module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 729,
"column": 8
} | {
"line": 729,
"column": 19
} | {
"line": 729,
"column": 20
} | [
{
"pp": "case refine_2.refine_2\nR : Type u_1\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDedekindDomain R\nK : Type u_2\nS : Type u_3\ninst✝³ : Field K\ninst✝² : CommSemiring S\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\nv : HeightOneSpectrum R\ns : Set (adicCompletion K v)\nx✝ : ∃ γ, {x | (valuation K v).restrict... | [
"case refine_2.refine_2\nR : Type u_1\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDedekindDomain R\nK : Type u_2\nS : Type u_3\ninst✝³ : Field K\ninst✝² : CommSemiring S\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\nv : HeightOneSpectrum R\ns : Set (adicCompletion K v)\nx✝ : ∃ γ, {x | (valuation K v).restrict x < ↑γ} ⊆ s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 803,
"column": 12
} | {
"line": 803,
"column": 23
} | {
"line": 803,
"column": 24
} | [
{
"pp": "R : Type u_1\ninst✝⁴ : CommRing R\ninst✝³ : IsDedekindDomain R\nK : Type u_2\ninst✝² : Field K\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\nv : HeightOneSpectrum R\nn : (WithZero (Multiplicative ℤ))ˣ\nx✝ : ∃ a, ¬(valuation K v) a = 0 ∧ ∃ x, (valuation K v) a * ↑n = (valuation K v) x\na : K\nha0 :... | [
"R : Type u_1\ninst✝⁴ : CommRing R\ninst✝³ : IsDedekindDomain R\nK : Type u_2\ninst✝² : Field K\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\nv : HeightOneSpectrum R\nn : (WithZero (Multiplicative ℤ))ˣ\nx✝ : ∃ a, ¬(valuation K v) a = 0 ∧ ∃ x, (valuation K v) a * ↑n = (valuation K v) x\na : K\nha0 : ¬(valuation... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 803,
"column": 36
} | {
"line": 803,
"column": 47
} | {
"line": 803,
"column": 48
} | [
{
"pp": "R : Type u_1\ninst✝⁴ : CommRing R\ninst✝³ : IsDedekindDomain R\nK : Type u_2\ninst✝² : Field K\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\nv : HeightOneSpectrum R\nn : (WithZero (Multiplicative ℤ))ˣ\nx✝ : ∃ a, ¬(valuation K v) a = 0 ∧ ∃ x, (valuation K v) a * ↑n = (valuation K v) x\na : K\nha0 :... | [
"R : Type u_1\ninst✝⁴ : CommRing R\ninst✝³ : IsDedekindDomain R\nK : Type u_2\ninst✝² : Field K\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\nv : HeightOneSpectrum R\nn : (WithZero (Multiplicative ℤ))ˣ\nx✝ : ∃ a, ¬(valuation K v) a = 0 ∧ ∃ x, (valuation K v) a * ↑n = (valuation K v) x\na : K\nha0 : ¬(valuation... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 901,
"column": 2
} | {
"line": 901,
"column": 13
} | {
"line": 901,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝⁴ : CommRing R\ninst✝³ : IsDedekindDomain R\nK : Type u_2\ninst✝² : Field K\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\nv : HeightOneSpectrum R\nr : R\n⊢ Valued.v ((WithVal.equiv (valuation K v)).symm ((algebraMap R K) r)) ≤ 1",
"ppTerm": "?m.68",
"assigned": true,
... | [
"R : Type u_1\ninst✝⁴ : CommRing R\ninst✝³ : IsDedekindDomain R\nK : Type u_2\ninst✝² : Field K\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\nv : HeightOneSpectrum R\nr : R\n⊢ (valuation K v) ((algebraMap R K) r) ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.PiTopology | {
"line": 152,
"column": 2
} | {
"line": 152,
"column": 30
} | {
"line": 152,
"column": 31
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝³ : TopologicalSpace R\ninst✝² : DecidableEq σ\ninst✝¹ : CommSemiring R\ninst✝ : Nonempty σ\nf : MvPowerSeries σ R\nd : σ →₀ ℕ\ns : σ\nh✝ : True\nn : σ →₀ ℕ\nhn : n ≥ d + Finsupp.single s 1\n⊢ d < d + Finsupp.single s 1",
"ppTerm": "?m.87",
"assigned": true,
... | [
"σ : Type u_1\nR : Type u_2\ninst✝³ : TopologicalSpace R\ninst✝² : DecidableEq σ\ninst✝¹ : CommSemiring R\ninst✝ : Nonempty σ\nf : MvPowerSeries σ R\nd : σ →₀ ℕ\ns : σ\nh✝ : True\nn : σ →₀ ℕ\nhn : n ≥ d + Finsupp.single s 1\n⊢ ∃ i, 0 < (Finsupp.single s 1) i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.PiTopology | {
"line": 208,
"column": 4
} | {
"line": 208,
"column": 39
} | {
"line": 209,
"column": 6
} | [
{
"pp": "case neg\nσ : Type u_1\nR : Type u_2\ninst✝¹ : TopologicalSpace R\ninst✝ : Semiring R\nd : σ →₀ ℕ\nh : ∀ (i : σ), d ≠ Finsupp.single i 1\n⊢ ∀ᶠ (x' : σ) in cofinite, (if d = Finsupp.single x' 1 then 1 else 0) = 0",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"case neg\nσ : Type u_1\nR : Type u_2\ninst✝¹ : TopologicalSpace R\ninst✝ : Semiring R\nd : σ →₀ ℕ\nh : ∀ (i : σ), d ≠ Finsupp.single i 1\n⊢ ∀ᶠ (x' : σ) in cofinite, d = Finsupp.single x' 1 → 1 = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.PiTopology | {
"line": 302,
"column": 2
} | {
"line": 302,
"column": 28
} | {
"line": 302,
"column": 29
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝¹ : TopologicalSpace R\ninst✝ : Semiring R\nf : MvPowerSeries σ R\nh : constantCoeff f = 0\nn m : ℕ\nhm : n + 1 ≤ m\n⊢ ↑m ≤ m • f.order",
"ppTerm": "?m.81",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",... | [
"σ : Type u_1\nR : Type u_2\ninst✝¹ : TopologicalSpace R\ninst✝ : Semiring R\nf : MvPowerSeries σ R\nh : constantCoeff f = 0\nn m : ℕ\nhm : n + 1 ≤ m\n⊢ ↑m ≤ ↑m * f.order"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 70,
