module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.GroupTheory.Perm.Fin | {
"line": 523,
"column": 29
} | {
"line": 523,
"column": 45
} | {
"line": 523,
"column": 46
} | [
{
"pp": "n : ℕ\nR : Type u_1\ninst✝ : CommRing R\nσ : Perm (Fin n)\nf : Fin n → Fin n → R\nhf : ∀ (i j : Fin n), f i j = -f j i\nD : Finset ((_ : Fin n) × Fin n) := Finset.univ.sigma Finset.Iio\nhD : D = Finset.univ.sigma Finset.Iio\nhφD : Finset.image (fun x ↦ ⟨max (σ x.fst) (σ x.snd), min (σ x.fst) (σ x.snd)⟩... | [
"n : ℕ\nR : Type u_1\ninst✝ : CommRing R\nσ : Perm (Fin n)\nf : Fin n → Fin n → R\nhf : ∀ (i j : Fin n), f i j = -f j i\nD : Finset ((_ : Fin n) × Fin n) := Finset.univ.sigma Finset.Iio\nhD : D = Finset.univ.sigma Finset.Iio\nhφD : Finset.image (fun x ↦ ⟨max (σ x.fst) (σ x.snd), min (σ x.fst) (σ x.snd)⟩) D = D\nx✝ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Factors | {
"line": 628,
"column": 2
} | {
"line": 628,
"column": 44
} | {
"line": 628,
"column": 45
} | [
{
"pp": "α : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf : Perm α\n⊢ f.cycleFactorsFinset = ∅ ↔ f = 1",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"False",
"Finset.coe_empty",
"Equiv.Perm.instOne",
"Function.onFun"... | [
"α : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf : Perm α\n⊢ 1 = f ↔ f = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Factors | {
"line": 654,
"column": 2
} | {
"line": 654,
"column": 17
} | {
"line": 654,
"column": 18
} | [
{
"pp": "α : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\nh : f.cycleFactorsFinset = g.cycleFactorsFinset\n⊢ f.cycleFactorsFinset.noncommProd id ⋯ = g",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Finset",
"Equiv.Perm.c... | [
"α : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\nh : f.cycleFactorsFinset = g.cycleFactorsFinset\n⊢ g.cycleFactorsFinset.noncommProd (fun x ↦ x) ⋯ = g"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Factors | {
"line": 754,
"column": 2
} | {
"line": 754,
"column": 26
} | {
"line": 754,
"column": 27
} | [
{
"pp": "α : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nk g : Perm α\nhk : ∀ c ∈ g.cycleFactorsFinset, Commute k c\n⊢ ∀ x ∈ g.cycleFactorsFinset, Commute k (id x)",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Monoid.toMulOneClass",
"Finset",
"Equiv.Perm.cycle... | [
"α : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nk g : Perm α\nhk : ∀ c ∈ g.cycleFactorsFinset, Commute k c\n⊢ ∀ x ∈ g.cycleFactorsFinset, Commute k x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Type | {
"line": 303,
"column": 50
} | {
"line": 309,
"column": 88
} | {
"line": 311,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝⁴ : Fintype α\ninst✝³ : DecidableEq α\nβ : Type u_2\ninst✝² : Fintype β\ninst✝¹ : DecidableEq β\np : β → Prop\ninst✝ : DecidablePred p\nf : α ≃ Subtype p\ng : Perm α\n⊢ (g.extendDomain f).cycleType = g.cycleType",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
... | [] | by
induction g using cycle_induction_on with
| base_one => rw [extendDomain_one, cycleType_one, cycleType_one]
| base_cycles σ hσ =>
rw [(hσ.extendDomain f).cycleType, hσ.cycleType, card_support_extend_domain]
| induction_disjoint σ τ hd _ hσ hτ =>
rw [hd.cycleType_mul, ← extendDomain_mul, (hd.extendDom... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.GroupTheory.Perm.Cycle.Factors | {
"line": 830,
"column": 12
} | {
"line": 830,
"column": 28
} | {
"line": 830,
"column": 29
} | [
{
"pp": "case pos\nα : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\ng f✝ σ τ : Perm α\nhd : σ.Disjoint τ\na✝ : σ.IsCycle\nhσ : ∀ {f : Perm α}, f ∈ σ.cycleFactorsFinset → (σ * f⁻¹).cycleFactorsFinset = σ.cycleFactorsFinset \\ {f}\nhτ : ∀ {f : Perm α}, f ∈ τ.cycleFactorsFinset → (τ * f⁻¹).cycleFactorsFins... | [
"case pos\nα : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\ng f✝ σ τ : Perm α\nhd : σ.Disjoint τ\na✝ : σ.IsCycle\nhσ : ∀ {f : Perm α}, f ∈ σ.cycleFactorsFinset → (σ * f⁻¹).cycleFactorsFinset = σ.cycleFactorsFinset \\ {f}\nhτ : ∀ {f : Perm α}, f ∈ τ.cycleFactorsFinset → (τ * f⁻¹).cycleFactorsFinset = τ.cycle... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Factors | {
"line": 845,
"column": 12
} | {
"line": 845,
"column": 28
} | {
"line": 845,
"column": 29
} | [
{
"pp": "case pos\nα : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\ng f✝ σ τ : Perm α\nhd : σ.Disjoint τ\na✝ : σ.IsCycle\nhσ : ∀ {f : Perm α}, f ∈ σ.cycleFactorsFinset → (σ * f⁻¹).cycleFactorsFinset = σ.cycleFactorsFinset \\ {f}\nhτ : ∀ {f : Perm α}, f ∈ τ.cycleFactorsFinset → (τ * f⁻¹).cycleFactorsFins... | [
"case pos\nα : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\ng f✝ σ τ : Perm α\nhd : σ.Disjoint τ\na✝ : σ.IsCycle\nhσ : ∀ {f : Perm α}, f ∈ σ.cycleFactorsFinset → (σ * f⁻¹).cycleFactorsFinset = σ.cycleFactorsFinset \\ {f}\nhτ : ∀ {f : Perm α}, f ∈ τ.cycleFactorsFinset → (τ * f⁻¹).cycleFactorsFinset = τ.cycle... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Type | {
"line": 604,
"column": 4
} | {
"line": 604,
"column": 58
} | {
"line": 604,
"column": 59
} | [
{
"pp": "case mp\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ : Perm α\nh : σ.IsSwap\n⊢ σ.cycleType = {2}",
"ppTerm": "?mp",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Equiv.Perm.support",
"Equiv.Perm.cycleType",
"congrArg",
"Equiv.Perm.IsSwap",
... | [
"case mp\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ : Perm α\nh : σ.IsSwap\n⊢ σ.IsSwap"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Type | {
"line": 633,
"column": 2
} | {
"line": 633,
"column": 13
} | {
"line": 633,
"column": 14
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nh : IsThreeCycle 1\n⊢ False",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nh : IsThreeCycle 1\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Type | {
"line": 709,
"column": 10
} | {
"line": 709,
"column": 21
} | {
"line": 709,
"column": 22
} | [
{
"pp": "case mpr.h₂.hnc\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\ng : Perm α\na : α\nhg3 : g.IsThreeCycle\nha : ¬g a = a\n⊢ g a ∉ {g (g a)}",
"ppTerm": "?mpr.h₂.hnc",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Equiv.instEquivLike",
"congrArg",
"Finset",
... | [
"case mpr.h₂.hnc\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\ng : Perm α\na : α\nhg3 : g.IsThreeCycle\nha : ¬g a = a\n⊢ ¬a = g a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Type | {
"line": 714,
"column": 36
} | {
"line": 714,
"column": 64
} | {
"line": 714,
"column": 65
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\ng : Perm α\na : α\nhg3 : g.IsThreeCycle\nha : a = g (g a)\nthis : (g ^ 3) a = a\n⊢ g a = a",
"ppTerm": "?m.141",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\ng : Perm α\na : α\nhg3 : g.IsThreeCycle\nha : a = g (g a)\nthis : (g ^ 3) a = a\n⊢ g a = a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.SemiringInverse | {
"line": 93,
"column": 2
} | {
"line": 93,
"column": 13
} | {
"line": 93,
"column": 14
} | [
{
"pp": "n : Type u_1\nR : Type u_3\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommSemiring R\nA : Matrix n n R\np q : n\nhpq : p ≠ q\nhcol : A.col p = A.col q\ns t : ℤˣ\n⊢ detp s A = detp t A",
"ppTerm": "?m.29",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals"... | [
"n : Type u_1\nR : Type u_3\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommSemiring R\nA : Matrix n n R\np q : n\nhpq : p ≠ q\nhcol : A.col p = A.col q\ns t : ℤˣ\n⊢ detp s A = detp t A"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.SemiringInverse | {
"line": 99,
"column": 2
} | {
"line": 99,
"column": 13
} | {
"line": 99,
"column": 14
} | [
{
"pp": "n : Type u_1\nR : Type u_3\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommSemiring R\ns : ℤˣ\nA : Matrix n n R\np : n\nhcol : A.col p = 0\n⊢ detp s A = 0",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"n : Type u_1\nR : Type u_3\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommSemiring R\ns : ℤˣ\nA : Matrix n n R\np : n\nhcol : A.col p = 0\n⊢ detp s A = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Multilinear.Basic | {
