module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.RingTheory.Jacobson.Ideal | {
"line": 328,
"column": 4
} | {
"line": 328,
"column": 15
} | {
"line": 328,
"column": 16
} | [
{
"pp": "case mpr\nR : Type u\ninst✝ : CommRing R\nI : Ideal R\nhf : Function.Surjective ⇑(Quotient.mk I)\nh : ⊥.radical = ⊥.jacobson\nthis : (RingHom.ker (Quotient.mk I)).radical = (RingHom.ker (Quotient.mk I)).jacobson\n⊢ I.radical = I.jacobson",
"ppTerm": "?mpr",
"assigned": false,
"usedConstants... | [
"case mpr\nR : Type u\ninst✝ : CommRing R\nI : Ideal R\nhf : Function.Surjective ⇑(Quotient.mk I)\nh : ⊥.radical = ⊥.jacobson\nthis : (RingHom.ker (Quotient.mk I)).radical = (RingHom.ker (Quotient.mk I)).jacobson\n⊢ I.radical = I.jacobson"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic | {
"line": 45,
"column": 4
} | {
"line": 45,
"column": 15
} | {
"line": 45,
"column": 16
} | [
{
"pp": "case right\nR : Type u_1\nS : Type u_2\nK : Type u_3\ninst✝¹ : CommSemiring R\ninst✝ : IsLocalRing R\nI : Ideal R\na✝ : maximalIdeal R ≤ I\nu : Rˣ\nH : ↑u ∈ I\n⊢ 1 ∈ I",
"ppTerm": "?right",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case right\nR : Type u_1\nS : Type u_2\nK : Type u_3\ninst✝¹ : CommSemiring R\ninst✝ : IsLocalRing R\nI : Ideal R\na✝ : maximalIdeal R ≤ I\nu : Rˣ\nH : ↑u ∈ I\n⊢ 1 ∈ I"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.LocalRing.RingHom.Basic | {
"line": 143,
"column": 25
} | {
"line": 143,
"column": 82
} | {
"line": 143,
"column": 83
} | [
{
"pp": "R✝ : Type u_1\nS : Type u_2\nT : Type u_3\nK : Type u_4\nR : Type u_5\ninst✝² : DivisionRing K\ninst✝¹ : CommRing R\ninst✝ : Nontrivial R\nf : K →+* R\nr : K\nhr : IsUnit (f r)\n⊢ IsUnit r",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoi... | [
"R✝ : Type u_1\nS : Type u_2\nT : Type u_3\nK : Type u_4\nR : Type u_5\ninst✝² : DivisionRing K\ninst✝¹ : CommRing R\ninst✝ : Nontrivial R\nf : K →+* R\nr : K\nhr : IsUnit (f r)\n⊢ ¬r = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Mon | {
"line": 125,
"column": 18
} | {
"line": 126,
"column": 65
} | {
"line": 127,
"column": 6
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\ninst✝¹ : MonoidalCategory C\nM X Y : C\ninst✝ : MonObj M\ne : M ≅ X\n⊢ ((e.inv ⊗ₘ e.inv) ≫ μ ≫ e.hom) ▷ X ≫ (e.inv ⊗ₘ e.inv) ≫ μ ≫ e.hom =\n (α_ X X X).hom ≫ X ◁ ((e.inv ⊗ₘ e.inv) ≫ μ ≫ e.hom) ≫ (e.inv ⊗ₘ e.inv) ≫ μ ≫ e.hom",
"ppTerm": "?m.99",
"ass... | [
"C : Type u₁\ninst✝² : Category.{v₁, u₁} C\ninst✝¹ : MonoidalCategory C\nM X Y : C\ninst✝ : MonObj M\ne : M ≅ X\n⊢ ((e.inv ⊗ₘ e.inv) ≫ μ ⊗ₘ e.inv) ≫ μ ≫ e.hom = (α_ X X X).hom ≫ (e.inv ⊗ₘ (e.inv ⊗ₘ e.inv) ≫ μ) ≫ μ ≫ e.hom"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Mon | {
"line": 463,
"column": 13
} | {
"line": 467,
"column": 30
} | {
"line": 469,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝¹¹ : Category.{v₁, u₁} C\ninst✝¹⁰ : MonoidalCategory C\nM N O X✝ : C\ninst✝⁹ : MonObj M\ninst✝⁸ : MonObj N\ninst✝⁷ : MonObj O\ninst✝⁶ : BraidedCategory C\nX Y Z W : C\ninst✝⁵ : MonObj X\ninst✝⁴ : MonObj Y\ninst✝³ : MonObj Z\ninst✝² : MonObj W\nf : X ⟶ Y\ng : Z ⟶ W\ninst✝¹ : IsMonHom f... | [] | by
dsimp [tensorObj.mul_def]
slice_rhs 1 2 => rw [tensorμ_natural]
slice_lhs 2 3 => rw [tensorHom_comp_tensorHom, mul_hom, mul_hom, ← tensorHom_comp_tensorHom]
simp only [Category.assoc] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Monoidal.Mon | {
"line": 474,
"column": 16
} | {
"line": 474,
"column": 27
} | {
"line": 474,
"column": 28
} | [
{
"pp": "C : Type u₁\ninst✝¹⁰ : Category.{v₁, u₁} C\ninst✝⁹ : MonoidalCategory C\nM N O X✝ : C\ninst✝⁸ : MonObj M\ninst✝⁷ : MonObj N\ninst✝⁶ : MonObj O\ninst✝⁵ : BraidedCategory C\nX Y Z W : C\ninst✝⁴ : MonObj X\ninst✝³ : MonObj Y\ninst✝² : MonObj Z\ninst✝¹ : MonObj W\nf : Y ⟶ Z\ninst✝ : IsMonHom f\n⊢ η ≫ X ◁ f... | [
"C : Type u₁\ninst✝¹⁰ : Category.{v₁, u₁} C\ninst✝⁹ : MonoidalCategory C\nM N O X✝ : C\ninst✝⁸ : MonObj M\ninst✝⁷ : MonObj N\ninst✝⁶ : MonObj O\ninst✝⁵ : BraidedCategory C\nX Y Z W : C\ninst✝⁴ : MonObj X\ninst✝³ : MonObj Y\ninst✝² : MonObj Z\ninst✝¹ : MonObj W\nf : Y ⟶ Z\ninst✝ : IsMonHom f\n⊢ η ≫ X ◁ f = η"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Mon | {
"line": 475,
"column": 16
} | {
"line": 475,
"column": 27
} | {
"line": 475,
"column": 28
} | [
{
"pp": "C : Type u₁\ninst✝¹⁰ : Category.{v₁, u₁} C\ninst✝⁹ : MonoidalCategory C\nM N O X✝ : C\ninst✝⁸ : MonObj M\ninst✝⁷ : MonObj N\ninst✝⁶ : MonObj O\ninst✝⁵ : BraidedCategory C\nX Y Z W : C\ninst✝⁴ : MonObj X\ninst✝³ : MonObj Y\ninst✝² : MonObj Z\ninst✝¹ : MonObj W\nf : Y ⟶ Z\ninst✝ : IsMonHom f\n⊢ μ ≫ X ◁ f... | [
"C : Type u₁\ninst✝¹⁰ : Category.{v₁, u₁} C\ninst✝⁹ : MonoidalCategory C\nM N O X✝ : C\ninst✝⁸ : MonObj M\ninst✝⁷ : MonObj N\ninst✝⁶ : MonObj O\ninst✝⁵ : BraidedCategory C\nX Y Z W : C\ninst✝⁴ : MonObj X\ninst✝³ : MonObj Y\ninst✝² : MonObj Z\ninst✝¹ : MonObj W\nf : Y ⟶ Z\ninst✝ : IsMonHom f\n⊢ μ ≫ X ◁ f = (X ◁ f ⊗ₘ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Mon | {
"line": 479,
"column": 16
} | {
"line": 479,
"column": 27
} | {
"line": 479,
"column": 28
} | [
{
"pp": "C : Type u₁\ninst✝¹⁰ : Category.{v₁, u₁} C\ninst✝⁹ : MonoidalCategory C\nM N O X✝ : C\ninst✝⁸ : MonObj M\ninst✝⁷ : MonObj N\ninst✝⁶ : MonObj O\ninst✝⁵ : BraidedCategory C\nX Y Z W : C\ninst✝⁴ : MonObj X\ninst✝³ : MonObj Y\ninst✝² : MonObj Z\ninst✝¹ : MonObj W\nf : X ⟶ Y\ninst✝ : IsMonHom f\n⊢ η ≫ f ▷ Z... | [
"C : Type u₁\ninst✝¹⁰ : Category.{v₁, u₁} C\ninst✝⁹ : MonoidalCategory C\nM N O X✝ : C\ninst✝⁸ : MonObj M\ninst✝⁷ : MonObj N\ninst✝⁶ : MonObj O\ninst✝⁵ : BraidedCategory C\nX Y Z W : C\ninst✝⁴ : MonObj X\ninst✝³ : MonObj Y\ninst✝² : MonObj Z\ninst✝¹ : MonObj W\nf : X ⟶ Y\ninst✝ : IsMonHom f\n⊢ η ≫ f ▷ Z = η"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Mon | {
"line": 480,
"column": 16
} | {
"line": 480,
"column": 27
} | {
"line": 480,
"column": 28
} | [
{
"pp": "C : Type u₁\ninst✝¹⁰ : Category.{v₁, u₁} C\ninst✝⁹ : MonoidalCategory C\nM N O X✝ : C\ninst✝⁸ : MonObj M\ninst✝⁷ : MonObj N\ninst✝⁶ : MonObj O\ninst✝⁵ : BraidedCategory C\nX Y Z W : C\ninst✝⁴ : MonObj X\ninst✝³ : MonObj Y\ninst✝² : MonObj Z\ninst✝¹ : MonObj W\nf : X ⟶ Y\ninst✝ : IsMonHom f\n⊢ μ ≫ f ▷ Z... | [
"C : Type u₁\ninst✝¹⁰ : Category.{v₁, u₁} C\ninst✝⁹ : MonoidalCategory C\nM N O X✝ : C\ninst✝⁸ : MonObj M\ninst✝⁷ : MonObj N\ninst✝⁶ : MonObj O\ninst✝⁵ : BraidedCategory C\nX Y Z W : C\ninst✝⁴ : MonObj X\ninst✝³ : MonObj Y\ninst✝² : MonObj Z\ninst✝¹ : MonObj W\nf : X ⟶ Y\ninst✝ : IsMonHom f\n⊢ μ ≫ f ▷ Z = (f ▷ Z ⊗ₘ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Mon | {
"line": 954,
"column": 30
} | {
"line": 954,
"column": 60
} | {
"line": 954,
"column": 61
} | [
{
"pp": "C : Type u₁\ninst✝¹¹ : Category.{v₁, u₁} C\ninst✝¹⁰ : MonoidalCategory C\nM N O X✝ : C\ninst✝⁹ : MonObj M\ninst✝⁸ : MonObj N\ninst✝⁷ : MonObj O\nD : Type u₂\ninst✝⁶ : Category.{v₂, u₂} D\ninst✝⁵ : MonoidalCategory D\nE : Type u₃\ninst✝⁴ : Category.{v₃, u₃} E\ninst✝³ : MonoidalCategory E\nF F' : C ⥤ D\n... | [
"C : Type u₁\ninst✝¹¹ : Category.{v₁, u₁} C\ninst✝¹⁰ : MonoidalCategory C\nM N O X✝ : C\ninst✝⁹ : MonObj M\ninst✝⁸ : MonObj N\ninst✝⁷ : MonObj O\nD : Type u₂\ninst✝⁶ : Category.{v₂, u₂} D\ninst✝⁵ : MonoidalCategory D\nE : Type u₃\ninst✝⁴ : Category.{v₃, u₃} E\ninst✝³ : MonoidalCategory E\nF F' : C ⥤ D\nG : D ⥤ E\ni... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Mon | {
"line": 956,
"column": 30
} | {
"line": 956,
"column": 60
} | {
"line": 956,
"column": 61
} | [
{
"pp": "C : Type u₁\ninst✝¹¹ : Category.{v₁, u₁} C\ninst✝¹⁰ : MonoidalCategory C\nM N O X✝ : C\ninst✝⁹ : MonObj M\ninst✝⁸ : MonObj N\ninst✝⁷ : MonObj O\nD : Type u₂\ninst✝⁶ : Category.{v₂, u₂} D\ninst✝⁵ : MonoidalCategory D\nE : Type u₃\ninst✝⁴ : Category.{v₃, u₃} E\ninst✝³ : MonoidalCategory E\nF F' : C ⥤ D\n... | [
"C : Type u₁\ninst✝¹¹ : Category.{v₁, u₁} C\ninst✝¹⁰ : MonoidalCategory C\nM N O X✝ : C\ninst✝⁹ : MonObj M\ninst✝⁸ : MonObj N\ninst✝⁷ : MonObj O\nD : Type u₂\ninst✝⁶ : Category.{v₂, u₂} D\ninst✝⁵ : MonoidalCategory D\nE : Type u₃\ninst✝⁴ : Category.{v₃, u₃} E\ninst✝³ : MonoidalCategory E\nF F' : C ⥤ D\nG : D ⥤ E\ni... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Localization.Module | {
"line": 71,
"column": 2
} | {
"line": 72,
"column": 74
} | {
"line": 72,
"column": 75
} | [
{
"pp": "R : Type u_1\nRₛ : Type u_2\ninst✝¹⁰ : CommSemiring R\nS : Submonoid R\ninst✝⁹ : CommSemiring Rₛ\ninst✝⁸ : Algebra R Rₛ\ninst✝⁷ : IsLocalization S Rₛ\nM : Type u_3\nMₛ : Type u_4\ninst✝⁶ : AddCommMonoid M\ninst✝⁵ : Module R M\ninst✝⁴ : AddCommMonoid Mₛ\ninst✝³ : Module R Mₛ\ninst✝² : Module Rₛ Mₛ\ninst... | [
"R : Type u_1\nRₛ : Type u_2\ninst✝¹⁰ : CommSemiring R\nS : Submonoid R\ninst✝⁹ : CommSemiring Rₛ\ninst✝⁸ : Algebra R Rₛ\ninst✝⁷ : IsLocalization S Rₛ\nM : Type u_3\nMₛ : Type u_4\ninst✝⁶ : AddCommMonoid M\ninst✝⁵ : Module R M\ninst✝⁴ : AddCommMonoid Mₛ\ninst✝³ : Module R Mₛ\ninst✝² : Module Rₛ Mₛ\ninst✝¹ : IsScala... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting | {
"line": 100,
"column": 44
} | {
"line": 100,
"column": 61
} | {
"line": 100,
"column": 62
