module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.RingTheory.TwoSidedIdeal.BigOperators | {
"line": 82,
"column": 2
} | {
"line": 82,
"column": 13
} | {
"line": 82,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nI : TwoSidedIdeal R\nι : Type u_2\nf : ι → R\nval✝ : Multiset ι\nnodup✝ : val✝.Nodup\nhs : ∃ x ∈ { val := val✝, nodup := nodup✝ }, f x ∈ I\n⊢ { val := val✝, nodup := nodup✝ }.prod f ∈ I",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"NonUni... | [
"R : Type u_1\ninst✝ : CommRing R\nI : TwoSidedIdeal R\nι : Type u_2\nf : ι → R\nval✝ : Multiset ι\nnodup✝ : val✝.Nodup\nhs : ∃ x ∈ { val := val✝, nodup := nodup✝ }, f x ∈ I\n⊢ (Multiset.map f val✝).prod ∈ I"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.TensorProduct.IsBaseChangeRightExact | {
"line": 60,
"column": 4
} | {
"line": 60,
"column": 15
} | {
"line": 60,
"column": 16
} | [
{
"pp": "case refine_1\nR : Type u_1\ninst✝²⁰ : CommRing R\nS : Type u_2\ninst✝¹⁹ : CommRing S\ninst✝¹⁸ : Algebra R S\nM₁ : Type u_3\nM₂ : Type u_4\nM₃ : Type u_5\nN₁ : Type u_6\nN₂ : Type u_7\nN₃ : Type u_8\ninst✝¹⁷ : AddCommGroup M₁\ninst✝¹⁶ : AddCommGroup M₂\ninst✝¹⁵ : AddCommGroup M₃\ninst✝¹⁴ : AddCommGroup... | [
"case refine_1\nR : Type u_1\ninst✝²⁰ : CommRing R\nS : Type u_2\ninst✝¹⁹ : CommRing S\ninst✝¹⁸ : Algebra R S\nM₁ : Type u_3\nM₂ : Type u_4\nM₃ : Type u_5\nN₁ : Type u_6\nN₂ : Type u_7\nN₃ : Type u_8\ninst✝¹⁷ : AddCommGroup M₁\ninst✝¹⁶ : AddCommGroup M₂\ninst✝¹⁵ : AddCommGroup M₃\ninst✝¹⁴ : AddCommGroup N₁\ninst✝¹³... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.TensorProduct.IsBaseChangeRightExact | {
"line": 62,
"column": 4
} | {
"line": 62,
"column": 15
} | {
"line": 62,
"column": 16
} | [
{
"pp": "case refine_2\nR : Type u_1\ninst✝²⁰ : CommRing R\nS : Type u_2\ninst✝¹⁹ : CommRing S\ninst✝¹⁸ : Algebra R S\nM₁ : Type u_3\nM₂ : Type u_4\nM₃ : Type u_5\nN₁ : Type u_6\nN₂ : Type u_7\nN₃ : Type u_8\ninst✝¹⁷ : AddCommGroup M₁\ninst✝¹⁶ : AddCommGroup M₂\ninst✝¹⁵ : AddCommGroup M₃\ninst✝¹⁴ : AddCommGroup... | [
"case refine_2\nR : Type u_1\ninst✝²⁰ : CommRing R\nS : Type u_2\ninst✝¹⁹ : CommRing S\ninst✝¹⁸ : Algebra R S\nM₁ : Type u_3\nM₂ : Type u_4\nM₃ : Type u_5\nN₁ : Type u_6\nN₂ : Type u_7\nN₃ : Type u_8\ninst✝¹⁷ : AddCommGroup M₁\ninst✝¹⁶ : AddCommGroup M₂\ninst✝¹⁵ : AddCommGroup M₃\ninst✝¹⁴ : AddCommGroup N₁\ninst✝¹³... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Smooth.Quotient | {
"line": 36,
"column": 6
} | {
"line": 36,
"column": 17
} | {
"line": 36,
"column": 18
} | [
{
"pp": "R : Type u_1\ninst✝⁵ : CommRing R\nM : Type u_2\nN : Type u_3\ninst✝⁴ : AddCommGroup M\ninst✝³ : AddCommGroup N\ninst✝² : Module R M\ninst✝¹ : Module R N\nI : Ideal R\nf : M →ₗ[R] N\nsurj : Function.Surjective ⇑f\ninst✝ : Module.Flat R N\nx : M\nhx : x ∈ f.ker ⊓ I • ⊤\ny : TensorProduct R (↥I) M\nhy : ... | [
"R : Type u_1\ninst✝⁵ : CommRing R\nM : Type u_2\nN : Type u_3\ninst✝⁴ : AddCommGroup M\ninst✝³ : AddCommGroup N\ninst✝² : Module R M\ninst✝¹ : Module R N\nI : Ideal R\nf : M →ₗ[R] N\nsurj : Function.Surjective ⇑f\ninst✝ : Module.Flat R N\nx : M\nhx : x ∈ f.ker ⊓ I • ⊤\ny : TensorProduct R (↥I) M\nhy : (↑(TensorPro... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.Extension | {
"line": 81,
"column": 2
} | {
"line": 81,
"column": 27
} | {
"line": 81,
"column": 28
} | [
{
"pp": "R : Type u_1\nA : Type u_2\nΓR : Type u_3\nΓA : Type u_4\ninst✝⁵ : CommRing R\ninst✝⁴ : Ring A\ninst✝³ : LinearOrderedCommMonoidWithZero ΓR\ninst✝² : LinearOrderedCommMonoidWithZero ΓA\ninst✝¹ : Algebra R A\nvR : Valuation R ΓR\nvA : Valuation A ΓA\ninst✝ : vR.HasExtension vA\nx y : R\n⊢ vA ((algebraMa... | [
"R : Type u_1\nA : Type u_2\nΓR : Type u_3\nΓA : Type u_4\ninst✝⁵ : CommRing R\ninst✝⁴ : Ring A\ninst✝³ : LinearOrderedCommMonoidWithZero ΓR\ninst✝² : LinearOrderedCommMonoidWithZero ΓA\ninst✝¹ : Algebra R A\nvR : Valuation R ΓR\nvA : Valuation A ΓA\ninst✝ : vR.HasExtension vA\nx y : R\n⊢ vA ((algebraMap R A) x) < ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.Extension | {
"line": 87,
"column": 2
} | {
"line": 87,
"column": 28
} | {
"line": 87,
"column": 29
} | [
{
"pp": "R : Type u_1\nA : Type u_2\nΓR : Type u_3\nΓA : Type u_4\ninst✝⁵ : CommRing R\ninst✝⁴ : Ring A\ninst✝³ : LinearOrderedCommMonoidWithZero ΓR\ninst✝² : LinearOrderedCommMonoidWithZero ΓA\ninst✝¹ : Algebra R A\nvR : Valuation R ΓR\nvA : Valuation A ΓA\ninst✝ : vR.HasExtension vA\nx : R\n⊢ vA ((algebraMap ... | [
"R : Type u_1\nA : Type u_2\nΓR : Type u_3\nΓA : Type u_4\ninst✝⁵ : CommRing R\ninst✝⁴ : Ring A\ninst✝³ : LinearOrderedCommMonoidWithZero ΓR\ninst✝² : LinearOrderedCommMonoidWithZero ΓA\ninst✝¹ : Algebra R A\nvR : Valuation R ΓR\nvA : Valuation A ΓA\ninst✝ : vR.HasExtension vA\nx : R\n⊢ vA ((algebraMap R A) x) ≤ 1 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Smooth.Quotient | {
"line": 57,
"column": 6
} | {
"line": 57,
"column": 43
} | {
"line": 57,
"column": 44
} | [
{
"pp": "case refine_2.smul\nR : Type u_1\ninst✝⁵ : CommRing R\nM : Type u_2\nN : Type u_3\ninst✝⁴ : AddCommGroup M\ninst✝³ : AddCommGroup N\ninst✝² : Module R M\ninst✝¹ : Module R N\nI : Ideal R\nf : M →ₗ[R] N\nsurj : Function.Surjective ⇑f\ninst✝ : Module.Flat R N\nx : M\nr : R\nhr : r ∈ I\nm : M\nhm : m ∈ f.... | [
"case refine_2.smul\nR : Type u_1\ninst✝⁵ : CommRing R\nM : Type u_2\nN : Type u_3\ninst✝⁴ : AddCommGroup M\ninst✝³ : AddCommGroup N\ninst✝² : Module R M\ninst✝¹ : Module R N\nI : Ideal R\nf : M →ₗ[R] N\nsurj : Function.Surjective ⇑f\ninst✝ : Module.Flat R N\nx : M\nr : R\nhr : r ∈ I\nm : M\nhm : m ∈ f.ker\n⊢ r • m... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.Extension | {
"line": 90,
"column": 2
} | {
"line": 90,
"column": 36
} | {
"line": 90,
"column": 37
} | [
{
"pp": "R : Type u_1\nA : Type u_2\nΓR : Type u_3\nΓA : Type u_4\ninst✝⁵ : CommRing R\ninst✝⁴ : Ring A\ninst✝³ : LinearOrderedCommMonoidWithZero ΓR\ninst✝² : LinearOrderedCommMonoidWithZero ΓA\ninst✝¹ : Algebra R A\nvR : Valuation R ΓR\nvA : Valuation A ΓA\ninst✝ : vR.HasExtension vA\nx : R\n⊢ vA ((algebraMap ... | [
"R : Type u_1\nA : Type u_2\nΓR : Type u_3\nΓA : Type u_4\ninst✝⁵ : CommRing R\ninst✝⁴ : Ring A\ninst✝³ : LinearOrderedCommMonoidWithZero ΓR\ninst✝² : LinearOrderedCommMonoidWithZero ΓA\ninst✝¹ : Algebra R A\nvR : Valuation R ΓR\nvA : Valuation A ΓA\ninst✝ : vR.HasExtension vA\nx : R\n⊢ vA ((algebraMap R A) x) < 1 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.Extension | {
"line": 93,
"column": 2
} | {
"line": 93,
"column": 45
} | {
"line": 94,
"column": 4
} | [
{
"pp": "R : Type u_1\nA : Type u_2\nΓR : Type u_3\nΓA : Type u_4\ninst✝⁵ : CommRing R\ninst✝⁴ : Ring A\ninst✝³ : LinearOrderedCommMonoidWithZero ΓR\ninst✝² : LinearOrderedCommMonoidWithZero ΓA\ninst✝¹ : Algebra R A\nvR : Valuation R ΓR\nvA : Valuation A ΓA\ninst✝ : vR.HasExtension vA\nx : R\n⊢ vA ((algebraMap ... | [
"R : Type u_1\nA : Type u_2\nΓR : Type u_3\nΓA : Type u_4\ninst✝⁵ : CommRing R\ninst✝⁴ : Ring A\ninst✝³ : LinearOrderedCommMonoidWithZero ΓR\ninst✝² : LinearOrderedCommMonoidWithZero ΓA\ninst✝¹ : Algebra R A\nvR : Valuation R ΓR\nvA : Valuation A ΓA\ninst✝ : vR.HasExtension vA\nx : R\n⊢ vA ((algebraMap R A) x) ≤ 1 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Trivial | {
