": 118,
"column": 2
} | {
"line": 118,
"column": 35
} | {
"line": 118,
"column": 36
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝ : AddCommSemigroup α\nh : Periodic f c\na x : α\n⊢ (fun x ↦ f (x + a)) (x + c) = (fun x ↦ f (x + a)) x",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"id",
"instHAdd",
"HAdd.hAdd",
"AddCommSemigroup.toAdd... | [
"α : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝ : AddCommSemigroup α\nh : Periodic f c\na x : α\n⊢ f (x + c + a) = f (x + a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Periodic | {
"line": 126,
"column": 2
} | {
"line": 126,
"column": 35
} | {
"line": 126,
"column": 36
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝ : SubtractionCommMonoid α\nh : Periodic f c\na : α\n⊢ Periodic (fun x ↦ f (x - a)) c",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"AddMonoid.toAddZeroClass",
"sub_eq_add_neg",
... | [
"α : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝ : SubtractionCommMonoid α\nh : Periodic f c\na : α\n⊢ Periodic (fun x ↦ f (x + -a)) c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Periodic | {
"line": 132,
"column": 2
} | {
"line": 132,
"column": 33
} | {
"line": 132,
"column": 34
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝ : NonAssocSemiring α\nh : Periodic f c\nn : ℕ\n⊢ Periodic f (↑n * c)",
"ppTerm": "?m.11",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝ : NonAssocSemiring α\nh : Periodic f c\nn : ℕ\n⊢ Periodic f (↑n * c)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Periodic | {
"line": 141,
"column": 2
} | {
"line": 141,
"column": 35
} | {
"line": 141,
"column": 36
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\nc x : α\ninst✝ : AddGroup α\nh : Periodic f c\nn : ℕ\n⊢ f (x - n • c) = f x",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHSMul",
"congrArg",
"AddMonoid.toAddZeroClass",
"sub_eq_add_neg",
"... | [
"α : Type u_1\nβ : Type u_2\nf : α → β\nc x : α\ninst✝ : AddGroup α\nh : Periodic f c\nn : ℕ\n⊢ f (x + -(n • c)) = f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Periodic | {
"line": 145,
"column": 2
} | {
"line": 145,
"column": 33
} | {
"line": 145,
"column": 34
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\nc x : α\ninst✝ : NonAssocRing α\nh : Periodic f c\nn : ℕ\n⊢ f (x - ↑n * c) = f x",
"ppTerm": "?m.13",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nβ : Type u_2\nf : α → β\nc x : α\ninst✝ : NonAssocRing α\nh : Periodic f c\nn : ℕ\n⊢ f (x - ↑n * c) = f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Periodic | {
"line": 153,
"column": 2
} | {
"line": 153,
"column": 35
} | {
"line": 153,
"column": 36
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\nc x : α\ninst✝ : NonAssocRing α\nh : Periodic f c\nn : ℕ\n⊢ f (↑n * c - x) = f (-x)",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"HMul.hMul",
"AddGroupWithOne.toAddGroup",
"cong... | [
"α : Type u_1\nβ : Type u_2\nf : α → β\nc x : α\ninst✝ : NonAssocRing α\nh : Periodic f c\nn : ℕ\n⊢ f (-x + ↑n * c) = f (-x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Periodic | {
"line": 157,
"column": 4
} | {
"line": 157,
"column": 58
} | {
"line": 157,
"column": 59
} | [
{
"pp": "case ofNat\nα : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝ : AddGroup α\nh : Periodic f c\nn : ℕ\n⊢ Periodic f (Int.ofNat n • c)",
"ppTerm": "?ofNat",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHSMul",
"AddMonoid.toAddSemigroup",
"congrArg",
"AddM... | [
"case ofNat\nα : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝ : AddGroup α\nh : Periodic f c\nn : ℕ\n⊢ Periodic f (n • c)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Periodic | {
"line": 158,
"column": 4
} | {
"line": 158,
"column": 36
} | {
"line": 158,
"column": 37
} | [
{
"pp": "case negSucc\nα : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝ : AddGroup α\nh : Periodic f c\nn : ℕ\n⊢ Periodic f (Int.negSucc n • c)",
"ppTerm": "?negSucc",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHSMul",
"AddMonoid.toAddSemigroup",
"congrArg",
... | [
"case negSucc\nα : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝ : AddGroup α\nh : Periodic f c\nn : ℕ\n⊢ Periodic f (-((n + 1) • c))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Periodic | {
"line": 162,
"column": 2
} | {
"line": 162,
"column": 33
} | {
"line": 162,
"column": 34
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝ : NonAssocRing α\nh : Periodic f c\nn : ℤ\n⊢ Periodic f (↑n * c)",
"ppTerm": "?m.11",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝ : NonAssocRing α\nh : Periodic f c\nn : ℤ\n⊢ Periodic f (↑n * c)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Periodic | {
"line": 179,
"column": 2
} | {
"line": 179,
"column": 29
} | {
"line": 179,
"column": 30
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝ : AddZeroClass α\nh : Periodic f c\n⊢ f c = f 0",
"ppTerm": "?m.7",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝ : AddZeroClass α\nh : Periodic f c\n⊢ f c = f 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Periodic | {
"line": 262,
"column": 2
} | {
"line": 262,
"column": 29
} | {
"line": 262,
"column": 30
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝¹ : AddZeroClass α\ninst✝ : Neg β\nh : Antiperiodic f c\n⊢ f c = -f 0",
"ppTerm": "?m.10",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝¹ : AddZeroClass α\ninst✝ : Neg β\nh : Antiperiodic f c\n⊢ f c = -f 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Periodic | {
"line": 301,
"column": 30
} | {
"line": 301,
"column": 63
} | {
"line": 301,
"column": 64
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\nc x : α\ninst✝¹ : SubtractionCommMonoid α\ninst✝ : Neg β\nh : Antiperiodic f c\n⊢ f (c - x) = -f (-x)",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"congrArg",