"line": 337,
"column": 2
} | {
"line": 337,
"column": 13
} | {
"line": 337,
"column": 14
} | [
{
"pp": "R : Type uR\nn : ℕ\nM : Fin n.succ → Type v\nM₂ : Type v₂\ninst✝⁴ : Semiring R\ninst✝³ : (i : Fin n.succ) → AddCommMonoid (M i)\ninst✝² : AddCommMonoid M₂\ninst✝¹ : (i : Fin n.succ) → Module R (M i)\ninst✝ : Module R M₂\nf : MultilinearMap R M M₂\np : Fin (n + 1)\nm : (i : Fin n) → M (p.succAbove i)\nx... | [
"R : Type uR\nn : ℕ\nM : Fin n.succ → Type v\nM₂ : Type v₂\ninst✝⁴ : Semiring R\ninst✝³ : (i : Fin n.succ) → AddCommMonoid (M i)\ninst✝² : AddCommMonoid M₂\ninst✝¹ : (i : Fin n.succ) → Module R (M i)\ninst✝ : Module R M₂\nf : MultilinearMap R M M₂\np : Fin (n + 1)\nm : (i : Fin n) → M (p.succAbove i)\nx y : M p\n⊢ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Multilinear.Basic | {
"line": 342,
"column": 2
} | {
"line": 342,
"column": 13
} | {
"line": 342,
"column": 14
} | [
{
"pp": "R : Type uR\nn : ℕ\nM : Fin n.succ → Type v\nM₂ : Type v₂\ninst✝⁴ : Semiring R\ninst✝³ : (i : Fin n.succ) → AddCommMonoid (M i)\ninst✝² : AddCommMonoid M₂\ninst✝¹ : (i : Fin n.succ) → Module R (M i)\ninst✝ : Module R M₂\nf : MultilinearMap R M M₂\np : Fin (n + 1)\nm : (i : Fin n) → M (p.succAbove i)\nc... | [
"R : Type uR\nn : ℕ\nM : Fin n.succ → Type v\nM₂ : Type v₂\ninst✝⁴ : Semiring R\ninst✝³ : (i : Fin n.succ) → AddCommMonoid (M i)\ninst✝² : AddCommMonoid M₂\ninst✝¹ : (i : Fin n.succ) → Module R (M i)\ninst✝ : Module R M₂\nf : MultilinearMap R M M₂\np : Fin (n + 1)\nm : (i : Fin n) → M (p.succAbove i)\nc : R\nx : M ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Multilinear.Basic | {
"line": 392,
"column": 4
} | {
"line": 393,
"column": 11
} | {
"line": 393,
"column": 12
} | [
{
"pp": "R : Type uR\nι : Type uι\nM₁ : ι → Type v₁\nM₁' : ι → Type v₁'\nM₂ : Type v₂\ninst✝⁶ : Semiring R\ninst✝⁵ : (i : ι) → AddCommMonoid (M₁ i)\ninst✝⁴ : AddCommMonoid M₂\ninst✝³ : (i : ι) → Module R (M₁ i)\ninst✝² : Module R M₂\ninst✝¹ : (i : ι) → AddCommMonoid (M₁' i)\ninst✝ : (i : ι) → Module R (M₁' i)\n... | [
"R : Type uR\nι : Type uι\nM₁ : ι → Type v₁\nM₁' : ι → Type v₁'\nM₂ : Type v₂\ninst✝⁶ : Semiring R\ninst✝⁵ : (i : ι) → AddCommMonoid (M₁ i)\ninst✝⁴ : AddCommMonoid M₂\ninst✝³ : (i : ι) → Module R (M₁ i)\ninst✝² : Module R M₂\ninst✝¹ : (i : ι) → AddCommMonoid (M₁' i)\ninst✝ : (i : ι) → Module R (M₁' i)\nf : (i : ι) ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Alternating.Basic | {
"line": 212,
"column": 47
} | {
"line": 212,
"column": 84
} | {
"line": 212,
"column": 85
} | [
{
"pp": "R : Type u_1\ninst✝¹³ : Semiring R\nM : Type u_2\ninst✝¹² : AddCommMonoid M\ninst✝¹¹ : Module R M\nN : Type u_3\ninst✝¹⁰ : AddCommMonoid N\ninst✝⁹ : Module R N\nP : Type u_4\ninst✝⁸ : AddCommMonoid P\ninst✝⁷ : Module R P\nM' : Type u_5\ninst✝⁶ : AddCommGroup M'\ninst✝⁵ : Module R M'\nN' : Type u_6\nins... | [] | by simp [f.map_eq_zero_of_eq v h hij] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.LinearAlgebra.Alternating.Basic | {
"line": 315,
"column": 47
} | {
"line": 315,
"column": 84
} | {
"line": 315,
"column": 85
} | [
{
"pp": "R : Type u_1\ninst✝¹⁰ : Semiring R\nM : Type u_2\ninst✝⁹ : AddCommMonoid M\ninst✝⁸ : Module R M\nN : Type u_3\ninst✝⁷ : AddCommMonoid N\ninst✝⁶ : Module R N\nP : Type u_4\ninst✝⁵ : AddCommMonoid P\ninst✝⁴ : Module R P\nM' : Type u_5\ninst✝³ : AddCommGroup M'\ninst✝² : Module R M'\nN' : Type u_6\ninst✝¹... | [] | by simp [f.map_eq_zero_of_eq v h hij] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.LinearAlgebra.Alternating.Basic | {
"line": 423,
"column": 36
} | {
"line": 423,
"column": 73
} | {
"line": 425,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝¹² : Semiring R\nM : Type u_2\ninst✝¹¹ : AddCommMonoid M\ninst✝¹⁰ : Module R M\nN : Type u_3\ninst✝⁹ : AddCommMonoid N\ninst✝⁸ : Module R N\nP : Type u_4\ninst✝⁷ : AddCommMonoid P\ninst✝⁶ : Module R P\nM' : Type u_5\ninst✝⁵ : AddCommGroup M'\ninst✝⁴ : Module R M'\nN' : Type u_6\ninst... | [] | by simp [f.map_eq_zero_of_eq v h hij] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.LinearAlgebra.Alternating.Basic | {
"line": 551,
"column": 4
} | {
"line": 551,
"column": 40
} | {
"line": 551,
"column": 41
} | [
{
"pp": "R : Type u_1\ninst✝⁶ : Semiring R\nM : Type u_2\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\nN : Type u_3\ninst✝³ : AddCommMonoid N\ninst✝² : Module R N\nι : Type u_7\nM₂ : Type u_10\ninst✝¹ : AddCommMonoid M₂\ninst✝ : Module R M₂\nf : M₂ →ₗ[R] M\nhf : Function.Surjective ⇑f\ng₁ g₂ : M [⋀^ι]→ₗ[R] N\... | [
"R : Type u_1\ninst✝⁶ : Semiring R\nM : Type u_2\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\nN : Type u_3\ninst✝³ : AddCommMonoid N\ninst✝² : Module R N\nι : Type u_7\nM₂ : Type u_10\ninst✝¹ : AddCommMonoid M₂\ninst✝ : Module R M₂\nf : M₂ →ₗ[R] M\nhf : Function.Surjective ⇑f\ng₁ g₂ : M [⋀^ι]→ₗ[R] N\nh : (fun g ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Alternating.Basic | {
"line": 694,
"column": 12
} | {
"line": 694,
"column": 23
} | {
"line": 694,
"column": 24
} | [
{
"pp": "R : Type u_1\ninst✝¹⁴ : Semiring R\nM : Type u_2\ninst✝¹³ : AddCommMonoid M\ninst✝¹² : Module R M\nN : Type u_3\ninst✝¹¹ : AddCommMonoid N\ninst✝¹⁰ : Module R N\nP : Type u_4\ninst✝⁹ : AddCommMonoid P\ninst✝⁸ : Module R P\nM' : Type u_5\ninst✝⁷ : AddCommGroup M'\ninst✝⁶ : Module R M'\nN' : Type u_6\nin... | [
"R : Type u_1\ninst✝¹⁴ : Semiring R\nM : Type u_2\ninst✝¹³ : AddCommMonoid M\ninst✝¹² : Module R M\nN : Type u_3\ninst✝¹¹ : AddCommMonoid N\ninst✝¹⁰ : Module R N\nP : Type u_4\ninst✝⁹ : AddCommMonoid P\ninst✝⁸ : Module R P\nM' : Type u_5\ninst✝⁷ : AddCommGroup M'\ninst✝⁶ : Module R M'\nN' : Type u_6\ninst✝⁵ : AddCo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Multilinear.Basic | {
"line": 474,
"column": 2
} | {
"line": 474,
"column": 13
} | {
"line": 474,
"column": 14
} | [
{
"pp": "R : Type uR\nι : Type uι\nM₁ : ι → Type v₁\nM₂ : Type v₂\ninst✝⁶ : Semiring R\ninst✝⁵ : (i : ι) → AddCommMonoid (M₁ i)\ninst✝⁴ : AddCommMonoid M₂\ninst✝³ : (i : ι) → Module R (M₁ i)\ninst✝² : Module R M₂\nf : MultilinearMap R M₁ M₂\ninst✝¹ : DecidableEq ι\ninst✝ : Fintype ι\nm m' : (i : ι) → M₁ i\n⊢ f ... | [
"R : Type uR\nι : Type uι\nM₁ : ι → Type v₁\nM₂ : Type v₂\ninst✝⁶ : Semiring R\ninst✝⁵ : (i : ι) → AddCommMonoid (M₁ i)\ninst✝⁴ : AddCommMonoid M₂\ninst✝³ : (i : ι) → Module R (M₁ i)\ninst✝² : Module R M₂\nf : MultilinearMap R M₁ M₂\ninst✝¹ : DecidableEq ι\ninst✝ : Fintype ι\nm m' : (i : ι) → M₁ i\n⊢ f (m + m') = ∑... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Category.Ring.Colimits | {
"line": 235,
"column": 16
} | {
"line": 235,
"column": 31
} | {
"line": 236,
"column": 4
} | [
{
"pp": "case a.zero\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ RingCat\ns : Cocone F\nx y : Prequotient F\nj : J\n⊢ descFunLift F s (Prequotient.of j 0) = descFunLift F s zero",
"ppTerm": "?a.zero",
"assigned": true,
"usedConstants": [
"RingHom.instRingHomClass",
"CategoryTheory.Func... | [] | simp +instances | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Category.Ring.Colimits | {
"line": 235,
"column": 16
} | {
"line": 235,
"column": 31
} | {
"line": 236,
"column": 4
} | [
{
"pp": "case a.zero\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ RingCat\ns : Cocone F\nx y : Prequotient F\nj : J\n⊢ descFunLift F s (Prequotient.of j 0) = descFunLift F s zero",
"ppTerm": "?a.zero",
"assigned": true,
"usedConstants": [
"RingHom.instRingHomClass",
"CategoryTheory.Func... | [] | simp +instances | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Category.Ring.Colimits | {
"line": 235,
"column": 16
} | {
"line": 235,
"column": 31
} | {
"line": 236,
"column": 4
} | [
{
"pp": "case a.zero\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ RingCat\ns : Cocone F\nx y : Prequotient F\nj : J\n⊢ descFunLift F s (Prequotient.of j 0) = descFunLift F s zero",
"ppTerm": "?a.zero",
"assigned": true,
"usedConstants": [
"RingHom.instRingHomClass",