"line": 45,
"column": 27
} | {
"line": 45,
"column": 38
} | {
"line": 45,
"column": 39
} | [
{
"pp": "R✝ Γ : Type\ninst✝⁶ : Ring R✝\ninst✝⁵ : DecidableEq R✝\ninst✝⁴ : IsDomain R✝\ninst✝³ : LinearOrderedCommGroupWithZero Γ\nR : Type\ninst✝² : Semiring R\ninst✝¹ : DecidableEq R\ninst✝ : IsDomain R\nx✝¹ x✝ : R\n⊢ if x✝ * x✝¹ = 0 then x✝¹ * x✝ = 0 else True",
"ppTerm": "?m.186",
"assigned": true,
... | [
"R✝ Γ : Type\ninst✝⁶ : Ring R✝\ninst✝⁵ : DecidableEq R✝\ninst✝⁴ : IsDomain R✝\ninst✝³ : LinearOrderedCommGroupWithZero Γ\nR : Type\ninst✝² : Semiring R\ninst✝¹ : DecidableEq R\ninst✝ : IsDomain R\nx✝¹ x✝ : R\n⊢ x✝ = 0 ∨ x✝¹ = 0 → x✝¹ = 0 ∨ x✝ = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Smooth.Quotient | {
"line": 95,
"column": 2
} | {
"line": 95,
"column": 20
} | {
"line": 95,
"column": 21
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nJ I : Ideal R\nsq : I * I = ⊥\nf : J.Cotangent →ₗ[R] J.Cotangent\nle : f.range ≤ Submodule.map J.toCotangent (Submodule.comap (Submodule.subtype J) (I * J))\nthis : ∀ {x : R} (h : x ∈ I * J), f (J.toCotangent ⟨x, ⋯⟩) = 0\nx : J.Cotangent\nhx : x ∈ Submodule.map J.toCot... | [
"R : Type u_1\ninst✝ : CommRing R\nJ I : Ideal R\nsq : I * I = ⊥\nf : J.Cotangent →ₗ[R] J.Cotangent\nle : f.range ≤ Submodule.map J.toCotangent (Submodule.comap (Submodule.subtype J) (I * J))\nthis : ∀ {x : R} (h : x ∈ I * J), f (J.toCotangent ⟨x, ⋯⟩) = 0\nx : J.Cotangent\nhx : x ∈ Submodule.map J.toCotangent (Subm... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.WittVector.DiscreteValuationRing | {
"line": 97,
"column": 4
} | {
"line": 97,
"column": 73
} | {
"line": 98,
"column": 6
} | [
{
"pp": "p : ℕ\nhp✝ : Fact (Nat.Prime p)\nk : Type u_1\ninst✝¹ : Field k\ninst✝ : CharP k p\nhp : IsUnit ↑p\n⊢ False",
"ppTerm": "?m.10",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"p : ℕ\nhp✝ : Fact (Nat.Prime p)\nk : Type u_1\ninst✝¹ : Field k\ninst✝ : CharP k p\nhp : IsUnit ↑p\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.WittVector.DiscreteValuationRing | {
"line": 101,
"column": 8
} | {
"line": 101,
"column": 25
} | {
"line": 101,
"column": 25
} | [
{
"pp": "p : ℕ\nhp✝ : Fact (Nat.Prime p)\nk : Type u_1\ninst✝¹ : Field k\ninst✝ : CharP k p\nhp : ¬IsUnit ↑p\na b : 𝕎 k\nhab : ↑p = a * b\n⊢ a ≠ 0 ∧ b ≠ 0",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"WittVector.instZero",
"Eq.mpr",
"IsDomain.to_noZeroDivisors",
... | [
"p : ℕ\nhp✝ : Fact (Nat.Prime p)\nk : Type u_1\ninst✝¹ : Field k\ninst✝ : CharP k p\nhp : ¬IsUnit ↑p\na b : 𝕎 k\nhab : ↑p = a * b\n⊢ a * b ≠ 0"
] | ← mul_ne_zero_iff | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.WittVector.MulCoeff | {
"line": 82,
"column": 4
} | {
"line": 82,
"column": 15
} | {
"line": 82,
"column": 16
} | [
{
"pp": "case refine_2\np : ℕ\nhp : Fact (Nat.Prime p)\nn x : ℕ\nhx : x ∈ range n\n⊢ range (x + 1) ⊆ range n",
"ppTerm": "?refine_2",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Nat.instOne",
"Finset",
"PartialOrder.toPreorder",
"Preorder.toLE... | [
"case refine_2\np : ℕ\nhp : Fact (Nat.Prime p)\nn x : ℕ\nhx : x ∈ range n\n⊢ x < n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.WittVector.MulCoeff | {
"line": 103,
"column": 6
} | {
"line": 103,
"column": 17
} | {
"line": 103,
"column": 18
} | [
{
"pp": "case refine_1\np : ℕ\nhp : Fact (Nat.Prime p)\nn x : ℕ\nhx : x ∈ range (n + 1)\n⊢ {(0, x)} ⊆ univ ×ˢ range (n + 1)",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"Finset.singleton_subset_iff._simp_1",
"Eq.mpr",
"Finset.mem_range._simp_1",
"Finset.univ"... | [
"case refine_1\np : ℕ\nhp : Fact (Nat.Prime p)\nn x : ℕ\nhx : x ∈ range (n + 1)\n⊢ x ≤ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.WittVector.MulCoeff | {
"line": 103,
"column": 6
} | {
"line": 103,
"column": 17
} | {
"line": 103,
"column": 18
} | [
{
"pp": "case refine_2\np : ℕ\nhp : Fact (Nat.Prime p)\nn x : ℕ\nhx : x ∈ range (n + 1)\n⊢ {(1, x)} ⊆ univ ×ˢ range (n + 1)",
"ppTerm": "?refine_2",
"assigned": true,
"usedConstants": [
"Finset.singleton_subset_iff._simp_1",
"Eq.mpr",
"Finset.mem_range._simp_1",
"Finset.univ"... | [
"case refine_2\np : ℕ\nhp : Fact (Nat.Prime p)\nn x : ℕ\nhx : x ∈ range (n + 1)\n⊢ x ≤ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.WittVector.FrobeniusFractionField | {
"line": 160,
"column": 4
} | {
"line": 160,
"column": 26
} | {
"line": 160,
"column": 27
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nk : Type u_1\ninst✝¹ : Field k\ninst✝ : IsAlgClosed k\na₁ a₂ : 𝕎 k\nha₁ : a₁.coeff 0 ≠ 0\nha₂ : a₂.coeff 0 ≠ 0\nh : solution p a₁ a₂ = 0\nthis : 0 = a₂.coeff 0 / a₁.coeff 0\n⊢ False",
"ppTerm": "?m.44",
"assigned": false,
"usedConstants": [],
"usedFVars"... | [
"p : ℕ\nhp : Fact (Nat.Prime p)\nk : Type u_1\ninst✝¹ : Field k\ninst✝ : IsAlgClosed k\na₁ a₂ : 𝕎 k\nha₁ : a₁.coeff 0 ≠ 0\nha₂ : a₂.coeff 0 ≠ 0\nh : solution p a₁ a₂ = 0\nthis : 0 = a₂.coeff 0 / a₁.coeff 0\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.WittVector.FrobeniusFractionField | {
"line": 195,
"column": 2
} | {
"line": 195,
"column": 62
} | {
"line": 195,
"column": 63
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nk : Type u_1\ninst✝² : Field k\ninst✝¹ : CharP k p\ninst✝ : IsAlgClosed k\na₁ a₂ : 𝕎 k\nha₁ : a₁.coeff 0 ≠ 0\nha₂ : a₂.coeff 0 ≠ 0\nh : frobeniusRotation p ha₁ ha₂ = 0\n⊢ solution p a₁ a₂ = 0",
"ppTerm": "?m.36",
"assigned": false,
"usedConstants": [],
"... | [
"p : ℕ\nhp : Fact (Nat.Prime p)\nk : Type u_1\ninst✝² : Field k\ninst✝¹ : CharP k p\ninst✝ : IsAlgClosed k\na₁ a₂ : 𝕎 k\nha₁ : a₁.coeff 0 ≠ 0\nha₂ : a₂.coeff 0 ≠ 0\nh : frobeniusRotation p ha₁ ha₂ = 0\n⊢ solution p a₁ a₂ = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.WittVector.FrobeniusFractionField | {
"line": 235,
"column": 4
} | {
"line": 235,
"column": 35
} | {
"line": 236,
"column": 6
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nk : Type u_1\ninst✝² : Field k\ninst✝¹ : CharP k p\ninst✝ : IsAlgClosed k\nm n : ℕ\nr' q' : 𝕎 k\nhr' : r'.coeff 0 ≠ 0\nhq' : q'.coeff 0 ≠ 0\nhq : ↑p ^ n * q' ∈ nonZeroDivisors (𝕎 k)\nb : 𝕎 k := frobeniusRotation p hr' hq'\nkey : frobenius b * r' = q' * b\nhq''' : q' ≠... | [
"p : ℕ\nhp : Fact (Nat.Prime p)\nk : Type u_1\ninst✝² : Field k\ninst✝¹ : CharP k p\ninst✝ : IsAlgClosed k\nm n : ℕ\nr' q' : 𝕎 k\nhr' : r'.coeff 0 ≠ 0\nhq' : q'.coeff 0 ≠ 0\nhq : ↑p ^ n * q' ∈ nonZeroDivisors (𝕎 k)\nb : 𝕎 k := frobeniusRotation p hr' hq'\nkey : frobenius b * r' = q' * b\nhq''' : q' ≠ 0\n⊢ ¬(alge... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.WittVector.Isocrystal | {
"line": 185,
"column": 29
} | {
"line": 185,
"column": 56
} | {
"line": 185,
"column": 57
} | [
{
"pp": "p : ℕ\ninst✝⁵ : Fact (Nat.Prime p)\nk : Type u_2\ninst✝⁴ : Field k\ninst✝³ : IsAlgClosed k\ninst✝² : CharP k p\nV : Type u_3\ninst✝¹ : AddCommGroup V\ninst✝ : Isocrystal p k V\nh_dim : finrank K(p, k) V = 1\nthis : Nontrivial V\nx : V\nhx : x ≠ 0\n⊢ Φ(p, k) x ≠ 0",
"ppTerm": "?m.67",
"assigned"... | [
"p : ℕ\ninst✝⁵ : Fact (Nat.Prime p)\nk : Type u_2\ninst✝⁴ : Field k\ninst✝³ : IsAlgClosed k\ninst✝² : CharP k p\nV : Type u_3\ninst✝¹ : AddCommGroup V\ninst✝ : Isocrystal p k V\nh_dim : finrank K(p, k) V = 1\nthis : Nontrivial V\nx : V\nhx : x ≠ 0\n⊢ Φ(p, k) x ≠ 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.WittVector.FrobeniusFractionField | {