"column": 2
} | {
"line": 70,
"column": 13
} | {
"line": 70,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝ : Semiring R\nφ : R⟦X⟧\n⊢ φ.order = ⊤ ↔ φ = 0",
"ppTerm": "?m.9",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_1\ninst✝ : Semiring R\nφ : R⟦X⟧\n⊢ φ.order = ⊤ ↔ φ = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 88,
"column": 4
} | {
"line": 88,
"column": 15
} | {
"line": 88,
"column": 16
} | [
{
"pp": "R : Type u_1\ninst✝ : Semiring R\nφ : R⟦X⟧\nn : ℕ\nh : (coeff n) φ ≠ 0\n⊢ ↑(Nat.find ⋯) ≤ ↑n",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.find_le_iff._simp_1",
"instDecidableNot",
"Semiring.toModule",
"instCharZeroENat",
"Power... | [
"R : Type u_1\ninst✝ : Semiring R\nφ : R⟦X⟧\nn : ℕ\nh : (coeff n) φ ≠ 0\n⊢ ∃ m ≤ n, ¬(coeff m) φ = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 117,
"column": 11
} | {
"line": 117,
"column": 22
} | {
"line": 117,
"column": 23
} | [
{
"pp": "case top\nR : Type u_1\ninst✝ : Semiring R\nφ : R⟦X⟧\nh : ∀ (i : ℕ), ↑i < ⊤ → (coeff i) φ = 0\n⊢ ⊤ ≤ φ.order",
"ppTerm": "?top",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MvPowerSeries.instZero",
"instTopENat",
"instLinearOrderENat",
"PartialOrder.toPreor... | [
"case top\nR : Type u_1\ninst✝ : Semiring R\nφ : R⟦X⟧\nh : ∀ (i : ℕ), ↑i < ⊤ → (coeff i) φ = 0\n⊢ φ = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 117,
"column": 31
} | {
"line": 117,
"column": 42
} | {
"line": 117,
"column": 43
} | [
{
"pp": "R : Type u_1\ninst✝ : Semiring R\nφ : R⟦X⟧\nh : ∀ (i : ℕ), ↑i < ⊤ → (coeff i) φ = 0\n⊢ ∀ (n : ℕ), (coeff n) φ = (coeff n) 0",
"ppTerm": "?m.40",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MvPowerSeries.instZero",
"Semiring.toModule",
"SemilinearMapClass.distribM... | [
"R : Type u_1\ninst✝ : Semiring R\nφ : R⟦X⟧\nh : ∀ (i : ℕ), ↑i < ⊤ → (coeff i) φ = 0\n⊢ φ = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 120,
"column": 4
} | {
"line": 120,
"column": 15
} | {
"line": 120,
"column": 16
} | [
{
"pp": "case coe\nR : Type u_1\ninst✝ : Semiring R\nφ : R⟦X⟧\nn : ℕ\nh : ∀ (i : ℕ), ↑i < ↑n → (coeff i) φ = 0\n⊢ ∀ i < n, (coeff i) φ = 0",
"ppTerm": "?coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case coe\nR : Type u_1\ninst✝ : Semiring R\nφ : R⟦X⟧\nn : ℕ\nh : ∀ (i : ℕ), ↑i < ↑n → (coeff i) φ = 0\n⊢ ∀ i < n, (coeff i) φ = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 118,
"column": 2
} | {
"line": 118,
"column": 12
} | {
"line": 119,
"column": 4
} | [
{
"pp": "case coe\nR : Type u_1\ninst✝ : Semiring R\nφ : R⟦X⟧\nn : ℕ\nh : ∀ (i : ℕ), ↑i < ↑n → (coeff i) φ = 0\n⊢ ↑n ≤ φ.order",
"ppTerm": "?coe",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Semiring.toModule",
"instCharZeroENat",
"instAddMonoidWith... | [] | | coe n => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | null |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 137,
"column": 2
} | {
"line": 137,
"column": 12
} | {
"line": 137,
"column": 13
} | [
{
"pp": "case coe\nR : Type u_1\ninst✝ : Semiring R\nφ : R⟦X⟧\nn : ℕ\n⊢ φ.order = ↑n ↔ (∀ (i : ℕ), ↑i = ↑n → (coeff i) φ ≠ 0) ∧ ∀ (i : ℕ), ↑i < ↑n → (coeff i) φ = 0",
"ppTerm": "?coe",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"Semiring.toModule",
"instCharZeroENat",
... | [] | | coe n => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | null |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 1049,
"column": 2
} | {
"line": 1049,
"column": 65
} | {
"line": 1049,
"column": 66
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDedekindDomain R\nv : HeightOneSpectrum R\nb : ℝ≥0\nhb : 1 < b\nr : R\n⊢ (v.intAdicAbv hb) r ≤ 1",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Int.instAddCommMonoid",
"LinearOrderedCommGroupWithZero.toLine... | [
"R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDedekindDomain R\nv : HeightOneSpectrum R\nb : ℝ≥0\nhb : 1 < b\nr : R\n⊢ v.intValuation r ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 1052,
"column": 2
} | {
"line": 1052,
"column": 65
} | {
"line": 1052,
"column": 66
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDedekindDomain R\nv : HeightOneSpectrum R\nb : ℝ≥0\nhb : 1 < b\nr : R\n⊢ (v.intAdicAbv hb) r < 1 ↔ r ∈ v.asIdeal",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Int.instAddCommMonoid",
"LinearOrderedCommGrou... | [
"R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDedekindDomain R\nv : HeightOneSpectrum R\nb : ℝ≥0\nhb : 1 < b\nr : R\n⊢ v.intValuation r < 1 ↔ r ∈ v.asIdeal"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 1117,
"column": 59
} | {
"line": 1117,
"column": 70
} | {
"line": 1117,
"column": 71
} | [
{
"pp": "R : Type u_4\ninst✝³ : CommRing R\ninst✝² : IsDedekindDomain R\ninst✝¹ : Algebra R ℚ\ninst✝ : IsFractionRing R ℚ\n𝔭 : HeightOneSpectrum R\nx : ℚ\n⊢ Function.Injective (⇑(algebraMap R ℚ) ∘ Nat.cast)",
"ppTerm": "?m.44",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSem... | [
"R : Type u_4\ninst✝³ : CommRing R\ninst✝² : IsDedekindDomain R\ninst✝¹ : Algebra R ℚ\ninst✝ : IsFractionRing R ℚ\n𝔭 : HeightOneSpectrum R\nx : ℚ\n⊢ Function.Injective Nat.cast"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 177,