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nX₃ Y₁ Y₂ Y₃ : C\ng₁ : Y₁ ⟶ Y₂\ng₂ : Y₂ ⟶ Y₃\ni₃ : X₃ ⟶ Y₃\nt₂ : PullbackCone g₂ i₃\ni₂ : t₂.pt ⟶ Y₂\nt₁ : PullbackCone g₁ i₂\nhi₂ : i₂ = t₂.fst\nH : IsLimit t₂\nH' : IsLimit t₁\ns : PullbackCone (g₁ ≫ g₂) i₃\nl₂ : s.pt ⟶ t₂.pt\nhl₂ : l₂ ≫ t₂.fst = s.fst ≫ g₁\nhl₂'... | [
"C : Type u\ninst✝ : Category.{v, u} C\nX₃ Y₁ Y₂ Y₃ : C\ng₁ : Y₁ ⟶ Y₂\ng₂ : Y₂ ⟶ Y₃\ni₃ : X₃ ⟶ Y₃\nt₂ : PullbackCone g₂ i₃\ni₂ : t₂.pt ⟶ Y₂\nt₁ : PullbackCone g₁ i₂\nhi₂ : i₂ = t₂.fst\nH : IsLimit t₂\nH' : IsLimit t₁\ns : PullbackCone (g₁ ≫ g₂) i₃\nl₂ : s.pt ⟶ t₂.pt\nhl₂ : l₂ ≫ t₂.fst = s.fst ≫ g₁\nhl₂' : l₂ ≫ t₂.s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting | {
"line": 104,
"column": 4
} | {
"line": 104,
"column": 28
} | {
"line": 104,
"column": 29
} | [
{
"pp": "case h₁\nC : Type u\ninst✝ : Category.{v, u} C\nX₃ Y₁ Y₂ Y₃ : C\ng₁ : Y₁ ⟶ Y₂\ng₂ : Y₂ ⟶ Y₃\ni₃ : X₃ ⟶ Y₃\nt₂ : PullbackCone g₂ i₃\ni₂ : t₂.pt ⟶ Y₂\nt₁ : PullbackCone g₁ i₂\nhi₂ : i₂ = t₂.fst\nH : IsLimit t₂\nH' : IsLimit t₁\ns : PullbackCone (g₁ ≫ g₂) i₃\nl₂ : s.pt ⟶ t₂.pt\nhl₂ : l₂ ≫ t₂.fst = s.fst ≫... | [
"case h₁\nC : Type u\ninst✝ : Category.{v, u} C\nX₃ Y₁ Y₂ Y₃ : C\ng₁ : Y₁ ⟶ Y₂\ng₂ : Y₂ ⟶ Y₃\ni₃ : X₃ ⟶ Y₃\nt₂ : PullbackCone g₂ i₃\ni₂ : t₂.pt ⟶ Y₂\nt₁ : PullbackCone g₁ i₂\nhi₂ : i₂ = t₂.fst\nH : IsLimit t₂\nH' : IsLimit t₁\ns : PullbackCone (g₁ ≫ g₂) i₃\nl₂ : s.pt ⟶ t₂.pt\nhl₂ : l₂ ≫ t₂.fst = s.fst ≫ g₁\nhl₂' : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting | {
"line": 129,
"column": 6
} | {
"line": 129,
"column": 17
} | {
"line": 129,
"column": 18
} | [
{
"pp": "case refine_1.h₁\nC : Type u\ninst✝ : Category.{v, u} C\nX₃ Y₁ Y₂ Y₃ : C\ng₁ : Y₁ ⟶ Y₂\ng₂ : Y₂ ⟶ Y₃\ni₃ : X₃ ⟶ Y₃\nt₂ : PullbackCone g₂ i₃\ni₂ : t₂.pt ⟶ Y₂\nt₁ : PullbackCone g₁ i₂\nhi₂ : i₂ = t₂.fst\nH : IsLimit t₂\nH' : IsLimit (t₂.pasteHoriz t₁ hi₂)\ns : PullbackCone g₁ i₂\nl : s.pt ⟶ (t₂.pasteHori... | [
"case refine_1.h₁\nC : Type u\ninst✝ : Category.{v, u} C\nX₃ Y₁ Y₂ Y₃ : C\ng₁ : Y₁ ⟶ Y₂\ng₂ : Y₂ ⟶ Y₃\ni₃ : X₃ ⟶ Y₃\nt₂ : PullbackCone g₂ i₃\ni₂ : t₂.pt ⟶ Y₂\nt₁ : PullbackCone g₁ i₂\nhi₂ : i₂ = t₂.fst\nH : IsLimit t₂\nH' : IsLimit (t₂.pasteHoriz t₁ hi₂)\ns : PullbackCone g₁ i₂\nl : s.pt ⟶ (t₂.pasteHoriz t₁ hi₂).pt... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting | {
"line": 133,
"column": 6
} | {
"line": 133,
"column": 23
} | {
"line": 133,
"column": 24
} | [
{
"pp": "case refine_2.h₀\nC : Type u\ninst✝ : Category.{v, u} C\nX₃ Y₁ Y₂ Y₃ : C\ng₁ : Y₁ ⟶ Y₂\ng₂ : Y₂ ⟶ Y₃\ni₃ : X₃ ⟶ Y₃\nt₂ : PullbackCone g₂ i₃\ni₂ : t₂.pt ⟶ Y₂\nt₁ : PullbackCone g₁ i₂\nhi₂ : i₂ = t₂.fst\nH : IsLimit t₂\nH' : IsLimit (t₂.pasteHoriz t₁ hi₂)\ns : PullbackCone g₁ i₂\nl : s.pt ⟶ (t₂.pasteHori... | [
"case refine_2.h₀\nC : Type u\ninst✝ : Category.{v, u} C\nX₃ Y₁ Y₂ Y₃ : C\ng₁ : Y₁ ⟶ Y₂\ng₂ : Y₂ ⟶ Y₃\ni₃ : X₃ ⟶ Y₃\nt₂ : PullbackCone g₂ i₃\ni₂ : t₂.pt ⟶ Y₂\nt₁ : PullbackCone g₁ i₂\nhi₂ : i₂ = t₂.fst\nH : IsLimit t₂\nH' : IsLimit (t₂.pasteHoriz t₁ hi₂)\ns : PullbackCone g₁ i₂\nl : s.pt ⟶ (t₂.pasteHoriz t₁ hi₂).pt... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting | {
"line": 134,
"column": 6
} | {
"line": 134,
"column": 25
} | {
"line": 134,
"column": 26
} | [
{
"pp": "case refine_2.h₁\nC : Type u\ninst✝ : Category.{v, u} C\nX₃ Y₁ Y₂ Y₃ : C\ng₁ : Y₁ ⟶ Y₂\ng₂ : Y₂ ⟶ Y₃\ni₃ : X₃ ⟶ Y₃\nt₂ : PullbackCone g₂ i₃\ni₂ : t₂.pt ⟶ Y₂\nt₁ : PullbackCone g₁ i₂\nhi₂ : i₂ = t₂.fst\nH : IsLimit t₂\nH' : IsLimit (t₂.pasteHoriz t₁ hi₂)\ns : PullbackCone g₁ i₂\nl : s.pt ⟶ (t₂.pasteHori... | [
"case refine_2.h₁\nC : Type u\ninst✝ : Category.{v, u} C\nX₃ Y₁ Y₂ Y₃ : C\ng₁ : Y₁ ⟶ Y₂\ng₂ : Y₂ ⟶ Y₃\ni₃ : X₃ ⟶ Y₃\nt₂ : PullbackCone g₂ i₃\ni₂ : t₂.pt ⟶ Y₂\nt₁ : PullbackCone g₁ i₂\nhi₂ : i₂ = t₂.fst\nH : IsLimit t₂\nH' : IsLimit (t₂.pasteHoriz t₁ hi₂)\ns : PullbackCone g₁ i₂\nl : s.pt ⟶ (t₂.pasteHoriz t₁ hi₂).pt... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | {
"line": 352,
"column": 8
} | {
"line": 352,
"column": 19
} | {
"line": 352,
"column": 20
} | [
{
"pp": "case refine_3.h₁\nC : Type u₁\ninst✝² : Category.{v₁, u₁} C\nA B : C\nf : A ⟶ B\nX : C\ninst✝¹ : HasBinaryProduct A X\ninst✝ : HasBinaryProduct B X\ns : PullbackCone f prod.fst\nm : s.pt ⟶ A ⨯ X\nh₁ : m ≫ prod.fst = s.fst\nh₂ : m ≫ prod.map f (𝟙 X) = s.snd\n⊢ m ≫ prod.fst = prod.lift s.fst (s.snd ≫ pr... | [
"case refine_3.h₁\nC : Type u₁\ninst✝² : Category.{v₁, u₁} C\nA B : C\nf : A ⟶ B\nX : C\ninst✝¹ : HasBinaryProduct A X\ninst✝ : HasBinaryProduct B X\ns : PullbackCone f prod.fst\nm : s.pt ⟶ A ⨯ X\nh₁ : m ≫ prod.fst = s.fst\nh₂ : m ≫ prod.map f (𝟙 X) = s.snd\n⊢ m ≫ prod.fst = s.fst"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting | {
"line": 292,
"column": 49
} | {
"line": 292,
"column": 67
} | {
"line": 292,
"column": 68
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nX₁ X₂ X₃ Y₁ : C\nf₁ : X₁ ⟶ X₂\nf₂ : X₂ ⟶ X₃\ni₁ : X₁ ⟶ Y₁\nt₁ : PushoutCocone i₁ f₁\ni₂ : X₂ ⟶ t₁.pt\nt₂ : PushoutCocone «i₂» f₂\nhi₂ : «i₂» = t₁.inr\nH : IsColimit t₁\nH' : IsColimit t₂\ns : PushoutCocone i₁ (f₁ ≫ f₂)\nl₁ : t₁.pt ⟶ s.pt\nhl₁ : t₁.inl ≫ l₁ = s.inl... | [
"C : Type u\ninst✝ : Category.{v, u} C\nX₁ X₂ X₃ Y₁ : C\nf₁ : X₁ ⟶ X₂\nf₂ : X₂ ⟶ X₃\ni₁ : X₁ ⟶ Y₁\nt₁ : PushoutCocone i₁ f₁\ni₂ : X₂ ⟶ t₁.pt\nt₂ : PushoutCocone «i₂» f₂\nhi₂ : «i₂» = t₁.inr\nH : IsColimit t₁\nH' : IsColimit t₂\ns : PushoutCocone i₁ (f₁ ≫ f₂)\nl₁ : t₁.pt ⟶ s.pt\nhl₁ : t₁.inl ≫ l₁ = s.inl\nhl₁' : t₁.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting | {
"line": 326,
"column": 6
} | {
"line": 326,
"column": 25
} | {
"line": 326,
"column": 26
} | [
{
"pp": "case refine_2.h₀\nC : Type u\ninst✝ : Category.{v, u} C\nX₁ X₂ X₃ Y₁ : C\nf₁ : X₁ ⟶ X₂\nf₂ : X₂ ⟶ X₃\ni₁ : X₁ ⟶ Y₁\nt₁ : PushoutCocone i₁ f₁\ni₂ : X₂ ⟶ t₁.pt\nt₂ : PushoutCocone «i₂» f₂\nhi₂ : «i₂» = t₁.inr\nH : IsColimit t₁\nH' : IsColimit (t₁.pasteHoriz t₂ hi₂)\ns : PushoutCocone «i₂» f₂\nl : (t₁.pas... | [
"case refine_2.h₀\nC : Type u\ninst✝ : Category.{v, u} C\nX₁ X₂ X₃ Y₁ : C\nf₁ : X₁ ⟶ X₂\nf₂ : X₂ ⟶ X₃\ni₁ : X₁ ⟶ Y₁\nt₁ : PushoutCocone i₁ f₁\ni₂ : X₂ ⟶ t₁.pt\nt₂ : PushoutCocone «i₂» f₂\nhi₂ : «i₂» = t₁.inr\nH : IsColimit t₁\nH' : IsColimit (t₁.pasteHoriz t₂ hi₂)\ns : PushoutCocone «i₂» f₂\nl : (t₁.pasteHoriz t₂ h... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting | {
"line": 327,
"column": 6
} | {
"line": 327,
"column": 25
} | {
"line": 327,
"column": 26
} | [
{
"pp": "case refine_2.h₁\nC : Type u\ninst✝ : Category.{v, u} C\nX₁ X₂ X₃ Y₁ : C\nf₁ : X₁ ⟶ X₂\nf₂ : X₂ ⟶ X₃\ni₁ : X₁ ⟶ Y₁\nt₁ : PushoutCocone i₁ f₁\ni₂ : X₂ ⟶ t₁.pt\nt₂ : PushoutCocone «i₂» f₂\nhi₂ : «i₂» = t₁.inr\nH : IsColimit t₁\nH' : IsColimit (t₁.pasteHoriz t₂ hi₂)\ns : PushoutCocone «i₂» f₂\nl : (t₁.pas... | [
"case refine_2.h₁\nC : Type u\ninst✝ : Category.{v, u} C\nX₁ X₂ X₃ Y₁ : C\nf₁ : X₁ ⟶ X₂\nf₂ : X₂ ⟶ X₃\ni₁ : X₁ ⟶ Y₁\nt₁ : PushoutCocone i₁ f₁\ni₂ : X₂ ⟶ t₁.pt\nt₂ : PushoutCocone «i₂» f₂\nhi₂ : «i₂» = t₁.inr\nH : IsColimit t₁\nH' : IsColimit (t₁.pasteHoriz t₂ hi₂)\ns : PushoutCocone «i₂» f₂\nl : (t₁.pasteHoriz t₂ h... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | {
"line": 734,
"column": 8
} | {
"line": 734,
"column": 19
} | {
"line": 734,
"column": 20
} | [
{
"pp": "case refine_3.h₁\nC : Type u₁\ninst✝² : Category.{v₁, u₁} C\nA B : C\nf : A ⟶ B\nX : C\ninst✝¹ : HasBinaryCoproduct A X\ninst✝ : HasBinaryCoproduct B X\ns : PushoutCocone coprod.inl f\nm : B ⨿ X ⟶ s.pt\nh₁ : coprod.map f (𝟙 X) ≫ m = s.inl\nh₂ : coprod.inl ≫ m = s.inr\n⊢ coprod.inl ≫ m = coprod.inl ≫ c... | [
"case refine_3.h₁\nC : Type u₁\ninst✝² : Category.{v₁, u₁} C\nA B : C\nf : A ⟶ B\nX : C\ninst✝¹ : HasBinaryCoproduct A X\ninst✝ : HasBinaryCoproduct B X\ns : PushoutCocone coprod.inl f\nm : B ⨿ X ⟶ s.pt\nh₁ : coprod.map f (𝟙 X) ≫ m = s.inl\nh₂ : coprod.inl ≫ m = s.inr\n⊢ coprod.inl ≫ m = s.inr"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | {
"line": 837,
"column": 36
} | {
"line": 837,
"column": 65
} | {
"line": 837,
"column": 66
} | [
{
"pp": "C : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝² : Category.{v₂, u₂} D\nF : C ⥤ D\nW X Y Z : C\nf : W ⟶ X\ng : W ⟶ Y\nh : X ⟶ Z\ni : Y ⟶ Z\ninst✝¹ : ReflectsLimit (cospan h i) F\ninst✝ : F.Faithful\nH : IsPullback (F.map f) (F.map g) (F.map h) (F.map i)\n⊢ F.map (f ≫ h) = F.map (g ≫ i)",
... | [
"C : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝² : Category.{v₂, u₂} D\nF : C ⥤ D\nW X Y Z : C\nf : W ⟶ X\ng : W ⟶ Y\nh : X ⟶ Z\ni : Y ⟶ Z\ninst✝¹ : ReflectsLimit (cospan h i) F\ninst✝ : F.Faithful\nH : IsPullback (F.map f) (F.map g) (F.map h) (F.map i)\n⊢ F.map f ≫ F.map h = F.map g ≫ F.map i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.FreeCommRing | {
"line": 269,
"column": 2
} | {
"line": 269,
"column": 96
} | {
"line": 271,
"column": 0
} | [
{
"pp": "case neg\nα : Type u\np : α\ns : Set α\nhps : (of p).IsSupported s\nthis✝ : DecidablePred fun x ↦ x ∈ s\nh : p ∉ s\nw : ℤ\nH : X = C ↑w\nthis : X.coeff 1 = (C w).coeff 1\n⊢ 1 = 0",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"Polynomial.C",
"NonAssocSemiring.toAddCom... | [] | rwa [Polynomial.coeff_C, if_neg (one_ne_zero : 1 ≠ 0), Polynomial.coeff_X, if_pos rfl] at this | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticRwa___1 | Lean.Parser.Tactic.tacticRwa__ |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | {
"line": 855,
"column": 36
} | {
"line": 855,
"column": 65
} | {
"line": 855,