"line": 254,
"column": 4
} | {
"line": 254,
"column": 31
} | {
"line": 255,
"column": 6
} | [
{
"pp": "case refine_1\np : ℕ\nhp : Fact (Nat.Prime p)\nk : Type u_1\ninst✝² : Field k\ninst✝¹ : CharP k p\ninst✝ : IsAlgClosed k\na : FractionRing (𝕎 k)\nm : ℕ\nr' : 𝕎 k\nhr' : r'.coeff 0 ≠ 0\nhr0 : ↑p ^ m * r' ≠ 0\nn : ℕ\nq' : 𝕎 k\nhq' : q'.coeff 0 ≠ 0\nhq : ↑p ^ n * q' ∈ nonZeroDivisors (𝕎 k)\nhq0 : ↑p ^... | [
"case refine_1\np : ℕ\nhp : Fact (Nat.Prime p)\nk : Type u_1\ninst✝² : Field k\ninst✝¹ : CharP k p\ninst✝ : IsAlgClosed k\na : FractionRing (𝕎 k)\nm : ℕ\nr' : 𝕎 k\nhr' : r'.coeff 0 ≠ 0\nhr0 : ↑p ^ m * r' ≠ 0\nn : ℕ\nq' : 𝕎 k\nhq' : q'.coeff 0 ≠ 0\nhq : ↑p ^ n * q' ∈ nonZeroDivisors (𝕎 k)\nhq0 : ↑p ^ n * q' ≠ 0\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.ZMod.Torsion | {
"line": 25,
"column": 2
} | {
"line": 25,
"column": 29
} | {
"line": 25,
"column": 30
} | [
{
"pp": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nx✝ : (ZMod p)ˣ\n⊢ x✝ ∈ rootsOfUnity (p - 1) (ZMod p) ↔ x✝ ∈ ⊤",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Units.val",
"Eq.mpr",
"MulOne.toOne",
"ZMod.commRing",
"Monoid.toMulOneClass",
"congrArg",
"H... | [
"p : ℕ\ninst✝ : Fact (Nat.Prime p)\nx✝ : (ZMod p)ˣ\n⊢ ↑x✝ ^ (p - 1) = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Cardinal.Cofinality.Club | {
"line": 109,
"column": 4
} | {
"line": 109,
"column": 15
} | {
"line": 109,
"column": 16
} | [
{
"pp": "α : Type v\ninst✝¹ : LinearOrder α\ninst✝ : WellFoundedLT α\ns : Set (Set α)\nhα✝ : cof α ≠ ℵ₀\nhsα : #↑s < cof α\nhs : ∀ x ∈ s, IsClub x\nh✝ : Nonempty α\nhα : ℵ₀ < cof α\na : α\nf : ↑s → α → α\nhf : ∀ (x : ↑s) (x_1 : α), f x x_1 ∈ ↑x ∧ x_1 ≤ f x x_1\ng : ℕ → α := fun t ↦ Nat.rec a (fun x IH ↦ sSup (r... | [
"α : Type v\ninst✝¹ : LinearOrder α\ninst✝ : WellFoundedLT α\ns : Set (Set α)\nhα✝ : cof α ≠ ℵ₀\nhsα : #↑s < cof α\nhs : ∀ x ∈ s, IsClub x\nh✝ : Nonempty α\nhα : ℵ₀ < cof α\na : α\nf : ↑s → α → α\nhf : ∀ (x : ↑s) (x_1 : α), f x x_1 ∈ ↑x ∧ x_1 ≤ f x x_1\ng : ℕ → α := fun t ↦ Nat.rec a (fun x IH ↦ sSup (range fun x ↦... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Cardinal.Cofinality.Club | {
"line": 142,
"column": 2
} | {
"line": 142,
"column": 22
} | {
"line": 142,
"column": 23
} | [
{
"pp": "α : Type v\ns t : Set α\ninst✝¹ : LinearOrder α\ninst✝ : WellFoundedLT α\nhα : cof α ≠ ℵ₀\nhs : IsClub s\nht : IsClub t\n⊢ IsClub (s ∩ t)",
"ppTerm": "?m.12",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type v\ns t : Set α\ninst✝¹ : LinearOrder α\ninst✝ : WellFoundedLT α\nhα : cof α ≠ ℵ₀\nhs : IsClub s\nht : IsClub t\n⊢ IsClub (s ∩ t)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Cardinal.Cofinality.Club | {
"line": 160,
"column": 6
} | {
"line": 160,
"column": 17
} | {
"line": 160,
"column": 18
} | [
{
"pp": "case inr.refine_2.inr\nα : Type v\ninst✝¹ : LinearOrder α\ninst✝ : WellFoundedLT α\nf : α → α\nhα : cof α ≠ ℵ₀\nhf : IsNormal f\nh✝¹ : Nonempty α\na : α\nh✝ : NoMaxOrder α\nh : IsCofinal (range fun n ↦ f^[n] a)\n⊢ #↑(range fun n ↦ f^[n] a) ≤ ℵ₀",
"ppTerm": "?inr.refine_2.inr",
"assigned": true,... | [
"case inr.refine_2.inr\nα : Type v\ninst✝¹ : LinearOrder α\ninst✝ : WellFoundedLT α\nf : α → α\nhα : cof α ≠ ℵ₀\nhf : IsNormal f\nh✝¹ : Nonempty α\na : α\nh✝ : NoMaxOrder α\nh : IsCofinal (range fun n ↦ f^[n] a)\n⊢ {x | ∃ y, f^[y] a = x}.Countable"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Cardinal.Cofinality.Club | {
"line": 189,
"column": 2
} | {
"line": 189,
"column": 13
} | {
"line": 189,
"column": 14
} | [
{
"pp": "α : Type v\ns : Set α\ninst✝ : LinearOrder α\nhs : IsStationary s\n⊢ s.Nonempty",
"ppTerm": "?m.4",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type v\ns : Set α\ninst✝ : LinearOrder α\nhs : IsStationary s\n⊢ s.Nonempty"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Cardinal.Cofinality.Club | {
"line": 202,
"column": 2
} | {
"line": 202,
"column": 13
} | {
"line": 202,
"column": 14
} | [
{
"pp": "α : Type v\ninst✝ : LinearOrder α\nh : IsStationary ∅\n⊢ False",
"ppTerm": "?m.6",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type v\ninst✝ : LinearOrder α\nh : IsStationary ∅\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Descriptive.Tree | {
"line": 43,
"column": 11
} | {
"line": 43,
"column": 22
} | {
"line": 43,
"column": 23
} | [
{
"pp": "case nil\nA : Type u_1\nT : ↥(tree A)\nx : List A\nh : x ++ [] ∈ T\n⊢ x ∈ T",
"ppTerm": "?nil",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case nil\nA : Type u_1\nT : ↥(tree A)\nx : List A\nh : x ++ [] ∈ T\n⊢ x ∈ T"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Descriptive.Tree | {
"line": 57,
"column": 21
} | {
"line": 57,
"column": 32
} | {
"line": 57,
"column": 33
} | [
{
"pp": "A : Type u_1\nT : ↥(tree A)\nh : [] ∉ T\nx : List A\n⊢ x ∈ T ↔ x ∈ ⊥",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"iff_false",
"congrArg",
"Membership.mem",
"id",
"Subtype",
"Bot.bot",
"Descriptive.tree",
... | [
"A : Type u_1\nT : ↥(tree A)\nh : [] ∉ T\nx : List A\n⊢ x ∉ T"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Descriptive.Tree | {
"line": 111,
"column": 4
} | {
"line": 111,
"column": 69
} | {
"line": 111,
"column": 70
} | [
{
"pp": "case right\nA : Type u_1\nT : ↥(tree A)\nx y : List A\nhl : x.length ≤ y.length\nh1 : List.take x.length y <+: x\nh2 : List.drop x.length y ∈ T\n⊢ List.take x.length y ++ List.drop x.length y = x ++ List.drop x.length y",
"ppTerm": "?right",
"assigned": true,
"usedConstants": [
"Eq.mp... | [
"case right\nA : Type u_1\nT : ↥(tree A)\nx y : List A\nhl : x.length ≤ y.length\nh1 : List.take x.length y <+: x\nh2 : List.drop x.length y ∈ T\n⊢ List.take x.length y = x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Descriptive.Tree | {
"line": 117,
"column": 2
} | {
"line": 117,
"column": 13
} | {
"line": 117,
"column": 14
} | [
{
"pp": "A : Type u_1\nT : ↥(tree A)\nx : List A\n⊢ x ∈ pullSub T x ↔ [] ∈ T",
"ppTerm": "?m.11",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"A : Type u_1\nT : ↥(tree A)\nx : List A\n⊢ x ∈ pullSub T x ↔ [] ∈ T"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Descriptive.Tree | {
"line": 124,
"column": 64
} | {
"line": 124,
"column": 75
} | {
"line": 124,
"column": 76
} | [
{
"pp": "A : Type u_1\nT : ↥(tree A)\nx y : List A\nh : y <+: x ∧ [] ∈ subAt T x\nh' : y.length ≤ x.length\n⊢ x ∈ T",
"ppTerm": "?m.53",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"A : Type u_1\nT : ↥(tree A)\nx y : List A\nh : y <+: x ∧ [] ∈ subAt T x\nh' : y.length ≤ x.length\n⊢ x ∈ T"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Cardinal.Cofinality.Club | {
"line": 282,
"column": 2
} | {
"line": 282,
"column": 13
} | {
"line": 282,
"column": 14
} | [
{
"pp": "α : Type v\ns t : Set α\ninst✝¹ : LinearOrder α\ninst✝ : WellFoundedLT α\nhα : cof α ≠ ℵ₀\n⊢ IsStationary (s ∪ t) ↔ IsStationary s ∨ IsStationary t",
"ppTerm": "?m.12",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type v\ns t : Set α\ninst✝¹ : LinearOrder α\ninst✝ : WellFoundedLT α\nhα : cof α ≠ ℵ₀\n⊢ IsStationary (s ∪ t) ↔ IsStationary s ∨ IsStationary t"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Lists | {
"line": 109,
"column": 24
} | {
"line": 109,
"column": 42
} | {
"line": 109,
"column": 43