"AddMonoid.toAddZeroClas... | [
"α : Type u_1\nβ : Type u_2\nf : α → β\nc x : α\ninst✝¹ : SubtractionCommMonoid α\ninst✝ : Neg β\nh : Antiperiodic f c\n⊢ f (-x + c) = -f (-x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Periodic | {
"line": 304,
"column": 30
} | {
"line": 304,
"column": 77
} | {
"line": 304,
"column": 78
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝¹ : AddGroup α\ninst✝ : InvolutiveNeg β\nh : Antiperiodic f c\n⊢ Antiperiodic f (-c)",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"AddMonoid.toAddSemigroup... | [
"α : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝¹ : AddGroup α\ninst✝ : InvolutiveNeg β\nh : Antiperiodic f c\n⊢ ∀ (x : α), f (x + -c) = -f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Periodic | {
"line": 308,
"column": 2
} | {
"line": 308,
"column": 29
} | {
"line": 308,
"column": 30
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝¹ : AddGroup α\ninst✝ : InvolutiveNeg β\nh : Antiperiodic f c\n⊢ f (-c) = -f 0",
"ppTerm": "?m.12",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝¹ : AddGroup α\ninst✝ : InvolutiveNeg β\nh : Antiperiodic f c\n⊢ f (-c) = -f 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.Injective | {
"line": 78,
"column": 15
} | {
"line": 78,
"column": 54
} | {
"line": 78,
"column": 55
} | [
{
"pp": "R : Type u\ninst✝⁴ : Ring R\nQ : Type v\ninst✝³ : AddCommGroup Q\ninst✝² : Module R Q\nM : Type u_1\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\ne : Q ≃ₗ[R] M\nh : Baer R Q\nI : Ideal R\ng : ↥I →ₗ[R] M\ng' : R →ₗ[R] Q\nh' : ∀ (x : R) (mem : x ∈ I), g' x = (↑e.symm ∘ₗ g) ⟨x, mem⟩\n⊢ ∀ (x : R) (mem : x ... | [
"R : Type u\ninst✝⁴ : Ring R\nQ : Type v\ninst✝³ : AddCommGroup Q\ninst✝² : Module R Q\nM : Type u_1\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\ne : Q ≃ₗ[R] M\nh : Baer R Q\nI : Ideal R\ng : ↥I →ₗ[R] M\ng' : R →ₗ[R] Q\nh' : ∀ (x : R) (mem : x ∈ I), g' x = (↑e.symm ∘ₗ g) ⟨x, mem⟩\n⊢ ∀ (x : R) (mem : x ∈ I), e (g' ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Periodic | {
"line": 329,
"column": 2
} | {
"line": 329,
"column": 65
} | {
"line": 329,
"column": 66
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\nc x : α\ninst✝¹ : AddGroup α\ninst✝ : SubtractionMonoid β\nh : Antiperiodic f c\nn : ℤ\n⊢ f (x - n • c) = ↑n.negOnePow • f x",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Units.val",
"Eq.mpr",
"instHSMul",
"congrArg... | [
"α : Type u_1\nβ : Type u_2\nf : α → β\nc x : α\ninst✝¹ : AddGroup α\ninst✝ : SubtractionMonoid β\nh : Antiperiodic f c\nn : ℤ\n⊢ f (x + -(n • c)) = ↑n.negOnePow • f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Periodic | {
"line": 338,
"column": 2
} | {
"line": 338,
"column": 33
} | {
"line": 338,
"column": 34
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\nc x : α\ninst✝¹ : NonAssocRing α\ninst✝ : NonAssocRing β\nh : Antiperiodic f c\nn : ℤ\n⊢ f (x + ↑n * c) = ↑↑n.negOnePow * f x",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nβ : Type u_2\nf : α → β\nc x : α\ninst✝¹ : NonAssocRing α\ninst✝ : NonAssocRing β\nh : Antiperiodic f c\nn : ℤ\n⊢ f (x + ↑n * c) = ↑↑n.negOnePow * f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Periodic | {
"line": 342,
"column": 2
} | {
"line": 342,
"column": 33
} | {
"line": 342,
"column": 34
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\nc x : α\ninst✝¹ : NonAssocRing α\ninst✝ : NonAssocRing β\nh : Antiperiodic f c\nn : ℤ\n⊢ f (x - ↑n * c) = ↑↑n.negOnePow * f x",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nβ : Type u_2\nf : α → β\nc x : α\ninst✝¹ : NonAssocRing α\ninst✝ : NonAssocRing β\nh : Antiperiodic f c\nn : ℤ\n⊢ f (x - ↑n * c) = ↑↑n.negOnePow * f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Periodic | {
"line": 346,
"column": 2
} | {
"line": 346,
"column": 33
} | {
"line": 346,
"column": 34
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\nc x : α\ninst✝¹ : NonAssocRing α\ninst✝ : NonAssocRing β\nh : Antiperiodic f c\nn : ℤ\n⊢ f (↑n * c - x) = ↑↑n.negOnePow * f (-x)",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nβ : Type u_2\nf : α → β\nc x : α\ninst✝¹ : NonAssocRing α\ninst✝ : NonAssocRing β\nh : Antiperiodic f c\nn : ℤ\n⊢ f (↑n * c - x) = ↑↑n.negOnePow * f (-x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.Injective | {
"line": 110,
"column": 2
} | {
"line": 112,
"column": 42
} | {
"line": 114,
"column": 0
} | [
{
"pp": "R : Type u\ninst✝⁶ : Ring R\nQ : Type v\ninst✝⁵ : AddCommGroup Q\ninst✝⁴ : Module R Q\nM : Type u_1\nN : Type u_2\ninst✝³ : AddCommGroup M\ninst✝² : AddCommGroup N\ninst✝¹ : Module R M\ninst✝ : Module R N\ni : M →ₗ[R] N\nf : M →ₗ[R] Q\na b : ExtensionOf i f\ndomain_eq : a.domain = b.domain\nto_fun_eq :... | [] | rcases a with ⟨a, a_le, e1⟩
congr
exact LinearPMap.ext domain_eq to_fun_eq | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Module.Injective | {
"line": 110,
"column": 2
} | {
"line": 112,
"column": 42
} | {
"line": 114,
"column": 0
} | [
{
"pp": "R : Type u\ninst✝⁶ : Ring R\nQ : Type v\ninst✝⁵ : AddCommGroup Q\ninst✝⁴ : Module R Q\nM : Type u_1\nN : Type u_2\ninst✝³ : AddCommGroup M\ninst✝² : AddCommGroup N\ninst✝¹ : Module R M\ninst✝ : Module R N\ni : M →ₗ[R] N\nf : M →ₗ[R] Q\na b : ExtensionOf i f\ndomain_eq : a.domain = b.domain\nto_fun_eq :... | [] | rcases a with ⟨a, a_le, e1⟩
congr
exact LinearPMap.ext domain_eq to_fun_eq | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Ring.Periodic | {
"line": 365,
"column": 55
} | {
"line": 365,
"column": 78
} | {
"line": 365,
"column": 79
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝¹ : AddSemigroup α\ninst✝ : Neg β\nh : Antiperiodic f c\na x : α\n⊢ (fun x ↦ f (a + x)) (x + c) = -(fun x ↦ f (a + x)) x",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"id",