"column": 66
} | [
{
"pp": "C : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝² : Category.{v₂, u₂} D\nF : C ⥤ D\nW X Y Z : C\nf : W ⟶ X\ng : W ⟶ Y\nh : X ⟶ Z\ni : Y ⟶ Z\ninst✝¹ : ReflectsColimit (span f g) F\ninst✝ : F.Faithful\nH : IsPushout (F.map f) (F.map g) (F.map h) (F.map i)\n⊢ F.map (f ≫ h) = F.map (g ≫ i)",
... | [
"C : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝² : Category.{v₂, u₂} D\nF : C ⥤ D\nW X Y Z : C\nf : W ⟶ X\ng : W ⟶ Y\nh : X ⟶ Z\ni : Y ⟶ Z\ninst✝¹ : ReflectsColimit (span f g) F\ninst✝ : F.Faithful\nH : IsPushout (F.map f) (F.map g) (F.map h) (F.map i)\n⊢ F.map f ≫ F.map h = F.map g ≫ F.map i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Localization.BaseChange | {
"line": 201,
"column": 4
} | {
"line": 201,
"column": 15
} | {
"line": 201,
"column": 16
} | [
{
"pp": "R : Type u_1\ninst✝⁶ : CommSemiring R\nA : Type u_2\ninst✝⁵ : CommSemiring A\ninst✝⁴ : Algebra R A\nT : Type u_5\ninst✝³ : CommSemiring T\ninst✝² : Algebra R T\ninst✝¹ : Algebra A T\ninst✝ : IsScalarTower R A T\nH : Function.Bijective ⇑(algebraMap A T)\n⊢ algebraMapSubmonoid T (algebraMapSubmonoid A (I... | [
"R : Type u_1\ninst✝⁶ : CommSemiring R\nA : Type u_2\ninst✝⁵ : CommSemiring A\ninst✝⁴ : Algebra R A\nT : Type u_5\ninst✝³ : CommSemiring T\ninst✝² : Algebra R T\ninst✝¹ : Algebra A T\ninst✝ : IsScalarTower R A T\nH : Function.Bijective ⇑(algebraMap A T)\n⊢ algebraMapSubmonoid T (IsUnit.submonoid R) ≤ IsUnit.submono... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Localization.BaseChange | {
"line": 220,
"column": 2
} | {
"line": 220,
"column": 57
} | {
"line": 221,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝¹⁸ : CommSemiring R\nS : Submonoid R\nA : Type u_2\ninst✝¹⁷ : CommSemiring A\ninst✝¹⁶ : Algebra R A\ninst✝¹⁵ : IsLocalization S A\nM : Type u_3\ninst✝¹⁴ : AddCommMonoid M\ninst✝¹³ : Module R M\nM' : Type u_4\ninst✝¹² : AddCommMonoid M'\ninst✝¹¹ : Module R M'\ninst✝¹⁰ : Module A M'\ni... | [
"R : Type u_1\ninst✝¹⁸ : CommSemiring R\nS : Submonoid R\nA : Type u_2\ninst✝¹⁷ : CommSemiring A\ninst✝¹⁶ : Algebra R A\ninst✝¹⁵ : IsLocalization S A\nM : Type u_3\ninst✝¹⁴ : AddCommMonoid M\ninst✝¹³ : Module R M\nM' : Type u_4\ninst✝¹² : AddCommMonoid M'\ninst✝¹¹ : Module R M'\ninst✝¹⁰ : Module A M'\ninst✝⁹ : IsSc... | apply (finsuppRight R R (Localization S) M α).injective | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | {
"line": 915,
"column": 4
} | {
"line": 915,
"column": 15
} | {
"line": 915,
"column": 16
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nF₁ F₂ F₃ F₄ : C ⥤ D\nf₁ : F₁ ⟶ F₂\nf₂ : F₁ ⟶ F₃\nf₃ : F₂ ⟶ F₄\nf₄ : F₃ ⟶ F₄\nh : ∀ (X : C), IsPullback (f₁.app X) (f₂.app X) (f₃.app X) (f₄.app X)\nX : C\n⊢ (f₁ ≫ f₃).app X = (f₂ ≫ f₄).app X",
"ppTerm": "?m.122",
... | [
"C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nF₁ F₂ F₃ F₄ : C ⥤ D\nf₁ : F₁ ⟶ F₂\nf₂ : F₁ ⟶ F₃\nf₃ : F₂ ⟶ F₄\nf₄ : F₃ ⟶ F₄\nh : ∀ (X : C), IsPullback (f₁.app X) (f₂.app X) (f₃.app X) (f₄.app X)\nX : C\n⊢ f₁.app X ≫ f₃.app X = f₂.app X ≫ f₄.app X"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | {
"line": 935,
"column": 4
} | {
"line": 935,
"column": 15
} | {
"line": 935,
"column": 16
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nF₁ F₂ F₃ F₄ : C ⥤ D\nf₁ : F₁ ⟶ F₂\nf₂ : F₁ ⟶ F₃\nf₃ : F₂ ⟶ F₄\nf₄ : F₃ ⟶ F₄\nh : ∀ (X : C), IsPushout (f₁.app X) (f₂.app X) (f₃.app X) (f₄.app X)\nX : C\n⊢ (f₁ ≫ f₃).app X = (f₂ ≫ f₄).app X",
"ppTerm": "?m.122",
... | [
"C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nF₁ F₂ F₃ F₄ : C ⥤ D\nf₁ : F₁ ⟶ F₂\nf₂ : F₁ ⟶ F₃\nf₃ : F₂ ⟶ F₄\nf₄ : F₃ ⟶ F₄\nh : ∀ (X : C), IsPushout (f₁.app X) (f₂.app X) (f₃.app X) (f₄.app X)\nX : C\n⊢ f₁.app X ≫ f₃.app X = f₂.app X ≫ f₄.app X"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | {
"line": 1025,
"column": 8
} | {
"line": 1025,
"column": 19
} | {
"line": 1025,
"column": 20
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nX Y Z : C\nf : X ⟶ Z\ng : Y ⟶ Z\ninst✝ : HasPullbacksAlong g\nP : C\np : P ⟶ X\ne : Over.mk p ≅ Over.mk (pullback.fst f g)\n⊢ ((Over.forget X).mapIso e).hom ≫ pullback.fst f g = p ≫ (Iso.refl X).hom",
"ppTerm": "?m.94",
"assigned": true,
"usedConst... | [
"C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nX Y Z : C\nf : X ⟶ Z\ng : Y ⟶ Z\ninst✝ : HasPullbacksAlong g\nP : C\np : P ⟶ X\ne : Over.mk p ≅ Over.mk (pullback.fst f g)\n⊢ Over.Hom.left e.hom ≫ pullback.fst f g = p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | {
"line": 1063,
"column": 2
} | {
"line": 1063,
"column": 13
} | {
"line": 1063,
"column": 14
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nX Y Z Z' : C\nf : X ⟶ Z\ng : Y ⟶ Z'\ni : Z ⟶ Z'\ninst✝¹ : IsIso i\ninst✝ : HasPullback (f ≫ i) g\n⊢ HasPullback f (g ≫ inv i)",
"ppTerm": "?m.36",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nX Y Z Z' : C\nf : X ⟶ Z\ng : Y ⟶ Z'\ni : Z ⟶ Z'\ninst✝¹ : IsIso i\ninst✝ : HasPullback (f ≫ i) g\n⊢ HasPullback f (g ≫ inv i)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.LocalizedModule.Basic | {
"line": 124,
"column": 26
} | {
"line": 124,
"column": 83
} | {
"line": 124,
"column": 84
} | [
{
"pp": "R : Type u\ninst✝⁸ : CommSemiring R\nS : Submonoid R\nM : Type v\ninst✝⁷ : AddCommMonoid M\ninst✝⁶ : Module R M\nT : Type u_1\ninst✝⁵ : CommSemiring T\ninst✝⁴ : Algebra R T\ninst✝³ : IsLocalization S T\nT' : Type u_2\ninst✝² : CommSemiring T'\ninst✝¹ : Algebra R T'\ninst✝ : IsLocalization S T'\nα : Typ... | [
"R : Type u\ninst✝⁸ : CommSemiring R\nS : Submonoid R\nM : Type v\ninst✝⁷ : AddCommMonoid M\ninst✝⁶ : Module R M\nT : Type u_1\ninst✝⁵ : CommSemiring T\ninst✝⁴ : Algebra R T\ninst✝³ : IsLocalization S T\nT' : Type u_2\ninst✝² : CommSemiring T'\ninst✝¹ : Algebra R T'\ninst✝ : IsLocalization S T'\nα : Type u_3\nx : L... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | {
"line": 1068,
"column": 37
} | {
"line": 1068,
"column": 48
} | {
"line": 1068,
"column": 49
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nX Y Z Z' : C\nf : X ⟶ Z\ng : Y ⟶ Z'\ni : Z ⟶ Z'\ninst✝ : IsIso i\nh : HasPullback f (g ≫ inv i)\n⊢ HasPullback (f ≫ i) g",
"ppTerm": "?m.42",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nX Y Z Z' : C\nf : X ⟶ Z\ng : Y ⟶ Z'\ni : Z ⟶ Z'\ninst✝ : IsIso i\nh : HasPullback f (g ≫ inv i)\n⊢ HasPullback (f ≫ i) g"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.LocalizedModule.Basic | {
"line": 134,
"column": 29
} | {
"line": 134,
"column": 86
} | {
"line": 134,
"column": 87
} | [
{
"pp": "R : Type u\ninst✝⁸ : CommSemiring R\nS : Submonoid R\nM : Type v\ninst✝⁷ : AddCommMonoid M\ninst✝⁶ : Module R M\nT : Type u_1\ninst✝⁵ : CommSemiring T\ninst✝⁴ : Algebra R T\ninst✝³ : IsLocalization S T\nT' : Type u_2\ninst✝² : CommSemiring T'\ninst✝¹ : Algebra R T'\ninst✝ : IsLocalization S T'\nα : Typ... | [
"R : Type u\ninst✝⁸ : CommSemiring R\nS : Submonoid R\nM : Type v\ninst✝⁷ : AddCommMonoid M\ninst✝⁶ : Module R M\nT : Type u_1\ninst✝⁵ : CommSemiring T\ninst✝⁴ : Algebra R T\ninst✝³ : IsLocalization S T\nT' : Type u_2\ninst✝² : CommSemiring T'\ninst✝¹ : Algebra R T'\ninst✝ : IsLocalization S T'\nα : Type u_3\nx y :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | {
"line": 1086,
"column": 2
} | {
"line": 1086,
"column": 13
} | {
"line": 1086,
"column": 14
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nX Y Z Z' : C\nf : Z ⟶ X\ng : Z' ⟶ Y\ni : Z' ⟶ Z\ninst✝¹ : IsIso i\ninst✝ : HasPushout (i ≫ f) g\n⊢ HasPushout f (inv i ≫ g)",
"ppTerm": "?m.36",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nX Y Z Z' : C\nf : Z ⟶ X\ng : Z' ⟶ Y\ni : Z' ⟶ Z\ninst✝¹ : IsIso i\ninst✝ : HasPushout (i ≫ f) g\n⊢ HasPushout f (inv i ≫ g)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | {
"line": 1091,
"column": 37
} | {
"line": 1091,
"column": 48
} | {
"line": 1091,
"column": 49
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nX Y Z Z' : C\nf : Z ⟶ X\ng : Z' ⟶ Y\ni : Z' ⟶ Z\ninst✝ : IsIso i\nh : HasPushout f (inv i ≫ g)\n⊢ HasPushout (i ≫ f) g",
"ppTerm": "?m.42",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nX Y Z Z' : C\nf : Z ⟶ X\ng : Z' ⟶ Y\ni : Z' ⟶ Z\ninst✝ : IsIso i\nh : HasPushout f (inv i ≫ g)\n⊢ HasPushout (i ≫ f) g"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.LocalizedModule.Basic | {
"line": 342,
"column": 55
} | {
"line": 342,
"column": 88
} | {
"line": 342,
"column": 88
} | [
{
"pp": "R : Type u\ninst✝⁵ : CommSemiring R\nS : Submonoid R\nM : Type v\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nT : Type u_1\ninst✝² : CommSemiring T\ninst✝¹ : Algebra R T\ninst✝ : IsLocalization S T\nx : T\nm : M\ns : ↥S\nn : M\nt : ↥S\n⊢ x • mk (t • m + s • n) (s * t) = IsLocalization.mk' T ?m.144 ?... | [
"R : Type u\ninst✝⁵ : CommSemiring R\nS : Submonoid R\nM : Type v\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nT : Type u_1\ninst✝² : CommSemiring T\ninst✝¹ : Algebra R T\ninst✝ : IsLocalization S T\nx : T\nm : M\ns : ↥S\nn : M\nt : ↥S\n⊢ x • mk (t • m + s • n) (s * t) = ?m.167 • ?m.147",
"R : Type u\ninst✝⁵ :... | IsLocalization.mk'_sec (M := S) T | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Monad.Products | {
"line": 82,
"column": 68
} | {
"line": 82,
"column": 79
} | {
"line": 82,
"column": 80