"column": 4
} | {
"line": 177,
"column": 41
} | {
"line": 177,
"column": 42
} | [
{
"pp": "case inr\nR : Type u_1\ninst✝ : Semiring R\nφ ψ : R⟦X⟧\nh : φ.order ≠ ψ.order\nψ_lt_φ : ψ.order < φ.order\n⊢ (φ + ψ).order ≤ min φ.order ψ.order",
"ppTerm": "?inr",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case inr\nR : Type u_1\ninst✝ : Semiring R\nφ ψ : R⟦X⟧\nh : φ.order ≠ ψ.order\nψ_lt_φ : ψ.order < φ.order\n⊢ (φ + ψ).order ≤ min φ.order ψ.order"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 221,
"column": 4
} | {
"line": 221,
"column": 15
} | {
"line": 221,
"column": 16
} | [
{
"pp": "case mp\nR : Type u_1\ninst✝ : Semiring R\nφ : R⟦X⟧\nh : 1 ≤ φ.order\n⊢ ↑0 < φ.order",
"ppTerm": "?mp",
"assigned": true,
"usedConstants": [
"CharP.cast_eq_zero",
"Eq.mpr",
"instCharZeroENat",
"instAddMonoidWithOneENat",
"ENat.instNatCast",
"congrArg",
... | [
"case mp\nR : Type u_1\ninst✝ : Semiring R\nφ : R⟦X⟧\nh : 1 ≤ φ.order\n⊢ 0 < φ.order"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.LinearTopology | {
"line": 306,
"column": 9
} | {
"line": 306,
"column": 20
} | {
"line": 306,
"column": 21
} | [
{
"pp": "R : Type u_1\ninst✝³ : Ring R\ninst✝² : TopologicalSpace R\ninst✝¹ : IsLinearTopology R R\ninst✝ : IsLinearTopology Rᵐᵒᵖ R\nI : AddSubgroup R\nx✝ : ↑I ∈ 𝓝 0 ∧ (∀ (r x : R), x ∈ I → r • x ∈ I) ∧ ∀ (r' : Rᵐᵒᵖ), ∀ x ∈ I, r' • x ∈ I\nhI : ↑I ∈ 𝓝 0\nhRI : ∀ (r x : R), x ∈ I → r • x ∈ I\nhRI' : ∀ (r' : Rᵐᵒ... | [
"R : Type u_1\ninst✝³ : Ring R\ninst✝² : TopologicalSpace R\ninst✝¹ : IsLinearTopology R R\ninst✝ : IsLinearTopology Rᵐᵒᵖ R\nI : AddSubgroup R\nx✝ : ↑I ∈ 𝓝 0 ∧ (∀ (r x : R), x ∈ I → r • x ∈ I) ∧ ∀ (r' : Rᵐᵒᵖ), ∀ x ∈ I, r' • x ∈ I\nhI : ↑I ∈ 𝓝 0\nhRI : ∀ (r x : R), x ∈ I → r • x ∈ I\nhRI' : ∀ (r' : Rᵐᵒᵖ), ∀ x ∈ I,... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 234,
"column": 2
} | {
"line": 234,
"column": 13
} | {
"line": 234,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝ : Semiring R\nφ : R⟦X⟧\nn : ℕ\nhf : constantCoeff φ = 0\n⊢ ↑n ≤ n • φ.order",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"instAddMonoidWithOneENat",
"HMul.hMul",
... | [
"R : Type u_1\ninst✝ : Semiring R\nφ : R⟦X⟧\nn : ℕ\nhf : constantCoeff φ = 0\n⊢ ↑n ≤ ↑n * φ.order"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 286,
"column": 21
} | {
"line": 286,
"column": 32
} | {
"line": 286,
"column": 33
} | [
{
"pp": "R : Type u_2\ninst✝ : Ring R\nφ : R⟦X⟧\nh : (-φ).order ≠ φ.order\n⊢ φ = 0",
"ppTerm": "?m.21",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_2\ninst✝ : Ring R\nφ : R⟦X⟧\nh : (-φ).order ≠ φ.order\n⊢ φ = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 325,
"column": 2
} | {
"line": 325,
"column": 34
} | {
"line": 325,
"column": 35
} | [
{
"pp": "R : Type u_1\ninst✝ : Semiring R\nφ : R⟦X⟧\n⊢ X ^ φ.order.toNat ∣ φ",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Dvd.dvd",
"Semiring.toModule",
"_private.Mathlib.RingTheory.PowerSeries.Order.0.PowerSeries.X_pow_order_dvd._simp_1_1",
"sem... | [
"R : Type u_1\ninst✝ : Semiring R\nφ : R⟦X⟧\n⊢ ∀ m < φ.order.toNat, (coeff m) φ = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Evaluation | {
"line": 171,
"column": 4
} | {
"line": 171,
"column": 15
} | {
"line": 171,
"column": 16
} | [
{
"pp": "case h\nσ : Type u_1\nR : Type u_2\ninst✝⁶ : CommRing R\ninst✝⁵ : UniformSpace R\nS : Type u_3\ninst✝⁴ : CommRing S\ninst✝³ : UniformSpace S\nφ : R →+* S\na : σ → S\ninst✝² : IsUniformAddGroup R\ninst✝¹ : IsUniformAddGroup S\ninst✝ : IsLinearTopology S S\nhφ : Continuous[inst✝⁵.toTopologicalSpace, inst... | [
"case h\nσ : Type u_1\nR : Type u_2\ninst✝⁶ : CommRing R\ninst✝⁵ : UniformSpace R\nS : Type u_3\ninst✝⁴ : CommRing S\ninst✝³ : UniformSpace S\nφ : R →+* S\na : σ → S\ninst✝² : IsUniformAddGroup R\ninst✝¹ : IsUniformAddGroup S\ninst✝ : IsLinearTopology S S\nhφ : Continuous[inst✝⁵.toTopologicalSpace, inst✝³.toTopolog... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Evaluation | {
"line": 175,
"column": 4
} | {
"line": 175,
"column": 84
} | {
"line": 175,
"column": 85
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝⁶ : CommRing R\ninst✝⁵ : UniformSpace R\nS : Type u_3\ninst✝⁴ : CommRing S\ninst✝³ : UniformSpace S\nφ : R →+* S\na : σ → S\ninst✝² : IsUniformAddGroup R\ninst✝¹ : IsUniformAddGroup S\ninst✝ : IsLinearTopology S S\nhφ : Continuous[inst✝⁵.toTopologicalSpace, inst✝³.toTop... | [
"σ : Type u_1\nR : Type u_2\ninst✝⁶ : CommRing R\ninst✝⁵ : UniformSpace R\nS : Type u_3\ninst✝⁴ : CommRing S\ninst✝³ : UniformSpace S\nφ : R →+* S\na : σ → S\ninst✝² : IsUniformAddGroup R\ninst✝¹ : IsUniformAddGroup S\ninst✝ : IsLinearTopology S S\nhφ : Continuous[inst✝⁵.toTopologicalSpace, inst✝³.toTopologicalSpac... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.PiTopology | {
"line": 153,
"column": 20
} | {
"line": 153,
"column": 31
} | {
"line": 153,
"column": 32
} | [
{
"pp": "R : Type u_1\ninst✝¹ : TopologicalSpace R\ninst✝ : Semiring R\nι : Type u_2\nf : ι → R⟦X⟧\na : ℕ → R\nh : ∀ (d : ℕ), HasSum (fun i ↦ (coeff d) (f i)) (a d)\n⊢ ∀ (d : ℕ), HasSum (fun i ↦ (coeff d) (f i)) ((coeff d) (mk a))",