} | [
{
"pp": "case cons'\nα : Type u_1\nb✝¹ b✝ : Bool\nb : Lists' α b✝\na : Lists' α true\na_ih✝ :\n ∀ (h : true = b✝),\n let l' := ⋯ ▸ b;\n ofList l'.toList = l'\nIH :\n ∀ (h : true = true),\n let l' := ⋯ ▸ a;\n ofList l'.toList = l'\nh : true = true\n⊢ let l' := ⋯ ▸ b.cons' a;\n ofList l'.toList = l... | [
"case cons'\nα : Type u_1\nb✝¹ b✝ : Bool\nb : Lists' α b✝\na : Lists' α true\na_ih✝ :\n ∀ (h : true = b✝),\n let l' := ⋯ ▸ b;\n ofList l'.toList = l'\nIH :\n ∀ (h : true = true),\n let l' := ⋯ ▸ a;\n ofList l'.toList = l'\nh : true = true\n⊢ ofList a.toList = a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Descriptive.Tree | {
"line": 145,
"column": 31
} | {
"line": 145,
"column": 59
} | {
"line": 145,
"column": 60
} | [
{
"pp": "A : Type u_1\nT : ↥(tree A)\nx y z : List A\nhl : x.length ≤ z.length\nhp : ¬x <+: z\nh : List.take (x ++ y).length z <+: x ++ y\nright✝ : List.drop (x ++ y).length z ∈ T\n⊢ ?m.103",
"ppTerm": "?m.104",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"A : Type u_1\nT : ↥(tree A)\nx y z : List A\nhl : x.length ≤ z.length\nhp : ¬x <+: z\nh : List.take (x ++ y).length z <+: x ++ y\nright✝ : List.drop (x ++ y).length z ∈ T\n⊢ ?m.103"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Descriptive.Tree | {
"line": 148,
"column": 4
} | {
"line": 148,
"column": 15
} | {
"line": 148,
"column": 16
} | [
{
"pp": "case inr\nA : Type u_1\nT : ↥(tree A)\nx y z : List A\nhl : z.length ≤ x.length\n⊢ z <+: x ∧ [] <+: y ∧ [] ∈ T ↔ z <+: x ++ y ∧ [] ∈ T",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Membership.mem",
"id",
"Subtype",
"List.... | [
"case inr\nA : Type u_1\nT : ↥(tree A)\nx y z : List A\nhl : z.length ≤ x.length\n⊢ [] ∈ T → (z <+: x ↔ z <+: x ++ y)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Commute | {
"line": 36,
"column": 39
} | {
"line": 36,
"column": 67
} | {
"line": 36,
"column": 68
} | [
{
"pp": "o₁ o₂ : Ordinal.{u_1}\nhcomm : AddCommute o₁ o₂\nih : ∀ y < o₁ + o₂, ∀ {o₁ o₂ : Ordinal.{u_1}}, AddCommute o₁ o₂ → o₁ + o₂ = y → ∃ o n₁ n₂, o * ↑n₁ = o₁ ∧ o * ↑n₂ = o₂\nhle : o₁ ≤ o₂\nh₁ : o₁ ≠ 0\no₃ : Ordinal.{u_1} := o₂ - o₁\nhsub : o₁ + o₃ = o₂\nhcomm' : AddCommute o₁ o₃\n⊢ o₁ + o₃ < o₁ + o₂",
"... | [
"o₁ o₂ : Ordinal.{u_1}\nhcomm : AddCommute o₁ o₂\nih : ∀ y < o₁ + o₂, ∀ {o₁ o₂ : Ordinal.{u_1}}, AddCommute o₁ o₂ → o₁ + o₂ = y → ∃ o n₁ n₂, o * ↑n₁ = o₁ ∧ o * ↑n₂ = o₂\nhle : o₁ ≤ o₂\nh₁ : o₁ ≠ 0\no₃ : Ordinal.{u_1} := o₂ - o₁\nhsub : o₁ + o₃ = o₂\nhcomm' : AddCommute o₁ o₃\n⊢ 0 < o₁"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.FixedPointApproximants | {
"line": 57,
"column": 4
} | {
"line": 57,
"column": 55
} | {
"line": 57,
"column": 56
} | [
{
"pp": "α : Type u\ng : Ordinal.{u} → α\nh_inj : InjOn g (Iio (succ #α).ord)\nh : lift.{u, u + 1} #↑(Iio (succ #α).ord) ≤ lift.{u + 1, u} #α\n⊢ #↑(Iio (succ #α).ord) = lift.{u + 1, u} (succ #α)",
"ppTerm": "?m.32",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}... | [
"α : Type u\ng : Ordinal.{u} → α\nh_inj : InjOn g (Iio (succ #α).ord)\nh : lift.{u, u + 1} #↑(Iio (succ #α).ord) ≤ lift.{u + 1, u} #α\n⊢ #↑(Iio (succ #α).ord) = lift.{u + 1, u} (succ #α)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.FixedPointApproximants | {
"line": 105,
"column": 2
} | {
"line": 105,
"column": 13
} | {
"line": 105,
"column": 14
} | [
{
"pp": "α : Type u\ninst✝ : CompleteLattice α\nf : α →o α\nx : α\nhx : x ≤ f x\na : Ordinal.{u}\n⊢ ⨆ b, ⨆ (_ : b < a + 1), f (lfpApprox f x b) ≤ f (lfpApprox f x a)",
"ppTerm": "?m.62",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Ordinal.instLinearOrder",
"Preorder.toLT",
... | [
"α : Type u\ninst✝ : CompleteLattice α\nf : α →o α\nx : α\nhx : x ≤ f x\na : Ordinal.{u}\n⊢ ∀ i ≤ a, f (lfpApprox f x i) ≤ f (lfpApprox f x a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.FixedPointApproximants | {
"line": 114,
"column": 4
} | {
"line": 114,
"column": 15
} | {
"line": 114,
"column": 16
} | [
{
"pp": "α : Type u\ninst✝ : CompleteLattice α\nf : α →o α\nx : α\na : Ordinal.{u}\nha : IsSuccLimit a\nb : Ordinal.{u}\nhab : b < a\n⊢ f (lfpApprox f x b) ≤ lfpApprox f x ↑⟨b + 1, ⋯⟩",
"ppTerm": "?m.106",
"assigned": true,
"usedConstants": [
"ChainCompletePartialOrder.instOfCompleteLattice",
... | [
"α : Type u\ninst✝ : CompleteLattice α\nf : α →o α\nx : α\na : Ordinal.{u}\nha : IsSuccLimit a\nb : Ordinal.{u}\nhab : b < a\n⊢ f (lfpApprox f x b) ≤ lfpApprox f x (b + 1)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Lists | {
"line": 309,
"column": 4
} | {
"line": 309,
"column": 15
} | {
"line": 309,
"column": 16
} | [
{
"pp": "case D1\nα : Type u_1\ntrans : Lists α → Prop := fun l₁ ↦ ∀ ⦃l₂ l₃ : Lists α⦄, l₁ ~ l₂ → l₂ ~ l₃ → l₁ ~ l₃\na : Lists α\nl : Lists' α true\nIH₁ : trans a\nIH₂ : ∀ (l' : Lists α), l' ∈ l.toList → trans l'\n⊢ ∀ (l' : Lists α), l' ∈ (Lists'.cons a l).toList → trans l'",
"ppTerm": "?D1",
"assigned"... | [
"case D1\nα : Type u_1\ntrans : Lists α → Prop := fun l₁ ↦ ∀ ⦃l₂ l₃ : Lists α⦄, l₁ ~ l₂ → l₂ ~ l₃ → l₁ ~ l₃\na : Lists α\nl : Lists' α true\nIH₁ : trans a\nIH₂ : ∀ (l' : Lists α), l' ∈ l.toList → trans l'\n⊢ trans a ∧ ∀ (a : Lists α), a ∈ l.toList → trans a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.CantorNormalForm | {
"line": 154,
"column": 8
} | {
"line": 155,
"column": 36
} | {
"line": 156,
"column": 6
} | [
{
"pp": "case refine_2.inr.inl\nb o✝ o : Ordinal.{u_1}\nho : o ≠ 0\nIH : List.Pairwise (fun x1 x2 ↦ x1 > x2) (map Prod.fst (CNF b (o % b ^ log b o)))\nhb : 1 < b\nhob : o < b\n⊢ List.Pairwise (fun x1 x2 ↦ x1 > x2) (map Prod.fst (CNF b o))",
"ppTerm": "?refine_2.inr.inl",
"assigned": true,
"usedConst... | [] | rw [CNF.of_lt ho hob]
exact pairwise_singleton _ _ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.SetTheory.Ordinal.CantorNormalForm | {
"line": 154,
"column": 8
} | {
"line": 155,
"column": 36
} | {
"line": 156,
"column": 6
} | [
{
"pp": "case refine_2.inr.inl\nb o✝ o : Ordinal.{u_1}\nho : o ≠ 0\nIH : List.Pairwise (fun x1 x2 ↦ x1 > x2) (map Prod.fst (CNF b (o % b ^ log b o)))\nhb : 1 < b\nhob : o < b\n⊢ List.Pairwise (fun x1 x2 ↦ x1 > x2) (map Prod.fst (CNF b o))",
"ppTerm": "?refine_2.inr.inl",
"assigned": true,
"usedConst... | [] | rw [CNF.of_lt ho hob]
exact pairwise_singleton _ _ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.SetTheory.Ordinal.CantorNormalForm | {
"line": 185,
"column": 4
} | {
"line": 185,
"column": 15
} | {
"line": 185,
"column": 16
} | [
{
"pp": "b o : Ordinal.{u_1}\na : Ordinal.{u_1} × Ordinal.{u_1}\nha : a ∈ CNF b o\n⊢ decide (a.toSigma.snd ≠ 0) = true",
"ppTerm": "?m.54",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instDecidableNot",
"Ordinal.instLinearOrder",
"Bool.not",
"Prod.toSigma",
"L... | [
"b o : Ordinal.{u_1}\na : Ordinal.{u_1} × Ordinal.{u_1}\nha : a ∈ CNF b o\n⊢ ¬a.2 = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.CantorNormalForm | {
"line": 228,
"column": 6
} | {
"line": 228,
"column": 17
} | {
"line": 228,
"column": 18
} | [
{
"pp": "case inr.inr\nb : Ordinal.{u_1}\nhb : b ≤ 1\no a : Ordinal.{u_1}\nho : o ≠ 0\nha : a ≠ 0\n⊢ a ∉ map Prod.fst [(0, o)]",
"ppTerm": "?inr.inr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"congrArg",
"List.map",
"Membership.mem",
"id",
"Pr... | [