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nX : C\ninst✝ : HasBinaryProducts C\nA : (prodComonad X).Coalgebra\n⊢ (((𝟭 (prodComonad X).Coalgebra).obj A).a ≫\n (prodComonad X).map (Iso.refl ((𝟭 (prodComonad X).Coalgebra).obj A).A).hom) ≫\n prod.snd =\n ((Iso.refl ((𝟭 (prodComonad X).Coalgeb... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nX : C\ninst✝ : HasBinaryProducts C\nA : (prodComonad X).Coalgebra\n⊢ A.a ≫ prod.snd = 𝟙 A.A"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monad.Products | {
"line": 130,
"column": 67
} | {
"line": 130,
"column": 78
} | {
"line": 130,
"column": 79
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nX : C\ninst✝ : HasBinaryCoproducts C\nA : (coprodMonad X).Algebra\n⊢ coprod.inr ≫\n (coprodMonad X).map (Iso.refl ((𝟭 (coprodMonad X).Algebra).obj A).A).hom ≫\n ((algebraToUnder X ⋙ underToAlgebra X).obj A).a =\n coprod.inr ≫ ((𝟭 (coprodMonad X).... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nX : C\ninst✝ : HasBinaryCoproducts C\nA : (coprodMonad X).Algebra\n⊢ 𝟙 A.A = coprod.inr ≫ A.a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.LocalizedModule.Basic | {
"line": 587,
"column": 29
} | {
"line": 587,
"column": 40
} | {
"line": 587,
"column": 41
} | [
{
"pp": "R : Type u_1\ninst✝¹¹ : CommSemiring R\nS : Submonoid R\nM : Type u_2\nM' : Type u_3\nM'' : Type u_4\ninst✝¹⁰ : AddCommMonoid M\ninst✝⁹ : AddCommMonoid M'\ninst✝⁸ : AddCommMonoid M''\nA : Type u_5\ninst✝⁷ : CommSemiring A\ninst✝⁶ : Algebra R A\ninst✝⁵ : Module A M'\ninst✝⁴ : IsLocalization S A\ninst✝³ ... | [
"R : Type u_1\ninst✝¹¹ : CommSemiring R\nS : Submonoid R\nM : Type u_2\nM' : Type u_3\nM'' : Type u_4\ninst✝¹⁰ : AddCommMonoid M\ninst✝⁹ : AddCommMonoid M'\ninst✝⁸ : AddCommMonoid M''\nA : Type u_5\ninst✝⁷ : CommSemiring A\ninst✝⁶ : Algebra R A\ninst✝⁵ : Module A M'\ninst✝⁴ : IsLocalization S A\ninst✝³ : Module R M... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.LocalizedModule.Basic | {
"line": 591,
"column": 17
} | {
"line": 592,
"column": 11
} | {
"line": 592,
"column": 12
} | [
{
"pp": "R : Type u_1\ninst✝¹¹ : CommSemiring R\nS : Submonoid R\nM : Type u_2\nM' : Type u_3\nM'' : Type u_4\ninst✝¹⁰ : AddCommMonoid M\ninst✝⁹ : AddCommMonoid M'\ninst✝⁸ : AddCommMonoid M''\nA : Type u_5\ninst✝⁷ : CommSemiring A\ninst✝⁶ : Algebra R A\ninst✝⁵ : Module A M'\ninst✝⁴ : IsLocalization S A\ninst✝³ ... | [
"R : Type u_1\ninst✝¹¹ : CommSemiring R\nS : Submonoid R\nM : Type u_2\nM' : Type u_3\nM'' : Type u_4\ninst✝¹⁰ : AddCommMonoid M\ninst✝⁹ : AddCommMonoid M'\ninst✝⁸ : AddCommMonoid M''\nA : Type u_5\ninst✝⁷ : CommSemiring A\ninst✝⁶ : Algebra R A\ninst✝⁵ : Module A M'\ninst✝⁴ : IsLocalization S A\ninst✝³ : Module R M... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Comma.Over.Pullback | {
"line": 88,
"column": 14
} | {
"line": 88,
"column": 25
} | {
"line": 88,
"column": 26
} | [
{
"pp": "case h₁\nC : Type u\ninst✝² : Category.{v, u} C\nX✝ Y✝ : C\nD : Type u₂\ninst✝¹ : Category.{v₂, u₂} D\nX Y : C\nf : X ⟶ Y\ninst✝ : HasPullbacksAlong f\nx : Over X\ny : Over Y\nv : x ⟶ (pullback f).obj y\n⊢ pullback.lift (Hom.left v ≫ pullback.fst y.hom f) x.hom ⋯ ≫ pullback.snd y.hom f = Hom.left v ≫ p... | [
"case h₁\nC : Type u\ninst✝² : Category.{v, u} C\nX✝ Y✝ : C\nD : Type u₂\ninst✝¹ : Category.{v₂, u₂} D\nX Y : C\nf : X ⟶ Y\ninst✝ : HasPullbacksAlong f\nx : Over X\ny : Over Y\nv : x ⟶ (pullback f).obj y\n⊢ x.hom = Hom.left v ≫ pullback.snd y.hom f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Comma.Over.Pullback | {
"line": 231,
"column": 10
} | {
"line": 231,
"column": 21
} | {
"line": 231,
"column": 22
} | [
{
"pp": "case h₁\nC : Type u\ninst✝² : Category.{v, u} C\nX✝ Y✝ : C\nD : Type u₂\ninst✝¹ : Category.{v₂, u₂} D\nX Y : C\nf : X ⟶ Y\ninst✝ : HasPushoutsAlong f\nx : Under X\ny : Under Y\nu : (pushout f).obj x ⟶ y\n⊢ pushout.inr x.hom f ≫ pushout.desc (pushout.inl x.hom f ≫ Hom.right u) y.hom ⋯ = pushout.inr x.ho... | [
"case h₁\nC : Type u\ninst✝² : Category.{v, u} C\nX✝ Y✝ : C\nD : Type u₂\ninst✝¹ : Category.{v₂, u₂} D\nX Y : C\nf : X ⟶ Y\ninst✝ : HasPushoutsAlong f\nx : Under X\ny : Under Y\nu : (pushout f).obj x ⟶ y\n⊢ y.hom = pushout.inr x.hom f ≫ Hom.right u"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.LocalizedModule.Basic | {
"line": 738,
"column": 25
} | {
"line": 738,
"column": 61
} | {
"line": 738,
"column": 62
} | [
{
"pp": "R : Type u_1\ninst✝¹¹ : CommSemiring R\nS : Submonoid R\nM : Type u_2\nM' : Type u_3\nM'' : Type u_4\ninst✝¹⁰ : AddCommMonoid M\ninst✝⁹ : AddCommMonoid M'\ninst✝⁸ : AddCommMonoid M''\nA : Type u_5\ninst✝⁷ : CommSemiring A\ninst✝⁶ : Algebra R A\ninst✝⁵ : Module A M'\ninst✝⁴ : IsLocalization S A\ninst✝³ ... | [
"R : Type u_1\ninst✝¹¹ : CommSemiring R\nS : Submonoid R\nM : Type u_2\nM' : Type u_3\nM'' : Type u_4\ninst✝¹⁰ : AddCommMonoid M\ninst✝⁹ : AddCommMonoid M'\ninst✝⁸ : AddCommMonoid M''\nA : Type u_5\ninst✝⁷ : CommSemiring A\ninst✝⁶ : Algebra R A\ninst✝⁵ : Module A M'\ninst✝⁴ : IsLocalization S A\ninst✝³ : Module R M... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.LocalizedModule.Basic | {
"line": 751,
"column": 29
} | {
"line": 751,
"column": 61
} | {
"line": 751,
"column": 62
} | [
{
"pp": "R : Type u_1\ninst✝¹⁰ : CommSemiring R\nM : Type u_2\ninst✝⁹ : AddCommMonoid M\nA : Type u_5\ninst✝⁸ : CommSemiring A\ninst✝⁷ : Algebra R A\ninst✝⁶ : Module R M\nS : Submonoid R\ninst✝⁵ : Module A M\nN : Type u_6\ninst✝⁴ : AddCommMonoid N\ninst✝³ : Module R N\ninst✝² : Module A N\ninst✝¹ : IsScalarTowe... | [
"R : Type u_1\ninst✝¹⁰ : CommSemiring R\nM : Type u_2\ninst✝⁹ : AddCommMonoid M\nA : Type u_5\ninst✝⁸ : CommSemiring A\ninst✝⁷ : Algebra R A\ninst✝⁶ : Module R M\nS : Submonoid R\ninst✝⁵ : Module A M\nN : Type u_6\ninst✝⁴ : AddCommMonoid N\ninst✝³ : Module R N\ninst✝² : Module A N\ninst✝¹ : IsScalarTower R A M\nins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.LocalizedModule.Basic | {
"line": 754,
"column": 23
} | {
"line": 754,
"column": 55
} | {
"line": 754,
"column": 56
} | [
{
"pp": "R : Type u_1\ninst✝¹⁰ : CommSemiring R\nM : Type u_2\ninst✝⁹ : AddCommMonoid M\nA : Type u_5\ninst✝⁸ : CommSemiring A\ninst✝⁷ : Algebra R A\ninst✝⁶ : Module R M\nS : Submonoid R\ninst✝⁵ : Module A M\nN : Type u_6\ninst✝⁴ : AddCommMonoid N\ninst✝³ : Module R N\ninst✝² : Module A N\ninst✝¹ : IsScalarTowe... | [
"R : Type u_1\ninst✝¹⁰ : CommSemiring R\nM : Type u_2\ninst✝⁹ : AddCommMonoid M\nA : Type u_5\ninst✝⁸ : CommSemiring A\ninst✝⁷ : Algebra R A\ninst✝⁶ : Module R M\nS : Submonoid R\ninst✝⁵ : Module A M\nN : Type u_6\ninst✝⁴ : AddCommMonoid N\ninst✝³ : Module R N\ninst✝² : Module A N\ninst✝¹ : IsScalarTower R A M\nins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.LocalizedModule.Basic | {
"line": 776,
"column": 37
} | {
"line": 776,
"column": 69
} | {
"line": 776,
"column": 70
} | [
{
"pp": "R : Type u_1\ninst✝¹¹ : CommSemiring R\nM : Type u_2\ninst✝¹⁰ : AddCommMonoid M\nA : Type u_5\ninst✝⁹ : CommSemiring A\ninst✝⁸ : Algebra R A\ninst✝⁷ : Module R M\nS : Submonoid R\nN : Type u_6\ninst✝⁶ : AddCommMonoid N\ninst✝⁵ : Module R N\ninst✝⁴ : Module A M\ninst✝³ : Module A N\ninst✝² : IsScalarTow... | [
"R : Type u_1\ninst✝¹¹ : CommSemiring R\nM : Type u_2\ninst✝¹⁰ : AddCommMonoid M\nA : Type u_5\ninst✝⁹ : CommSemiring A\ninst✝⁸ : Algebra R A\ninst✝⁷ : Module R M\nS : Submonoid R\nN : Type u_6\ninst✝⁶ : AddCommMonoid N\ninst✝⁵ : Module R N\ninst✝⁴ : Module A M\ninst✝³ : Module A N\ninst✝² : IsScalarTower R A M\nin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Category.Ring.Constructions | {
"line": 397,
"column": 6
} | {
"line": 397,
"column": 17
} | {
"line": 397,
"column": 18
} | [
{
"pp": "A B : CommRingCat\nf g : A ⟶ B\nx : ↑A\ne : x ∈ (Hom.hom f).eqLocus (Hom.hom g)\n⊢ (Hom.hom (ofHom ((Hom.hom f).eqLocus (Hom.hom g)).subtype ≫ f)) ⟨x, e⟩ =\n (Hom.hom (ofHom ((Hom.hom f).eqLocus (Hom.hom g)).subtype ≫ g)) ⟨x, e⟩",
"ppTerm": "?m.51",
"assigned": true,
"usedConstants": [
... | [
"A B : CommRingCat\nf g : A ⟶ B\nx : ↑A\ne : x ∈ (Hom.hom f).eqLocus (Hom.hom g)\n⊢ (Hom.hom f) x = (Hom.hom g) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Comma | {
"line": 242,
"column": 2
} | {
"line": 244,
"column": 22
} | {
"line": 246,
"column": 0
} | [
{
"pp": "J : Type w\ninst✝³ : Category.{w', w} J\nA : Type u₁\ninst✝² : Category.{v₁, u₁} A\nB : Type u₂\ninst✝¹ : Category.{v₂, u₂} B\nT : Type u₃\ninst✝ : Category.{v₃, u₃} T\nX : T\nG : A ⥤ T\nF : J ⥤ StructuredArrow X G\ni₁ : HasLimit (F ⋙ proj X G)\ni₂ : PreservesLimit (F ⋙ proj X G) G\n⊢ HasLimit F",
... | [] | haveI : HasLimit (F ⋙ Comma.snd (Functor.fromPUnit X) G) := i₁
haveI : PreservesLimit (F ⋙ Comma.snd (Functor.fromPUnit X) G) _ := i₂
apply Comma.hasLimit | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Limits.Comma | {
"line": 242,
"column": 2
} | {
"line": 244,
"column": 22
} | {
"line": 246,
"column": 0
} | [
{
"pp": "J : Type w\ninst✝³ : Category.{w', w} J\nA : Type u₁\ninst✝² : Category.{v₁, u₁} A\nB : Type u₂\ninst✝¹ : Category.{v₂, u₂} B\nT : Type u₃\ninst✝ : Category.{v₃, u₃} T\nX : T\nG : A ⥤ T\nF : J ⥤ StructuredArrow X G\ni₁ : HasLimit (F ⋙ proj X G)\ni₂ : PreservesLimit (F ⋙ proj X G) G\n⊢ HasLimit F",
... | [] | haveI : HasLimit (F ⋙ Comma.snd (Functor.fromPUnit X) G) := i₁