"instHAdd",
"AddSemigroup.toAdd",
... | [
"α : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝¹ : AddSemigroup α\ninst✝ : Neg β\nh : Antiperiodic f c\na x : α\n⊢ f (a + (x + c)) = -f (a + x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Periodic | {
"line": 369,
"column": 2
} | {
"line": 369,
"column": 35
} | {
"line": 369,
"column": 36
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝¹ : AddCommSemigroup α\ninst✝ : Neg β\nh : Antiperiodic f c\na x : α\n⊢ (fun x ↦ f (x + a)) (x + c) = -(fun x ↦ f (x + a)) x",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"id",
"instHAdd",
"HAdd.hAdd",
"A... | [
"α : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝¹ : AddCommSemigroup α\ninst✝ : Neg β\nh : Antiperiodic f c\na x : α\n⊢ f (x + c + a) = -f (x + a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Periodic | {
"line": 377,
"column": 2
} | {
"line": 377,
"column": 35
} | {
"line": 377,
"column": 36
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝¹ : SubtractionCommMonoid α\ninst✝ : Neg β\nh : Antiperiodic f c\na : α\n⊢ Antiperiodic (fun x ↦ f (x - a)) c",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"AddMonoid.toAddZeroClass",
... | [
"α : Type u_1\nβ : Type u_2\nf : α → β\nc : α\ninst✝¹ : SubtractionCommMonoid α\ninst✝ : Neg β\nh : Antiperiodic f c\na : α\n⊢ Antiperiodic (fun x ↦ f (x + -a)) c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Periodic | {
"line": 384,
"column": 2
} | {
"line": 384,
"column": 44
} | {
"line": 384,
"column": 45
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : α → β\nc : α\ninst✝³ : AddMonoid α\ninst✝² : Neg β\ninst✝¹ : Group γ\ninst✝ : DistribMulAction γ α\nh : Antiperiodic f c\na : γ\nx : α\n⊢ (fun x ↦ f (a • x)) (x + a⁻¹ • c) = -(fun x ↦ f (a • x)) x",
"ppTerm": "?m.23",
"assigned": true,
"usedCons... | [
"α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : α → β\nc : α\ninst✝³ : AddMonoid α\ninst✝² : Neg β\ninst✝¹ : Group γ\ninst✝ : DistribMulAction γ α\nh : Antiperiodic f c\na : γ\nx : α\n⊢ f (a • x + c) = -f (a • x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Periodic | {
"line": 388,
"column": 2
} | {
"line": 388,
"column": 28
} | {
"line": 388,
"column": 29
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : α → β\nc : α\ninst✝³ : AddMonoid α\ninst✝² : Neg β\ninst✝¹ : Group γ\ninst✝ : DistribMulAction γ α\nh : Antiperiodic f c\na : γ\n⊢ Antiperiodic (fun x ↦ f (a⁻¹ • x)) (a • c)",
"ppTerm": "?m.22",
"assigned": false,
"usedConstants": [],
"usedF... | [
"α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : α → β\nc : α\ninst✝³ : AddMonoid α\ninst✝² : Neg β\ninst✝¹ : Group γ\ninst✝ : DistribMulAction γ α\nh : Antiperiodic f c\na : γ\n⊢ Antiperiodic (fun x ↦ f (a⁻¹ • x)) (a • c)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Periodic | {
"line": 395,
"column": 2
} | {
"line": 395,
"column": 35
} | {
"line": 395,
"column": 36
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\nc₁ c₂ : α\ninst✝¹ : AddGroup α\ninst✝ : InvolutiveNeg β\nh1 : Antiperiodic f c₁\nh2 : Antiperiodic f c₂\n⊢ Periodic f (c₁ - c₂)",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"AddMonoid.toAddSemigroup",
"congrArg"... | [
"α : Type u_1\nβ : Type u_2\nf : α → β\nc₁ c₂ : α\ninst✝¹ : AddGroup α\ninst✝ : InvolutiveNeg β\nh1 : Antiperiodic f c₁\nh2 : Antiperiodic f c₂\n⊢ Periodic f (c₁ + -c₂)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Periodic | {
"line": 402,
"column": 2
} | {
"line": 402,
"column": 35
} | {
"line": 402,
"column": 36
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\nc₁ c₂ : α\ninst✝¹ : AddGroup α\ninst✝ : InvolutiveNeg β\nh1 : Periodic f c₁\nh2 : Antiperiodic f c₂\n⊢ Antiperiodic f (c₁ - c₂)",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"AddMonoid.toAddSemigroup",
"congrArg"... | [
"α : Type u_1\nβ : Type u_2\nf : α → β\nc₁ c₂ : α\ninst✝¹ : AddGroup α\ninst✝ : InvolutiveNeg β\nh1 : Periodic f c₁\nh2 : Antiperiodic f c₂\n⊢ Antiperiodic f (c₁ + -c₂)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.Group | {
"line": 195,
"column": 2
} | {
"line": 195,
"column": 28
} | {
"line": 195,
"column": 29
} | [
{
"pp": "α : Type u_1\ninst✝² : CommGroup α\ninst✝¹ : PartialOrder α\ninst✝ : IsOrderedMonoid α\nb : α\n⊢ Pairwise (Disjoint on fun n ↦ Ioc (b ^ n) (b ^ (n + 1)))",
"ppTerm": "?m.27",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝² : CommGroup α\ninst✝¹ : PartialOrder α\ninst✝ : IsOrderedMonoid α\nb : α\n⊢ Pairwise (Disjoint on fun n ↦ Ioc (b ^ n) (b ^ (n + 1)))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.Group | {
"line": 200,
"column": 2
} | {
"line": 200,
"column": 28
} | {
"line": 200,
"column": 29
} | [
{
"pp": "α : Type u_1\ninst✝² : CommGroup α\ninst✝¹ : PartialOrder α\ninst✝ : IsOrderedMonoid α\nb : α\n⊢ Pairwise (Disjoint on fun n ↦ Ico (b ^ n) (b ^ (n + 1)))",
"ppTerm": "?m.27",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝² : CommGroup α\ninst✝¹ : PartialOrder α\ninst✝ : IsOrderedMonoid α\nb : α\n⊢ Pairwise (Disjoint on fun n ↦ Ico (b ^ n) (b ^ (n + 1)))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.Group | {
"line": 205,
"column": 2
} | {
"line": 205,
"column": 28
} | {
"line": 205,
"column": 29
} | [
{
"pp": "α : Type u_1\ninst✝² : CommGroup α\ninst✝¹ : PartialOrder α\ninst✝ : IsOrderedMonoid α\nb : α\n⊢ Pairwise (Disjoint on fun n ↦ Ioo (b ^ n) (b ^ (n + 1)))",
"ppTerm": "?m.27",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝² : CommGroup α\ninst✝¹ : PartialOrder α\ninst✝ : IsOrderedMonoid α\nb : α\n⊢ Pairwise (Disjoint on fun n ↦ Ioo (b ^ n) (b ^ (n + 1)))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.Group | {
"line": 215,
"column": 2
} | {
"line": 215,
"column": 71