"case inr.inr\nb : Ordinal.{u_1}\nhb : b ≤ 1\no a : Ordinal.{u_1}\nho : o ≠ 0\nha : a ≠ 0\n⊢ ¬a = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.CantorNormalForm | {
"line": 242,
"column": 2
} | {
"line": 242,
"column": 16
} | {
"line": 243,
"column": 2
} | [
{
"pp": "b e x y : Ordinal.{u_1}\nhb : 1 < b\nhx : x ≠ 0\nhxb : x < b\nhy : y < b ^ e\ne' : Ordinal.{u_1}\n⊢ (coeff b (b ^ e * x + y)) e' = (single e x + coeff b y) e'",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"Finsupp.instFunLike",
"Eq.mpr",
"HMul.hMul",
"Mul... | [
"b e x y : Ordinal.{u_1}\nhb : 1 < b\nhx : x ≠ 0\nhxb : x < b\nhy : y < b ^ e\ne' : Ordinal.{u_1}\n⊢ (coeff b (b ^ e * x + y)) e' = (single e x) e' + (coeff b y) e'"
] | rw [add_apply] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.SetTheory.Ordinal.CantorNormalForm | {
"line": 290,
"column": 2
} | {
"line": 290,
"column": 13
} | {
"line": 290,
"column": 14
} | [
{
"pp": "b e x : Ordinal.{u_1}\n⊢ eval b (single e x) = b ^ e * x",
"ppTerm": "?m.13",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"b e x : Ordinal.{u_1}\n⊢ eval b (single e x) = b ^ e * x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.FixedPointApproximants | {
"line": 192,
"column": 6
} | {
"line": 192,
"column": 87
} | {
"line": 193,
"column": 8
} | [
{
"pp": "α : Type u\ninst✝ : CompleteLattice α\nf : α →o α\n⊢ ∃ y, lfpApprox f ⊥ (succ #α).ord = ↑y",
"ppTerm": "?m.83",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"Order.succ",
"ChainCompletePartialOrder.instOfCompleteLattice",
"Cardinal... | [
"α : Type u\ninst✝ : CompleteLattice α\nf : α →o α\n⊢ IsFixedPt (⇑f) (lfpApprox f ⊥ (succ #α).ord)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.CantorNormalForm | {
"line": 303,
"column": 6
} | {
"line": 303,
"column": 27
} | {
"line": 303,
"column": 28
} | [
{
"pp": "b x e' y : Ordinal.{u_1}\nf : Ordinal.{u_1} →₀ Ordinal.{u_1}\nhf : ∀ c ∈ f.support, c < e'\nhy : y ≠ 0\na : Ordinal.{u_1}\nha : a ∈ (single e' y + f).support\nh : ∀ e'_1 ∈ (single e' y + f).support, e'_1 ≤ a\na✝ : single e' y + f = f → eval b (single a x + (single e' y + f)) = b ^ a * x + eval b (singl... | [
"b x e' y : Ordinal.{u_1}\nf : Ordinal.{u_1} →₀ Ordinal.{u_1}\nhf : ∀ c ∈ f.support, c < e'\nhy : y ≠ 0\na : Ordinal.{u_1}\nha : a ∈ (single e' y + f).support\nh : ∀ e'_1 ∈ (single e' y + f).support, e'_1 ≤ a\na✝ : single e' y + f = f → eval b (single a x + (single e' y + f)) = b ^ a * x + eval b (single e' y + f)\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Order.SuccPred | {
"line": 44,
"column": 65
} | {
"line": 44,
"column": 76
} | {
"line": 44,
"column": 77
} | [
{
"pp": "α : Type u_1\ninst✝⁴ : LinearOrder α\ninst✝³ : TopologicalSpace α\ninst✝² : OrderTopology α\na : α\ninst✝¹ : SuccOrder α\ninst✝ : NoMaxOrder α\na✝ : Nontrivial α\nh : IsOpen[inst✝³] {a}\nha : IsSuccLimit a\n⊢ ∃ l, l < a",
"ppTerm": "?m.34",
"assigned": false,
"usedConstants": [],
"usedF... | [
"α : Type u_1\ninst✝⁴ : LinearOrder α\ninst✝³ : TopologicalSpace α\ninst✝² : OrderTopology α\na : α\ninst✝¹ : SuccOrder α\ninst✝ : NoMaxOrder α\na✝ : Nontrivial α\nh : IsOpen[inst✝³] {a}\nha : IsSuccLimit a\n⊢ ∃ l, l < a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Order.SuccPred | {
"line": 45,
"column": 10
} | {
"line": 45,
"column": 42
} | {
"line": 45,
"column": 43
} | [
{
"pp": "α : Type u_1\ninst✝⁴ : LinearOrder α\ninst✝³ : TopologicalSpace α\ninst✝² : OrderTopology α\na : α\ninst✝¹ : SuccOrder α\ninst✝ : NoMaxOrder α\na✝ : Nontrivial α\nh : IsOpen[inst✝³] {a}\nha : IsSuccLimit a\n⊢ ∃ u, a < u",
"ppTerm": "?m.35",
"assigned": false,
"usedConstants": [],
"usedF... | [
"α : Type u_1\ninst✝⁴ : LinearOrder α\ninst✝³ : TopologicalSpace α\ninst✝² : OrderTopology α\na : α\ninst✝¹ : SuccOrder α\ninst✝ : NoMaxOrder α\na✝ : Nontrivial α\nh : IsOpen[inst✝³] {a}\nha : IsSuccLimit a\n⊢ ∃ u, a < u"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Notation | {
"line": 231,
"column": 2
} | {
"line": 231,
"column": 32
} | {
"line": 231,
"column": 33
} | [
{
"pp": "e : ONote\nn : ℕ+\na : ONote\nh : (e.oadd n a).NF\ne0 : e = 0\n⊢ a = 0",
"ppTerm": "?m.10",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"e : ONote\nn : ℕ+\na : ONote\nh : (e.oadd n a).NF\ne0 : e = 0\n⊢ a = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Veblen | {
"line": 134,
"column": 2
} | {
"line": 134,
"column": 13
} | {
"line": 134,
"column": 14
} | [
{
"pp": "f : Ordinal.{u} → Ordinal.{u}\nhf : IsNormal f\n⊢ veblenWith f 1 = deriv f",
"ppTerm": "?m.8",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"f : Ordinal.{u} → Ordinal.{u}\nhf : IsNormal f\n⊢ veblenWith f 1 = deriv f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Veblen | {
"line": 206,
"column": 18
} | {
"line": 206,
"column": 29
} | {
"line": 206,
"column": 30
} | [
{
"pp": "case h\nf : Ordinal.{u} → Ordinal.{u}\nhf : IsNormal f\nhp : 0 < f 0\no : Ordinal.{u}\nho : IsSuccLimit o\na : Ordinal.{u}\nIH : ∀ b < o, veblenWith f b 0 ≤ a\n⊢ 0 < o ∧ List.foldr (fun x ↦ veblenWith f ↑x) 0 [] ≤ veblenWith f 0 0",
"ppTerm": "?h",
"assigned": true,
"usedConstants": [
... | [
"case h\nf : Ordinal.{u} → Ordinal.{u}\nhf : IsNormal f\nhp : 0 < f 0\no : Ordinal.{u}\nho : IsSuccLimit o\na : Ordinal.{u}\nIH : ∀ b < o, veblenWith f b 0 ≤ a\n⊢ 0 < o"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Veblen | {
"line": 224,
"column": 87
} | {
"line": 226,
"column": 49
} | {
"line": 228,
"column": 0
} | [
{
"pp": "f : Ordinal.{u} → Ordinal.{u}\no₁ o₂ a : Ordinal.{u}\nhf : IsNormal f\nh : o₂ ≤ o₁\n⊢ veblenWith f o₂ a < veblenWith f o₁ (veblenWith f o₂ a) ↔ a < veblenWith f o₁ a",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Ordinal.partialOrder"... | [] | by
simp_rw [(right_le_veblenWith hf ..).lt_iff_ne', ne_eq,
veblenWith_veblenWith_eq_veblenWith_iff hf h] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.SetTheory.Ordinal.Veblen | {
"line": 229,
"column": 2
} | {
"line": 229,
"column": 13
} | {
"line": 229,
"column": 14
} | [
{
"pp": "f : Ordinal.{u} → Ordinal.{u}\no a : Ordinal.{u}\nhf : IsNormal f\n⊢ veblenWith f o (f a) = f a ↔ veblenWith f o a = a",
"ppTerm": "?m.7",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"f : Ordinal.{u} → Ordinal.{u}\no a : Ordinal.{u}\nhf : IsNormal f\n⊢ veblenWith f o (f a) = f a ↔ veblenWith f o a = a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Veblen | {
"line": 232,
"column": 2
} | {
"line": 232,
"column": 13
} | {
"line": 232,
"column": 14
} | [
{
"pp": "f : Ordinal.{u} → Ordinal.{u}\no a : Ordinal.{u}\nhf : IsNormal f\n⊢ f a < veblenWith f o (f a) ↔ a < veblenWith f o a",
"ppTerm": "?m.9",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"f : Ordinal.{u} → Ordinal.{u}\no a : Ordinal.{u}\nhf : IsNormal f\n⊢ f a < veblenWith f o (f a) ↔ a < veblenWith f o a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Veblen | {
"line": 439,
"column": 2
} | {
"line": 439,
"column": 13
} | {
"line": 439,
"column": 14
} | [
{
"pp": "o x : Ordinal.{u}\nh : o < x.invVeblen₁\n⊢ veblen o x = x",
"ppTerm": "?m.4",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"o x : Ordinal.{u}\nh : o < x.invVeblen₁\n⊢ veblen o x = x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Veblen | {
"line": 555,
"column": 2
} | {
"line": 555,
"column": 23
} | {
"line": 555,
"column": 24