"ppTerm": "?m.47",
"assigned": true,
"usedConstants": [
"Eq.m... | [
"R : Type u_1\ninst✝¹ : TopologicalSpace R\ninst✝ : Semiring R\nι : Type u_2\nf : ι → R⟦X⟧\na : ℕ → R\nh : ∀ (d : ℕ), HasSum (fun i ↦ (coeff d) (f i)) (a d)\n⊢ ∀ (d : ℕ), HasSum (fun i ↦ (coeff d) (f i)) (a d)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 334,
"column": 2
} | {
"line": 334,
"column": 12
} | {
"line": 335,
"column": 4
} | [
{
"pp": "case inr.coe\nR : Type u_2\ninst✝ : Semiring R\nφ : R⟦X⟧\nhφ : φ ≠ 0\nn : ℕ\nho : φ.order = ↑n\n⊢ ↑n = emultiplicity X φ",
"ppTerm": "?inr.coe",
"assigned": true,
"usedConstants": [
"not_le",
"PowerSeries.coeff_mul_of_lt_order",
"Eq.mpr",
"NonAssocSemiring.toAddCommM... | [] | | coe n => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | null |
Mathlib.RingTheory.MvPowerSeries.Evaluation | {
"line": 183,
"column": 4
} | {
"line": 183,
"column": 15
} | {
"line": 183,
"column": 16
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝⁶ : CommRing R\ninst✝⁵ : UniformSpace R\nS : Type u_3\ninst✝⁴ : CommRing S\ninst✝³ : UniformSpace S\nφ : R →+* S\na : σ → S\ninst✝² : IsUniformAddGroup R\ninst✝¹ : IsUniformAddGroup S\ninst✝ : IsLinearTopology S S\nhφ : Continuous[inst✝⁵.toTopologicalSpace, inst✝³.toTop... | [
"σ : Type u_1\nR : Type u_2\ninst✝⁶ : CommRing R\ninst✝⁵ : UniformSpace R\nS : Type u_3\ninst✝⁴ : CommRing S\ninst✝³ : UniformSpace S\nφ : R →+* S\na : σ → S\ninst✝² : IsUniformAddGroup R\ninst✝¹ : IsUniformAddGroup S\ninst✝ : IsLinearTopology S S\nhφ : Continuous[inst✝⁵.toTopologicalSpace, inst✝³.toTopologicalSpac... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 361,
"column": 2
} | {
"line": 361,
"column": 13
} | {
"line": 361,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝¹ : Semiring R\ninst✝ : Nontrivial R\n⊢ order 1 = 0",
"ppTerm": "?m.8",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_1\ninst✝¹ : Semiring R\ninst✝ : Nontrivial R\n⊢ order 1 = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.PiTopology | {
"line": 168,
"column": 34
} | {
"line": 168,
"column": 45
} | {
"line": 168,
"column": 46
} | [
{
"pp": "R : Type u_1\ninst✝³ : TopologicalSpace R\ninst✝² : Semiring R\nι : Type u_2\nf : ι → R⟦X⟧\ninst✝¹ : LinearOrder ι\ninst✝ : LocallyFiniteOrderBot ι\nhempty : Nonempty ι\nn : ℕ\nh : ∀ (n : ℕ), ∃ a, ∀ (b : ι), a ≤ b → ↑n < (f b).order\ni : ι\nhi : ∀ (b : ι), i ≤ b → ↑n < (f b).order\nk : ι\nhk : i < k\n⊢... | [
"R : Type u_1\ninst✝³ : TopologicalSpace R\ninst✝² : Semiring R\nι : Type u_2\nf : ι → R⟦X⟧\ninst✝¹ : LinearOrder ι\ninst✝ : LocallyFiniteOrderBot ι\nhempty : Nonempty ι\nn : ℕ\nh : ∀ (n : ℕ), ∃ a, ∀ (b : ι), a ≤ b → ↑n < (f b).order\ni : ι\nhi : ∀ (b : ι), i ≤ b → ↑n < (f b).order\nk : ι\nhk : i < k\n⊢ ↑n < (f k).... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.LinearTopology | {
"line": 98,
"column": 22
} | {
"line": 98,
"column": 64
} | {
"line": 99,
"column": 6
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝ : Ring R\nJ K : TwoSidedIdeal R\nd e : σ →₀ ℕ\nhK : K ≠ ⊤\nh : ∀ (a : MvPowerSeries σ R), (∀ e ≤ d, (coeff e) a ∈ J) → ∀ e_1 ≤ e, (coeff e_1) a ∈ K\nx : R\nhx : x ∈ ↑J\nd' : σ →₀ ℕ\n⊢ (if d' = 0 then x else 0) ∈ J",
"ppTerm": "?m.59",
"assigned": true,
"use... | [] | split_ifs <;> [exact hx; exact J.zero_mem] | Batteries.Tactic._aux_Batteries_Tactic_SeqFocus___macroRules_Batteries_Tactic_seq_focus_1 | Batteries.Tactic.seq_focus |
Mathlib.RingTheory.MvPowerSeries.LinearTopology | {
"line": 99,
"column": 6
} | {
"line": 99,
"column": 17
} | {
"line": 99,
"column": 18
} | [
{
"pp": "case mp.left\nσ : Type u_1\nR : Type u_2\ninst✝ : Ring R\nJ K : TwoSidedIdeal R\nd e : σ →₀ ℕ\nhK : K ≠ ⊤\nh : ∀ (a : MvPowerSeries σ R), (∀ e ≤ d, (coeff e) a ∈ J) → ∀ e_1 ≤ e, (coeff e_1) a ∈ K\nx : R\nhx : x ∈ ↑J\nthis : ∀ (d' : σ →₀ ℕ), (coeff d') (C x) ∈ J\n⊢ x ∈ ↑K",
"ppTerm": "?mp.left",
... | [
"case mp.left\nσ : Type u_1\nR : Type u_2\ninst✝ : Ring R\nJ K : TwoSidedIdeal R\nd e : σ →₀ ℕ\nhK : K ≠ ⊤\nh : ∀ (a : MvPowerSeries σ R), (∀ e ≤ d, (coeff e) a ∈ J) → ∀ e_1 ≤ e, (coeff e_1) a ∈ K\nx : R\nhx : x ∈ ↑J\nthis : ∀ (d' : σ →₀ ℕ), (coeff d') (C x) ∈ J\n⊢ x ∈ K"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.LinearTopology | {
"line": 107,
"column": 6
} | {
"line": 107,
"column": 17
} | {
"line": 107,
"column": 18
} | [
{
"pp": "case mp.right\nσ : Type u_1\nR : Type u_2\ninst✝ : Ring R\nJ K : TwoSidedIdeal R\nd e : σ →₀ ℕ\nhK : K ≠ ⊤\nh : ∀ (a : MvPowerSeries σ R), (∀ e ≤ d, (coeff e) a ∈ J) → ∀ e_1 ≤ e, (coeff e_1) a ∈ K\nh' : ¬e ≤ d\nx : R\na✝ : x ∈ ⊤\nthis : ∀ d' ≤ d, (coeff d') ((monomial e) x) ∈ J\n⊢ x ∈ K",
"ppTerm":... | [
"case mp.right\nσ : Type u_1\nR : Type u_2\ninst✝ : Ring R\nJ K : TwoSidedIdeal R\nd e : σ →₀ ℕ\nhK : K ≠ ⊤\nh : ∀ (a : MvPowerSeries σ R), (∀ e ≤ d, (coeff e) a ∈ J) → ∀ e_1 ≤ e, (coeff e_1) a ∈ K\nh' : ¬e ≤ d\nx : R\na✝ : x ∈ ⊤\nthis : ∀ d' ≤ d, (coeff d') ((monomial e) x) ∈ J\n⊢ x ∈ K"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Evaluation | {
"line": 248,
"column": 4
} | {
"line": 248,
"column": 43
} | {
"line": 249,
"column": 6
} | [
{