"CategoryTheory.Func... | [] | simp +instances | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Multilinear.Basic | {
"line": 552,
"column": 8
} | {
"line": 552,
"column": 23
} | {
"line": 552,
"column": 24
} | [
{
"pp": "R : Type uR\nι : Type uι\nM₁ : ι → Type v₁\nM₂ : Type v₂\ninst✝⁶ : Semiring R\ninst✝⁵ : (i : ι) → AddCommMonoid (M₁ i)\ninst✝⁴ : AddCommMonoid M₂\ninst✝³ : (i : ι) → Module R (M₁ i)\ninst✝² : Module R M₂\nf : MultilinearMap R M₁ M₂\nα : ι → Type u_1\ng : (i : ι) → α i → M₁ i\ninst✝¹ : DecidableEq ι\nin... | [
"R : Type uR\nι : Type uι\nM₁ : ι → Type v₁\nM₂ : Type v₂\ninst✝⁶ : Semiring R\ninst✝⁵ : (i : ι) → AddCommMonoid (M₁ i)\ninst✝⁴ : AddCommMonoid M₂\ninst✝³ : (i : ι) → Module R (M₁ i)\ninst✝² : Module R M₂\nf : MultilinearMap R M₁ M₂\nα : ι → Type u_1\ng : (i : ι) → α i → M₁ i\ninst✝¹ : DecidableEq ι\ninst✝ : Fintyp... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Category.Ring.Colimits | {
"line": 236,
"column": 15
} | {
"line": 236,
"column": 30
} | {
"line": 237,
"column": 4
} | [
{
"pp": "case a.one\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ RingCat\ns : Cocone F\nx y : Prequotient F\nj : J\n⊢ descFunLift F s (Prequotient.of j 1) = descFunLift F s one",
"ppTerm": "?a.one",
"assigned": true,
"usedConstants": [
"RingHom.instRingHomClass",
"CategoryTheory.Functor... | [] | simp +instances | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Category.Ring.Colimits | {
"line": 236,
"column": 15
} | {
"line": 236,
"column": 30
} | {
"line": 237,
"column": 4
} | [
{
"pp": "case a.one\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ RingCat\ns : Cocone F\nx y : Prequotient F\nj : J\n⊢ descFunLift F s (Prequotient.of j 1) = descFunLift F s one",
"ppTerm": "?a.one",
"assigned": true,
"usedConstants": [
"RingHom.instRingHomClass",
"CategoryTheory.Functor... | [] | simp +instances | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Category.Ring.Colimits | {
"line": 236,
"column": 15
} | {
"line": 236,
"column": 30
} | {
"line": 237,
"column": 4
} | [
{
"pp": "case a.one\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ RingCat\ns : Cocone F\nx y : Prequotient F\nj : J\n⊢ descFunLift F s (Prequotient.of j 1) = descFunLift F s one",
"ppTerm": "?a.one",
"assigned": true,
"usedConstants": [
"RingHom.instRingHomClass",
"CategoryTheory.Functor... | [] | simp +instances | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Category.Ring.Colimits | {
"line": 237,
"column": 17
} | {
"line": 237,
"column": 32
} | {
"line": 238,
"column": 4
} | [
{
"pp": "case a.neg\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ RingCat\ns : Cocone F\nx✝ y : Prequotient F\nj : J\nx : ↑(F.obj j)\n⊢ descFunLift F s (Prequotient.of j (-x)) = descFunLift F s (Prequotient.of j x).neg",
"ppTerm": "?a.neg",
"assigned": true,
"usedConstants": [
"NegZeroClass.to... | [] | simp +instances | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Category.Ring.Colimits | {
"line": 237,
"column": 17
} | {
"line": 237,
"column": 32
} | {
"line": 238,
"column": 4
} | [
{
"pp": "case a.neg\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ RingCat\ns : Cocone F\nx✝ y : Prequotient F\nj : J\nx : ↑(F.obj j)\n⊢ descFunLift F s (Prequotient.of j (-x)) = descFunLift F s (Prequotient.of j x).neg",
"ppTerm": "?a.neg",
"assigned": true,
"usedConstants": [
"NegZeroClass.to... | [] | simp +instances | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Category.Ring.Colimits | {
"line": 237,
"column": 17
} | {
"line": 237,
"column": 32
} | {
"line": 238,
"column": 4
} | [
{
"pp": "case a.neg\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ RingCat\ns : Cocone F\nx✝ y : Prequotient F\nj : J\nx : ↑(F.obj j)\n⊢ descFunLift F s (Prequotient.of j (-x)) = descFunLift F s (Prequotient.of j x).neg",
"ppTerm": "?a.neg",
"assigned": true,
"usedConstants": [
"NegZeroClass.to... | [] | simp +instances | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Category.Ring.Colimits | {
"line": 238,
"column": 19
} | {
"line": 238,
"column": 34
} | {
"line": 239,
"column": 4
} | [
{
"pp": "case a.add\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ RingCat\ns : Cocone F\nx✝ y✝ : Prequotient F\nj : J\nx y : ↑(F.obj j)\n⊢ descFunLift F s (Prequotient.of j (x + y)) = descFunLift F s ((Prequotient.of j x).add (Prequotient.of j y))",
"ppTerm": "?a.add",
"assigned": true,
"usedConstan... | [] | simp +instances | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Category.Ring.Colimits | {
"line": 238,
"column": 19
} | {
"line": 238,
"column": 34
} | {
"line": 239,
"column": 4
} | [
{
"pp": "case a.add\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ RingCat\ns : Cocone F\nx✝ y✝ : Prequotient F\nj : J\nx y : ↑(F.obj j)\n⊢ descFunLift F s (Prequotient.of j (x + y)) = descFunLift F s ((Prequotient.of j x).add (Prequotient.of j y))",
"ppTerm": "?a.add",
"assigned": true,
"usedConstan... | [] | simp +instances | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Category.Ring.Colimits | {
"line": 238,
"column": 19
} | {
"line": 238,
"column": 34
} | {
"line": 239,
"column": 4
} | [
{
"pp": "case a.add\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ RingCat\ns : Cocone F\nx✝ y✝ : Prequotient F\nj : J\nx y : ↑(F.obj j)\n⊢ descFunLift F s (Prequotient.of j (x + y)) = descFunLift F s ((Prequotient.of j x).add (Prequotient.of j y))",
"ppTerm": "?a.add",
"assigned": true,
"usedConstan... | [] | simp +instances | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Category.Ring.Colimits | {
"line": 239,
"column": 19
} | {
"line": 239,
"column": 34
} | {
"line": 240,
"column": 4
} | [
{
"pp": "case a.mul\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ RingCat\ns : Cocone F\nx✝ y✝ : Prequotient F\nj : J\nx y : ↑(F.obj j)\n⊢ descFunLift F s (Prequotient.of j (x * y)) = descFunLift F s ((Prequotient.of j x).mul (Prequotient.of j y))",
"ppTerm": "?a.mul",
"assigned": true,
"usedConstan... | [] | simp +instances | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Category.Ring.Colimits | {
"line": 239,
"column": 19
} | {
"line": 239,
"column": 34
} | {
"line": 240,
"column": 4
} | [
{
"pp": "case a.mul\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ RingCat\ns : Cocone F\nx✝ y✝ : Prequotient F\nj : J\nx y : ↑(F.obj j)\n⊢ descFunLift F s (Prequotient.of j (x * y)) = descFunLift F s ((Prequotient.of j x).mul (Prequotient.of j y))",
"ppTerm": "?a.mul",
"assigned": true,
"usedConstan... | [] | simp +instances | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Category.Ring.Colimits | {
"line": 239,
"column": 19
} | {
"line": 239,
"column": 34
} | {
"line": 240,
"column": 4
} | [
{
"pp": "case a.mul\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ RingCat\ns : Cocone F\nx✝ y✝ : Prequotient F\nj : J\nx y : ↑(F.obj j)\n⊢ descFunLift F s (Prequotient.of j (x * y)) = descFunLift F s ((Prequotient.of j x).mul (Prequotient.of j y))",
"ppTerm": "?a.mul",
"assigned": true,
"usedConstan... | [] | simp +instances | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Matrix.Determinant.Basic | {
"line": 145,
"column": 6
} | {
"line": 145,
"column": 40
} | {
"line": 145,
"column": 41
} | [
{
"pp": "n : Type u_2\ninst✝² : DecidableEq n\ninst✝¹ : Fintype n\nR : Type v\ninst✝ : CommRing R\nM N : Matrix n n R\nf : n → n\nx✝ : f ∈ univ\nhbij : f ∉ {p | Bijective p}\n⊢ ¬Bijective f",
"ppTerm": "?m.386",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"n : Type u_2\ninst✝² : DecidableEq n\ninst✝¹ : Fintype n\nR : Type v\ninst✝ : CommRing R\nM N : Matrix n n R\nf : n → n\nx✝ : f ∈ univ\nhbij : f ∉ {p | Bijective p}\n⊢ ¬Bijective f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.Determinant.Basic | {
"line": 143,
"column": 92
} | {
"line": 145,
"column": 45
} | {
"line": 146,
"column": 4
} | [
{
"pp": "n : Type u_2\ninst✝² : DecidableEq n\ninst✝¹ : Fintype n\nR : Type v\ninst✝ : CommRing R\nM N : Matrix n n R\n⊢ ∑ p, ∑ σ, ↑↑(sign σ) * ∏ i, M (σ i) (p i) * N (p i) i =\n ∑ p with Bijective p, ∑ σ, ↑↑(sign σ) * ∏ i, M (σ i) (p i) * N (p i) i",