haveI : PreservesLimit (F ⋙ Comma.snd (Functor.fromPUnit X) G) _ := i₂
apply Comma.hasLimit | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Category.Ring.Constructions | {
"line": 423,
"column": 4
} | {
"line": 423,
"column": 39
} | {
"line": 425,
"column": 0
} | [
{
"pp": "case one\nA B : CommRingCat\nf g : A ⟶ B\nF : WalkingParallelPair ⥤ CommRingCat\nx : ↑(limit.cone F).pt\nhx : IsUnit ((ConcreteCategory.hom ((limit.cone F).π.app zero)) x)\n⊢ (ConcreteCategory.hom (limit.π F one)) x =\n (ConcreteCategory.hom (F.map left)) ((ConcreteCategory.hom (limit.π F zero)) x)"... | [] | exact (limit.w_apply F left x).symm | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Algebra.Category.Ring.Constructions | {
"line": 458,
"column": 6
} | {
"line": 458,
"column": 37
} | {
"line": 458,
"column": 38
} | [
{
"pp": "A B C : CommRingCat\nf : A ⟶ C\ng : B ⟶ C\nx : ↑A × ↑B\ne : x ∈ ((Hom.hom f).comp (RingHom.fst ↑A ↑B)).eqLocus ((Hom.hom g).comp (RingHom.snd ↑A ↑B))\n⊢ (Hom.hom\n (ofHom\n ((RingHom.fst ↑A ↑B).comp\n (((Hom.hom f).comp (RingHom.fst ↑A ↑B)).eqLocus ((Hom.hom g).comp (Ring... | [
"A B C : CommRingCat\nf : A ⟶ C\ng : B ⟶ C\nx : ↑A × ↑B\ne : x ∈ ((Hom.hom f).comp (RingHom.fst ↑A ↑B)).eqLocus ((Hom.hom g).comp (RingHom.snd ↑A ↑B))\n⊢ (Hom.hom f) x.1 = (Hom.hom g) x.2"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.LocalizedModule.Basic | {
"line": 1333,
"column": 8
} | {
"line": 1333,
"column": 40
} | {
"line": 1333,
"column": 41
} | [
{
"pp": "R : Type u_6\nS : Type u_7\nS' : Type u_8\ninst✝⁴ : CommSemiring R\ninst✝³ : Ring S\ninst✝² : Ring S'\ninst✝¹ : Algebra R S\ninst✝ : Algebra R S'\nM : Submonoid R\nf : S →ₐ[R] S'\nh₁ : ∀ x ∈ M, IsUnit ((algebraMap R S') x)\nh₂ : ∀ (y : S'), ∃ x, x.2 • y = f x.1\nh₃ : ∀ (x : S), f x = 0 → ∃ m, m • x = 0... | [
"R : Type u_6\nS : Type u_7\nS' : Type u_8\ninst✝⁴ : CommSemiring R\ninst✝³ : Ring S\ninst✝² : Ring S'\ninst✝¹ : Algebra R S\ninst✝ : Algebra R S'\nM : Submonoid R\nf : S →ₐ[R] S'\nh₁ : ∀ x ∈ M, IsUnit ((algebraMap R S') x)\nh₂ : ∀ (y : S'), ∃ x, x.2 • y = f x.1\nh₃ : ∀ (x : S), f x = 0 → ∃ m, m • x = 0\nx : S\nx✝ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.LocalizedModule.Basic | {
"line": 1373,
"column": 2
} | {
"line": 1373,
"column": 13
} | {
"line": 1373,
"column": 14
} | [
{
"pp": "R : Type u_6\nM : Type u_8\nM' : Type u_9\ninst✝⁵ : CommSemiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\ninst✝² : AddCommMonoid M'\ninst✝¹ : Module R M'\nS : Submonoid R\ng : M →ₗ[R] M'\ninst✝ : IsLocalizedModule S g\nm : M\n⊢ m ∈ g.ker ↔ ∃ r ∈ S, r • m = 0",
"ppTerm": "?m.161",
"assi... | [
"R : Type u_6\nM : Type u_8\nM' : Type u_9\ninst✝⁵ : CommSemiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\ninst✝² : AddCommMonoid M'\ninst✝¹ : Module R M'\nS : Submonoid R\ng : M →ₗ[R] M'\ninst✝ : IsLocalizedModule S g\nm : M\n⊢ g m = 0 ↔ ∃ r ∈ S, r • m = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.LocalizedModule.Basic | {
"line": 1381,
"column": 2
} | {
"line": 1381,
"column": 13
} | {
"line": 1381,
"column": 14
} | [
{
"pp": "R : Type u_6\nM : Type u_8\nM' : Type u_9\ninst✝⁵ : CommSemiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\ninst✝² : AddCommMonoid M'\ninst✝¹ : Module R M'\nS : Submonoid R\ng : M →ₗ[R] M'\ninst✝ : IsLocalizedModule S g\nH : ⊤ ≤ g.ker\nx : M\ns : ↥S\n⊢ Function.uncurry (mk' g) (x, s) = 0",
"... | [
"R : Type u_6\nM : Type u_8\nM' : Type u_9\ninst✝⁵ : CommSemiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\ninst✝² : AddCommMonoid M'\ninst✝¹ : Module R M'\nS : Submonoid R\ng : M →ₗ[R] M'\ninst✝ : IsLocalizedModule S g\nH : ⊤ ≤ g.ker\nx : M\ns : ↥S\n⊢ g x = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.LocalizedModule.Basic | {
"line": 1446,
"column": 4
} | {
"line": 1446,
"column": 56
} | {
"line": 1446,
"column": 57
} | [
{
"pp": "case neg\nR : Type u_1\nM : Type u_2\nA : Type u_3\nN : Type u_4\ninst✝¹¹ : CommRing R\ninst✝¹⁰ : AddCommMonoid M\ninst✝⁹ : Module R M\ninst✝⁸ : CommRing A\ninst✝⁷ : AddCommMonoid N\ninst✝⁶ : Module A N\ninst✝⁵ : Algebra R A\ninst✝⁴ : Module R N\ninst✝³ : IsScalarTower R A N\nf : M →ₗ[R] N\nS : Submono... | [
"case neg\nR : Type u_1\nM : Type u_2\nA : Type u_3\nN : Type u_4\ninst✝¹¹ : CommRing R\ninst✝¹⁰ : AddCommMonoid M\ninst✝⁹ : Module R M\ninst✝⁸ : CommRing A\ninst✝⁷ : AddCommMonoid N\ninst✝⁶ : Module A N\ninst✝⁵ : Algebra R A\ninst✝⁴ : Module R N\ninst✝³ : IsScalarTower R A N\nf : M →ₗ[R] N\nS : Submonoid R\ninst✝²... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Bicategory.Functor.Pseudofunctor | {
"line": 131,
"column": 38
} | {
"line": 131,
"column": 49
} | {
"line": 131,
"column": 49
} | [
{
"pp": "B : Type u₁\ninst✝² : Bicategory B\nC : Type u₂\ninst✝¹ : Bicategory C\nD : Type u₃\ninst✝ : Bicategory D\nF : B ⥤ᵖ C\na✝ b✝ : B\nf : a✝ ⟶ b✝\n⊢ (λ_ (F.map f)).hom ≫ (F.map₂Iso (λ_ f)).inv = (F.mapId a✝).inv ▷ F.map f ≫ (F.mapComp (𝟙 a✝) f).inv",
"ppTerm": "?m.73",
"assigned": true,
"usedC... | [
"B : Type u₁\ninst✝² : Bicategory B\nC : Type u₂\ninst✝¹ : Bicategory C\nD : Type u₃\ninst✝ : Bicategory D\nF : B ⥤ᵖ C\na✝ b✝ : B\nf : a✝ ⟶ b✝\n⊢ (λ_ (F.map f)).hom = ((F.mapId a✝).inv ▷ F.map f ≫ (F.mapComp (𝟙 a✝) f).inv) ≫ (F.map₂Iso (λ_ f)).hom"
] | comp_inv_eq | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Bicategory.Functor.Pseudofunctor | {
"line": 134,
"column": 38
} | {
"line": 134,
"column": 49
} | {
"line": 134,
"column": 49
} | [
{
"pp": "B : Type u₁\ninst✝² : Bicategory B\nC : Type u₂\ninst✝¹ : Bicategory C\nD : Type u₃\ninst✝ : Bicategory D\nF : B ⥤ᵖ C\na✝ b✝ : B\nf : a✝ ⟶ b✝\n⊢ (ρ_ (F.map f)).hom ≫ (F.map₂Iso (ρ_ f)).inv = F.map f ◁ (F.mapId b✝).inv ≫ (F.mapComp f (𝟙 b✝)).inv",
"ppTerm": "?m.102",
"assigned": true,
"used... | [
"B : Type u₁\ninst✝² : Bicategory B\nC : Type u₂\ninst✝¹ : Bicategory C\nD : Type u₃\ninst✝ : Bicategory D\nF : B ⥤ᵖ C\na✝ b✝ : B\nf : a✝ ⟶ b✝\n⊢ (ρ_ (F.map f)).hom = (F.map f ◁ (F.mapId b✝).inv ≫ (F.mapComp f (𝟙 b✝)).inv) ≫ (F.map₂Iso (ρ_ f)).hom"
] | comp_inv_eq | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Bicategory.Functor.Pseudofunctor | {
"line": 219,
"column": 2
} | {
"line": 219,
"column": 13
} | {
"line": 219,
"column": 14
} | [
{
"pp": "B : Type u₁\ninst✝¹ : Bicategory B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤ᵖ C\na b : B\nf : a ⟶ b\n⊢ (F.mapId a).inv ▷ F.map f = (λ_ (F.map f)).hom ≫ F.map₂ (λ_ f).inv ≫ (F.mapComp (𝟙 a) f).hom",
"ppTerm": "?m.84",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedG... | [
"B : Type u₁\ninst✝¹ : Bicategory B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤ᵖ C\na b : B\nf : a ⟶ b\n⊢ (F.mapId a).inv ▷ F.map f = (λ_ (F.map f)).hom ≫ F.map₂ (λ_ f).inv ≫ (F.mapComp (𝟙 a) f).hom"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Bicategory.Functor.Pseudofunctor | {
"line": 218,
"column": 72
} | {
"line": 219,
"column": 58
} | {
"line": 221,
"column": 0
} | [
{
"pp": "B : Type u₁\ninst✝¹ : Bicategory B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤ᵖ C\na b : B\nf : a ⟶ b\n⊢ (F.mapId a).inv ▷ F.map f = (λ_ (F.map f)).hom ≫ F.map₂ (λ_ f).inv ≫ (F.mapComp (𝟙 a) f).hom",
"ppTerm": "?m.84",
"assigned": true,
"usedConstants": [
"CategoryTheory.Category.ass... | [] | by
simpa using congrArg (·.inv) (F.whiskerRightIso_mapId f) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Bicategory.Functor.Pseudofunctor | {
"line": 247,
"column": 2
} | {
"line": 247,
"column": 13
} | {
"line": 247,
"column": 14
} | [
{
"pp": "B : Type u₁\ninst✝¹ : Bicategory B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤ᵖ C\na b : B\nf : a ⟶ b\n⊢ F.map f ◁ (F.mapId b).inv = (ρ_ (F.map f)).hom ≫ F.map₂ (ρ_ f).inv ≫ (F.mapComp f (𝟙 b)).hom",
"ppTerm": "?m.84",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedG... | [
"B : Type u₁\ninst✝¹ : Bicategory B\nC : Type u₂\ninst✝ : Bicategory C\nF : B ⥤ᵖ C\na b : B\nf : a ⟶ b\n⊢ F.map f ◁ (F.mapId b).inv = (ρ_ (F.map f)).hom ≫ F.map₂ (ρ_ f).inv ≫ (F.mapComp f (𝟙 b)).hom"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Finiteness.Ideal | {
"line": 60,
"column": 4
} | {
"line": 60,
"column": 15
} | {
"line": 60,
"column": 16
} | [
{
"pp": "R : Type u_3\ninst✝ : CommSemiring R\nI : Ideal R\nh : I.radical.FG\nhJ : ∀ (J : Ideal R), J.FG → J ≤ I.radical → ∃ n, J ^ n ≤ I\n⊢ ∃ n, I.radical ^ n ≤ I",
"ppTerm": "?m.33",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_3\ninst✝ : CommSemiring R\nI : Ideal R\nh : I.radical.FG\nhJ : ∀ (J : Ideal R), J.FG → J ≤ I.radical → ∃ n, J ^ n ≤ I\n⊢ ∃ n, I.radical ^ n ≤ I"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Bicategory.Functor.Pseudofunctor | {
"line": 339,
"column": 66
} | {
"line": 339,
"column": 86
} | {
"line": 340,
"column": 6
} | [
{
"pp": "B : Type u₁\ninst✝² : Bicategory B\nC : Type u₂\ninst✝¹ : Bicategory C\nD : Type u₃\ninst✝ : Bicategory D\nF✝ : B ⥤ᵖ C\nF : B ⥤ᴸ C\nF' : F.PseudoCore\na✝ b✝ c✝ : B\nf : a✝ ⟶ b✝\ng h : b✝ ⟶ c✝\nη : g ⟶ h\n⊢ F.map₂ (f ◁ η) = (F'.mapCompIso f g).hom ≫ F.mapComp f g ≫ F.map₂ (f ◁ η)",
"ppTerm": "?m.92"... | [
"B : Type u₁\ninst✝² : Bicategory B\nC : Type u₂\ninst✝¹ : Bicategory C\nD : Type u₃\ninst✝ : Bicategory D\nF✝ : B ⥤ᵖ C\nF : B ⥤ᴸ C\nF' : F.PseudoCore\na✝ b✝ c✝ : B\nf : a✝ ⟶ b✝\ng h : b✝ ⟶ c✝\nη : g ⟶ h\n⊢ F.map₂ (f ◁ η) = (F'.mapCompIso f g).hom ≫ (F'.mapCompIso f g).inv ≫ F.map₂ (f ◁ η)"