} | {
"line": 216,
"column": 4
} | [
{
"pp": "α : Type u_1\ninst✝² : Ring α\ninst✝¹ : PartialOrder α\ninst✝ : IsOrderedRing α\na : α\n⊢ Pairwise (Disjoint on fun n ↦ Ioc (a + ↑n) (a + ↑n + 1))",
"ppTerm": "?m.28",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝² : Ring α\ninst✝¹ : PartialOrder α\ninst✝ : IsOrderedRing α\na : α\n⊢ Pairwise (Disjoint on fun n ↦ Ioc (a + ↑n) (a + ↑n + 1))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.Group | {
"line": 220,
"column": 2
} | {
"line": 220,
"column": 71
} | {
"line": 221,
"column": 4
} | [
{
"pp": "α : Type u_1\ninst✝² : Ring α\ninst✝¹ : PartialOrder α\ninst✝ : IsOrderedRing α\na : α\n⊢ Pairwise (Disjoint on fun n ↦ Ico (a + ↑n) (a + ↑n + 1))",
"ppTerm": "?m.28",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝² : Ring α\ninst✝¹ : PartialOrder α\ninst✝ : IsOrderedRing α\na : α\n⊢ Pairwise (Disjoint on fun n ↦ Ico (a + ↑n) (a + ↑n + 1))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.Group | {
"line": 225,
"column": 2
} | {
"line": 225,
"column": 71
} | {
"line": 226,
"column": 4
} | [
{
"pp": "α : Type u_1\ninst✝² : Ring α\ninst✝¹ : PartialOrder α\ninst✝ : IsOrderedRing α\na : α\n⊢ Pairwise (Disjoint on fun n ↦ Ioo (a + ↑n) (a + ↑n + 1))",
"ppTerm": "?m.28",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝² : Ring α\ninst✝¹ : PartialOrder α\ninst✝ : IsOrderedRing α\na : α\n⊢ Pairwise (Disjoint on fun n ↦ Ioo (a + ↑n) (a + ↑n + 1))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.Group | {
"line": 232,
"column": 2
} | {
"line": 232,
"column": 29
} | {
"line": 232,
"column": 30
} | [
{
"pp": "α : Type u_1\ninst✝² : Ring α\ninst✝¹ : PartialOrder α\ninst✝ : IsOrderedRing α\n⊢ Pairwise (Disjoint on fun n ↦ Ico (↑n) (↑n + 1))",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝² : Ring α\ninst✝¹ : PartialOrder α\ninst✝ : IsOrderedRing α\n⊢ Pairwise (Disjoint on fun n ↦ Ico (↑n) (↑n + 1))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.Group | {
"line": 236,
"column": 2
} | {
"line": 236,
"column": 29
} | {
"line": 236,
"column": 30
} | [
{
"pp": "α : Type u_1\ninst✝² : Ring α\ninst✝¹ : PartialOrder α\ninst✝ : IsOrderedRing α\n⊢ Pairwise (Disjoint on fun n ↦ Ioo (↑n) (↑n + 1))",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝² : Ring α\ninst✝¹ : PartialOrder α\ninst✝ : IsOrderedRing α\n⊢ Pairwise (Disjoint on fun n ↦ Ioo (↑n) (↑n + 1))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.Group | {
"line": 240,
"column": 2
} | {
"line": 240,
"column": 29
} | {
"line": 240,
"column": 30
} | [
{
"pp": "α : Type u_1\ninst✝² : Ring α\ninst✝¹ : PartialOrder α\ninst✝ : IsOrderedRing α\n⊢ Pairwise (Disjoint on fun n ↦ Ioc (↑n) (↑n + 1))",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝² : Ring α\ninst✝¹ : PartialOrder α\ninst✝ : IsOrderedRing α\n⊢ Pairwise (Disjoint on fun n ↦ Ioc (↑n) (↑n + 1))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Count | {
"line": 109,
"column": 4
} | {
"line": 109,
"column": 21
} | {
"line": 109,
"column": 22
} | [
{
"pp": "p✝ : ℕ → Prop\ninst✝¹ : DecidablePred p✝\np : ℕ → Prop\ninst✝ : DecidablePred p\nm n : ℕ\nhm : p m\nhn : p n\nheq : count p m = count p n\nh : m ≠ n\nhmn : m < n\n⊢ False",
"ppTerm": "?m.28",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"p✝ : ℕ → Prop\ninst✝¹ : DecidablePred p✝\np : ℕ → Prop\ninst✝ : DecidablePred p\nm n : ℕ\nhm : p m\nhn : p n\nheq : count p m = count p n\nh : m ≠ n\nhmn : m < n\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Factorization.Induction | {
"line": 89,
"column": 12
} | {
"line": 89,
"column": 23
} | {
"line": 89,
"column": 24
} | [
{
"pp": "case zero\nmotive : ℕ → Prop\nzero : motive 0\none : motive 1\nprime_mul : ∀ (p a : ℕ), Prime p → motive a → motive (p * a)\na p : ℕ\nhp : Prime p\nha : motive a\n⊢ motive (p ^ 0 * a)",
"ppTerm": "?zero",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"HMul... | [
"case zero\nmotive : ℕ → Prop\nzero : motive 0\none : motive 1\nprime_mul : ∀ (p a : ℕ), Prime p → motive a → motive (p * a)\na p : ℕ\nhp : Prime p\nha : motive a\n⊢ motive a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Count | {
"line": 119,
"column": 2
} | {
"line": 119,
"column": 65
} | {
"line": 120,
"column": 4
} | [
{
"pp": "p : ℕ → Prop\ninst✝ : DecidablePred p\nn : ℕ\n⊢ count p n = n ↔ ∀ n' < n, p n'",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.count_eq_card_filter_range",
"congrArg",
"id",
"Finset.range",
"Iff",
"Nat",
"LT.lt",
... | [
"p : ℕ → Prop\ninst✝ : DecidablePred p\nn : ℕ\n⊢ #({x ∈ range n | p x}) = n ↔ ∀ n' < n, p n'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Factorization.Induction | {
"line": 101,
"column": 4
} | {
"line": 101,
"column": 15
} | {
"line": 101,
"column": 16
} | [
{
"pp": "case succ.zero\nmotive : ℕ → Prop\nzero : motive 0\none : motive 1\nprime : ∀ (p : ℕ), Prime p → motive p\ncomposite : ∀ (a : ℕ), 2 ≤ a → motive a → ∀ (b : ℕ), 2 ≤ b → motive b → motive (a * b)\nn p : ℕ\nhp : Prime p\nha : motive (0 + 1)\n⊢ motive (p * (0 + 1))",
"ppTerm": "?succ.zero",
"assign... | [
"case succ.zero\nmotive : ℕ → Prop\nzero : motive 0\none : motive 1\nprime : ∀ (p : ℕ), Prime p → motive p\ncomposite : ∀ (a : ℕ), 2 ≤ a → motive a → ∀ (b : ℕ), 2 ≤ b → motive b → motive (a * b)\nn p : ℕ\nhp : Prime p\nha : motive (0 + 1)\n⊢ motive p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.Injective | {
"line": 410,
"column": 50
} | {
"line": 410,
"column": 70
} | {
"line": 410,
"column": 71
} | [
{
"pp": "R : Type u\ninst✝³ : Ring R\nQ : Type v\ninst✝² : AddCommGroup Q\ninst✝¹ : Module R Q\ninst✝ : Small.{v, u} R\ninj : Injective R Q\nI : Ideal R\ng : ↥I →ₗ[R] Q\neI : Shrink.{v, u} ↥I ≃ₗ[R] ↥I := Shrink.linearEquiv R ↥I\neR : Shrink.{v, u} R ≃ₗ[R] R := Shrink.linearEquiv R R\ng' : Shrink.{v, u} R →ₗ[R] ... | [