"pp": "case pos\nσ : Type u_1\nR : Type u_2\ninst✝¹⁰ : CommRing R\ninst✝⁹ : UniformSpace R\nS : Type u_3\ninst✝⁸ : CommRing S\ninst✝⁷ : UniformSpace S\nφ : R →+* S\na : σ → S\ninst✝⁶ : IsTopologicalSemiring R\ninst✝⁵ : IsUniformAddGroup R\ninst✝⁴ : IsUniformAddGroup S\ninst✝³ : CompleteSpace S\ninst✝² : T2Spa... | [
"case pos\nσ : Type u_1\nR : Type u_2\ninst✝¹⁰ : CommRing R\ninst✝⁹ : UniformSpace R\nS : Type u_3\ninst✝⁸ : CommRing S\ninst✝⁷ : UniformSpace S\nφ : R →+* S\na : σ → S\ninst✝⁶ : IsTopologicalSemiring R\ninst✝⁵ : IsUniformAddGroup R\ninst✝⁴ : IsUniformAddGroup S\ninst✝³ : CompleteSpace S\ninst✝² : T2Space S\ninst✝¹... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.LinearTopology | {
"line": 160,
"column": 2
} | {
"line": 160,
"column": 28
} | {
"line": 160,
"column": 29
} | [
{
"pp": "case h\nσ : Type u_1\nR : Type u_3\ninst✝² : CommRing R\ninst✝¹ : TopologicalSpace R\ninst✝ : IsLinearTopology R R\nf : MvPowerSeries σ R\nd : σ →₀ ℕ\nI : Ideal R\nhI : ↑I ∈ 𝓝 0\nN : ℕ\nhN : ∀ (b : ℕ), N ≤ b → constantCoeff ((map (Ideal.Quotient.mk I)) f) ^ b = 0\nn : ℕ\nhn : N + Finsupp.degree d ≤ n\... | [
"case h\nσ : Type u_1\nR : Type u_3\ninst✝² : CommRing R\ninst✝¹ : TopologicalSpace R\ninst✝ : IsLinearTopology R R\nf : MvPowerSeries σ R\nd : σ →₀ ℕ\nI : Ideal R\nhI : ↑I ∈ 𝓝 0\nN : ℕ\nhN : ∀ (b : ℕ), N ≤ b → constantCoeff ((map (Ideal.Quotient.mk I)) f) ^ b = 0\nn : ℕ\nhn : N + Finsupp.degree d ≤ n\n⊢ (coeff d)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Evaluation | {
"line": 205,
"column": 2
} | {
"line": 205,
"column": 46
} | {
"line": 205,
"column": 47
} | [
{
"pp": "R : Type u_1\ninst✝¹⁷ : CommRing R\nS : Type u_2\ninst✝¹⁶ : CommRing S\nφ : R →+* S\na : S\ninst✝¹⁵ : UniformSpace R\ninst✝¹⁴ : UniformSpace S\ninst✝¹³ : IsUniformAddGroup R\ninst✝¹² : IsTopologicalSemiring R\ninst✝¹¹ : IsUniformAddGroup S\ninst✝¹⁰ : T2Space S\ninst✝⁹ : CompleteSpace S\ninst✝⁸ : IsTopo... | [
"R : Type u_1\ninst✝¹⁷ : CommRing R\nS : Type u_2\ninst✝¹⁶ : CommRing S\nφ : R →+* S\na : S\ninst✝¹⁵ : UniformSpace R\ninst✝¹⁴ : UniformSpace S\ninst✝¹³ : IsUniformAddGroup R\ninst✝¹² : IsTopologicalSemiring R\ninst✝¹¹ : IsUniformAddGroup S\ninst✝¹⁰ : T2Space S\ninst✝⁹ : CompleteSpace S\ninst✝⁸ : IsTopologicalRing ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Cardinal.Continuum | {
"line": 72,
"column": 34
} | {
"line": 72,
"column": 45
} | {
"line": 72,
"column": 46
} | [
{
"pp": "⊢ ℶ_ 1 = 𝔠",
"ppTerm": "?m.4",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"⊢ ℶ_ 1 = 𝔠"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Cardinal.Continuum | {
"line": 182,
"column": 8
} | {
"line": 182,
"column": 32
} | {
"line": 182,
"column": 32
} | [
{
"pp": "case a\nx : Cardinal.{u_1}\nh₁ : 2 ≤ x\nh₂ : x ≤ 𝔠\n⊢ x ^ ℵ₀ ≤ 𝔠",
"ppTerm": "?a✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Cardinal.instPowCardinal",
"Cardinal",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"id",
"Cardina... | [
"case a\nx : Cardinal.{u_1}\nh₁ : 2 ≤ x\nh₂ : x ≤ 𝔠\n⊢ x ^ ℵ₀ ≤ 𝔠 ^ ℵ₀"
] | ← continuum_power_aleph0 | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.MvPowerSeries.Substitution | {
"line": 127,
"column": 2
} | {
"line": 127,
"column": 56
} | {
"line": 127,
"column": 57
} | [
{
"pp": "σ : Type u_1\nS : Type u_5\ninst✝ : CommRing S\nthis : UniformSpace S := ⊥\n⊢ HasSubst fun s ↦ X s",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MvPowerSeries.WithPiTopology.instTopologicalSpace",
"CommSemiring.toSemiring",
"MvPowerSeries",
... | [
"σ : Type u_1\nS : Type u_5\ninst✝ : CommRing S\nthis : UniformSpace S := ⊥\n⊢ HasEval fun s ↦ X s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Real.Cardinality | {
"line": 75,
"column": 4
} | {
"line": 75,
"column": 20
} | {
"line": 75,
"column": 21
} | [
{
"pp": "case true\nc : ℝ\nf : ℕ → Bool\nn : ℕ\nh : 0 ≤ c\nh' : f n = true\n⊢ 0 ≤ cantorFunctionAux c f n",
"ppTerm": "?true",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real.instLE",
"Real",
"Real.instZero",
"congrArg",
"id",
"LE.le",
"Cardinal.c... | [
"case true\nc : ℝ\nf : ℕ → Bool\nn : ℕ\nh : 0 ≤ c\nh' : f n = true\n⊢ 0 ≤ c ^ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Substitution | {
"line": 364,
"column": 2
} | {
"line": 364,
"column": 76
} | {
"line": 365,
"column": 2
} | [
{
"pp": "σ : Type u_1\nR : Type u_3\ninst✝² : CommRing R\nτ : Type u_4\nS : Type u_5\ninst✝¹ : CommRing S\ninst✝ : Algebra R S\nf : MvPowerSeries σ R\nn : τ →₀ ℕ\n⊢ (coeff n) (subst 0 f) = (coeff n) ((map (algebraMap R S)) (C (constantCoeff f)))",
"ppTerm": "?m.45",
"assigned": true,
"usedConstants"... | [
"σ : Type u_1\nR : Type u_3\ninst✝² : CommRing R\nτ : Type u_4\nS : Type u_5\ninst✝¹ : CommRing S\ninst✝ : Algebra R S\nf : MvPowerSeries σ R\nn : τ →₀ ℕ\n⊢ (coeff 0) f • (coeff n) (Finsupp.prod 0 fun s e ↦ 0 s ^ e) = (algebraMap R S) ((coeff n) (C (constantCoeff f)))",
"σ : Type u_1\nR : Type u_3\ninst✝² : CommR... | rw [coeff_subst (by simp [hasSubst_def]), coeff_map, finsum_eq_single _ 0] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.RingTheory.MvPowerSeries.Substitution | {
"line": 421,
"column": 2
} | {