"ppTerm": "?m.110",
"assigned": true,
"usedCo... | [] | by
refine (sum_subset (filter_subset _ _) fun f _ hbij ↦ det_mul_aux ?_).symm
simpa only [mem_filter_univ] using hbij | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Category.Ring.Colimits | {
"line": 535,
"column": 16
} | {
"line": 535,
"column": 31
} | {
"line": 536,
"column": 4
} | [
{
"pp": "case a.zero\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ CommRingCat\ns : Cocone F\nx y : Prequotient F\nj : J\n⊢ descFunLift F s (Prequotient.of j 0) = descFunLift F s zero",
"ppTerm": "?a.zero",
"assigned": true,
"usedConstants": [
"RingHom.instRingHomClass",
"CategoryTheory.... | [] | simp +instances | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Category.Ring.Colimits | {
"line": 535,
"column": 16
} | {
"line": 535,
"column": 31
} | {
"line": 536,
"column": 4
} | [
{
"pp": "case a.zero\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ CommRingCat\ns : Cocone F\nx y : Prequotient F\nj : J\n⊢ descFunLift F s (Prequotient.of j 0) = descFunLift F s zero",
"ppTerm": "?a.zero",
"assigned": true,
"usedConstants": [
"RingHom.instRingHomClass",
"CategoryTheory.... | [] | simp +instances | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Category.Ring.Colimits | {
"line": 535,
"column": 16
} | {
"line": 535,
"column": 31
} | {
"line": 536,
"column": 4
} | [
{
"pp": "case a.zero\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ CommRingCat\ns : Cocone F\nx y : Prequotient F\nj : J\n⊢ descFunLift F s (Prequotient.of j 0) = descFunLift F s zero",
"ppTerm": "?a.zero",
"assigned": true,
"usedConstants": [
"RingHom.instRingHomClass",
"CategoryTheory.... | [] | simp +instances | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Category.Ring.Colimits | {
"line": 536,
"column": 15
} | {
"line": 536,
"column": 30
} | {
"line": 537,
"column": 4
} | [
{
"pp": "case a.one\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ CommRingCat\ns : Cocone F\nx y : Prequotient F\nj : J\n⊢ descFunLift F s (Prequotient.of j 1) = descFunLift F s one",
"ppTerm": "?a.one",
"assigned": true,
"usedConstants": [
"RingHom.instRingHomClass",
"CategoryTheory.Fun... | [] | simp +instances | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Category.Ring.Colimits | {
"line": 536,
"column": 15
} | {
"line": 536,
"column": 30
} | {
"line": 537,
"column": 4
} | [
{
"pp": "case a.one\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ CommRingCat\ns : Cocone F\nx y : Prequotient F\nj : J\n⊢ descFunLift F s (Prequotient.of j 1) = descFunLift F s one",
"ppTerm": "?a.one",
"assigned": true,
"usedConstants": [
"RingHom.instRingHomClass",
"CategoryTheory.Fun... | [] | simp +instances | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Category.Ring.Colimits | {
"line": 536,
"column": 15
} | {
"line": 536,
"column": 30
} | {
"line": 537,
"column": 4
} | [
{
"pp": "case a.one\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ CommRingCat\ns : Cocone F\nx y : Prequotient F\nj : J\n⊢ descFunLift F s (Prequotient.of j 1) = descFunLift F s one",
"ppTerm": "?a.one",
"assigned": true,
"usedConstants": [
"RingHom.instRingHomClass",
"CategoryTheory.Fun... | [] | simp +instances | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Category.Ring.Colimits | {
"line": 537,
"column": 17
} | {
"line": 537,
"column": 32
} | {
"line": 538,
"column": 4
} | [
{
"pp": "case a.neg\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ CommRingCat\ns : Cocone F\nx✝ y : Prequotient F\nj : J\nx : ↑(F.obj j)\n⊢ descFunLift F s (Prequotient.of j (-x)) = descFunLift F s (Prequotient.of j x).neg",
"ppTerm": "?a.neg",
"assigned": true,
"usedConstants": [
"NegZeroClas... | [] | simp +instances | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Category.Ring.Colimits | {
"line": 537,
"column": 17
} | {
"line": 537,
"column": 32
} | {
"line": 538,
"column": 4
} | [
{
"pp": "case a.neg\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ CommRingCat\ns : Cocone F\nx✝ y : Prequotient F\nj : J\nx : ↑(F.obj j)\n⊢ descFunLift F s (Prequotient.of j (-x)) = descFunLift F s (Prequotient.of j x).neg",
"ppTerm": "?a.neg",
"assigned": true,
"usedConstants": [
"NegZeroClas... | [] | simp +instances | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Category.Ring.Colimits | {
"line": 537,
"column": 17
} | {
"line": 537,
"column": 32
} | {
"line": 538,
"column": 4
} | [
{
"pp": "case a.neg\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ CommRingCat\ns : Cocone F\nx✝ y : Prequotient F\nj : J\nx : ↑(F.obj j)\n⊢ descFunLift F s (Prequotient.of j (-x)) = descFunLift F s (Prequotient.of j x).neg",
"ppTerm": "?a.neg",
"assigned": true,
"usedConstants": [
"NegZeroClas... | [] | simp +instances | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Category.Ring.Colimits | {
"line": 538,
"column": 19
} | {
"line": 538,
"column": 34
} | {
"line": 539,
"column": 4
} | [
{
"pp": "case a.add\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ CommRingCat\ns : Cocone F\nx✝ y✝ : Prequotient F\nj : J\nx y : ↑(F.obj j)\n⊢ descFunLift F s (Prequotient.of j (x + y)) = descFunLift F s ((Prequotient.of j x).add (Prequotient.of j y))",
"ppTerm": "?a.add",
"assigned": true,
"usedCon... | [] | simp +instances | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Category.Ring.Colimits | {
"line": 538,
"column": 19
} | {
"line": 538,
"column": 34
} | {
"line": 539,
"column": 4
} | [
{
"pp": "case a.add\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ CommRingCat\ns : Cocone F\nx✝ y✝ : Prequotient F\nj : J\nx y : ↑(F.obj j)\n⊢ descFunLift F s (Prequotient.of j (x + y)) = descFunLift F s ((Prequotient.of j x).add (Prequotient.of j y))",
"ppTerm": "?a.add",
"assigned": true,
"usedCon... | [] | simp +instances | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Category.Ring.Colimits | {
"line": 538,
"column": 19
} | {
"line": 538,
"column": 34
} | {
"line": 539,
"column": 4
} | [
{
"pp": "case a.add\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ CommRingCat\ns : Cocone F\nx✝ y✝ : Prequotient F\nj : J\nx y : ↑(F.obj j)\n⊢ descFunLift F s (Prequotient.of j (x + y)) = descFunLift F s ((Prequotient.of j x).add (Prequotient.of j y))",
"ppTerm": "?a.add",
"assigned": true,
"usedCon... | [] | simp +instances | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Category.Ring.Colimits | {
"line": 539,
"column": 19
} | {
"line": 539,
"column": 34
} | {
"line": 540,
"column": 4
} | [
{
"pp": "case a.mul\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ CommRingCat\ns : Cocone F\nx✝ y✝ : Prequotient F\nj : J\nx y : ↑(F.obj j)\n⊢ descFunLift F s (Prequotient.of j (x * y)) = descFunLift F s ((Prequotient.of j x).mul (Prequotient.of j y))",
"ppTerm": "?a.mul",
"assigned": true,
"usedCon... | [] | simp +instances | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Category.Ring.Colimits | {
"line": 539,
"column": 19
} | {
"line": 539,
"column": 34
} | {
"line": 540,
"column": 4
} | [
{
"pp": "case a.mul\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ CommRingCat\ns : Cocone F\nx✝ y✝ : Prequotient F\nj : J\nx y : ↑(F.obj j)\n⊢ descFunLift F s (Prequotient.of j (x * y)) = descFunLift F s ((Prequotient.of j x).mul (Prequotient.of j y))",
"ppTerm": "?a.mul",
"assigned": true,
"usedCon... | [] | simp +instances | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Category.Ring.Colimits | {
"line": 539,
"column": 19
} | {
"line": 539,
"column": 34
} | {
"line": 540,
"column": 4
} | [
{
"pp": "case a.mul\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ CommRingCat\ns : Cocone F\nx✝ y✝ : Prequotient F\nj : J\nx y : ↑(F.obj j)\n⊢ descFunLift F s (Prequotient.of j (x * y)) = descFunLift F s ((Prequotient.of j x).mul (Prequotient.of j y))",
"ppTerm": "?a.mul",
"assigned": true,
"usedCon... | [] | simp +instances | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.Matrix.Determinant.Basic | {
"line": 513,
"column": 6
} | {
"line": 513,
"column": 31
} | {
"line": 513,
"column": 32
} | [
{