} | [
{
"pp": "o : Ordinal.{u_1}\n⊢ ε_ o = deriv (fun a ↦ ω ^ a) o",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Ordinal.omega0",
"id",
"HPow.hPow",
"Ordinal.deriv",
"Ordinal.epsilon",
"instHPow",
"Ordinal.instPow",
"Eq",
"Ordinal"
],
... | [
"o : Ordinal.{u_1}\n⊢ veblen 1 o = deriv (fun a ↦ ω ^ a) o"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Cardinal | {
"line": 40,
"column": 2
} | {
"line": 40,
"column": 35
} | {
"line": 40,
"column": 36
} | [
{
"pp": "x y : ZFSet.{u}\nh : x ⊆ y\n⊢ x.card ≤ y.card",
"ppTerm": "?m.5",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"x y : ZFSet.{u}\nh : x ⊆ y\n⊢ x.card ≤ y.card"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Cardinal | {
"line": 57,
"column": 2
} | {
"line": 57,
"column": 32
} | {
"line": 57,
"column": 33
} | [
{
"pp": "x : ZFSet.{u}\n⊢ {x}.card = 1",
"ppTerm": "?m.7",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"x : ZFSet.{u}\n⊢ {x}.card = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Cardinal | {
"line": 70,
"column": 2
} | {
"line": 70,
"column": 37
} | {
"line": 70,
"column": 38
} | [
{
"pp": "x : ZFSet.{u}\n⊢ lift.{u + 1, u} x.powerset.card = lift.{u + 1, u} (2 ^ x.card)",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Cardinal.instPowCardinal",
"Cardinal",
"congrArg",
"ZFSet",
"PartialOrder.toPreorder",
"Nat.instAtLe... | [
"x : ZFSet.{u}\n⊢ #{ x_1 // x_1 ⊆ x } = 2 ^ #↥x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Cardinal | {
"line": 74,
"column": 2
} | {
"line": 74,
"column": 60
} | {
"line": 74,
"column": 61
} | [
{
"pp": "x : ZFSet.{u}\nf : ZFSet.{u} → ZFSet.{u}\ninst✝ : Definable₁ f\n⊢ (image f x).card ≤ x.card",
"ppTerm": "?m.4",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"x : ZFSet.{u}\nf : ZFSet.{u} → ZFSet.{u}\ninst✝ : Definable₁ f\n⊢ (image f x).card ≤ x.card"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Cardinal | {
"line": 79,
"column": 2
} | {
"line": 79,
"column": 60
} | {
"line": 79,
"column": 61
} | [
{
"pp": "α : Type u\ninst✝ : Small.{v, u} α\nf : α → ZFSet.{v}\n⊢ lift.{max u (v + 1), max u v} (lift.{u, v} (range f).card) ≤ lift.{v + 1, u} #α",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Cardinal",
"Cardinal.lift_lift",
"congrArg",
"Cardinal.... | [
"α : Type u\ninst✝ : Small.{v, u} α\nf : α → ZFSet.{v}\n⊢ lift.{max u (v + 1), v} (range f).card ≤ lift.{v + 1, u} #α"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Cardinal | {
"line": 83,
"column": 2
} | {
"line": 83,
"column": 93
} | {
"line": 84,
"column": 4
} | [
{
"pp": "α : Type u\ninst✝ : Small.{v, u} α\nf : α → ZFSet.{v}\n⊢ ⨆ i, (f i).card ≤ (⋃ (i : α), f i).card",
"ppTerm": "?m.11",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\ninst✝ : Small.{v, u} α\nf : α → ZFSet.{v}\n⊢ ⨆ i, (f i).card ≤ (⋃ (i : α), f i).card"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Cardinal | {
"line": 89,
"column": 2
} | {
"line": 89,
"column": 62
} | {
"line": 90,
"column": 4
} | [
{
"pp": "α : Type u\ninst✝ : Small.{v, u} α\nf : α → ZFSet.{v}\n⊢ lift.{v + 1, max u v} (lift.{u, v} (⋃ (i : α), f i).card) ≤ lift.{v + 1, max u v} (sum fun i ↦ (f i).card)",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Cardinal",
"Cardinal.lift_lift",
"... | [
"α : Type u\ninst✝ : Small.{v, u} α\nf : α → ZFSet.{v}\n⊢ lift.{max u (v + 1), v} (⋃ (i : α), f i).card ≤ sum fun i ↦ lift.{v + 1, v} (f i).card"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Veblen | {
"line": 595,
"column": 2
} | {
"line": 595,
"column": 13
} | {
"line": 595,
"column": 14
} | [
{
"pp": "o : Ordinal.{u_1}\n⊢ ω < veblen 1 0",
"ppTerm": "?m.9",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"o : Ordinal.{u_1}\n⊢ ω < veblen 1 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Veblen | {
"line": 687,
"column": 2
} | {
"line": 687,
"column": 13
} | {
"line": 687,
"column": 14
} | [
{
"pp": "o : Ordinal.{u_1}\n⊢ ε_ 0 < Γ_ 0",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"o : Ordinal.{u_1}\n⊢ ε_ 0 < Γ_ 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Notation | {
"line": 444,
"column": 8
} | {
"line": 444,
"column": 19
} | {
"line": 444,
"column": 20
} | [
{
"pp": "case oadd.lt.h₂\ne : ONote\nn : ℕ+\na o : ONote\nh₁ : (e.oadd n a).NF\nh₂ : o.NF\nthis✝¹ : a.NF\nh' : (a.add o).repr = a.repr + o.repr\ne' : ONote\nn' : ℕ+\na' : ONote\nh : a.add o = e'.oadd n' a'\nnf : (e'.oadd n' a').NF\nthis✝ : e.NF\nthis : e'.NF\nhe : e.cmp e' = Ordering.lt\nee : e < e'\n⊢ ω ^ e'.r... | [
"case oadd.lt.h₂\ne : ONote\nn : ℕ+\na o : ONote\nh₁ : (e.oadd n a).NF\nh₂ : o.NF\nthis✝¹ : a.NF\nh' : (a.add o).repr = a.repr + o.repr\ne' : ONote\nn' : ℕ+\na' : ONote\nh : a.add o = e'.oadd n' a'\nnf : (e'.oadd n' a').NF\nthis✝ : e.NF\nthis : e'.NF\nhe : e.cmp e' = Ordering.lt\nee : e < e'\n⊢ ω ^ e'.repr ≤ ω ^ e'... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Notation | {
"line": 457,
"column": 6
} | {
"line": 457,
"column": 21
} | {
"line": 458,
"column": 6
} | [
{
"pp": "case eq\ne₁ : ONote\nn₁ : ℕ+\na₁ e₂ : ONote\nn₂ : ℕ+\na₂ : ONote\nb : Ordinal.{0}\nh₁ : (e₁.oadd n₁ a₁).NFBelow b\nh₂ : (e₂.oadd n₂ a₂).NF\nh' : (a₁.sub a₂).NFBelow e₁.repr\nthis : (e₁.cmp e₂).Compares e₁ e₂\nh : e₁.cmp e₂ = Ordering.eq\n⊢ (match Ordering.eq with\n | Ordering.lt => 0\n | Orde... | [
"case eq\ne₁ : ONote\nn₁ : ℕ+\na₁ e₂ : ONote\nn₂ : ℕ+\na₂ : ONote\nb : Ordinal.{0}\nh₁ : (e₁.oadd n₁ a₁).NFBelow b\nh₂ : (e₂.oadd n₂ a₂).NF\nh' : (a₁.sub a₂).NFBelow e₁.repr\nthis : (e₁.cmp e₂).Compares e₁ e₂\nh : e₁.cmp e₂ = Ordering.eq\n⊢ (match Ordering.eq with\n | Ordering.lt => 0\n | Ordering.gt => e... | rw [Nat.sub_eq] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.SetTheory.ZFC.Rank | {
"line": 109,
"column": 72
} | {
"line": 117,
"column": 10
} | {
"line": 119,
"column": 0
} | [
{
"pp": "x : PSet.{u_1}\n⊢ x.rank ≤ succ (⋃₀ x).rank",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Order.succ",
"PSet.instMembership",
"Ordinal.partialOrder",
"PSet.rank_mono",
"congrArg",
"PSet.powerset",
"PartialOrder.toPreorder... | [] | by
rw [← rank_powerset]
apply rank_mono
rw [subset_iff]
intro z _
rw [mem_powerset, subset_iff]
intro _ _
rw [mem_sUnion]
exists z | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.SetTheory.ZFC.Rank | {
"line": 127,
"column": 4
} | {
"line": 127,
"column": 37
} | {
"line": 127,
"column": 38
} | [
{
"pp": "x✝ x : PSet.{u}\nih : ∀ y ∈ x, lift.{u + 1, u} y.rank = IsWellFounded.rank (fun x1 x2 ↦ x1 ∈ x2) y\no : Ordinal.{u}\nh : o < x.rank\n⊢ lift.{u + 1, u} o < ⨆ i, succ (lift.{u + 1, u} (↑i).rank)",
"ppTerm": "?m.66",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Ordinal.instLinea... | [
"x✝ x : PSet.{u}\nih : ∀ y ∈ x, lift.{u + 1, u} y.rank = IsWellFounded.rank (fun x1 x2 ↦ x1 ∈ x2) y\no : Ordinal.{u}\nh : o < x.rank\n⊢ ∃ a ∈ x, o ≤ a.rank"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Rank | {
"line": 128,
"column": 4
} | {
"line": 128,
"column": 15
} | {
"line": 128,
"column": 16
} | [
{
"pp": "x✝ x : PSet.{u}\nih : ∀ y ∈ x, lift.{u + 1, u} y.rank = IsWellFounded.rank (fun x1 x2 ↦ x1 ∈ x2) y\nh : { b // b ∈ x }\n⊢ succ (lift.{u + 1, u} (↑h).rank) ≤ lift.{u + 1, u} x.rank",
"ppTerm": "?m.40",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Order.s... | [