"line": 423,
"column": 9
} | {
"line": 423,
"column": 10
} | [
{
"pp": "σ : Type u_1\nR : Type u_3\ninst✝¹⁶ : CommRing R\nτ : Type u_4\nS : Type u_5\ninst✝¹⁵ : CommRing S\ninst✝¹⁴ : Algebra R S\na : σ → MvPowerSeries τ S\nT : Type u_6\ninst✝¹³ : CommRing T\ninst✝¹² : UniformSpace T\ninst✝¹¹ : T2Space T\ninst✝¹⁰ : CompleteSpace T\ninst✝⁹ : IsUniformAddGroup T\ninst✝⁸ : IsTo... | [
"σ : Type u_1\nR : Type u_3\ninst✝¹⁶ : CommRing R\nτ : Type u_4\nS : Type u_5\ninst✝¹⁵ : CommRing S\ninst✝¹⁴ : Algebra R S\na : σ → MvPowerSeries τ S\nT : Type u_6\ninst✝¹³ : CommRing T\ninst✝¹² : UniformSpace T\ninst✝¹¹ : T2Space T\ninst✝¹⁰ : CompleteSpace T\ninst✝⁹ : IsUniformAddGroup T\ninst✝⁸ : IsTopologicalRin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Substitution | {
"line": 438,
"column": 4
} | {
"line": 438,
"column": 15
} | {
"line": 438,
"column": 16
} | [
{
"pp": "case pos\nσ : Type u_1\nR : Type u_3\ninst✝² : CommRing R\nτ : Type u_4\nS : Type u_5\ninst✝¹ : CommRing S\ninst✝ : Algebra R S\na : σ → MvPowerSeries τ S\nha : HasSubst a\nf : MvPowerSeries σ R\nhf : IsNilpotent (constantCoeff f)\nd : σ →₀ ℕ\nhd : d = 0\n⊢ IsNilpotent ((algebraMap R S) ((coeff 0) f))"... | [
"case pos\nσ : Type u_1\nR : Type u_3\ninst✝² : CommRing R\nτ : Type u_4\nS : Type u_5\ninst✝¹ : CommRing S\ninst✝ : Algebra R S\na : σ → MvPowerSeries τ S\nha : HasSubst a\nf : MvPowerSeries σ R\nhf : IsNilpotent (constantCoeff f)\nd : σ →₀ ℕ\nhd : d = 0\n⊢ IsNilpotent ((algebraMap R S) (constantCoeff f))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ArithmeticFunction.LFunction | {
"line": 106,
"column": 14
} | {
"line": 106,
"column": 25
} | {
"line": 106,
"column": 26
} | [
{
"pp": "case pos\nR : Type u_1\ninst✝ : CommSemiring R\nq : ℕ\nf g : PowerSeries R\nhq : 1 < q\nk : ℕ\nhs :\n Finset.map ({ toFun := fun k ↦ q ^ k, inj' := ⋯ }.prodMap { toFun := fun k ↦ q ^ k, inj' := ⋯ })\n (Finset.antidiagonal k) ⊆\n (q ^ k).divisorsAntidiagonal\ni j : ℕ\nhab : i + j = k ∧ q ^ k ≠ ... | [
"case pos\nR : Type u_1\ninst✝ : CommSemiring R\nq : ℕ\nf g : PowerSeries R\nhq : 1 < q\nk : ℕ\nhs :\n Finset.map ({ toFun := fun k ↦ q ^ k, inj' := ⋯ }.prodMap { toFun := fun k ↦ q ^ k, inj' := ⋯ })\n (Finset.antidiagonal k) ⊆\n (q ^ k).divisorsAntidiagonal\ni j : ℕ\nhab : i + j = k ∧ q ^ k ≠ 0\nh :\n ∀ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ArithmeticFunction.LFunction | {
"line": 106,
"column": 14
} | {
"line": 106,
"column": 40
} | {
"line": 107,
"column": 12
} | [
{
"pp": "case pos\nR : Type u_1\ninst✝ : CommSemiring R\nq : ℕ\nf g : PowerSeries R\nhq : 1 < q\nk : ℕ\nhs :\n Finset.map ({ toFun := fun k ↦ q ^ k, inj' := ⋯ }.prodMap { toFun := fun k ↦ q ^ k, inj' := ⋯ })\n (Finset.antidiagonal k) ⊆\n (q ^ k).divisorsAntidiagonal\ni j : ℕ\nhab : i + j = k ∧ q ^ k ≠ ... | [] | simpa using h (i, j) hab.1 | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.RingTheory.MvPowerSeries.Substitution | {
"line": 448,
"column": 2
} | {
"line": 448,
"column": 13
} | {
"line": 448,
"column": 14
} | [
{
"pp": "σ : Type u_1\nR : Type u_3\ninst✝² : CommRing R\nτ : Type u_4\nS : Type u_5\ninst✝¹ : CommRing S\ninst✝ : Algebra R S\na : σ → MvPowerSeries τ S\nha : HasSubst a\nf : MvPowerSeries σ R\nhf : IsNilpotent (constantCoeff f)\n⊢ IsNilpotent (constantCoeff ((substAlgHom ha) f))",
"ppTerm": "?m.66",
"... | [
"σ : Type u_1\nR : Type u_3\ninst✝² : CommRing R\nτ : Type u_4\nS : Type u_5\ninst✝¹ : CommRing S\ninst✝ : Algebra R S\na : σ → MvPowerSeries τ S\nha : HasSubst a\nf : MvPowerSeries σ R\nhf : IsNilpotent (constantCoeff f)\n⊢ IsNilpotent (constantCoeff (subst a f))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Substitution | {
"line": 466,
"column": 2
} | {
"line": 466,
"column": 43
} | {
"line": 466,
"column": 44
} | [
{
"pp": "σ : Type u_1\nR : Type u_3\ninst✝⁶ : CommRing R\nτ : Type u_4\nS : Type u_5\ninst✝⁵ : CommRing S\ninst✝⁴ : Algebra R S\na : σ → MvPowerSeries τ S\nυ : Type u_7\nT : Type u_8\ninst✝³ : CommRing T\ninst✝² : Algebra R T\ninst✝¹ : Algebra S T\ninst✝ : IsScalarTower R S T\nb : τ → MvPowerSeries υ T\nha : Ha... | [
"σ : Type u_1\nR : Type u_3\ninst✝⁶ : CommRing R\nτ : Type u_4\nS : Type u_5\ninst✝⁵ : CommRing S\ninst✝⁴ : Algebra R S\na : σ → MvPowerSeries τ S\nυ : Type u_7\nT : Type u_8\ninst✝³ : CommRing T\ninst✝² : Algebra R T\ninst✝¹ : Algebra S T\ninst✝ : IsScalarTower R S T\nb : τ → MvPowerSeries υ T\nha : HasSubst a\nhb... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Substitution | {
"line": 475,
"column": 2
} | {
"line": 475,
"column": 44
} | {
"line": 475,
"column": 45
} | [
{
"pp": "σ : Type u_1\nR : Type u_3\ninst✝⁶ : CommRing R\nτ : Type u_4\nS : Type u_5\ninst✝⁵ : CommRing S\ninst✝⁴ : Algebra R S\na : σ → MvPowerSeries τ S\nυ : Type u_7\nT : Type u_8\ninst✝³ : CommRing T\ninst✝² : Algebra R T\ninst✝¹ : Algebra S T\ninst✝ : IsScalarTower R S T\nb : τ → MvPowerSeries υ T\nha : Ha... | [
"σ : Type u_1\nR : Type u_3\ninst✝⁶ : CommRing R\nτ : Type u_4\nS : Type u_5\ninst✝⁵ : CommRing S\ninst✝⁴ : Algebra R S\na : σ → MvPowerSeries τ S\nυ : Type u_7\nT : Type u_8\ninst✝³ : CommRing T\ninst✝² : Algebra R T\ninst✝¹ : Algebra S T\ninst✝ : IsScalarTower R S T\nb : τ → MvPowerSeries υ T\nha : HasSubst a\nhb... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Substitution | {