"pp": "n : Type u_2\ninst✝³ : DecidableEq n\ninst✝² : Fintype n\nR : Type v\ninst✝¹ : CommRing R\ninst✝ : Nontrivial n\nu v : n → R\ni j : n\nhij : i ≠ j\nuv' : Matrix n n R := ((vecMulVec u v).updateRow i v).updateRow j v\nhuv' : uv'.det = 0\n⊢ vecMulVec u v = ((vecMulVec u v).updateRow j (u j • v)).updateRo... | [
"n : Type u_2\ninst✝³ : DecidableEq n\ninst✝² : Fintype n\nR : Type v\ninst✝¹ : CommRing R\ninst✝ : Nontrivial n\nu v : n → R\ni j : n\nhij : i ≠ j\nuv' : Matrix n n R := ((vecMulVec u v).updateRow i v).updateRow j v\nhuv' : uv'.det = 0\n⊢ vecMulVec u v = (vecMulVec (update u j (u j)) v).updateRow i (u i • v)"
] | ← update_vecMulVec u v j, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.LinearAlgebra.Matrix.Determinant.Basic | {
"line": 564,
"column": 4
} | {
"line": 564,
"column": 57
} | {
"line": 565,
"column": 2
} | [
{
"pp": "case refine_1\nR : Type v\ninst✝ : CommRing R\nn : ℕ\nk : Fin (n + 1)\nc : Fin n → R\nhc : ∀ (i : Fin n), 0 < i.succ → c i = 0\nM N : Matrix (Fin n.succ) (Fin n.succ) R\nh0 : ∀ (j : Fin n.succ), M 0 j = N 0 j\nhsucc : ∀ (i : Fin n) (j : Fin n.succ), M i.succ j = N i.succ j + c i * M i.castSucc j\ni✝ j ... | [] | rw [hsucc, hc i (Fin.succ_pos _), zero_mul, add_zero] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.CategoryTheory.Limits.Types.ColimitType | {
"line": 287,
"column": 6
} | {
"line": 287,
"column": 17
} | {
"line": 287,
"column": 18
} | [
{
"pp": "J : Type u\ninst✝ : Category.{v, u} J\nF : J ⥤ Type w₀\nc : F.CoconeTypes\nhc : c.IsColimitCore\nT : Type w₂\nf g : c.pt → T\nh : ∀ (j : J), f ∘ c.ι j = g ∘ c.ι j\nthis : Equiv.ulift.invFun ∘ f = Equiv.ulift.invFun ∘ g\nx : c.pt\n⊢ f x = g x",
"ppTerm": "?m.82",
"assigned": false,
"usedCons... | [
"J : Type u\ninst✝ : Category.{v, u} J\nF : J ⥤ Type w₀\nc : F.CoconeTypes\nhc : c.IsColimitCore\nT : Type w₂\nf g : c.pt → T\nh : ∀ (j : J), f ∘ c.ι j = g ∘ c.ι j\nthis : Equiv.ulift.invFun ∘ f = Equiv.ulift.invFun ∘ g\nx : c.pt\n⊢ f x = g x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Filtered.Basic | {
"line": 682,
"column": 24
} | {
"line": 682,
"column": 57
} | {
"line": 682,
"column": 58
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : IsCofilteredOrEmpty C\ni j j' : C\nf : j ⟶ i\nf' : j' ⟶ i\nK : C\nG : K ⟶ j\nG' : K ⟶ j'\nh✝ : True\nk : C\ne : k ⟶ K\nhe : e ≫ G ≫ f = e ≫ G' ≫ f'\n⊢ (e ≫ G) ≫ f = (e ≫ G') ≫ f'",
"ppTerm": "?m.77",
"assigned": true,
"usedConstants": [
... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : IsCofilteredOrEmpty C\ni j j' : C\nf : j ⟶ i\nf' : j' ⟶ i\nK : C\nG : K ⟶ j\nG' : K ⟶ j'\nh✝ : True\nk : C\ne : k ⟶ K\nhe : e ≫ G ≫ f = e ≫ G' ≫ f'\n⊢ e ≫ G ≫ f = e ≫ G' ≫ f'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Multilinear.Basic | {
"line": 741,
"column": 2
} | {
"line": 741,
"column": 29
} | {
"line": 741,
"column": 30
} | [
{
"pp": "ι : Sort u_2\ninst✝² : DecidableEq ι\nP : ι → Prop\ninst✝¹ : DecidablePred P\nM₁ : ι → Type u_1\ninst✝ : DecidableEq { a // ¬P a }\nx : (i : { a // P a }) → M₁ ↑i\nz : (i : { a // ¬P a }) → M₁ ↑i\ni : { a // ¬P a }\nc : M₁ ↑i\n⊢ (fun j ↦ if h : P j then x ⟨j, h⟩ else update z i c ⟨j, h⟩) =\n update ... | [
"ι : Sort u_2\ninst✝² : DecidableEq ι\nP : ι → Prop\ninst✝¹ : DecidablePred P\nM₁ : ι → Type u_1\ninst✝ : DecidableEq { a // ¬P a }\nx : (i : { a // P a }) → M₁ ↑i\nz : (i : { a // ¬P a }) → M₁ ↑i\ni : { a // ¬P a }\nc : M₁ ↑i\n⊢ (fun j ↦ if h : P j then x ⟨j, h⟩ else update z i c ⟨j, h⟩) =\n update (fun j ↦ if ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Types.Colimits | {
"line": 71,
"column": 28
} | {
"line": 71,
"column": 43
} | {
"line": 71,
"column": 44
} | [
{
"pp": "J : Type v\ninst✝ : Category.{w, v} J\nF : J ⥤ Type u\nc : F.CoconeTypes\nhc : Limits.IsColimit (F.coconeTypesEquiv c)\nx y : F.ColimitType\nh : F.descColimitType c x = F.descColimitType c y\nf : F.ColimitType → ULift.{u, 0} Bool := fun z ↦ { down := decide (x = z) }\nthis : f x = f y\n⊢ x = y",
"p... | [
"J : Type v\ninst✝ : Category.{w, v} J\nF : J ⥤ Type u\nc : F.CoconeTypes\nhc : Limits.IsColimit (F.coconeTypesEquiv c)\nx y : F.ColimitType\nh : F.descColimitType c x = F.descColimitType c y\nf : F.ColimitType → ULift.{u, 0} Bool := fun z ↦ { down := decide (x = z) }\nthis : f x = f y\n⊢ x = y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Types.Colimits | {
"line": 83,
"column": 8
} | {
"line": 83,
"column": 28
} | {
"line": 83,
"column": 29
} | [
{
"pp": "J : Type v\ninst✝ : Category.{w, v} J\nF : J ⥤ Type u\nc : F.CoconeTypes\nhc : Limits.IsColimit (F.coconeTypesEquiv c)\nx : c.pt\nf₁ : (F.coconeTypesEquiv c).pt ⟶ ULift.{u, 0} Bool := ↾fun x ↦ { down := true }\nf₂ : (F.coconeTypesEquiv c).pt ⟶ ULift.{u, 0} Bool := ↾fun x ↦ { down := decide (∃ a, F.desc... | [
"J : Type v\ninst✝ : Category.{w, v} J\nF : J ⥤ Type u\nc : F.CoconeTypes\nhc : Limits.IsColimit (F.coconeTypesEquiv c)\nx : c.pt\nf₁ : (F.coconeTypesEquiv c).pt ⟶ ULift.{u, 0} Bool := ↾fun x ↦ { down := true }\nf₂ : (F.coconeTypesEquiv c).pt ⟶ ULift.{u, 0} Bool := ↾fun x ↦ { down := decide (∃ a, F.descColimitType ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Types.Colimits | {
"line": 86,
"column": 6
} | {
"line": 86,
"column": 26
} | {
"line": 86,
"column": 27
} | [
{
"pp": "case mpr.refine_2\nJ : Type v\ninst✝ : Category.{w, v} J\nF : J ⥤ Type u\nc : F.CoconeTypes\nhc : Limits.IsColimit (F.coconeTypesEquiv c)\nx✝ : c.pt\nf₁ : (F.coconeTypesEquiv c).pt ⟶ ULift.{u, 0} Bool := ⋯\nf₂ : (F.coconeTypesEquiv c).pt ⟶ ULift.{u, 0} Bool := ⋯\nj : J\nx : F.obj j\n⊢ ((ConcreteCategor... | [
"case mpr.refine_2\nJ : Type v\ninst✝ : Category.{w, v} J\nF : J ⥤ Type u\nc : F.CoconeTypes\nhc : Limits.IsColimit (F.coconeTypesEquiv c)\nx✝ : c.pt\nf₁ : (F.coconeTypesEquiv c).pt ⟶ ULift.{u, 0} Bool := ↾fun x ↦ { down := true }\nf₂ : (F.coconeTypesEquiv c).pt ⟶ ULift.{u, 0} Bool := ↾fun x ↦ { down := decide (∃ a... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Types.Filtered | {
"line": 96,
"column": 78
} | {
"line": 96,
"column": 89
} | {
"line": 96,
"column": 90
} | [
{
"pp": "J : Type v\ninst✝¹ : Category.{w, v} J\nF : J ⥤ Type u\ninst✝ : IsFilteredOrEmpty J\nt : Cocone F\nhsurj : ∀ (x : t.pt), ∃ i xi, x = (hom (t.ι.app i)) xi\nhinj :\n ∀ (i : J) (x y : (fun X ↦ X) (F.obj i)),\n (hom (t.ι.app i)) x = (hom (t.ι.app i)) y → ∃ k f, (hom (F.map f)) x = (hom (F.map f)) y\ni ... | [
"J : Type v\ninst✝¹ : Category.{w, v} J\nF : J ⥤ Type u\ninst✝ : IsFilteredOrEmpty J\nt : Cocone F\nhsurj : ∀ (x : t.pt), ∃ i xi, x = (hom (t.ι.app i)) xi\nhinj :\n ∀ (i : J) (x y : (fun X ↦ X) (F.obj i)),\n (hom (t.ι.app i)) x = (hom (t.ι.app i)) y → ∃ k f, (hom (F.map f)) x = (hom (F.map f)) y\ni j : J\nxi : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.Determinant.Basic | {
"line": 642,
"column": 48
} | {
"line": 642,
"column": 69
} | {
"line": 642,
"column": 70
} | [
{
"pp": "n : Type u_2\ninst✝⁴ : DecidableEq n\ninst✝³ : Fintype n\nR : Type v\ninst✝² : CommRing R\no : Type u_3\ninst✝¹ : Fintype o\ninst✝ : DecidableEq o\nM : o → Matrix n n R\npreserving_snd : Finset (Perm (n × o)) := {σ | ∀ (x : n × o), (σ x).2 = x.2}\nmem_preserving_snd : ∀ {σ : Perm (n × o)}, σ ∈ preservi... | [
"n : Type u_2\ninst✝⁴ : DecidableEq n\ninst✝³ : Fintype n\nR : Type v\ninst✝² : CommRing R\no : Type u_3\ninst✝¹ : Fintype o\ninst✝ : DecidableEq o\nM : o → Matrix n n R\npreserving_snd : Finset (Perm (n × o)) := {σ | ∀ (x : n × o), (σ x).2 = x.2}\nmem_preserving_snd : ∀ {σ : Perm (n × o)}, σ ∈ preserving_snd ↔ ∀ (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Category.Grp.FilteredColimits | {
"line": 80,
"column": 2
} | {
"line": 80,
"column": 13
} | {
"line": 80,
"column": 14
} | [
{
"pp": "J : Type v\ninst✝¹ : SmallCategory J\ninst✝ : IsFiltered J\nF : J ⥤ GrpCat\nj : J\nx y : ↑(F.obj j)\nthis :\n G.mk F ⟨j, x⟩ * G.mk F ⟨j, y⟩ =\n G.mk F\n ⟨j,\n (ConcreteCategory.hom (F.map (𝟙 ⟨j, x⟩.fst))) ⟨j, x⟩.snd *\n (ConcreteCategory.hom (F.map (𝟙 ⟨j, y⟩.fst))) ⟨j, y⟩.snd... | [