"R : Type u\ninst✝³ : Ring R\nQ : Type v\ninst✝² : AddCommGroup Q\ninst✝¹ : Module R Q\ninst✝ : Small.{v, u} R\ninj : Injective R Q\nI : Ideal R\ng : ↥I →ₗ[R] Q\neI : Shrink.{v, u} ↥I ≃ₗ[R] ↥I := Shrink.linearEquiv R ↥I\neR : Shrink.{v, u} R ≃ₗ[R] R := Shrink.linearEquiv R R\ng' : Shrink.{v, u} R →ₗ[R] Q\nhg' : ∀ (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Totient | {
"line": 59,
"column": 67
} | {
"line": 59,
"column": 83
} | {
"line": 59,
"column": 83
} | [
{
"pp": "n : ℕ\ne : ↑{m | m < n ∧ n.Coprime m} ≃ ↥({x ∈ range n | n.Coprime x}) :=\n { toFun := fun m ↦ ⟨↑m, ⋯⟩, invFun := fun m ↦ ⟨↑m, ⋯⟩, left_inv := ⋯, right_inv := ⋯ }\n⊢ #({a ∈ range n | n.Coprime a}) = Fintype.card ↥({x ∈ range n | n.Coprime x})",
"ppTerm": "?m.60",
"assigned": true,
"usedCon... | [
"n : ℕ\ne : ↑{m | m < n ∧ n.Coprime m} ≃ ↥({x ∈ range n | n.Coprime x}) :=\n { toFun := fun m ↦ ⟨↑m, ⋯⟩, invFun := fun m ↦ ⟨↑m, ⋯⟩, left_inv := ⋯, right_inv := ⋯ }\n⊢ #({a ∈ range n | n.Coprime a}) = #({x ∈ range n | n.Coprime x})"
] | Fintype.card_coe | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.Filter.AtTopBot.Finite | {
"line": 82,
"column": 2
} | {
"line": 82,
"column": 32
} | {
"line": 82,
"column": 33
} | [
{
"pp": "β : Type u_4\ninst✝¹ : LinearOrder β\ninst✝ : NoMaxOrder β\nu : ℕ → β\nhu : Tendsto u atTop atTop\n⊢ ∃ᶠ (n : ℕ) in atTop, ∀ k < n, u k < u n",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"instDistribL... | [
"β : Type u_4\ninst✝¹ : LinearOrder β\ninst✝ : NoMaxOrder β\nu : ℕ → β\nhu : Tendsto u atTop atTop\n⊢ ∀ (a : ℕ), ∃ b, a ≤ b ∧ ∀ k < b, u k < u b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.AtTopBot.Prod | {
"line": 30,
"column": 2
} | {
"line": 30,
"column": 65
} | {
"line": 30,
"column": 66
} | [
{
"pp": "case inr.inr\nα : Type u_3\nβ : Type u_4\ninst✝¹ : Preorder α\ninst✝ : Preorder β\nh✝¹ : Nonempty α\nh✝ : Nonempty β\n⊢ atTop ×ˢ atTop = atTop",
"ppTerm": "?inr.inr",
"assigned": true,
"usedConstants": [
"Set.instSProd",
"Eq.mpr",
"iInf",
"Filter.prod_iInf_left",
... | [
"case inr.inr\nα : Type u_3\nβ : Type u_4\ninst✝¹ : Preorder α\ninst✝ : Preorder β\nh✝¹ : Nonempty α\nh✝ : Nonempty β\n⊢ ⨅ i, ⨅ i_1, 𝓟 (Ici (i_1, i)) = ⨅ i, ⨅ j, 𝓟 (Ici (i, j))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.AtTopBot.Finite | {
"line": 150,
"column": 4
} | {
"line": 150,
"column": 71
} | {
"line": 151,
"column": 2
} | [
{
"pp": "case inr.hbd\nc d d' : ℕ\nhn : 2 * (c ^ 2 + d + 1) ≤ 2 * (c ^ 2 + d + 1) + d'\nc0 : c > 0\n⊢ (c ^ 2) ^ (c ^ 2 + d' + d + 1) < (c ^ 2 + 1) ^ (c ^ 2 + d' + d + 1)",
"ppTerm": "?inr.hbd",
"assigned": true,
"usedConstants": [
"Nat.instMonoid",
"Nat.lt_succ_self",
"instOfNatNat... | [] | exact Nat.pow_lt_pow_left (Nat.lt_succ_self _) (Nat.succ_ne_zero _) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Order.Filter.AtTopBot.Finite | {
"line": 150,
"column": 4
} | {
"line": 150,
"column": 71
} | {
"line": 151,
"column": 2
} | [
{
"pp": "case inr.hbd\nc d d' : ℕ\nhn : 2 * (c ^ 2 + d + 1) ≤ 2 * (c ^ 2 + d + 1) + d'\nc0 : c > 0\n⊢ (c ^ 2) ^ (c ^ 2 + d' + d + 1) < (c ^ 2 + 1) ^ (c ^ 2 + d' + d + 1)",
"ppTerm": "?inr.hbd",
"assigned": true,
"usedConstants": [
"Nat.instMonoid",
"Nat.lt_succ_self",
"instOfNatNat... | [] | exact Nat.pow_lt_pow_left (Nat.lt_succ_self _) (Nat.succ_ne_zero _) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Filter.AtTopBot.Prod | {
"line": 37,
"column": 4
} | {
"line": 37,
"column": 15
} | {
"line": 37,
"column": 16
} | [
{
"pp": "case hf\nι : Type u_1\nι' : Type u_2\np q : Finset ι × Finset ι'\nhpq : p ≤ q\n⊢ (fun p ↦ p.1 ×ˢ p.2) p ⊆ (fun p ↦ p.1 ×ˢ p.2) q",
"ppTerm": "?hf",
"assigned": true,
"usedConstants": [
"SProd.sprod",
"Finset",
"PartialOrder.toPreorder",
"Preorder.toLE",
"id",
... | [
"case hf\nι : Type u_1\nι' : Type u_2\np q : Finset ι × Finset ι'\nhpq : p ≤ q\n⊢ p.1 ×ˢ p.2 ⊆ q.1 ×ˢ q.2"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.AtTopBot.Finite | {
"line": 150,
"column": 4
} | {
"line": 150,
"column": 71
} | {
"line": 151,
"column": 2
} | [
{
"pp": "case inr.hbd\nc d d' : ℕ\nhn : 2 * (c ^ 2 + d + 1) ≤ 2 * (c ^ 2 + d + 1) + d'\nc0 : c > 0\n⊢ (c ^ 2) ^ (c ^ 2 + d' + d + 1) < (c ^ 2 + 1) ^ (c ^ 2 + d' + d + 1)",
"ppTerm": "?inr.hbd",
"assigned": true,
"usedConstants": [
"Nat.instMonoid",
"Nat.lt_succ_self",
"instOfNatNat... | [] | exact Nat.pow_lt_pow_left (Nat.lt_succ_self _) (Nat.succ_ne_zero _) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Filter.AtTopBot.CountablyGenerated | {
"line": 115,
"column": 2
} | {
"line": 115,
"column": 13
} | {
"line": 115,
"column": 14
} | [
{
"pp": "ι : Type u_3\nl : Filter ι\np : ι → Prop\ninst✝ : l.IsCountablyGenerated\n⊢ (∀ᶠ (n : ι) in l, p n) ↔ ∀ (x : ℕ → ι), Tendsto x atTop l → ∀ᶠ (n : ℕ) in atTop, p (x n)",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"instDistrib... | [
"ι : Type u_3\nl : Filter ι\np : ι → Prop\ninst✝ : l.IsCountablyGenerated\n⊢ (∀ᶠ (n : ι) in l, p n) ↔ ∀ (x : ℕ → ι), Tendsto x atTop l → ∃ a, ∀ (b : ℕ), a ≤ b → p (x b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Totient | {
"line": 308,
"column": 2
} | {
"line": 309,
"column": 60
} | {
"line": 310,
"column": 2
} | [
{
"pp": "n : ℕ\n⊢ φ n = (n / ∏ p ∈ n.primeFactors, p) * ∏ p ∈ n.primeFactors, (p - 1)",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHDiv",
"HMul.hMul",
"CommSemiring.toNonUnitalCommSemiring",
"congrArg",
"Nat.prod_primeFactors_dvd",
... | [
"n : ℕ\n⊢ 0 < ∏ p ∈ n.primeFactors, p"
] | rw [← mul_div_left n.totient, totient_mul_prod_primeFactors, mul_comm,
Nat.mul_div_assoc _ (prod_primeFactors_dvd n), mul_comm] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Nat.Totient | {
"line": 332,
"column": 4
} | {
"line": 332,
"column": 33
} | {