"line": 497,
"column": 2
} | {
"line": 497,
"column": 68
} | {
"line": 498,
"column": 2
} | [
{
"pp": "case neg\nσ : Type u_1\nR : Type u_3\ninst✝² : CommRing R\nτ : Type u_4\nS : Type u_5\ninst✝¹ : CommRing S\ninst✝ : Algebra R S\na : σ → MvPowerSeries τ S\nw : τ → ℕ\nha : HasSubst a\nf : MvPowerSeries σ R\nd : τ →₀ ℕ\nhd : ↑((Finsupp.weight w) d) < ⨅ d, ⨅ (_ : (coeff d) f ≠ 0), (Finsupp.weight (weight... | [
"case neg\nσ : Type u_1\nR : Type u_3\ninst✝² : CommRing R\nτ : Type u_4\nS : Type u_5\ninst✝¹ : CommRing S\ninst✝ : Algebra R S\na : σ → MvPowerSeries τ S\nw : τ → ℕ\nha : HasSubst a\nf : MvPowerSeries σ R\nd : τ →₀ ℕ\nhd : ↑((Finsupp.weight w) d) < ⨅ d, ⨅ (_ : (coeff d) f ≠ 0), (Finsupp.weight (weightedOrder w ∘ ... | simp only [Finsupp.weight_apply, Finsupp.sum, Function.comp_apply] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.RingTheory.MvPowerSeries.Substitution | {
"line": 514,
"column": 4
} | {
"line": 514,
"column": 43
} | {
"line": 515,
"column": 2
} | [
{
"pp": "σ : Type u_1\nR : Type u_3\ninst✝² : CommRing R\nτ : Type u_4\nS : Type u_5\ninst✝¹ : CommRing S\ninst✝ : Algebra R S\na : σ → MvPowerSeries τ S\nha : HasSubst a\nf : MvPowerSeries σ R\ni : σ →₀ ℕ\nhi : ¬(coeff i) f = 0\n⊢ (⨅ i, (a i).order) * f.order ≤ (⨅ i, (order ∘ a) i) * ↑(Finsupp.degree i)",
... | [] | refine mul_le_mul_right (order_le hi) _ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.RingTheory.MvPowerSeries.Substitution | {
"line": 514,
"column": 4
} | {
"line": 514,
"column": 43
} | {
"line": 515,
"column": 2
} | [
{
"pp": "σ : Type u_1\nR : Type u_3\ninst✝² : CommRing R\nτ : Type u_4\nS : Type u_5\ninst✝¹ : CommRing S\ninst✝ : Algebra R S\na : σ → MvPowerSeries τ S\nha : HasSubst a\nf : MvPowerSeries σ R\ni : σ →₀ ℕ\nhi : ¬(coeff i) f = 0\n⊢ (⨅ i, (a i).order) * f.order ≤ (⨅ i, (order ∘ a) i) * ↑(Finsupp.degree i)",
... | [] | refine mul_le_mul_right (order_le hi) _ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.MvPowerSeries.Substitution | {
"line": 514,
"column": 4
} | {
"line": 514,
"column": 43
} | {
"line": 515,
"column": 2
} | [
{
"pp": "σ : Type u_1\nR : Type u_3\ninst✝² : CommRing R\nτ : Type u_4\nS : Type u_5\ninst✝¹ : CommRing S\ninst✝ : Algebra R S\na : σ → MvPowerSeries τ S\nha : HasSubst a\nf : MvPowerSeries σ R\ni : σ →₀ ℕ\nhi : ¬(coeff i) f = 0\n⊢ (⨅ i, (a i).order) * f.order ≤ (⨅ i, (order ∘ a) i) * ↑(Finsupp.degree i)",
... | [] | refine mul_le_mul_right (order_le hi) _ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Complex.Cardinality | {
"line": 34,
"column": 2
} | {
"line": 34,
"column": 14
} | {
"line": 35,
"column": 0
} | [
{
"pp": "⊢ ℵ₀ < 𝔠",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Cardinal.aleph0",
"Cardinal.cantor"
],
"usedFVars": [],
"usedGoals": []
}
] | [] | apply cantor | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.LinearAlgebra.Complex.FiniteDimensional | {
"line": 68,
"column": 2
} | {
"line": 68,
"column": 23
} | {
"line": 68,
"column": 24
} | [
{
"pp": "⊢ lift.{0, 0} #ℚ < lift.{0, 0} #ℝ",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"Preorder.toLT",
"NoMinOrder.infinite",
"Cardinal",
"congrArg",
"Rat.nontrivial",
"Rat",
"PartialOrder.toPreorder",
"Card... | [
"⊢ ℵ₀ < 𝔠"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Complex.FiniteDimensional | {
"line": 74,
"column": 2
} | {
"line": 74,
"column": 13
} | {
"line": 74,
"column": 14
} | [
{
"pp": "⊢ Cardinal.lift.{0, 0} #ℚ < Cardinal.lift.{0, 0} #ℂ",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"NoMinOrder.infinite",
"Cardinal",
"congrArg",
"Rat.nontrivial",
"Rat",
"PartialOrder.toPreorder",
"... | [
"⊢ ℵ₀ < 𝔠"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.LSeries.Basic | {
"line": 122,
"column": 2
} | {
"line": 122,
"column": 26
} | {
"line": 123,
"column": 2
} | [
{
"pp": "f g : ℕ → ℂ\ns : ℂ\nn : ℕ\nh : ‖f n‖ ≤ ‖g n‖\n⊢ ‖term f s n‖ ≤ ‖term g s n‖",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"Real.instPow",
"Real.instLE",
"Real",
"instHDiv",
"Real.instZero",
"congrArg",
... | [
"f g : ℕ → ℂ\ns : ℂ\nn : ℕ\nh : ‖f n‖ ≤ ‖g n‖\n⊢ (if n = 0 then 0 else ‖f n‖ / ↑n ^ s.re) ≤ if n = 0 then 0 else ‖g n‖ / ↑n ^ s.re"
] | simp only [norm_term_eq] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.NumberTheory.LSeries.Basic | {
"line": 129,
"column": 2
} | {
"line": 129,
"column": 26
} | {
"line": 130,
"column": 2
} | [
{
"pp": "f : ℕ → ℂ\ns s' : ℂ\nh : s.re ≤ s'.re\nn : ℕ\n⊢ ‖term f s' n‖ ≤ ‖term f s n‖",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"Real.instPow",
"Real.instLE",
"Real",
"instHDiv",
"Real.instZero",
"congrArg",
... | [
"f : ℕ → ℂ\ns s' : ℂ\nh : s.re ≤ s'.re\nn : ℕ\n⊢ (if n = 0 then 0 else ‖f n‖ / ↑n ^ s'.re) ≤ if n = 0 then 0 else ‖f n‖ / ↑n ^ s.re"
] | simp only [norm_term_eq] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.RingTheory.PowerSeries.Substitution | {
"line": 62,
"column": 61
} | {
"line": 63,
"column": 21
} | {
"line": 65,
"column": 0