] | ← F'.mapCompIso_inv, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Bicategory.Functor.Pseudofunctor | {
"line": 342,
"column": 65
} | {
"line": 342,
"column": 85
} | {
"line": 343,
"column": 6
} | [
{
"pp": "B : Type u₁\ninst✝² : Bicategory B\nC : Type u₂\ninst✝¹ : Bicategory C\nD : Type u₃\ninst✝ : Bicategory D\nF✝ : B ⥤ᵖ C\nF : B ⥤ᴸ C\nF' : F.PseudoCore\na✝ b✝ c✝ : B\nf✝ g✝ : a✝ ⟶ b✝\nη : f✝ ⟶ g✝\nh : b✝ ⟶ c✝\n⊢ F.map₂ (η ▷ h) = (F'.mapCompIso f✝ h).hom ≫ F.mapComp f✝ h ≫ F.map₂ (η ▷ h)",
"ppTerm": "... | [
"B : Type u₁\ninst✝² : Bicategory B\nC : Type u₂\ninst✝¹ : Bicategory C\nD : Type u₃\ninst✝ : Bicategory D\nF✝ : B ⥤ᵖ C\nF : B ⥤ᴸ C\nF' : F.PseudoCore\na✝ b✝ c✝ : B\nf✝ g✝ : a✝ ⟶ b✝\nη : f✝ ⟶ g✝\nh : b✝ ⟶ c✝\n⊢ F.map₂ (η ▷ h) = (F'.mapCompIso f✝ h).hom ≫ (F'.mapCompIso f✝ h).inv ≫ F.map₂ (η ▷ h)"
] | ← F'.mapCompIso_inv, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.IsConnected | {
"line": 150,
"column": 2
} | {
"line": 150,
"column": 13
} | {
"line": 151,
"column": 4
} | [
{
"pp": "J : Type u₁\ninst✝¹ : Category.{v₁, u₁} J\ninst✝ : IsPreconnected J\nα : Type u₂\nF : J → α\nh : ∀ (j₁ j₂ : J) (x : j₁ ⟶ j₂), F j₁ = F j₂\nj j' : J\n⊢ F j = F j'",
"ppTerm": "?m.6",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"J : Type u₁\ninst✝¹ : Category.{v₁, u₁} J\ninst✝ : IsPreconnected J\nα : Type u₂\nF : J → α\nh : ∀ (j₁ j₂ : J) (x : j₁ ⟶ j₂), F j₁ = F j₂\nj j' : J\n⊢ F j = F j'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.IsConnected | {
"line": 203,
"column": 2
} | {
"line": 203,
"column": 92
} | {
"line": 204,
"column": 2
} | [
{
"pp": "J : Type u₁\ninst✝¹ : Category.{v₁, u₁} J\ninst✝ : IsPreconnected J\np : Set J\nj₀ : J\nh0 : j₀ ∈ p\nh1 : ∀ {j₁ j₂ : J} (x : j₁ ⟶ j₂), j₁ ∈ p ↔ j₂ ∈ p\nj : J\naux : ∀ (j₁ j₂ : J) (f : j₁ ⟶ j₂), { down := j₁ ∈ p } = { down := j₂ ∈ p } :=\n fun j₁ j₂ f ↦ congrArg ULift.up (Iff.eq (h1 f))\n⊢ j ∈ p",
... | [
"J : Type u₁\ninst✝¹ : Category.{v₁, u₁} J\ninst✝ : IsPreconnected J\np : Set J\nj₀ : J\nh0 : j₀ ∈ p\nh1 : ∀ {j₁ j₂ : J} (x : j₁ ⟶ j₂), j₁ ∈ p ↔ j₂ ∈ p\nj : J\naux : ∀ (j₁ j₂ : J) (f : j₁ ⟶ j₂), { down := j₁ ∈ p } = { down := j₂ ∈ p } :=\n fun j₁ j₂ f ↦ congrArg ULift.up (Iff.eq (h1 f))\ni : (j ∈ p) = (j₀ ∈ p)\n⊢ ... | injection constant_of_preserves_morphisms (fun k => ULift.up.{u₁} (k ∈ p)) aux j j₀ with i | Lean.Elab.Tactic.evalInjection | Lean.Parser.Tactic.injection |
Mathlib.CategoryTheory.IsConnected | {
"line": 485,
"column": 4
} | {
"line": 485,
"column": 15
} | {
"line": 485,
"column": 16
} | [
{
"pp": "J : Type u₁\ninst✝² : Category.{v₁, u₁} J\nC : Type w₂\ninst✝¹ : Category.{w₁, w₂} C\ninst✝ : IsPreconnected J\nX Y : C\nα : (const J).obj X ⟶ (const J).obj Y\nx✝¹ x✝ : J\nf : x✝¹ ⟶ x✝\n⊢ α.app x✝¹ = α.app x✝",
"ppTerm": "?m.48",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"J : Type u₁\ninst✝² : Category.{v₁, u₁} J\nC : Type w₂\ninst✝¹ : Category.{w₁, w₂} C\ninst✝ : IsPreconnected J\nX Y : C\nα : (const J).obj X ⟶ (const J).obj Y\nx✝¹ x✝ : J\nf : x✝¹ ⟶ x✝\n⊢ α.app x✝¹ = α.app x✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Elements | {
"line": 163,
"column": 28
} | {
"line": 163,
"column": 49
} | {
"line": 163,
"column": 50
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF F₁ F₂ : C ⥤ Type w\nα : F₁ ⟶ F₂\nt₁ t₂ : F₁.Elements\nk : t₁ ⟶ t₂\n⊢ (ConcreteCategory.hom (F₂.map ↑k)) ⟨t₁.fst, (ConcreteCategory.hom (α.app t₁.fst)) t₁.snd⟩.snd =\n ⟨t₂.fst, (ConcreteCategory.hom (α.app t₂.fst)) t₂.snd⟩.snd",
"ppTerm": "?m.46",
"ass... | [
"C : Type u\ninst✝ : Category.{v, u} C\nF F₁ F₂ : C ⥤ Type w\nα : F₁ ⟶ F₂\nt₁ t₂ : F₁.Elements\nk : t₁ ⟶ t₂\n⊢ (ConcreteCategory.hom (F₂.map ↑k)) ((ConcreteCategory.hom (α.app t₁.fst)) t₁.snd) =\n (ConcreteCategory.hom (α.app t₂.fst)) t₂.snd"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Elements | {
"line": 300,
"column": 4
} | {
"line": 300,
"column": 43
} | {
"line": 301,
"column": 6
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF✝ : C ⥤ Type w\nF : Cᵒᵖ ⥤ Type (max w v)\nx : F.Elementsᵒᵖ\n⊢ (ConcreteCategory.hom (F.map (𝟙 (unop x).1))) (uliftYonedaEquiv (uliftYonedaEquiv.symm (unop x).snd)) = (unop x).snd",
"ppTerm": "?m.234",
"assigned": true,
"usedConstants": [
"Eq.mp... | [
"C : Type u\ninst✝ : Category.{v, u} C\nF✝ : C ⥤ Type w\nF : Cᵒᵖ ⥤ Type (max w v)\nx : F.Elementsᵒᵖ\n⊢ uliftYonedaEquiv (uliftYonedaEquiv.symm (unop x).snd) = (unop x).snd"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.MorphismProperty.Comma | {
"line": 386,
"column": 59
} | {
"line": 386,
"column": 70
} | {
"line": 386,
"column": 71
} | [
{
"pp": "A : Type u_1\ninst✝⁶ : Category.{v_1, u_1} A\nB : Type u_2\ninst✝⁵ : Category.{v_2, u_2} B\nT : Type u_3\ninst✝⁴ : Category.{v_3, u_3} T\nL : A ⥤ T\nR : B ⥤ T\nP : MorphismProperty T\nQ : MorphismProperty A\nW : MorphismProperty B\ninst✝³ : Q.IsMultiplicative\ninst✝² : W.IsMultiplicative\nL₁ L₂ L₃ : A ... | [
"A : Type u_1\ninst✝⁶ : Category.{v_1, u_1} A\nB : Type u_2\ninst✝⁵ : Category.{v_2, u_2} B\nT : Type u_3\ninst✝⁴ : Category.{v_3, u_3} T\nL : A ⥤ T\nR : B ⥤ T\nP : MorphismProperty T\nQ : MorphismProperty A\nW : MorphismProperty B\ninst✝³ : Q.IsMultiplicative\ninst✝² : W.IsMultiplicative\nL₁ L₂ L₃ : A ⥤ T\nR₁ R₂ R... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.MorphismProperty.Comma | {
"line": 421,
"column": 50
} | {
"line": 421,
"column": 61
} | {
"line": 421,
"column": 62
} | [
{
"pp": "A : Type u_1\ninst✝⁷ : Category.{v_1, u_1} A\nB : Type u_2\ninst✝⁶ : Category.{v_2, u_2} B\nT : Type u_3\ninst✝⁵ : Category.{v_3, u_3} T\nL : A ⥤ T\nR : B ⥤ T\nP : MorphismProperty T\nQ : MorphismProperty A\nW : MorphismProperty B\ninst✝⁴ : Q.IsMultiplicative\ninst✝³ : W.IsMultiplicative\nL₁ L₂ L₃ : A ... | [
"A : Type u_1\ninst✝⁷ : Category.{v_1, u_1} A\nB : Type u_2\ninst✝⁶ : Category.{v_2, u_2} B\nT : Type u_3\ninst✝⁵ : Category.{v_3, u_3} T\nL : A ⥤ T\nR : B ⥤ T\nP : MorphismProperty T\nQ : MorphismProperty A\nW : MorphismProperty B\ninst✝⁴ : Q.IsMultiplicative\ninst✝³ : W.IsMultiplicative\nL₁ L₂ L₃ : A ⥤ T\nR₁ R₂ R... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.MorphismProperty.Comma | {
"line": 448,
"column": 60
} | {
"line": 448,
"column": 71
} | {
"line": 448,
"column": 72
} | [
{
"pp": "A : Type u_1\ninst✝⁶ : Category.{v_1, u_1} A\nB : Type u_2\ninst✝⁵ : Category.{v_2, u_2} B\nT : Type u_3\ninst✝⁴ : Category.{v_3, u_3} T\nL : A ⥤ T\nR : B ⥤ T\nP : MorphismProperty T\nQ : MorphismProperty A\nW : MorphismProperty B\ninst✝³ : Q.IsMultiplicative\ninst✝² : W.IsMultiplicative\nL₁ L₂ L₃ : A ... | [
"A : Type u_1\ninst✝⁶ : Category.{v_1, u_1} A\nB : Type u_2\ninst✝⁵ : Category.{v_2, u_2} B\nT : Type u_3\ninst✝⁴ : Category.{v_3, u_3} T\nL : A ⥤ T\nR : B ⥤ T\nP : MorphismProperty T\nQ : MorphismProperty A\nW : MorphismProperty B\ninst✝³ : Q.IsMultiplicative\ninst✝² : W.IsMultiplicative\nL₁ L₂ L₃ : A ⥤ T\nR₁ R₂ R... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.MorphismProperty.Comma | {
"line": 483,
"column": 51
} | {
"line": 483,
"column": 62
} | {
"line": 483,
"column": 63
} | [
{
"pp": "A : Type u_1\ninst✝⁷ : Category.{v_1, u_1} A\nB : Type u_2\ninst✝⁶ : Category.{v_2, u_2} B\nT : Type u_3\ninst✝⁵ : Category.{v_3, u_3} T\nL : A ⥤ T\nR : B ⥤ T\nP : MorphismProperty T\nQ : MorphismProperty A\nW : MorphismProperty B\ninst✝⁴ : Q.IsMultiplicative\ninst✝³ : W.IsMultiplicative\nL₁ L₂ L₃ : A ... | [
"A : Type u_1\ninst✝⁷ : Category.{v_1, u_1} A\nB : Type u_2\ninst✝⁶ : Category.{v_2, u_2} B\nT : Type u_3\ninst✝⁵ : Category.{v_3, u_3} T\nL : A ⥤ T\nR : B ⥤ T\nP : MorphismProperty T\nQ : MorphismProperty A\nW : MorphismProperty B\ninst✝⁴ : Q.IsMultiplicative\ninst✝³ : W.IsMultiplicative\nL₁ L₂ L₃ : A ⥤ T\nR₁ R₂ R... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.MorphismProperty.Comma | {
"line": 824,
"column": 4
} | {
"line": 824,
"column": 15
} | {
"line": 824,
"column": 16
} | [
{
"pp": "case refine_1\nC : Type u_1\nD : Type u_2\ninst✝³ : Category.{u_3, u_1} C\ninst✝² : Category.{u_4, u_2} D\nP : MorphismProperty D\nQ : MorphismProperty C\ninst✝¹ : Q.IsMultiplicative\nF : C ⥤ D\nX : D\ninst✝ : F.Full\nA B : P.CostructuredArrow ⊤ F X\nf : (CostructuredArrow.toOver P F X).obj A ⟶ (Costru... | [
"case refine_1\nC : Type u_1\nD : Type u_2\ninst✝³ : Category.{u_3, u_1} C\ninst✝² : Category.{u_4, u_2} D\nP : MorphismProperty D\nQ : MorphismProperty C\ninst✝¹ : Q.IsMultiplicative\nF : C ⥤ D\nX : D\ninst✝ : F.Full\nA B : P.CostructuredArrow ⊤ F X\nf : (CostructuredArrow.toOver P F X).obj A ⟶ (CostructuredArrow.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.WithTerminal.Basic | {
"line": 382,
"column": 32
} | {
"line": 382,
"column": 62
} | {
"line": 382,
"column": 63
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nD : Type u_1\ninst✝ : Category.{v_1, u_1} D\nc c' : Comma (𝟭 (C ⥤ D)) (Functor.const C)\nφ : c ⟶ c'\nx y : WithTerminal C\nf : x ⟶ y\na : C\nx✝ : of a ⟶ star\n⊢ c.hom.app a ≫ φ.right = φ.left.app a ≫ c'.hom.app a",
"ppTerm": "?m.157",
"assigned": false,
... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nD : Type u_1\ninst✝ : Category.{v_1, u_1} D\nc c' : Comma (𝟭 (C ⥤ D)) (Functor.const C)\nφ : c ⟶ c'\nx y : WithTerminal C\nf : x ⟶ y\na : C\nx✝ : of a ⟶ star\n⊢ c.hom.app a ≫ φ.right = φ.left.app a ≫ c'.hom.app a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Connected | {
"line": 75,
"column": 22
} | {
"line": 75,
"column": 33
} | {
"line": 75,
"column": 34
} | [
{
"pp": "J : Type u₁\ninst✝² : Category.{v₁, u₁} J\nC : Type u₂\ninst✝¹ : Category.{v₂, u₂} C\nX : C\ninst✝ : IsConnected J\ns : Cone ((Functor.const J).obj X)\nj x✝¹ x✝ : J\nf : x✝¹ ⟶ x✝\n⊢ s.π.app x✝¹ = s.π.app x✝",
"ppTerm": "?m.55",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"J : Type u₁\ninst✝² : Category.{v₁, u₁} J\nC : Type u₂\ninst✝¹ : Category.{v₂, u₂} C\nX : C\ninst✝ : IsConnected J\ns : Cone ((Functor.const J).obj X)\nj x✝¹ x✝ : J\nf : x✝¹ ⟶ x✝\n⊢ s.π.app x✝¹ = s.π.app x✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Connected | {
"line": 76,
"column": 20
} | {
"line": 76,
"column": 31
} | {
"line": 76,
"column": 32
} | [
{
"pp": "J : Type u₁\ninst✝² : Category.{v₁, u₁} J\nC : Type u₂\ninst✝¹ : Category.{v₂, u₂} C\nX : C\ninst✝ : IsConnected J\ns : Cone ((Functor.const J).obj X)\nm : s.pt ⟶ (constCone J X).pt\nhm : ∀ (j : J), m ≫ (constCone J X).π.app j = s.π.app j\n⊢ m = s.π.app (Classical.arbitrary J)",
"ppTerm": "?m.75",
... | [
"J : Type u₁\ninst✝² : Category.{v₁, u₁} J\nC : Type u₂\ninst✝¹ : Category.{v₂, u₂} C\nX : C\ninst✝ : IsConnected J\ns : Cone ((Functor.const J).obj X)\nm : s.pt ⟶ (constCone J X).pt\nhm : ∀ (j : J), m ≫ (constCone J X).π.app j = s.π.app j\n⊢ m = s.π.app (Classical.arbitrary J)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Connected | {
"line": 87,
"column": 22
} | {
"line": 87,
"column": 33
} | {
"line": 87,
"column": 34
} | [
{
"pp": "J : Type u₁\ninst✝² : Category.{v₁, u₁} J\nC : Type u₂\ninst✝¹ : Category.{v₂, u₂} C\nX : C\ninst✝ : IsConnected J\ns : Cocone ((Functor.const J).obj X)\nj x✝¹ x✝ : J\nf : x✝¹ ⟶ x✝\n⊢ s.ι.app x✝¹ = s.ι.app x✝",
"ppTerm": "?m.55",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"J : Type u₁\ninst✝² : Category.{v₁, u₁} J\nC : Type u₂\ninst✝¹ : Category.{v₂, u₂} C\nX : C\ninst✝ : IsConnected J\ns : Cocone ((Functor.const J).obj X)\nj x✝¹ x✝ : J\nf : x✝¹ ⟶ x✝\n⊢ s.ι.app x✝¹ = s.ι.app x✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Connected | {
"line": 88,
"column": 20
} | {
"line": 88,
"column": 31
} | {
"line": 88,
"column": 32
} | [
{
"pp": "J : Type u₁\ninst✝² : Category.{v₁, u₁} J\nC : Type u₂\ninst✝¹ : Category.{v₂, u₂} C\nX : C\ninst✝ : IsConnected J\ns : Cocone ((Functor.const J).obj X)\nm : (constCocone J X).pt ⟶ s.pt\nhm : ∀ (j : J), (constCocone J X).ι.app j ≫ m = s.ι.app j\n⊢ m = s.ι.app (Classical.arbitrary J)",
"ppTerm": "?m... | [
"J : Type u₁\ninst✝² : Category.{v₁, u₁} J\nC : Type u₂\ninst✝¹ : Category.{v₂, u₂} C\nX : C\ninst✝ : IsConnected J\ns : Cocone ((Functor.const J).obj X)\nm : (constCocone J X).pt ⟶ s.pt\nhm : ∀ (j : J), (constCocone J X).ι.app j ≫ m = s.ι.app j\n⊢ m = s.ι.app (Classical.arbitrary J)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.WithTerminal.Basic | {
"line": 778,
"column": 20
} | {
"line": 778,
"column": 31
} | {
"line": 778,
"column": 32
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nD : Type u_1\ninst✝ : Category.{v_1, u_1} D\nc : Comma (Functor.const C) (𝟭 (C ⥤ D))\nx y : C\nf : x ⟶ y\n⊢ c.hom.app x ≫ c.right.map f = c.hom.app y",
"ppTerm": "?m.55",
"assigned": true,
"usedConstants": [
"CategoryTheory.Functor",
"Cat... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nD : Type u_1\ninst✝ : Category.{v_1, u_1} D\nc : Comma (Functor.const C) (𝟭 (C ⥤ D))\nx y : C\nf : x ⟶ y\n⊢ c.hom.app x ≫ c.right.map f = c.hom.app y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.EffectiveEpi.Basic | {
"line": 111,
"column": 6
} | {
"line": 111,
"column": 49
} | {
"line": 111,
"column": 50
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nX Y : C\nf : X ⟶ Y\ninst✝ : EffectiveEpi f\nA B : C\nz : A ⟶ B\nhz : Mono z\nu : X ⟶ A\nv : Y ⟶ B\nsq : CommSq u f z v\nZ✝ : C\nx✝¹ x✝ : Z✝ ⟶ X\nh : x✝¹ ≫ f = x✝ ≫ f\n⊢ x✝¹ ≫ u = x✝ ≫ u",
"ppTerm": "?m.53",
"assigned": false,
"usedConstants": []... | [
"C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nX Y : C\nf : X ⟶ Y\ninst✝ : EffectiveEpi f\nA B : C\nz : A ⟶ B\nhz : Mono z\nu : X ⟶ A\nv : Y ⟶ B\nsq : CommSq u f z v\nZ✝ : C\nx✝¹ x✝ : Z✝ ⟶ X\nh : x✝¹ ≫ f = x✝ ≫ f\n⊢ x✝¹ ≫ u = x✝ ≫ u"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.WithTerminal.Basic | {
"line": 793,
"column": 26
} | {
"line": 793,
"column": 56
} | {
"line": 793,
"column": 57
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nD : Type u_1\ninst✝ : Category.{v_1, u_1} D\nc c' : Comma (Functor.const C) (𝟭 (C ⥤ D))\nφ : c ⟶ c'\nx y : WithInitial C\nf : x ⟶ y\na : C\nx✝ : star ⟶ of a\n⊢ ((ofCommaObject c).map x✝ ≫\n match of a with\n | of x => φ.right.app x\n | star => φ.l... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nD : Type u_1\ninst✝ : Category.{v_1, u_1} D\nc c' : Comma (Functor.const C) (𝟭 (C ⥤ D))\nφ : c ⟶ c'\nx y : WithInitial C\nf : x ⟶ y\na : C\nx✝ : star ⟶ of a\n⊢ c.hom.app a ≫ φ.right.app a = φ.left ≫ c'.hom.app a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.EffectiveEpi.Basic | {
"line": 255,
"column": 21
} | {
"line": 255,
"column": 32
} | {
"line": 255,
"column": 33
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nX Y : C\nf : X ⟶ Y\ninst✝ : IsIso f\nW✝ : C\nx✝² : X ⟶ W✝\nx✝¹ : ∀ {Z : C} (g₁ g₂ : Z ⟶ X), g₁ ≫ f = g₂ ≫ f → g₁ ≫ x✝² = g₂ ≫ x✝²\nx✝ : Y ⟶ W✝\nh : f ≫ x✝ = x✝²\n⊢ x✝ = inv f ≫ x✝²",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
... | [
"C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nX Y : C\nf : X ⟶ Y\ninst✝ : IsIso f\nW✝ : C\nx✝² : X ⟶ W✝\nx✝¹ : ∀ {Z : C} (g₁ g₂ : Z ⟶ X), g₁ ≫ f = g₂ ≫ f → g₁ ≫ x✝² = g₂ ≫ x✝²\nx✝ : Y ⟶ W✝\nh : f ≫ x✝ = x✝²\n⊢ f ≫ x✝ = x✝²"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Final | {
"line": 627,
"column": 4
} | {
"line": 627,
"column": 15
} | {
"line": 627,
"column": 16
} | [
{
"pp": "case h₁\nC : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝² : Category.{v₂, u₂} D\nF : C ⥤ D\ninst✝¹ : F.Initial\nE : Type u₃\ninst✝ : Category.{v₃, u₃} E\nG : D ⥤ E\ns : Cone (F ⋙ G)\nj j₁ j₂ : C\nk₁ : F.obj j₁ ⟶ F.obj j\nk₂ : F.obj j₂ ⟶ F.obj j\nf : j₁ ⟶ j₂\nw : F.map f ≫ k₂ = k₁\nh : s.π... | [
"case h₁\nC : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝² : Category.{v₂, u₂} D\nF : C ⥤ D\ninst✝¹ : F.Initial\nE : Type u₃\ninst✝ : Category.{v₃, u₃} E\nG : D ⥤ E\ns : Cone (F ⋙ G)\nj j₁ j₂ : C\nk₁ : F.obj j₁ ⟶ F.obj j\nk₂ : F.obj j₂ ⟶ F.obj j\nf : j₁ ⟶ j₂\nw : F.map f ≫ k₂ = k₁\nh : s.π.app j₁ ≫ G.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Final | {
"line": 631,
"column": 4
} | {
"line": 631,
"column": 15
} | {
"line": 631,
"column": 16
} | [
{
"pp": "case h₂\nC : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝² : Category.{v₂, u₂} D\nF : C ⥤ D\ninst✝¹ : F.Initial\nE : Type u₃\ninst✝ : Category.{v₃, u₃} E\nG : D ⥤ E\ns : Cone (F ⋙ G)\nj j₁ j₂ : C\nk₁ : F.obj j₁ ⟶ F.obj j\nk₂ : F.obj j₂ ⟶ F.obj j\nf : j₁ ⟶ j₂\nw : F.map f ≫ k₂ = k₁\nh : (s.... | [
"case h₂\nC : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝² : Category.{v₂, u₂} D\nF : C ⥤ D\ninst✝¹ : F.Initial\nE : Type u₃\ninst✝ : Category.{v₃, u₃} E\nG : D ⥤ E\ns : Cone (F ⋙ G)\nj j₁ j₂ : C\nk₁ : F.obj j₁ ⟶ F.obj j\nk₂ : F.obj j₂ ⟶ F.obj j\nf : j₁ ⟶ j₂\nw : F.map f ≫ k₂ = k₁\nh : (s.π.app j₁ ≫ (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.Assoc | {
"line": 111,
"column": 2
} | {
"line": 111,
"column": 39
} | {
"line": 111,
"column": 40
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nX₁ X₂ X₃ Y₁ Y₂ : C\nf₁ : X₁ ⟶ Y₁\nf₂ : X₂ ⟶ Y₁\nf₃ : X₂ ⟶ Y₂\nf₄ : X₃ ⟶ Y₂\ninst✝² : HasPullback f₁ f₂\ninst✝¹ : HasPullback f₃ f₄\ninst✝ : HasPullback (pullback.snd f₁ f₂ ≫ f₃) f₄\n⊢ IsLimit\n ((PullbackCone.mk (pullback.fst f₃ f₄) (pullback.snd f₃ f₄) ⋯).pas... | [
"C : Type u\ninst✝³ : Category.{v, u} C\nX₁ X₂ X₃ Y₁ Y₂ : C\nf₁ : X₁ ⟶ Y₁\nf₂ : X₂ ⟶ Y₁\nf₃ : X₂ ⟶ Y₂\nf₄ : X₃ ⟶ Y₂\ninst✝² : HasPullback f₁ f₂\ninst✝¹ : HasPullback f₃ f₄\ninst✝ : HasPullback (pullback.snd f₁ f₂ ≫ f₃) f₄\n⊢ IsLimit (PullbackCone.mk (pullback.fst (pullback.snd f₁ f₂ ≫ f₃) f₄) (pullback.snd (pullbac... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.Assoc | {
"line": 130,
"column": 2
} | {
"line": 130,
"column": 38
} | {
"line": 130,
"column": 39
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nX₁ X₂ X₃ Y₁ Y₂ : C\nf₁ : X₁ ⟶ Y₁\nf₂ : X₂ ⟶ Y₁\nf₃ : X₂ ⟶ Y₂\nf₄ : X₃ ⟶ Y₂\ninst✝² : HasPullback f₁ f₂\ninst✝¹ : HasPullback f₃ f₄\ninst✝ : HasPullback f₁ (pullback.fst f₃ f₄ ≫ f₂)\n⊢ IsLimit\n ((PullbackCone.mk (pullback.fst f₁ f₂) (pullback.snd f₁ f₂) ⋯).pas... | [
"C : Type u\ninst✝³ : Category.{v, u} C\nX₁ X₂ X₃ Y₁ Y₂ : C\nf₁ : X₁ ⟶ Y₁\nf₂ : X₂ ⟶ Y₁\nf₃ : X₂ ⟶ Y₂\nf₄ : X₃ ⟶ Y₂\ninst✝² : HasPullback f₁ f₂\ninst✝¹ : HasPullback f₃ f₄\ninst✝ : HasPullback f₁ (pullback.fst f₃ f₄ ≫ f₂)\n⊢ IsLimit (PullbackCone.mk (pullback.fst f₁ (pullback.fst f₃ f₄ ≫ f₂)) (pullback.snd f₁ (pull... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.KernelPair | {
"line": 191,
"column": 6
} | {
"line": 191,
"column": 17
} | {
"line": 191,
"column": 18
} | [
{