"line": 333,
"column": 4
} | [
{
"pp": "a b : ℕ\n⊢ ∀ (a1 a2 b1 b2 c1 c2 : ℕ), b1 ∣ a1 → b2 ∣ a2 → a1 / b1 * c1 * (a2 / b2 * c2) = a1 * a2 / (b1 * b2) * (c1 * c2)",
"ppTerm": "?m.64",
"assigned": true,
"usedConstants": [
"Dvd.dvd",
"Nat.instDvd",
"Nat"
],
"usedFVars": [],
"usedGoals": [
{
... | [
"a b a1 a2 b1 b2 c1 c2 : ℕ\nh1 : b1 ∣ a1\nh2 : b2 ∣ a2\n⊢ a1 / b1 * c1 * (a2 / b2 * c2) = a1 * a2 / (b1 * b2) * (c1 * c2)"
] | intro a1 a2 b1 b2 c1 c2 h1 h2 | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.Data.Nat.Totient | {
"line": 369,
"column": 2
} | {
"line": 369,
"column": 52
} | {
"line": 369,
"column": 53
} | [
{
"pp": "p n : ℕ\nhp : Prime p\nh : p ∣ n\nh1 : φ p * φ (p * n) = φ p * (φ n * p)\n⊢ φ (p * n) = p * φ n",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"p n : ℕ\nhp : Prime p\nh : p ∣ n\nh1 : φ p * φ (p * n) = φ p * (φ n * p)\n⊢ φ (p * n) = p * φ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Totient | {
"line": 374,
"column": 2
} | {
"line": 374,
"column": 17
} | {
"line": 374,
"column": 18
} | [
{
"pp": "p n : ℕ\nhp : Prime p\nh : ¬p ∣ n\n⊢ p.Coprime n",
"ppTerm": "?m.21",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"p n : ℕ\nhp : Prime p\nh : ¬p ∣ n\n⊢ p.Coprime n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Basic | {
"line": 48,
"column": 31
} | {
"line": 48,
"column": 61
} | {
"line": 48,
"column": 62
} | [
{
"pp": "X : Type u\nT : Set (Set X)\nempty_mem : ∅ ∈ T\nsInter_mem : ∀ A ⊆ T, ⋂₀ A ∈ T\nunion_mem : ∀ A ∈ T, ∀ B ∈ T, A ∪ B ∈ T\ns t : Set X\nhs : sᶜ ∈ T\nht : tᶜ ∈ T\n⊢ (s ∩ t)ᶜ ∈ T",
"ppTerm": "?m.45",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Compl.compl",
... | [
"X : Type u\nT : Set (Set X)\nempty_mem : ∅ ∈ T\nsInter_mem : ∀ A ⊆ T, ⋂₀ A ∈ T\nunion_mem : ∀ A ∈ T, ∀ B ∈ T, A ∪ B ∈ T\ns t : Set X\nhs : sᶜ ∈ T\nht : tᶜ ∈ T\n⊢ sᶜ ∪ tᶜ ∈ T"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Basic | {
"line": 142,
"column": 2
} | {
"line": 142,
"column": 52
} | {
"line": 142,
"column": 53
} | [
{
"pp": "X : Type u\ns₁ s₂ : Set X\ninst✝ : TopologicalSpace X\n⊢ IsClosed[inst✝] s₁ → IsClosed[inst✝] s₂ → IsClosed[inst✝] (s₁ ∪ s₂)",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.compl_union",
"congrArg",
"Compl.compl",
"Set.instUnion",
... | [
"X : Type u\ns₁ s₂ : Set X\ninst✝ : TopologicalSpace X\n⊢ IsOpen[inst✝] s₁ᶜ → IsOpen[inst✝] s₂ᶜ → IsOpen[inst✝] (s₁ᶜ ∩ s₂ᶜ)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Basic | {
"line": 145,
"column": 2
} | {
"line": 145,
"column": 67
} | {
"line": 145,
"column": 68
} | [
{
"pp": "X : Type u\ninst✝ : TopologicalSpace X\ns : Set (Set X)\n⊢ (∀ t ∈ s, IsClosed[inst✝] t) → IsClosed[inst✝] (⋂₀ s)",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.compl_sInter",
"congrArg",
"Compl.compl",
"Set.sUnion",
"Membership.m... | [
"X : Type u\ninst✝ : TopologicalSpace X\ns : Set (Set X)\n⊢ (∀ t ∈ s, IsOpen[inst✝] tᶜ) → IsOpen[inst✝] (⋃ a ∈ s, aᶜ)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Neighborhoods | {
"line": 120,
"column": 27
} | {
"line": 120,
"column": 38
} | {
"line": 120,
"column": 39
} | [
{
"pp": "X : Type u\ninst✝ : TopologicalSpace X\ns U : Set X\nh : U ∈ ⨆ x ∈ s, 𝓝 x\n⊢ ∀ x ∈ s, U ∈ 𝓝 x",
"ppTerm": "?m.31",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"X : Type u\ninst✝ : TopologicalSpace X\ns U : Set X\nh : U ∈ ⨆ x ∈ s, 𝓝 x\n⊢ ∀ x ∈ s, U ∈ 𝓝 x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Neighborhoods | {
"line": 251,
"column": 48
} | {
"line": 251,
"column": 91
} | {
"line": 251,
"column": 91
} | [
{
"pp": "X : Type u_2\nt t' : TopologicalSpace X\nH : ∀ (x : X), 𝓝 x = 𝓝 x\n⊢ t = t'",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"nhds",
"id",
"Topologi... | [] | by ext; simp_rw [@isOpen_iff_nhds _ _ _, H] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Topology.Neighborhoods | {
"line": 301,
"column": 2
} | {
"line": 301,
"column": 35
} | {
"line": 301,
"column": 36
} | [
{
"pp": "X : Type u\ninst✝ : TopologicalSpace X\ns t : Set X\nh : IsClosed[inst✝] t\n⊢ interior (s ∪ t) ⊆ interior s ∪ t",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Set.instUnion",
"id",
"Set.union_comm",
"LE.le",
"Set.in... | [
"X : Type u\ninst✝ : TopologicalSpace X\ns t : Set X\nh : IsClosed[inst✝] t\n⊢ interior (t ∪ s) ⊆ t ∪ interior s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Neighborhoods | {
"line": 305,
"column": 4
} | {
"line": 305,
"column": 52
} | {
"line": 305,
"column": 53
} | [
{
"pp": "X : Type u\ninst✝ : TopologicalSpace X\ns t : Set X\nh : IsOpen[inst✝] s\n⊢ (closure[inst✝] (s ∩ t))ᶜ ⊆ (s ∩ closure[inst✝] t)ᶜ",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Compl.compl",
"Set.compl_inter",
"Set.instUnion",
... | [
"X : Type u\ninst✝ : TopologicalSpace X\ns t : Set X\nh : IsOpen[inst✝] s\n⊢ interior (sᶜ ∪ tᶜ) ⊆ sᶜ ∪ interior tᶜ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Neighborhoods | {
"line": 308,
"column": 2
} | {
"line": 308,
"column": 33
} | {
"line": 308,
"column": 34
} | [
{
"pp": "X : Type u\ninst✝ : TopologicalSpace X\ns t : Set X\nh : IsOpen[inst✝] t\n⊢ closure[inst✝] s ∩ t ⊆ closure[inst✝] (s ∩ t)",
"ppTerm": "?m.13",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"X : Type u\ninst✝ : TopologicalSpace X\ns t : Set X\nh : IsOpen[inst✝] t\n⊢ closure[inst✝] s ∩ t ⊆ closure[inst✝] (s ∩ t)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Closure | {
"line": 183,
"column": 4
} | {
"line": 183,
"column": 44
} | {
"line": 183,
"column": 45
} | [
{
"pp": "X : Type u\ninst✝ : TopologicalSpace X\nι : Sort v\nl : Filter X\np : ι → Prop\ns : ι → Set X\nh : l.HasBasis p s\nho : ∀ (i : ι), p i → IsOpen (s i)\ni : ι\nhi : p i\n⊢ interior (s i) ∈ l",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Filter.instMembership",