"x✝ x : PSet.{u}\nih : ∀ y ∈ x, lift.{u + 1, u} y.rank = IsWellFounded.rank (fun x1 x2 ↦ x1 ∈ x2) y\nh : { b // b ∈ x }\n⊢ (↑h).rank < x.rank"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Basic | {
"line": 558,
"column": 75
} | {
"line": 558,
"column": 86
} | {
"line": 558,
"column": 87
} | [
{
"pp": "x y : ZFSet.{u}\nhxy : x ⊆ y\nz✝ : ZFSet.{u}\n⊢ z✝ ∈ x ∩ y ↔ z✝ ∈ x",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"ZFSet",
"Membership.mem",
"ZFSet.mem_inter._simp_1",
"id",
"Inter.inter",
"And",
"Iff",
... | [
"x y : ZFSet.{u}\nhxy : x ⊆ y\nz✝ : ZFSet.{u}\n⊢ z✝ ∈ x → z✝ ∈ y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Basic | {
"line": 559,
"column": 76
} | {
"line": 559,
"column": 87
} | {
"line": 559,
"column": 88
} | [
{
"pp": "x y : ZFSet.{u}\nhyx : y ⊆ x\nz✝ : ZFSet.{u}\n⊢ z✝ ∈ x ∩ y ↔ z✝ ∈ y",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"ZFSet",
"Membership.mem",
"ZFSet.mem_inter._simp_1",
"id",
"Inter.inter",
"And",
"Iff",
... | [
"x y : ZFSet.{u}\nhyx : y ⊆ x\nz✝ : ZFSet.{u}\n⊢ z✝ ∈ y → z✝ ∈ x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Basic | {
"line": 650,
"column": 6
} | {
"line": 650,
"column": 22
} | {
"line": 650,
"column": 23
} | [
{
"pp": "case h\nα : Type u_1\ninst✝ : Small.{u, u_1} α\nf : α → ZFSet.{u}\nx : ZFSet.{u}\ny : PSet.{u}\nz : α\nhz : f z = ⟦y⟧\n⊢ y.Equiv ((PSet.mk (Shrink.{u, u_1} α) (Quotient.out ∘ f ∘ ⇑(equivShrink α).symm)).Func ((equivShrink α) z))",
"ppTerm": "?h",
"assigned": true,
"usedConstants": [
"... | [
"case h\nα : Type u_1\ninst✝ : Small.{u, u_1} α\nf : α → ZFSet.{u}\nx : ZFSet.{u}\ny : PSet.{u}\nz : α\nhz : f z = ⟦y⟧\n⊢ y.Equiv (Quotient.out (mk y))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Basic | {
"line": 674,
"column": 2
} | {
"line": 674,
"column": 13
} | {
"line": 674,
"column": 14
} | [
{
"pp": "α : Type u_1\ninst✝ : Small.{u, u_1} α\nf : α → ZFSet.{u}\ni : α\nx : ZFSet.{u}\nhx : x ∈ f i\n⊢ x ∈ ⋃ (i : α), f i",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"ZFSet",
"Membership.mem",
"Exists",
"id",
"ZFSet.mem_iUnion._simp_1",
... | [
"α : Type u_1\ninst✝ : Small.{u, u_1} α\nf : α → ZFSet.{u}\ni : α\nx : ZFSet.{u}\nhx : x ∈ f i\n⊢ ∃ i, x ∈ f i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Basic | {
"line": 698,
"column": 40
} | {
"line": 698,
"column": 65
} | {
"line": 698,
"column": 66
} | [
{
"pp": "x x' y y' : ZFSet.{u_1}\nH : ∀ (z : ZFSet.{u_1}), z = {x} ∨ z = {x, y} ↔ z = {x'} ∨ z = {x', y'}\n⊢ x = x' ∧ ?m.27",
"ppTerm": "?m.28",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"x x' y y' : ZFSet.{u_1}\nH : ∀ (z : ZFSet.{u_1}), z = {x} ∨ z = {x, y} ↔ z = {x'} ∨ z = {x', y'}\n⊢ x = x' ∧ ?m.27"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Basic | {
"line": 698,
"column": 40
} | {
"line": 698,
"column": 88
} | {
"line": 699,
"column": 2
} | [
{
"pp": "x x' y y' : ZFSet.{u_1}\nH : ∀ (z : ZFSet.{u_1}), z = {x} ∨ z = {x, y} ↔ z = {x'} ∨ z = {x', y'}\n⊢ x = x' ∧ ?m.27",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"congrArg",
"ZFSet",
"Eq.mp",
"Insert.insert",
"_private.Mathlib.SetTheory.ZFC.Basic.0.Z... | [] | simpa [or_and_left] using (H {x}).1 (Or.inl rfl) | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.SetTheory.ZFC.Basic | {
"line": 698,
"column": 40
} | {
"line": 698,
"column": 88
} | {
"line": 699,
"column": 2
} | [
{
"pp": "x x' y y' : ZFSet.{u_1}\nH : ∀ (z : ZFSet.{u_1}), z = {x} ∨ z = {x, y} ↔ z = {x'} ∨ z = {x', y'}\n⊢ x = x' ∧ ?m.27",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"congrArg",
"ZFSet",
"Eq.mp",
"Insert.insert",
"_private.Mathlib.SetTheory.ZFC.Basic.0.Z... | [] | simpa [or_and_left] using (H {x}).1 (Or.inl rfl) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.SetTheory.ZFC.Basic | {
"line": 698,
"column": 40
} | {
"line": 698,
"column": 88
} | {
"line": 699,
"column": 2
} | [
{
"pp": "x x' y y' : ZFSet.{u_1}\nH : ∀ (z : ZFSet.{u_1}), z = {x} ∨ z = {x, y} ↔ z = {x'} ∨ z = {x', y'}\n⊢ x = x' ∧ ?m.27",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"congrArg",
"ZFSet",
"Eq.mp",
"Insert.insert",
"_private.Mathlib.SetTheory.ZFC.Basic.0.Z... | [] | simpa [or_and_left] using (H {x}).1 (Or.inl rfl) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.SetTheory.ZFC.Basic | {
"line": 701,
"column": 4
} | {
"line": 701,
"column": 25
} | {
"line": 701,
"column": 26
} | [
{
"pp": "y y' : ZFSet.{u_1}\nH : ∀ (z : ZFSet.{u_1}), z = {y} ∨ z = {y, y} ↔ z = {y} ∨ z = {y, y'}\n⊢ y = y'",
"ppTerm": "?m.71",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"y y' : ZFSet.{u_1}\nH : ∀ (z : ZFSet.{u_1}), z = {y} ∨ z = {y, y} ↔ z = {y} ∨ z = {y, y'}\n⊢ y = y'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Basic | {
"line": 705,
"column": 2
} | {
"line": 705,
"column": 13
} | {
"line": 705,
"column": 14
} | [
{
"pp": "x y y' : ZFSet.{u_1}\nH : ∀ (z : ZFSet.{u_1}), z = {x} ∨ z = {x, y} ↔ z = {x} ∨ z = {x, y'}\nhe : y = x → y = y'\nhx : y = x ∨ {x, y} = {x, y'}\nhy : {x, y} = {x, y'}\n⊢ y = x ∨ y = y'",
"ppTerm": "?m.128",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}... | [
"x y y' : ZFSet.{u_1}\nH : ∀ (z : ZFSet.{u_1}), z = {x} ∨ z = {x, y} ↔ z = {x} ∨ z = {x, y'}\nhe : y = x → y = y'\nhx : y = x ∨ {x, y} = {x, y'}\nhy : {x, y} = {x, y'}\n⊢ y = x ∨ y = y'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Rank | {
"line": 207,
"column": 4
} | {
"line": 207,
"column": 47
} | {
"line": 207,
"column": 48
} | [
{
"pp": "α : Type u_1\ninst✝ : Small.{u, u_1} α\nf : α → ZFSet.{u}\n⊢ (range f).rank ≤ ⨆ i, succ (f i).rank",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"_private.Mathlib.SetTheory.ZFC.Rank.0.ZFSet.rank_range._simp_1_1",
"ZFSet.mem_range._simp_1",
"Preo... | [
"α : Type u_1\ninst✝ : Small.{u, u_1} α\nf : α → ZFSet.{u}\n⊢ ∀ (a : α), (f a).rank + 1 ≤ ⨆ i, (f i).rank + 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Rank | {
"line": 206,
"column": 2
} | {
"line": 208,
"column": 25
} | {
"line": 210,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : Small.{u, u_1} α\nf : α → ZFSet.{u}\n⊢ (range f).rank = ⨆ i, succ (f i).rank",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"_private.Mathlib.SetTheory.ZFC.Rank.0.ZFSet.rank_range._simp_1_1",
"_private.Mathlib.SetTheory.ZFC.Rank.0... | [] | apply (Ordinal.iSup_le _).antisymm'
· simpa [rank_le_iff, ← add_one_le_iff] using Ordinal.le_iSup _
· simp [rank_lt_of_mem] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.SetTheory.ZFC.Rank | {
"line": 206,
"column": 2
} | {
"line": 208,
"column": 25
} | {
"line": 210,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : Small.{u, u_1} α\nf : α → ZFSet.{u}\n⊢ (range f).rank = ⨆ i, succ (f i).rank",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"_private.Mathlib.SetTheory.ZFC.Rank.0.ZFSet.rank_range._simp_1_1",
"_private.Mathlib.SetTheory.ZFC.Rank.0... | [] | apply (Ordinal.iSup_le _).antisymm'
· simpa [rank_le_iff, ← add_one_le_iff] using Ordinal.le_iSup _
· simp [rank_lt_of_mem] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.SetTheory.ZFC.Class | {
"line": 265,
"column": 2
} | {
"line": 265,
"column": 39
} | {
"line": 265,
"column": 40
} | [
{
"pp": "x : Class.{u}\nz : ZFSet.{u}\nhz : z ∈ x\ny : ZFSet.{u}\nright✝ : ↑z y\nH : ∀ z ∈ x, ↑y ∈ z\nw : ZFSet.{u}\nhxw : x w\n⊢ y ∈ w",