"J : Type v\ninst✝¹ : SmallCategory J\ninst✝ : IsFiltered J\nF : J ⥤ GrpCat\nj : J\nx y : ↑(F.obj j)\nthis :\n G.mk F ⟨j, x⟩ * G.mk F ⟨j, y⟩ =\n G.mk F\n ⟨j,\n (ConcreteCategory.hom (F.map (𝟙 ⟨j, x⟩.fst))) ⟨j, x⟩.snd *\n (ConcreteCategory.hom (F.map (𝟙 ⟨j, y⟩.fst))) ⟨j, y⟩.snd⟩\n⊢ G.mk F ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Multilinear.Basic | {
"line": 1162,
"column": 12
} | {
"line": 1162,
"column": 23
} | {
"line": 1162,
"column": 24
} | [
{
"pp": "R : Type uR\nι : Type uι\nM₁ : ι → Type v₁\nM₂ : Type v₂\ninst✝⁵ : CommSemiring R\ninst✝⁴ : (i : ι) → AddCommMonoid (M₁ i)\ninst✝³ : AddCommMonoid M₂\ninst✝² : (i : ι) → Module R (M₁ i)\ninst✝¹ : Module R M₂\nf : MultilinearMap R M₁ M₂\ninst✝ : Fintype ι\nc : ι → R\nm : (i : ι) → M₁ i\n⊢ (f fun i ↦ c i... | [
"R : Type uR\nι : Type uι\nM₁ : ι → Type v₁\nM₂ : Type v₂\ninst✝⁵ : CommSemiring R\ninst✝⁴ : (i : ι) → AddCommMonoid (M₁ i)\ninst✝³ : AddCommMonoid M₂\ninst✝² : (i : ι) → Module R (M₁ i)\ninst✝¹ : Module R M₂\nf : MultilinearMap R M₁ M₂\ninst✝ : Fintype ι\nc : ι → R\nm : (i : ι) → M₁ i\n⊢ (f fun i ↦ c i • m i) = (∏... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Multilinear.Basic | {
"line": 1171,
"column": 2
} | {
"line": 1171,
"column": 42
} | {
"line": 1171,
"column": 43
} | [
{
"pp": "R : Type uR\nι : Type uι\nM₁ : ι → Type v₁\nM₂ : Type v₂\ninst✝⁶ : CommSemiring R\ninst✝⁵ : (i : ι) → AddCommMonoid (M₁ i)\ninst✝⁴ : AddCommMonoid M₂\ninst✝³ : (i : ι) → Module R (M₁ i)\ninst✝² : Module R M₂\nf : MultilinearMap R M₁ M₂\ninst✝¹ : DecidableEq ι\ninst✝ : Fintype ι\nm : (i : ι) → M₁ i\ni :... | [
"R : Type uR\nι : Type uι\nM₁ : ι → Type v₁\nM₂ : Type v₂\ninst✝⁶ : CommSemiring R\ninst✝⁵ : (i : ι) → AddCommMonoid (M₁ i)\ninst✝⁴ : AddCommMonoid M₂\ninst✝³ : (i : ι) → Module R (M₁ i)\ninst✝² : Module R M₂\nf : MultilinearMap R M₁ M₂\ninst✝¹ : DecidableEq ι\ninst✝ : Fintype ι\nm : (i : ι) → M₁ i\ni : ι\nc : R\nx... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Multilinear.Basic | {
"line": 1272,
"column": 4
} | {
"line": 1272,
"column": 15
} | {
"line": 1272,
"column": 16
} | [
{
"pp": "case mp\nR : Type uR\nι : Type uι\nM₂ : Type v₂\ninst✝³ : CommSemiring R\ninst✝² : AddCommMonoid M₂\ninst✝¹ : Module R M₂\ninst✝ : Fintype ι\nz₁ z₂ : M₂\nh : ∀ (x : ι → R), (∏ i, x i) • z₁ = (∏ i, x i) • z₂\n⊢ z₁ = z₂",
"ppTerm": "?mp",
"assigned": false,
"usedConstants": [],
"usedFVars... | [
"case mp\nR : Type uR\nι : Type uι\nM₂ : Type v₂\ninst✝³ : CommSemiring R\ninst✝² : AddCommMonoid M₂\ninst✝¹ : Module R M₂\ninst✝ : Fintype ι\nz₁ z₂ : M₂\nh : ∀ (x : ι → R), (∏ i, x i) • z₁ = (∏ i, x i) • z₂\n⊢ z₁ = z₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.Determinant.Basic | {
"line": 711,
"column": 8
} | {
"line": 711,
"column": 98
} | {
"line": 712,
"column": 10
} | [
{
"pp": "m : Type u_1\nn : Type u_2\ninst✝⁴ : DecidableEq n\ninst✝³ : Fintype n\ninst✝² : DecidableEq m\ninst✝¹ : Fintype m\nR : Type v\ninst✝ : CommRing R\nA : Matrix m m R\nB : Matrix m n R\nD : Matrix n n R\nσ : Perm (m ⊕ n)\nhσn : σ ∉ ↑(sumCongrHom m n).range\n⊢ ¬∀ (x : m), ∃ y, Sum.inl y = σ (Sum.inl x)",
... | [
"m : Type u_1\nn : Type u_2\ninst✝⁴ : DecidableEq n\ninst✝³ : Fintype n\ninst✝² : DecidableEq m\ninst✝¹ : Fintype m\nR : Type v\ninst✝ : CommRing R\nA : Matrix m m R\nB : Matrix m n R\nD : Matrix n n R\nσ : Perm (m ⊕ n)\nhσn : σ ∉ ↑(sumCongrHom m n).range\n⊢ ¬∀ (x : m), ∃ y, Sum.inl y = σ (Sum.inl x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Category.Ring.FilteredColimits | {
"line": 171,
"column": 8
} | {
"line": 172,
"column": 53
} | {
"line": 173,
"column": 8
} | [
{
"pp": "J : Type v\ninst✝¹ : SmallCategory J\nF : J ⥤ SemiRingCat\ninst✝ : IsFiltered J\nt : Cocone F\nx y : ↑(R F)\n⊢ (↑(descAddMonoidHom t)).toFun (x * y) = (↑(descAddMonoidHom t)).toFun x * (↑(descAddMonoidHom t)).toFun y",
"ppTerm": "?m.64",
"assigned": true,
"usedConstants": [
"SemiRingC... | [
"J : Type v\ninst✝¹ : SmallCategory J\nF : J ⥤ SemiRingCat\ninst✝ : IsFiltered J\nt : Cocone F\nx y : ↑(R F)\n⊢ (descAddMonoidHom t) (x * y) = (descAddMonoidHom t) x * (descAddMonoidHom t) y"
] | change descAddMonoidHom t (x * y) =
descAddMonoidHom t x * descAddMonoidHom t y | Lean.Elab.Tactic.evalChange | Lean.Parser.Tactic.change |
Mathlib.CategoryTheory.Limits.Creates | {
"line": 340,
"column": 14
} | {
"line": 340,
"column": 25
} | {
"line": 340,
"column": 26
} | [
{
"pp": "C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝³ : Category.{v₂, u₂} D\nJ : Type w\ninst✝² : Category.{w', w} J\nK✝ K : J ⥤ C\nF : C ⥤ D\ninst✝¹ : F.Full\ninst✝ : F.Faithful\nl : Cone (K ⋙ F)\nhl : IsLimit l\nX : C\ni : F.obj X ≅ l.pt\nY Z : J\nf : Y ⟶ Z\n⊢ F.map (((const J).obj X).map f ... | [
"C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝³ : Category.{v₂, u₂} D\nJ : Type w\ninst✝² : Category.{w', w} J\nK✝ K : J ⥤ C\nF : C ⥤ D\ninst✝¹ : F.Full\ninst✝ : F.Faithful\nl : Cone (K ⋙ F)\nhl : IsLimit l\nX : C\ni : F.obj X ≅ l.pt\nY Z : J\nf : Y ⟶ Z\n⊢ l.π.app Z = l.π.app Y ≫ F.map (K.map f)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Types.Yoneda | {
"line": 113,
"column": 27
} | {
"line": 113,
"column": 38
} | {
"line": 113,
"column": 39
} | [
{
"pp": "J : Type v\ninst✝¹ : SmallCategory J\nC : Type u\ninst✝ : Category.{v, u} C\nF : J ⥤ C\nX : C\na : limit (F.op ⋙ yoneda.obj X)\nx✝¹ x✝ : J\nf : x✝¹ ⟶ x✝\n⊢ F.map f ≫ (ConcreteCategory.hom (limit.π (F.op ⋙ yoneda.obj X) (op x✝))) a =\n (ConcreteCategory.hom (limit.π (F.op ⋙ yoneda.obj X) (op x✝¹))) a... | [
"J : Type v\ninst✝¹ : SmallCategory J\nC : Type u\ninst✝ : Category.{v, u} C\nF : J ⥤ C\nX : C\na : limit (F.op ⋙ yoneda.obj X)\nx✝¹ x✝ : J\nf : x✝¹ ⟶ x✝\n⊢ F.map f ≫ (ConcreteCategory.hom (limit.π (F.op ⋙ yoneda.obj X) (op x✝))) a =\n (ConcreteCategory.hom (limit.π (F.op ⋙ yoneda.obj X) (op x✝¹))) a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.FunctorCategory.Basic | {
"line": 60,
"column": 10
} | {
"line": 60,
"column": 21
} | {
"line": 61,
"column": 12
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nD : Type u'\ninst✝² : Category.{v', u'} D\nJ : Type u₁\ninst✝¹ : Category.{v₁, u₁} J\nK : Type u₂\ninst✝ : Category.{v₂, u₂} K\nF : J ⥤ K ⥤ C\nc : Cone F\nt : (k : K) → IsLimit (((evaluation K C).obj k).mapCone c)\ns : Cone F\nX Y : K\nf : X ⟶ Y\nj : J\n⊢ s.pt.ma... | [
"C : Type u\ninst✝³ : Category.{v, u} C\nD : Type u'\ninst✝² : Category.{v', u'} D\nJ : Type u₁\ninst✝¹ : Category.{v₁, u₁} J\nK : Type u₂\ninst✝ : Category.{v₂, u₂} K\nF : J ⥤ K ⥤ C\nc : Cone F\nt : (k : K) → IsLimit (((evaluation K C).obj k).mapCone c)\ns : Cone F\nX Y : K\nf : X ⟶ Y\nj : J\n⊢ (s.π.app j).app X ≫... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Creates | {
"line": 464,
"column": 14
} | {
"line": 464,
"column": 47
} | {
"line": 464,
"column": 48
} | [
{
"pp": "C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝³ : Category.{v₂, u₂} D\nJ : Type w\ninst✝² : Category.{w', w} J\nK✝ K : J ⥤ C\nF : C ⥤ D\ninst✝¹ : F.Full\ninst✝ : F.Faithful\nl : Cocone (K ⋙ F)\nhl : IsColimit l\nX : C\ni : F.obj X ≅ l.pt\nY Z : J\nf : Y ⟶ Z\n⊢ F.map (K.map f ≫ F.preimage... | [
"C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝³ : Category.{v₂, u₂} D\nJ : Type w\ninst✝² : Category.{w', w} J\nK✝ K : J ⥤ C\nF : C ⥤ D\ninst✝¹ : F.Full\ninst✝ : F.Faithful\nl : Cocone (K ⋙ F)\nhl : IsColimit l\nX : C\ni : F.obj X ≅ l.pt\nY Z : J\nf : Y ⟶ Z\n⊢ F.map (K.map f) ≫ l.ι.app Z = l.ι.app Y... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Yoneda | {
"line": 52,
"column": 4
} | {
"line": 52,
"column": 15
} | {
"line": 52,
"column": 16
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nX : Cᵒᵖ\ns : Cocone (coyoneda.obj X)\nY : C\nf : (coyoneda.obj X).obj Y\n⊢ (hom ((colimitCocone X).ι.app Y ≫ ↾fun x ↦ (hom (s.ι.app (unop X))) (𝟙 (unop X)))).toFun f = (hom (s.ι.app Y)).toFun f",
"ppTerm": "?m.65",
"assigned": true,
"usedConstants": [... | [
"C : Type u\ninst✝ : Category.{v, u} C\nX : Cᵒᵖ\ns : Cocone (coyoneda.obj X)\nY : C\nf : (coyoneda.obj X).obj Y\n⊢ (hom (s.ι.app (unop X))) (𝟙 (unop X)) = (hom (s.ι.app Y)) f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Yoneda | {