"Eq.mpr... | [
"X : Type u\ninst✝ : TopologicalSpace X\nι : Sort v\nl : Filter X\np : ι → Prop\ns : ι → Set X\nh : l.HasBasis p s\nho : ∀ (i : ι), p i → IsOpen (s i)\ni : ι\nhi : p i\n⊢ s i ∈ l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Closure | {
"line": 337,
"column": 53
} | {
"line": 337,
"column": 94
} | {
"line": 337,
"column": 95
} | [
{
"pp": "X : Type u\ninst✝ : TopologicalSpace X\ns t : Set X\nh : Disjoint (closure s) (closure t)\n⊢ interior sᶜ ∪ interior tᶜ = univ",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.compl_univ_iff._simp_1",
"congrArg",
"Compl.compl",
"Set.univ"... | [
"X : Type u\ninst✝ : TopologicalSpace X\ns t : Set X\nh : Disjoint (closure s) (closure t)\n⊢ closure s ∩ closure t = ∅"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Defs.Induced | {
"line": 89,
"column": 26
} | {
"line": 89,
"column": 60
} | {
"line": 89,
"column": 61
} | [
{
"pp": "X : Type u_1\nY : Type u_2\nf : X → Y\nt : TopologicalSpace X\ns : Set (Set Y)\nh : ∀ t_1 ∈ s, IsOpen[t] (f ⁻¹' t_1)\n⊢ IsOpen[t] (f ⁻¹' ⋃₀ s)",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Set.sUnion",
"Membership.mem",
"id",
... | [
"X : Type u_1\nY : Type u_2\nf : X → Y\nt : TopologicalSpace X\ns : Set (Set Y)\nh : ∀ t_1 ∈ s, IsOpen[t] (f ⁻¹' t_1)\n⊢ IsOpen[t] (⋃ t ∈ s, f ⁻¹' t)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Closure | {
"line": 545,
"column": 2
} | {
"line": 545,
"column": 50
} | {
"line": 545,
"column": 51
} | [
{
"pp": "X : Type u\ninst✝ : TopologicalSpace X\ns t : Set X\n⊢ frontier (s ∪ t) ⊆ frontier s ∩ closure tᶜ ∪ closure sᶜ ∩ frontier t",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"X : Type u\ninst✝ : TopologicalSpace X\ns t : Set X\n⊢ frontier (s ∪ t) ⊆ frontier s ∩ closure tᶜ ∪ closure sᶜ ∩ frontier t"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Closure | {
"line": 570,
"column": 23
} | {
"line": 570,
"column": 38
} | {
"line": 570,
"column": 39
} | [
{
"pp": "X : Type u\ninst✝ : TopologicalSpace X\ns : Set X\nh : IsClosed s\nA : frontier s = s \\ interior s\nB : interior (frontier s) ⊆ interior s\nC : interior (frontier s) ⊆ frontier s\n⊢ interior (frontier s) ⊆ s \\ interior s",
"ppTerm": "?m.73",
"assigned": true,
"usedConstants": [
"Eq.... | [
"X : Type u\ninst✝ : TopologicalSpace X\ns : Set X\nh : IsClosed s\nA : frontier s = s \\ interior s\nB : interior (frontier s) ⊆ interior s\nC : interior (frontier s) ⊆ frontier s\n⊢ interior (s \\ interior s) ⊆ s \\ interior s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Closure | {
"line": 566,
"column": 2
} | {
"line": 571,
"column": 50
} | {
"line": 573,
"column": 0
} | [
{
"pp": "X : Type u\ninst✝ : TopologicalSpace X\ns : Set X\nh : IsClosed s\n⊢ interior (frontier s) = ∅",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"frontier",
"interior_subset",
"interior_mono",
"congrArg",
"IsClosed.frontier_eq",
"E... | [] | have A : frontier s = s \ interior s := h.frontier_eq
have B : interior (frontier s) ⊆ interior s := by rw [A]; exact interior_mono sdiff_subset
have C : interior (frontier s) ⊆ frontier s := interior_subset
have : interior (frontier s) ⊆ interior s ∩ (s \ interior s) :=
subset_inter B (by simpa [A] using C)
... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Closure | {
"line": 566,
"column": 2
} | {
"line": 571,
"column": 50
} | {
"line": 573,
"column": 0
} | [
{
"pp": "X : Type u\ninst✝ : TopologicalSpace X\ns : Set X\nh : IsClosed s\n⊢ interior (frontier s) = ∅",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"frontier",
"interior_subset",
"interior_mono",
"congrArg",
"IsClosed.frontier_eq",
"E... | [] | have A : frontier s = s \ interior s := h.frontier_eq
have B : interior (frontier s) ⊆ interior s := by rw [A]; exact interior_mono sdiff_subset
have C : interior (frontier s) ⊆ frontier s := interior_subset
have : interior (frontier s) ⊆ interior s ∩ (s \ interior s) :=
subset_inter B (by simpa [A] using C)
... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.ClusterPt | {
"line": 329,
"column": 4
} | {
"line": 329,
"column": 15
} | {
"line": 329,
"column": 16
} | [
{
"pp": "case mpr\nX : Type u\ninst✝ : TopologicalSpace X\nx : X\nF : Filter X\nU : Set X\nhU : U ∈ F.lift' closure[inst✝]\nh : ∀ (s : Set X), (∃ t₁ ∈ pure x, ∃ t₂ ∈ F.lift' closure[inst✝], s = t₁ ∩ t₂) → s.Nonempty\n⊢ U ∈ pure x",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"Pure.p... | [
"case mpr\nX : Type u\ninst✝ : TopologicalSpace X\nx : X\nF : Filter X\nU : Set X\nhU : U ∈ F.lift' closure[inst✝]\nh : ∀ (s : Set X), (∃ t₁ ∈ pure x, ∃ t₂ ∈ F.lift' closure[inst✝], s = t₁ ∩ t₂) → s.Nonempty\n⊢ x ∈ U"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 204,
"column": 4
} | {
"line": 204,
"column": 57
} | {
"line": 204,
"column": 58
} | [
{
"pp": "α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\nm : ℤ\n⊢ b + m • p - (toIcoDiv hp a b + m) • p ∈ Set.Ico a (a + p)",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"in... | [
"α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\nm : ℤ\n⊢ b - toIcoDiv hp a b • p ∈ Set.Ico a (a + p)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 215,
"column": 2
} | {
"line": 215,
"column": 13
} | {
"line": 215,
"column": 14
} | [
{
"pp": "α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\nm : ℤ\n⊢ b - toIcoDiv hp a b • p + m • p ∈ Set.Ico (a + m • p) (a + p + m • p)",
"ppTerm": "?m.66",
"assigned": true,
"usedConstants": [
"IsRigh... | [
"α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\nm : ℤ\n⊢ a ≤ toIcoMod hp a b ∧ toIcoMod hp a b < a + p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 224,
"column": 4
} | {
"line": 224,
"column": 57
} | {
"line": 224,
"column": 58
} | [
{