"ppTerm": "?m.70",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"x : Class.{u}\nz : ZFSet.{u}\nhz : z ∈ x\ny : ZFSet.{u}\nright✝ : ↑z y\nH : ∀ z ∈ x, ↑y ∈ z\nw : ZFSet.{u}\nhxw : x w\n⊢ y ∈ w"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Rank | {
"line": 227,
"column": 4
} | {
"line": 227,
"column": 37
} | {
"line": 227,
"column": 38
} | [
{
"pp": "x✝ x : ZFSet.{u}\nih : ∀ y ∈ x, lift.{u + 1, u} y.rank = IsWellFounded.rank (fun x1 x2 ↦ x1 ∈ x2) y\no : Ordinal.{u}\nh : o < x.rank\n⊢ lift.{u + 1, u} o < ⨆ i, succ (lift.{u + 1, u} (↑i).rank)",
"ppTerm": "?m.63",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Ordinal.instLine... | [
"x✝ x : ZFSet.{u}\nih : ∀ y ∈ x, lift.{u + 1, u} y.rank = IsWellFounded.rank (fun x1 x2 ↦ x1 ∈ x2) y\no : Ordinal.{u}\nh : o < x.rank\n⊢ ∃ a ∈ x, o ≤ a.rank"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Rank | {
"line": 228,
"column": 4
} | {
"line": 228,
"column": 15
} | {
"line": 228,
"column": 16
} | [
{
"pp": "x✝ x : ZFSet.{u}\nih : ∀ y ∈ x, lift.{u + 1, u} y.rank = IsWellFounded.rank (fun x1 x2 ↦ x1 ∈ x2) y\nh : ↥x\n⊢ succ (lift.{u + 1, u} (↑h).rank) ≤ lift.{u + 1, u} x.rank",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Order.succ",
... | [
"x✝ x : ZFSet.{u}\nih : ∀ y ∈ x, lift.{u + 1, u} y.rank = IsWellFounded.rank (fun x1 x2 ↦ x1 ∈ x2) y\nh : ↥x\n⊢ (↑h).rank < x.rank"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.VonNeumann | {
"line": 129,
"column": 17
} | {
"line": 129,
"column": 45
} | {
"line": 129,
"column": 46
} | [
{
"pp": "o : Ordinal.{u}\nh : IsSuccPrelimit o\nz : ZFSet.{u}\n⊢ z ∈ V_ o ↔ z ∈ ⋃ (a : ↑(Set.Iio o)), V_ ↑a",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Ordinal.partialOrder",
"Iff.of_eq",
"congrArg",
"ZFSet",
"Partia... | [
"o : Ordinal.{u}\nh : IsSuccPrelimit o\nz : ZFSet.{u}\n⊢ z.rank < o ↔ ∃ a < o, z.rank < a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.VonNeumann | {
"line": 138,
"column": 2
} | {
"line": 138,
"column": 13
} | {
"line": 138,
"column": 14
} | [
{
"pp": "o : Ordinal.{u_1}\n⊢ o.card ≤ (V_ o).card",
"ppTerm": "?m.3",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"o : Ordinal.{u_1}\n⊢ o.card ≤ (V_ o).card"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Ordinal | {
"line": 211,
"column": 4
} | {
"line": 211,
"column": 15
} | {
"line": 211,
"column": 16
} | [
{
"pp": "x : ZFSet.{u}\nh : x.IsOrdinal\na : ZFSet.{u}\nha : a ∈ x\nb : ZFSet.{u}\nhb : b ∈ x\n⊢ Subrel (fun x1 x2 ↦ x1 ∈ x2) (fun x_1 ↦ x_1 ∈ x) ⟨a, ha⟩ ⟨b, hb⟩ ∨\n ⟨a, ha⟩ = ⟨b, hb⟩ ∨ Subrel (fun x1 x2 ↦ x1 ∈ x2) (fun x_1 ↦ x_1 ∈ x) ⟨b, hb⟩ ⟨a, ha⟩",
"ppTerm": "?m.51",
"assigned": true,
"usedCo... | [
"x : ZFSet.{u}\nh : x.IsOrdinal\na : ZFSet.{u}\nha : a ∈ x\nb : ZFSet.{u}\nhb : b ∈ x\n⊢ a ∈ b ∨ a = b ∨ b ∈ a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Ordinal | {
"line": 293,
"column": 2
} | {
"line": 293,
"column": 13
} | {
"line": 293,
"column": 14
} | [
{
"pp": "o : Ordinal.{u_1}\nx : PSet.{u_1}\n⊢ (∃ b, x.Equiv ((PSet.mk o.ToType fun a ↦ (↑a.toOrd).toPSet).Func b)) ↔ ∃ a < o, x.Equiv a.toPSet",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"Ordinal.ToType.toOrd",
"Ordinal.partialOrder",
"PartialOr... | [
"o : Ordinal.{u_1}\nx : PSet.{u_1}\n⊢ (∃ b, x.Equiv (↑b.toOrd).toPSet) ↔ ∃ a < o, x.Equiv a.toPSet"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Ordinal | {
"line": 371,
"column": 2
} | {
"line": 371,
"column": 88
} | {
"line": 372,
"column": 4
} | [
{
"pp": "o : Ordinal.{u_1}\n⊢ o.toZFSet.card = o.card",
"ppTerm": "?m.2",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"o : Ordinal.{u_1}\n⊢ o.toZFSet.card = o.card"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Ordinal | {
"line": 405,
"column": 32
} | {
"line": 405,
"column": 43
} | {
"line": 405,
"column": 44
} | [
{
"pp": "x✝¹ y z w : ZFSet.{u}\nx✝ : { x // x.IsOrdinal }\nx : ZFSet.{?u.18}\nhx : x.IsOrdinal\n⊢ (fun o ↦ ⟨o.toZFSet, ⋯⟩) ((fun x ↦ (↑x).rank) ⟨x, hx⟩) = ⟨x, hx⟩",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"ZFSet",
"ZFSet.IsOrdinal",
"id",
"Subt... | [
"x✝¹ y z w : ZFSet.{u}\nx✝ : { x // x.IsOrdinal }\nx : ZFSet.{?u.18}\nhx : x.IsOrdinal\n⊢ x.rank.toZFSet = x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Notation | {
"line": 721,
"column": 2
} | {
"line": 721,
"column": 13
} | {
"line": 721,
"column": 14
} | [
{
"pp": "o e : ONote\nn : ℕ+\na : ONote\nm : ℕ\ninst✝ : o.NF\nh : o.split = (e.oadd n a, m)\nh₁ : (e.oadd n a).NF\nh₂ : o.repr = (e.oadd n a).repr + ↑m\ne0 : e.repr ≠ 0\nd : ω ∣ a.repr\n⊢ ω ≤ ω ^ e.repr",
"ppTerm": "?m.65",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals"... | [
"o e : ONote\nn : ℕ+\na : ONote\nm : ℕ\ninst✝ : o.NF\nh : o.split = (e.oadd n a, m)\nh₁ : (e.oadd n a).NF\nh₂ : o.repr = (e.oadd n a).repr + ↑m\ne0 : e.repr ≠ 0\nd : ω ∣ a.repr\n⊢ ω ≤ ω ^ e.repr"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Notation | {
"line": 726,
"column": 58
} | {
"line": 726,
"column": 69
} | {
"line": 726,
"column": 70
} | [
{
"pp": "o : ONote\ninst✝ : o.NF\nn : ℕ\n⊢ (o.mulNat n).NF",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"ONote.NF",
"Eq.mpr",
"ONote.instMul",
"HMul.hMul",
"congrArg",
"ONote.ofNat",
"id",
"ONote.mulNat",
"ONote.mulNat_eq_mul",
... | [
"o : ONote\ninst✝ : o.NF\nn : ℕ\n⊢ (o * ↑n).NF"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Notation | {
"line": 811,
"column": 6
} | {
"line": 811,
"column": 17
} | {
"line": 811,
"column": 18
} | [
{
"pp": "case inr\ne a : ONote\nNe : e.NF\nNa : a.NF\ne0 : e.repr ≠ 0\nn : ℕ+\nh✝ : a.repr < ω ^ e.repr\nNo : (e.oadd n a).NF\nthis✝ : ω ^ e.repr ≤ ω ^ e.repr * ↑↑n + a.repr\nb : Ordinal.{0}\nl : b < ω\nthis : ω ^ e.repr * ↑↑n + a.repr < ω ^ succ e.repr\nh : e.repr < ω\n⊢ ω ^ ω ≤ ω ^ (e.repr * ω)",
"ppTerm"... | [
"case inr\ne a : ONote\nNe : e.NF\nNa : a.NF\ne0 : e.repr ≠ 0\nn : ℕ+\nh✝ : a.repr < ω ^ e.repr\nNo : (e.oadd n a).NF\nthis✝ : ω ^ e.repr ≤ ω ^ e.repr * ↑↑n + a.repr\nb : Ordinal.{0}\nl : b < ω\nthis : ω ^ e.repr * ↑↑n + a.repr < ω ^ succ e.repr\nh : e.repr < ω\n⊢ ω ≤ e.repr * ω"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Lemmas | {
"line": 44,
"column": 2
} | {
"line": 44,
"column": 62
} | {
"line": 44,
"column": 63
} | [
{
"pp": "α : Type u_1\n𝕜 : Type u_2\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nl : Filter α\nf : 𝕜 → α\nc : 𝕜\nh : Tendsto (fun x ↦ f (c + x⁻¹)) atTop l\n⊢ Tendsto f (𝓝[>] c) l",
"ppTerm": "?m.23",
"assigned":... | [
"α : Type u_1\n𝕜 : Type u_2\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nl : Filter α\nf : 𝕜 → α\nc : 𝕜\nh : Tendsto (fun x ↦ f (c + x⁻¹)) atTop l\n⊢ map f (𝓝[>] c) ≤ l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Lemmas | {
"line": 51,
"column": 2
} | {
"line": 51,
"column": 41
} | {
"line": 51,
"column": 42
} | [
{
"pp": "α : Type u_1\n𝕜 : Type u_2\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nl : Filter α\nf : 𝕜 → α\nc : 𝕜\nh : Tendsto (f ∘ (fun x ↦ c + x) ∘ Neg.neg ∘ Inv.inv) atTop l\n⊢ Tendsto f (𝓝[<] c) l",
"ppTerm": "?m.... | [
"α : Type u_1\n𝕜 : Type u_2\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nl : Filter α\nf : 𝕜 → α\nc : 𝕜\nh : Tendsto (f ∘ (fun x ↦ c + x) ∘ Neg.neg ∘ Inv.inv) atTop l\n⊢ map f (𝓝[<] c) ≤ l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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