"line": 111,
"column": 4
} | {
"line": 111,
"column": 15
} | {
"line": 111,
"column": 16
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nJ : Type w\ninst✝ : Category.{t, w} J\nF : J ⥤ Cᵒᵖ\nc : Cone F\nhc : (X : C) → IsLimit ((yoneda.obj X).mapCone c)\ns : Cone F\nj : J\n⊢ (Quiver.Hom.op ((hom ((hc (unop s.pt)).lift ((yoneda.obj (unop s.pt)).mapCone s))) (𝟙 (unop s.pt))) ≫\n c.π.app j).unop... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nJ : Type w\ninst✝ : Category.{t, w} J\nF : J ⥤ Cᵒᵖ\nc : Cone F\nhc : (X : C) → IsLimit ((yoneda.obj X).mapCone c)\ns : Cone F\nj : J\n⊢ (c.π.app j).unop ≫ (hom ((hc (unop s.pt)).lift ((yoneda.obj (unop s.pt)).mapCone s))) (𝟙 (unop s.pt)) =\n (s.π.app j).unop"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Yoneda | {
"line": 156,
"column": 16
} | {
"line": 156,
"column": 27
} | {
"line": 156,
"column": 28
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nJ : Type w\ninst✝ : Category.{t, w} J\nF : J ⥤ C\nc : Cone F\nhc : (X : Cᵒᵖ) → IsLimit ((coyoneda.obj X).mapCone c)\ns : Cone F\nj : J\n⊢ (hom ((hc (op s.pt)).lift ((coyoneda.obj (op s.pt)).mapCone s))) (𝟙 (unop (op s.pt))) ≫ c.π.app j = s.π.app j",
"ppTerm"... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nJ : Type w\ninst✝ : Category.{t, w} J\nF : J ⥤ C\nc : Cone F\nhc : (X : Cᵒᵖ) → IsLimit ((coyoneda.obj X).mapCone c)\ns : Cone F\nj : J\n⊢ (hom ((hc (op s.pt)).lift ((coyoneda.obj (op s.pt)).mapCone s))) (𝟙 s.pt) ≫ c.π.app j = s.π.app j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Yoneda | {
"line": 159,
"column": 4
} | {
"line": 163,
"column": 13
} | {
"line": 165,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nJ : Type w\ninst✝ : Category.{t, w} J\nF : J ⥤ C\nc : Cone F\nhc : (X : Cᵒᵖ) → IsLimit ((coyoneda.obj X).mapCone c)\ns : Cone F\nm : s.pt ⟶ c.pt\nhm : ∀ (j : J), m ≫ c.π.app j = s.π.app j\n⊢ m = (hom ((hc (op s.pt)).lift ((coyoneda.obj (op s.pt)).mapCone s))) (𝟙... | [] | apply (Types.isLimitEquivSections (hc (op s.pt))).injective
ext j
dsimp [Types.isLimitEquivSections, Types.sectionOfCone]
have eq := congr_hom ((hc (op s.pt)).fac ((coyoneda.obj (op s.pt)).mapCone s) j) (𝟙 s.pt)
cat_disch | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Limits.Yoneda | {
"line": 159,
"column": 4
} | {
"line": 163,
"column": 13
} | {
"line": 165,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nJ : Type w\ninst✝ : Category.{t, w} J\nF : J ⥤ C\nc : Cone F\nhc : (X : Cᵒᵖ) → IsLimit ((coyoneda.obj X).mapCone c)\ns : Cone F\nm : s.pt ⟶ c.pt\nhm : ∀ (j : J), m ≫ c.π.app j = s.π.app j\n⊢ m = (hom ((hc (op s.pt)).lift ((coyoneda.obj (op s.pt)).mapCone s))) (𝟙... | [] | apply (Types.isLimitEquivSections (hc (op s.pt))).injective
ext j
dsimp [Types.isLimitEquivSections, Types.sectionOfCone]
have eq := congr_hom ((hc (op s.pt)).fac ((coyoneda.obj (op s.pt)).mapCone s) j) (𝟙 s.pt)
cat_disch | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Limits.FunctorCategory.Basic | {
"line": 272,
"column": 2
} | {
"line": 272,
"column": 13
} | {
"line": 272,
"column": 14
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nJ : Type u₁\ninst✝² : Category.{v₁, u₁} J\nK : Type u₂\ninst✝¹ : Category.{v₂, u₂} K\nH : J ⥤ K ⥤ C\ninst✝ : HasLimitsOfShape J C\nk : K\nW : C\nf g : W ⟶ (limit H).obj k\nw : ∀ (j : J), f ≫ (limit.π H j).app k = g ≫ (limit.π H j).app k\nj : J\n⊢ (f ≫ (limitObjIs... | [
"C : Type u\ninst✝³ : Category.{v, u} C\nJ : Type u₁\ninst✝² : Category.{v₁, u₁} J\nK : Type u₂\ninst✝¹ : Category.{v₂, u₂} K\nH : J ⥤ K ⥤ C\ninst✝ : HasLimitsOfShape J C\nk : K\nW : C\nf g : W ⟶ (limit H).obj k\nw : ∀ (j : J), f ≫ (limit.π H j).app k = g ≫ (limit.π H j).app k\nj : J\n⊢ f ≫ (limit.π H j).app k = g ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.FunctorCategory.Basic | {
"line": 291,
"column": 2
} | {
"line": 292,
"column": 44
} | {
"line": 294,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\nD : Type u'\ninst✝³ : Category.{v', u'} D\nJ : Type u₁\ninst✝² : Category.{v₁, u₁} J\nK : Type u₂\ninst✝¹ : Category.{v₂, u₂} K\nF : J ⥤ K ⥤ C\nG : D ⥤ K\ninst✝ : HasLimitsOfShape J C\nj : J\n⊢ (limitCompWhiskeringLeftIsoCompLimit F G).hom ≫ G.whiskerLeft (limit.... | [] | ext d
simp [limitCompWhiskeringLeftIsoCompLimit] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Limits.FunctorCategory.Basic | {
"line": 291,
"column": 2
} | {
"line": 292,
"column": 44
} | {
"line": 294,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\nD : Type u'\ninst✝³ : Category.{v', u'} D\nJ : Type u₁\ninst✝² : Category.{v₁, u₁} J\nK : Type u₂\ninst✝¹ : Category.{v₂, u₂} K\nF : J ⥤ K ⥤ C\nG : D ⥤ K\ninst✝ : HasLimitsOfShape J C\nj : J\n⊢ (limitCompWhiskeringLeftIsoCompLimit F G).hom ≫ G.whiskerLeft (limit.... | [] | ext d
simp [limitCompWhiskeringLeftIsoCompLimit] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Limits.FunctorCategory.Basic | {
"line": 369,
"column": 2
} | {
"line": 369,
"column": 13
} | {
"line": 369,
"column": 14
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nJ : Type u₁\ninst✝² : Category.{v₁, u₁} J\nK : Type u₂\ninst✝¹ : Category.{v₂, u₂} K\nH : J ⥤ K ⥤ C\ninst✝ : HasColimitsOfShape J C\nk : K\nW : C\nf g : (colimit H).obj k ⟶ W\nw : ∀ (j : J), (colimit.ι H j).app k ≫ f = (colimit.ι H j).app k ≫ g\nj : J\n⊢ colimit.... | [
"C : Type u\ninst✝³ : Category.{v, u} C\nJ : Type u₁\ninst✝² : Category.{v₁, u₁} J\nK : Type u₂\ninst✝¹ : Category.{v₂, u₂} K\nH : J ⥤ K ⥤ C\ninst✝ : HasColimitsOfShape J C\nk : K\nW : C\nf g : (colimit H).obj k ⟶ W\nw : ∀ (j : J), (colimit.ι H j).app k ≫ f = (colimit.ι H j).app k ≫ g\nj : J\n⊢ (colimit.ι H j).app ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.ShrinkYoneda | {
"line": 144,
"column": 4
} | {
"line": 144,
"column": 30
} | {
"line": 144,
"column": 31
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : LocallySmall.{w, v, u} C\nX : C\nP : Cᵒᵖ ⥤ Type w\nτ : shrinkYoneda.{w, v, u}.obj X ⟶ P\nY : Cᵒᵖ\nf : (yoneda.obj X).obj Y\n⊢ (ConcreteCategory.hom\n (((fun x ↦\n {\n app := fun Y ↦\n ↾fun ... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : LocallySmall.{w, v, u} C\nX : C\nP : Cᵒᵖ ⥤ Type w\nτ : shrinkYoneda.{w, v, u}.obj X ⟶ P\nY : Cᵒᵖ\nf : (yoneda.obj X).obj Y\n⊢ (ConcreteCategory.hom (P.map (Quiver.Hom.op f)))\n ((ConcreteCategory.hom (τ.app (op X))) ((equivShrink ((yoneda.obj X).obj (op X))) (𝟙... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.ShrinkYoneda | {
"line": 170,
"column": 2
} | {
"line": 171,
"column": 9
} | {
"line": 171,
"column": 10
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : LocallySmall.{w, v, u} C\nX Y : C\nP : Cᵒᵖ ⥤ Type w\nf : shrinkYoneda.{w, v, u}.obj X ⟶ P\ng : Y ⟶ X\n⊢ (ConcreteCategory.hom (P.map g.op)) (shrinkYonedaEquiv f) = shrinkYonedaEquiv (shrinkYoneda.{w, v, u}.map g ≫ f)",
"ppTerm": "?m.53",
"assigned... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : LocallySmall.{w, v, u} C\nX Y : C\nP : Cᵒᵖ ⥤ Type w\nf : shrinkYoneda.{w, v, u}.obj X ⟶ P\ng : Y ⟶ X\n⊢ (ConcreteCategory.hom (P.map g.op))\n ((ConcreteCategory.hom (f.app (op X))) ((equivShrink ((yoneda.obj X).obj (op X))) (𝟙 X))) =\n (ConcreteCategory.hom ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.ShrinkYoneda | {
"line": 231,
"column": 6
} | {
"line": 232,
"column": 72
} | {
"line": 232,
"column": 72
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : LocallySmall.{w, v, u} C\nX✝ Y✝ : C\ng : X✝ ⟶ Y✝\n⊢ uliftYoneda.{w', v, u}.map g ≫\n (NatIso.ofComponents (fun Y ↦ (Equiv.ulift.trans shrinkYonedaObjObjEquiv.symm).toIso) ⋯).hom =\n (NatIso.ofComponents (fun Y ↦ (Equiv.ulift.trans shrinkYonedaObjO... | [] | ext
exact (shrinkYoneda_map_app_shrinkYonedaObjObjEquiv_symm _ _).symm | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.ShrinkYoneda | {
"line": 231,
"column": 6
} | {
"line": 232,
"column": 72
} | {
"line": 232,
"column": 72
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : LocallySmall.{w, v, u} C\nX✝ Y✝ : C\ng : X✝ ⟶ Y✝\n⊢ uliftYoneda.{w', v, u}.map g ≫\n (NatIso.ofComponents (fun Y ↦ (Equiv.ulift.trans shrinkYonedaObjObjEquiv.symm).toIso) ⋯).hom =\n (NatIso.ofComponents (fun Y ↦ (Equiv.ulift.trans shrinkYonedaObjO... | [] | ext