"pp": "case refine_5.h₀\nC : Type u\ninst✝² : Category.{v, u} C\nX Y Z A : C\ng : Y ⟶ Z\na₁ a₂ : A ⟶ Y\nh : IsKernelPair g a₁ a₂\nf : X ⟶ Z\ninst✝¹ : HasPullback f g\ninst✝ : HasPullback f (a₁ ≫ g)\ns : PullbackCone (pullback.fst f g) (pullback.fst f g)\nm : s.pt ⟶ pullback f (a₁ ≫ g)\nhm :\n ∀ (j : WalkingC... | [
"case refine_5.h₀\nC : Type u\ninst✝² : Category.{v, u} C\nX Y Z A : C\ng : Y ⟶ Z\na₁ a₂ : A ⟶ Y\nh : IsKernelPair g a₁ a₂\nf : X ⟶ Z\ninst✝¹ : HasPullback f g\ninst✝ : HasPullback f (a₁ ≫ g)\ns : PullbackCone (pullback.fst f g) (pullback.fst f g)\nm : s.pt ⟶ pullback f (a₁ ≫ g)\nhm :\n ∀ (j : WalkingCospan),\n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.Assoc | {
"line": 283,
"column": 2
} | {
"line": 283,
"column": 39
} | {
"line": 284,
"column": 4
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nX₁ X₂ X₃ Z₁ Z₂ : C\ng₁ : Z₁ ⟶ X₁\ng₂ : Z₁ ⟶ X₂\ng₃ : Z₂ ⟶ X₂\ng₄ : Z₂ ⟶ X₃\ninst✝² : HasPushout g₁ g₂\ninst✝¹ : HasPushout g₃ g₄\ninst✝ : HasPushout (g₃ ≫ pushout.inr g₁ g₂) g₄\n⊢ IsColimit\n ((PushoutCocone.mk (pushout.inl g₃ g₄) (pushout.inr g₃ g₄) ⋯).pasteV... | [
"C : Type u\ninst✝³ : Category.{v, u} C\nX₁ X₂ X₃ Z₁ Z₂ : C\ng₁ : Z₁ ⟶ X₁\ng₂ : Z₁ ⟶ X₂\ng₃ : Z₂ ⟶ X₂\ng₄ : Z₂ ⟶ X₃\ninst✝² : HasPushout g₁ g₂\ninst✝¹ : HasPushout g₃ g₄\ninst✝ : HasPushout (g₃ ≫ pushout.inr g₁ g₂) g₄\n⊢ IsColimit (PushoutCocone.mk (pushout.inl (g₃ ≫ pushout.inr g₁ g₂) g₄) (pushout.inr (g₃ ≫ pushou... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.KernelPair | {
"line": 193,
"column": 8
} | {
"line": 193,
"column": 19
} | {
"line": 193,
"column": 20
} | [
{
"pp": "case h₁.h₀\nC : Type u\ninst✝² : Category.{v, u} C\nX Y Z A : C\ng : Y ⟶ Z\na₁ a₂ : A ⟶ Y\nh : IsKernelPair g a₁ a₂\nf : X ⟶ Z\ninst✝¹ : HasPullback f g\ninst✝ : HasPullback f (a₁ ≫ g)\ns : PullbackCone (pullback.fst f g) (pullback.fst f g)\nm : s.pt ⟶ pullback f (a₁ ≫ g)\nhm :\n ∀ (j : WalkingCospan)... | [
"case h₁.h₀\nC : Type u\ninst✝² : Category.{v, u} C\nX Y Z A : C\ng : Y ⟶ Z\na₁ a₂ : A ⟶ Y\nh : IsKernelPair g a₁ a₂\nf : X ⟶ Z\ninst✝¹ : HasPullback f g\ninst✝ : HasPullback f (a₁ ≫ g)\ns : PullbackCone (pullback.fst f g) (pullback.fst f g)\nm : s.pt ⟶ pullback f (a₁ ≫ g)\nhm :\n ∀ (j : WalkingCospan),\n m ≫\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.Assoc | {
"line": 303,
"column": 2
} | {
"line": 303,
"column": 40
} | {
"line": 303,
"column": 41
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nX₁ X₂ X₃ Z₁ Z₂ : C\ng₁ : Z₁ ⟶ X₁\ng₂ : Z₁ ⟶ X₂\ng₃ : Z₂ ⟶ X₂\ng₄ : Z₂ ⟶ X₃\ninst✝² : HasPushout g₁ g₂\ninst✝¹ : HasPushout g₃ g₄\ninst✝ : HasPushout g₁ (g₂ ≫ pushout.inl g₃ g₄)\n⊢ IsColimit\n ((PushoutCocone.mk (pushout.inl g₁ g₂) (pushout.inr g₁ g₂) ⋯).pasteH... | [
"C : Type u\ninst✝³ : Category.{v, u} C\nX₁ X₂ X₃ Z₁ Z₂ : C\ng₁ : Z₁ ⟶ X₁\ng₂ : Z₁ ⟶ X₂\ng₃ : Z₂ ⟶ X₂\ng₄ : Z₂ ⟶ X₃\ninst✝² : HasPushout g₁ g₂\ninst✝¹ : HasPushout g₃ g₄\ninst✝ : HasPushout g₁ (g₂ ≫ pushout.inl g₃ g₄)\n⊢ IsColimit (PushoutCocone.mk (pushout.inl g₁ (g₂ ≫ pushout.inl g₃ g₄)) (pushout.inr g₁ (g₂ ≫ pus... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.KernelPair | {
"line": 194,
"column": 8
} | {
"line": 194,
"column": 19
} | {
"line": 194,
"column": 20
} | [
{
"pp": "case h₁.h₁\nC : Type u\ninst✝² : Category.{v, u} C\nX Y Z A : C\ng : Y ⟶ Z\na₁ a₂ : A ⟶ Y\nh : IsKernelPair g a₁ a₂\nf : X ⟶ Z\ninst✝¹ : HasPullback f g\ninst✝ : HasPullback f (a₁ ≫ g)\ns : PullbackCone (pullback.fst f g) (pullback.fst f g)\nm : s.pt ⟶ pullback f (a₁ ≫ g)\nhm :\n ∀ (j : WalkingCospan)... | [
"case h₁.h₁\nC : Type u\ninst✝² : Category.{v, u} C\nX Y Z A : C\ng : Y ⟶ Z\na₁ a₂ : A ⟶ Y\nh : IsKernelPair g a₁ a₂\nf : X ⟶ Z\ninst✝¹ : HasPullback f g\ninst✝ : HasPullback f (a₁ ≫ g)\ns : PullbackCone (pullback.fst f g) (pullback.fst f g)\nm : s.pt ⟶ pullback f (a₁ ≫ g)\nhm :\n ∀ (j : WalkingCospan),\n m ≫\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.Assoc | {
"line": 328,
"column": 2
} | {
"line": 333,
"column": 32
} | {
"line": 335,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\nX₁ X₂ X₃ Z₁ Z₂ : C\ng₁ : Z₁ ⟶ X₁\ng₂ : Z₁ ⟶ X₂\ng₃ : Z₂ ⟶ X₂\ng₄ : Z₂ ⟶ X₃\ninst✝³ : HasPushout g₁ g₂\ninst✝² : HasPushout g₃ g₄\ninst✝¹ : HasPushout (g₃ ≫ pushout.inr g₁ g₂) g₄\ninst✝ : HasPushout g₁ (g₂ ≫ pushout.inl g₃ g₄)\n⊢ pushout.inl g₁ g₂ ≫ pushout.inl (g... | [] | trans f₁ ≫ l₁
· congr 1
exact
(pushoutPushoutLeftIsPushout g₁ g₂ g₃ g₄).comp_coconePointUniqueUpToIso_hom _
WalkingCospan.left
· exact pushout.inl_desc _ _ _ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.Assoc | {
"line": 328,
"column": 2
} | {
"line": 333,
"column": 32
} | {
"line": 335,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\nX₁ X₂ X₃ Z₁ Z₂ : C\ng₁ : Z₁ ⟶ X₁\ng₂ : Z₁ ⟶ X₂\ng₃ : Z₂ ⟶ X₂\ng₄ : Z₂ ⟶ X₃\ninst✝³ : HasPushout g₁ g₂\ninst✝² : HasPushout g₃ g₄\ninst✝¹ : HasPushout (g₃ ≫ pushout.inr g₁ g₂) g₄\ninst✝ : HasPushout g₁ (g₂ ≫ pushout.inl g₃ g₄)\n⊢ pushout.inl g₁ g₂ ≫ pushout.inl (g... | [] | trans f₁ ≫ l₁
· congr 1
exact
(pushoutPushoutLeftIsPushout g₁ g₂ g₃ g₄).comp_coconePointUniqueUpToIso_hom _
WalkingCospan.left
· exact pushout.inl_desc _ _ _ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.MorphismProperty.Limits | {
"line": 239,
"column": 2
} | {
"line": 239,
"column": 13
} | {
"line": 239,
"column": 14
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nP : MorphismProperty C\ninst✝² : P.IsStableUnderBaseChange\nS S' X Y : C\nf : S' ⟶ S\nv₂₂ : Y ⟶ S\ng : X ⟶ Y\ninst✝¹ : HasPullback v₂₂ f\nH : P g\ninst✝ : HasPullback (g ≫ v₂₂) f\n⊢ IsPullback (pullback.fst (g ≫ v₂₂) f)\n (pullback.lift (pullback.fst (g ≫ v₂₂)... | [
"C : Type u\ninst✝³ : Category.{v, u} C\nP : MorphismProperty C\ninst✝² : P.IsStableUnderBaseChange\nS S' X Y : C\nf : S' ⟶ S\nv₂₂ : Y ⟶ S\ng : X ⟶ Y\ninst✝¹ : HasPullback v₂₂ f\nH : P g\ninst✝ : HasPullback (g ≫ v₂₂) f\n⊢ IsPullback (pullback.fst (g ≫ v₂₂) f) (pullback.snd (g ≫ v₂₂) f) (g ≫ v₂₂) f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.RingHomProperties | {
"line": 124,
"column": 2
} | {
"line": 125,
"column": 44
} | {
"line": 127,
"column": 0
} | [
{
"pp": "P Q : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop\nhP : StableUnderComposition fun {R S} [CommRing R] [CommRing S] ↦ P\nhQ : StableUnderComposition fun {R S} [CommRing R] [CommRing S] ↦ Q\n⊢ StableUnderComposition fun {R S} [CommRing R] [CommRing S] f ↦ P f ∧ Q f",
... | [] | introv R hf hg
exact ⟨hP f g hf.1 hg.1, hQ f g hf.2 hg.2⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.RingHomProperties | {
"line": 124,
"column": 2
} | {
"line": 125,
"column": 44
} | {
"line": 127,
"column": 0
} | [
{
"pp": "P Q : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop\nhP : StableUnderComposition fun {R S} [CommRing R] [CommRing S] ↦ P\nhQ : StableUnderComposition fun {R S} [CommRing R] [CommRing S] ↦ Q\n⊢ StableUnderComposition fun {R S} [CommRing R] [CommRing S] f ↦ P f ∧ Q f",
... | [] | introv R hf hg
exact ⟨hP f g hf.1 hg.1, hQ f g hf.2 hg.2⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Category.CommAlgCat.FiniteType | {
"line": 76,
"column": 52
} | {
"line": 94,
"column": 38
} | {
"line": 96,
"column": 0
} | [
{
"pp": "R : Type u\ninst✝ : CommRing R\n⊢ EssentiallySmall.{u, v, max (v + 1) u} (FGAlgCat R)",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"CategoryTheory.toSkeleton",
"instFaithfulFGAlgCatUliftFunctor",
"Eq.mpr",
"CommAlgCat.instConcreteCategoryAlgHomCarrier",
... | [] | by
suffices h : EssentiallySmall.{u} (FGAlgCat.{max u v} R) by
exact essentiallySmall_of_fully_faithful (FGAlgCat.uliftFunctor R)
rw [essentiallySmall_iff]
refine ⟨?_, ?_⟩
· let f := toSkeleton ∘ (FGAlgCat.uliftFunctor R).obj ∘ FGAlgCatSkeleton.eval R
refine small_of_surjective (f := f) fun A ↦ ?_
s... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.MorphismProperty.Limits | {
"line": 360,
"column": 2
} | {
"line": 360,
"column": 13
} | {
"line": 360,
"column": 14
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nP : MorphismProperty C\ninst✝² : P.IsStableUnderCobaseChange\nS S' X Y : C\nf : S ⟶ S'\nv₂₂ : S ⟶ Y\ng : Y ⟶ X\ninst✝¹ : HasPushout v₂₂ f\nH : P g\ninst✝ : HasPushout (v₂₂ ≫ g) f\n⊢ IsPushout f (v₂₂ ≫ g) (pushout.inr v₂₂ f ≫ pushout.desc (g ≫ pushout.inl (v₂₂ ≫ g... | [
"C : Type u\ninst✝³ : Category.{v, u} C\nP : MorphismProperty C\ninst✝² : P.IsStableUnderCobaseChange\nS S' X Y : C\nf : S ⟶ S'\nv₂₂ : S ⟶ Y\ng : Y ⟶ X\ninst✝¹ : HasPushout v₂₂ f\nH : P g\ninst✝ : HasPushout (v₂₂ ≫ g) f\n⊢ IsPushout f (v₂₂ ≫ g) (pushout.inr (v₂₂ ≫ g) f) (pushout.inl (v₂₂ ≫ g) f)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Presentation | {
"line": 144,
"column": 2
} | {
"line": 144,
"column": 13
} | {
"line": 144,
"column": 14
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nJ : Type w\ninst✝ : Category.{t, w} J\nX : C\npres : LimitPresentation J X\ni j : J\nf : i ⟶ j\n⊢ pres.π.app i ≫ pres.diag.map f = pres.π.app j",
"ppTerm": "?m.45",
"assigned": true,
"usedConstants": [
"CategoryTheory.Functor",
"CategoryTh... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nJ : Type w\ninst✝ : Category.{t, w} J\nX : C\npres : LimitPresentation J X\ni j : J\nf : i ⟶ j\n⊢ pres.π.app i ≫ pres.diag.map f = pres.π.app j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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