"pp": "α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\nm : ℤ\n⊢ b + m • p - (toIocDiv hp a b + m) • p ∈ Set.Ioc a (a + p)",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Se... | [
"α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\nm : ℤ\n⊢ b - toIocDiv hp a b • p ∈ Set.Ioc a (a + p)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 235,
"column": 2
} | {
"line": 235,
"column": 13
} | {
"line": 235,
"column": 14
} | [
{
"pp": "α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\nm : ℤ\n⊢ b - toIocDiv hp a b • p + m • p ∈ Set.Ioc (a + m • p) (a + p + m • p)",
"ppTerm": "?m.66",
"assigned": true,
"usedConstants": [
"IsRigh... | [
"α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\nm : ℤ\n⊢ a < toIocMod hp a b ∧ toIocMod hp a b ≤ a + p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 274,
"column": 2
} | {
"line": 274,
"column": 70
} | {
"line": 276,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\nm : ℤ\n⊢ toIcoDiv hp (a - m • p) b = toIcoDiv hp a b + m",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NegZeroClass... | [] | rw [sub_eq_add_neg, ← neg_smul, toIcoDiv_add_zsmul', sub_neg_eq_add] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 274,
"column": 2
} | {
"line": 274,
"column": 70
} | {
"line": 276,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\nm : ℤ\n⊢ toIcoDiv hp (a - m • p) b = toIcoDiv hp a b + m",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NegZeroClass... | [] | rw [sub_eq_add_neg, ← neg_smul, toIcoDiv_add_zsmul', sub_neg_eq_add] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 274,
"column": 2
} | {
"line": 274,
"column": 70
} | {
"line": 276,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\nm : ℤ\n⊢ toIcoDiv hp (a - m • p) b = toIcoDiv hp a b + m",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NegZeroClass... | [] | rw [sub_eq_add_neg, ← neg_smul, toIcoDiv_add_zsmul', sub_neg_eq_add] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 299,
"column": 2
} | {
"line": 299,
"column": 30
} | {
"line": 299,
"column": 31
} | [
{
"pp": "α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIcoDiv hp a (b + p) = toIcoDiv hp a b + 1",
"ppTerm": "?m.32",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIcoDiv hp a (b + p) = toIcoDiv hp a b + 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 303,
"column": 2
} | {
"line": 303,
"column": 30
} | {
"line": 303,
"column": 31
} | [
{
"pp": "α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIcoDiv hp (a + p) b = toIcoDiv hp a b - 1",
"ppTerm": "?m.32",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIcoDiv hp (a + p) b = toIcoDiv hp a b - 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 307,
"column": 2
} | {
"line": 307,
"column": 30
} | {
"line": 307,
"column": 31
} | [
{
"pp": "α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIocDiv hp a (b + p) = toIocDiv hp a b + 1",
"ppTerm": "?m.32",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIocDiv hp a (b + p) = toIocDiv hp a b + 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 311,
"column": 2
} | {
"line": 311,
"column": 30
} | {
"line": 311,
"column": 31
} | [
{
"pp": "α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIocDiv hp (a + p) b = toIocDiv hp a b - 1",
"ppTerm": "?m.32",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIocDiv hp (a + p) b = toIocDiv hp a b - 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 331,
"column": 2
} | {
"line": 331,
"column": 30
} | {
"line": 331,
"column": 31
} | [
{
"pp": "α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIcoDiv hp a (b - p) = toIcoDiv hp a b - 1",
"ppTerm": "?m.32",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIcoDiv hp a (b - p) = toIcoDiv hp a b - 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 335,
"column": 2
} | {
"line": 335,
"column": 30
} | {
"line": 335,
"column": 31
} | [
{
"pp": "α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIcoDiv hp (a - p) b = toIcoDiv hp a b + 1",
"ppTerm": "?m.32",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIcoDiv hp (a - p) b = toIcoDiv hp a b + 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 339,
"column": 2
} | {
"line": 339,
"column": 30
} | {
"line": 339,
"column": 31
} | [
{
"pp": "α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIocDiv hp a (b - p) = toIocDiv hp a b - 1",
"ppTerm": "?m.32",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIocDiv hp a (b - p) = toIocDiv hp a b - 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 343,
"column": 2
} | {
"line": 343,
"column": 30
} | {
"line": 343,
"column": 31
} | [
{
"pp": "α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIocDiv hp (a - p) b = toIocDiv hp a b + 1",
"ppTerm": "?m.32",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIocDiv hp (a - p) b = toIocDiv hp a b + 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 377,
"column": 2
} | {
"line": 377,
"column": 28
} | {
"line": 377,
"column": 29
} | [
{
"pp": "α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIcoDiv hp (-a) b = -(toIocDiv hp a (-b) + 1)",
"ppTerm": "?m.34",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []... | [
"α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIcoDiv hp (-a) b = -(toIocDiv hp a (-b) + 1)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 383,
"column": 2
} | {
"line": 383,
"column": 28
} | {
"line": 383,
"column": 29
} | [
{
"pp": "α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIocDiv hp (-a) b = -(toIcoDiv hp a (-b) + 1)",
"ppTerm": "?m.34",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []... | [
"α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIocDiv hp (-a) b = -(toIcoDiv hp a (-b) + 1)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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