exact (shrinkYoneda_map_app_shrinkYonedaObjObjEquiv_symm _ _).symm | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.ShrinkYoneda | {
"line": 328,
"column": 4
} | {
"line": 328,
"column": 30
} | {
"line": 328,
"column": 31
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : LocallySmall.{w, v, u} C\nX : Cᵒᵖ\nP : C ⥤ Type w\nτ : shrinkCoyoneda.{w, v, u}.obj X ⟶ P\nY : C\nf : (yoneda.obj Y).obj X\n⊢ (ConcreteCategory.hom\n (((fun x ↦\n { app := fun Y ↦ ↾fun f ↦ (ConcreteCategory.hom (P.map ((equivShri... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : LocallySmall.{w, v, u} C\nX : Cᵒᵖ\nP : C ⥤ Type w\nτ : shrinkCoyoneda.{w, v, u}.obj X ⟶ P\nY : C\nf : (yoneda.obj Y).obj X\n⊢ (ConcreteCategory.hom (P.map f))\n ((ConcreteCategory.hom (τ.app (unop X))) ((equivShrink ((yoneda.obj (unop X)).obj X)) (𝟙 (unop X))))... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.ShrinkYoneda | {
"line": 354,
"column": 2
} | {
"line": 355,
"column": 9
} | {
"line": 355,
"column": 10
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : LocallySmall.{w, v, u} C\nX Y : Cᵒᵖ\nP : C ⥤ Type w\nf : shrinkCoyoneda.{w, v, u}.obj X ⟶ P\ng : Y ⟶ X\n⊢ (ConcreteCategory.hom (P.map g.unop)) (shrinkCoyonedaEquiv f) =\n shrinkCoyonedaEquiv (shrinkCoyoneda.{w, v, u}.map g ≫ f)",
"ppTerm": "?m.53"... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : LocallySmall.{w, v, u} C\nX Y : Cᵒᵖ\nP : C ⥤ Type w\nf : shrinkCoyoneda.{w, v, u}.obj X ⟶ P\ng : Y ⟶ X\n⊢ (ConcreteCategory.hom (P.map g.unop))\n ((ConcreteCategory.hom (f.app (unop X))) ((equivShrink ((yoneda.obj (unop X)).obj X)) (𝟙 (unop X)))) =\n (Concre... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Category.Grp.Limits | {
"line": 142,
"column": 2
} | {
"line": 143,
"column": 18
} | {
"line": 145,
"column": 0
} | [
{
"pp": "case mpr\nJ : Type v\ninst✝ : Category.{w, v} J\nF : J ⥤ GrpCat\n⊢ Small.{u, max u v} ↑(F ⋙ forget GrpCat).sections → HasLimit F",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"GrpCat.instConcreteCategoryMonoidHomCarrier",
"GrpCat",
"MonoidHom.instFunLike",
... | [] | · intro
infer_instance | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Algebra.Category.ModuleCat.Limits | {
"line": 52,
"column": 6
} | {
"line": 52,
"column": 36
} | {
"line": 52,
"column": 37
} | [
{
"pp": "R : Type u\ninst✝¹ : Ring R\nJ : Type v\ninst✝ : Category.{t, v} J\nF : J ⥤ ModuleCat R\nr : R\ns : (j : J) → ↑(F.obj j)\nsh : s ∈ (F ⋙ forget (ModuleCat R)).sections\nj j' : J\nf : j ⟶ j'\n⊢ (ConcreteCategory.hom ((F ⋙ forget (ModuleCat R)).map f)) ((r • s) j) = (r • s) j'",
"ppTerm": "?m.79",
... | [
"R : Type u\ninst✝¹ : Ring R\nJ : Type v\ninst✝ : Category.{t, v} J\nF : J ⥤ ModuleCat R\nr : R\ns : (j : J) → ↑(F.obj j)\nsh : s ∈ (F ⋙ forget (ModuleCat R)).sections\nj j' : J\nf : j ⟶ j'\n⊢ r • (ConcreteCategory.hom (F.map f)) (s j) = r • s j'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Category.Grp.Limits | {
"line": 310,
"column": 2
} | {
"line": 311,
"column": 18
} | {
"line": 313,
"column": 0
} | [
{
"pp": "case mpr\nJ : Type v\ninst✝ : Category.{w, v} J\nF : J ⥤ CommGrpCat\n⊢ Small.{u, max u v} ↑(F ⋙ forget CommGrpCat).sections → HasLimit F",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"CommGrpCat... | [] | · intro
infer_instance | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.CategoryTheory.Functor.Trifunctor | {
"line": 83,
"column": 38
} | {
"line": 86,
"column": 78
} | {
"line": 86,
"column": 79
} | [
{
"pp": "C₁ : Type u_1\nC₂ : Type u_2\nC₃ : Type u_3\nC₄ : Type u_4\nC₁₂ : Type u_5\nC₂₃ : Type u_6\ninst✝⁵ : Category.{v_1, u_1} C₁\ninst✝⁴ : Category.{v_2, u_2} C₂\ninst✝³ : Category.{v_3, u_3} C₃\ninst✝² : Category.{v_4, u_4} C₄\ninst✝¹ : Category.{v_5, u_5} C₁₂\ninst✝ : Category.{v_6, u_6} C₂₃\nF₁₂ F₁₂' : C... | [] | by
ext X₃
dsimp
simp only [← NatTrans.comp_app, NatTrans.naturality, ← G.map_comp] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Adjunction.FullyFaithful | {
"line": 59,
"column": 64
} | {
"line": 59,
"column": 75
} | {
"line": 59,
"column": 76
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nD : Type u₂\ninst✝¹ : Category.{v₂, u₂} D\nL : C ⥤ D\nR : D ⥤ C\nh : L ⊣ R\ninst✝ : L.Faithful\nX Y : C\nf g : Y ⟶ (𝟭 C).obj X\nhfg : f ≫ h.unit.app X = g ≫ h.unit.app X\n⊢ (h.homEquiv Y (L.obj X)) (L.map f) = (h.homEquiv Y (L.obj X)) (L.map g)",
"ppTerm"... | [
"C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nD : Type u₂\ninst✝¹ : Category.{v₂, u₂} D\nL : C ⥤ D\nR : D ⥤ C\nh : L ⊣ R\ninst✝ : L.Faithful\nX Y : C\nf g : Y ⟶ (𝟭 C).obj X\nhfg : f ≫ h.unit.app X = g ≫ h.unit.app X\n⊢ f ≫ h.unit.app X = g ≫ h.unit.app X"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Adjunction.FullyFaithful | {
"line": 131,
"column": 4
} | {
"line": 131,
"column": 15
} | {
"line": 131,
"column": 16
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nD : Type u₂\ninst✝¹ : Category.{v₂, u₂} D\nL : C ⥤ D\nR : D ⥤ C\nh : L ⊣ R\ninst✝ : ∀ (X : C), Mono (h.unit.app X)\nX Y : C\nf g : X ⟶ Y\nhfg : L.map f = L.map g\n⊢ (h.homEquiv X (L.obj Y)).symm (f ≫ h.unit.app Y) = (h.homEquiv X (L.obj Y)).symm (g ≫ h.unit.ap... | [
"C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nD : Type u₂\ninst✝¹ : Category.{v₂, u₂} D\nL : C ⥤ D\nR : D ⥤ C\nh : L ⊣ R\ninst✝ : ∀ (X : C), Mono (h.unit.app X)\nX Y : C\nf g : X ⟶ Y\nhfg : L.map f = L.map g\n⊢ L.map f = L.map g"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Adjunction.FullyFaithful | {
"line": 154,
"column": 4
} | {
"line": 154,
"column": 15
} | {
"line": 154,
"column": 16
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nD : Type u₂\ninst✝¹ : Category.{v₂, u₂} D\nL : C ⥤ D\nR : D ⥤ C\nh : L ⊣ R\ninst✝ : ∀ (X : D), Epi (h.counit.app X)\nX Y : D\nf g : X ⟶ Y\nhfg : R.map f = R.map g\n⊢ (h.homEquiv (R.obj X) Y) (h.counit.app X ≫ f) = (h.homEquiv (R.obj X) Y) (h.counit.app X ≫ g)"... | [
"C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nD : Type u₂\ninst✝¹ : Category.{v₂, u₂} D\nL : C ⥤ D\nR : D ⥤ C\nh : L ⊣ R\ninst✝ : ∀ (X : D), Epi (h.counit.app X)\nX Y : D\nf g : X ⟶ Y\nhfg : R.map f = R.map g\n⊢ R.map f = R.map g"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Category | {
"line": 295,
"column": 2
} | {
"line": 295,
"column": 28
} | {
"line": 296,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : MonoidalCategory C\nX Y Z Z' : C\nf : Z ⟶ Z'\n⊢ (X ⊗ Y) ◁ f = (α_ X Y Z).hom ≫ X ◁ Y ◁ f ≫ (α_ X Y Z').inv",
"ppTerm": "?m.47",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : MonoidalCategory C\nX Y Z Z' : C\nf : Z ⟶ Z'\n⊢ 𝟙 (X ⊗ Y) ⊗ₘ f = (α_ X Y Z).hom ≫ (𝟙 X ⊗ₘ 𝟙 Y ⊗ₘ f) ≫ (α_ X Y Z').inv"
] | simp only [← id_tensorHom] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.CategoryTheory.Monoidal.Category | {
"line": 907,
"column": 4
} | {
"line": 907,
"column": 15
} | {
"line": 907,
"column": 16
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : MonoidalCategory C\nW X✝ Y✝ Z X Y : C\nf g : X ⟶ Y\nh : f ▷ 𝟙_ C = g ▷ 𝟙_ C\n⊢ f = g",
"ppTerm": "?m.37",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : MonoidalCategory C\nW X✝ Y✝ Z X Y : C\nf g : X ⟶ Y\nh : f ▷ 𝟙_ C = g ▷ 𝟙_ C\n⊢ f = g"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Monoidal.Category | {
"line": 920,
"column": 4
} | {
"line": 920,
"column": 15
} | {
"line": 920,
"column": 16
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : MonoidalCategory C\nW X✝ Y✝ Z X Y : C\nf g : X ⟶ Y\nh : ((curriedTensor C).obj (𝟙_ C)).map f = ((curriedTensor C).obj (𝟙_ C)).map g\n⊢ f = g",
"ppTerm": "?m.37",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": [... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : MonoidalCategory C\nW X✝ Y✝ Z X Y : C\nf g : X ⟶ Y\nh : ((curriedTensor C).obj (𝟙_ C)).map f = ((curriedTensor C).obj (𝟙_ C)).map g\n⊢ f = g"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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