} | [
{
"pp": "τ : Type u_3\nS : Type u_4\ninst✝ : CommRing S\na : MvPowerSeries τ S\nha : MvPowerSeries.constantCoeff a = 0\n⊢ HasSubst a",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"congrArg",
"CommSemiring.toSemiring",
"IsNilpotent.zero._simp_1",
"MvPowerSeries",
... | [] | by
simp [HasSubst, ha] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.LSeries.Basic | {
"line": 345,
"column": 55
} | {
"line": 345,
"column": 66
} | {
"line": 345,
"column": 67
} | [
{
"pp": "f : ℕ → ℂ\nx : ℝ\ns : ℂ\nhs : x < s.re\nC : ℝ\nhC : ∀ (n : ℕ), n ≠ 0 → ‖f n‖ ≤ C * ↑n ^ (x - 1)\n⊢ ‖f 1‖ ≤ C",
"ppTerm": "?m.52",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"f : ℕ → ℂ\nx : ℝ\ns : ℂ\nhs : x < s.re\nC : ℝ\nhC : ∀ (n : ℕ), n ≠ 0 → ‖f n‖ ≤ C * ↑n ^ (x - 1)\n⊢ ‖f 1‖ ≤ C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Substitution | {
"line": 602,
"column": 74
} | {
"line": 607,
"column": 6
} | {
"line": 609,
"column": 0
} | [
{
"pp": "σ : Type u_1\nR : Type u_3\ninst✝⁴ : CommRing R\nτ : Type u_4\nS : Type u_5\ninst✝³ : CommRing S\ninst✝² : Algebra R S\na : σ → MvPowerSeries τ S\nf : MvPowerSeries σ R\ninst✝¹ : Finite τ\nx : σ → ℕ\nk : ℕ\ninst✝ : Finite σ\nh : ∀ (i : σ), constantCoeff (a i) = 0\nhx : ∀ (i : σ), k ≤ x i\n⊢ (truncTotal... | [] | by
rw [truncTotal_subst_eq_truncTotal_sum_subst_truncTotal_of_le
(hasSubst_of_constantCoeff_zero h) h hx,
truncTotal_eq_sum, ← substAlgHom_apply
(hasSubst_of_constantCoeff_zero h).truncTotal, map_sum]
simp | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.LSeries.Basic | {
"line": 358,
"column": 4
} | {
"line": 358,
"column": 43
} | {
"line": 358,
"column": 44
} | [
{
"pp": "case inl\nf : ℕ → ℂ\nx : ℝ\ns : ℂ\nhs : x < s.re\nC : ℝ\nhC : ∀ (n : ℕ), n ≠ 0 → ‖f n‖ ≤ C * ↑n ^ (x - 1)\nhC₀ : 0 ≤ C\nhsum : Summable fun n ↦ ‖↑C / ↑n ^ (s + (1 - ↑x))‖\n⊢ ‖term f s 0‖ ≤ ‖↑C / ↑0 ^ (s + (1 - ↑x))‖",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Norm.norm",... | [
"case inl\nf : ℕ → ℂ\nx : ℝ\ns : ℂ\nhs : x < s.re\nC : ℝ\nhC : ∀ (n : ℕ), n ≠ 0 → ‖f n‖ ≤ C * ↑n ^ (x - 1)\nhC₀ : 0 ≤ C\nhsum : Summable fun n ↦ ‖↑C / ↑n ^ (s + (1 - ↑x))‖\n⊢ 0 ≤ ‖↑C / ↑0 ^ (s + (1 - ↑x))‖"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.LSeries.Basic | {
"line": 363,
"column": 2
} | {
"line": 363,
"column": 13
} | {
"line": 363,
"column": 14
} | [
{
"pp": "case inr\nf : ℕ → ℂ\nx : ℝ\ns : ℂ\nhs : x < s.re\nC : ℝ\nhC : ∀ (n : ℕ), n ≠ 0 → ‖f n‖ ≤ C * ↑n ^ (x - 1)\nhC₀ : 0 ≤ C\nhsum : Summable fun n ↦ ‖↑C / ↑n ^ (s + (1 - ↑x))‖\nn : ℕ\nhn : n > 0\nhn' : 0 < ↑n ^ s.re\n⊢ ‖f n‖ ≤ C * ↑n ^ (-(s + (1 - ↑x)).re + s.re)",
"ppTerm": "?inr",
"assigned": true... | [
"case inr\nf : ℕ → ℂ\nx : ℝ\ns : ℂ\nhs : x < s.re\nC : ℝ\nhC : ∀ (n : ℕ), n ≠ 0 → ‖f n‖ ≤ C * ↑n ^ (x - 1)\nhC₀ : 0 ≤ C\nhsum : Summable fun n ↦ ‖↑C / ↑n ^ (s + (1 - ↑x))‖\nn : ℕ\nhn : n > 0\nhn' : 0 < ↑n ^ s.re\n⊢ ‖f n‖ ≤ C * ↑n ^ (x - 1)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Substitution | {
"line": 389,
"column": 2
} | {
"line": 389,
"column": 61
} | {
"line": 389,
"column": 62
} | [
{
"pp": "R : Type u_2\ninst✝⁶ : CommRing R\nS : Type u_4\ninst✝⁵ : CommRing S\nυ : Type u_5\nT : Type u_6\ninst✝⁴ : CommRing T\ninst✝³ : Algebra R S\ninst✝² : Algebra R T\ninst✝¹ : Algebra S T\na : S⟦X⟧\nb : MvPowerSeries υ T\ninst✝ : IsScalarTower R S T\nha : HasSubst a\nhb : HasSubst b\n⊢ subst b ∘ subst a = ... | [
"R : Type u_2\ninst✝⁶ : CommRing R\nS : Type u_4\ninst✝⁵ : CommRing S\nυ : Type u_5\nT : Type u_6\ninst✝⁴ : CommRing T\ninst✝³ : Algebra R S\ninst✝² : Algebra R T\ninst✝¹ : Algebra S T\na : S⟦X⟧\nb : MvPowerSeries υ T\ninst✝ : IsScalarTower R S T\nha : HasSubst a\nhb : HasSubst b\n⊢ ∀ (x : R⟦X⟧), subst b (subst a x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.EGauge | {
"line": 149,
"column": 2
} | {
"line": 149,
"column": 13
} | {
"line": 149,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NormedDivisionRing 𝕜\nE : Type u_2\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\ns : Set E\nhs : s.Nonempty\nthis : 0 ∈ 0 • s\n⊢ egauge 𝕜 s 0 = 0",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"𝕜 : Type u_1\ninst✝² : NormedDivisionRing 𝕜\nE : Type u_2\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\ns : Set E\nhs : s.Nonempty\nthis : 0 ∈ 0 • s\n⊢ egauge 𝕜 s 0 = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.EGauge | {
"line": 155,
"column": 2
} | {
"line": 155,
"column": 13
} | {
"line": 155,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NormedDivisionRing 𝕜\nE : Type u_2\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\ns : Set E\nx : E\nh : x ∈ 1 • s\n⊢ egauge 𝕜 s x ≤ 1",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"𝕜 : Type u_1\ninst✝² : NormedDivisionRing 𝕜\nE : Type u_2\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\ns : Set E\nx : E\nh : x ∈ 1 • s\n⊢ egauge 𝕜 s x ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Substitution | {
"line": 690,
"column": 4
} | {
"line": 690,
"column": 15
} | {
"line": 690,
"column": 16
} | [
{
"pp": "σ : Type u_1\nR : Type u_9\ninst✝ : CommSemiring R\nx : MvPowerSeries σ R\nn : σ →₀ ℕ\ns : σ\nh : ¬n s = 0\n⊢ s ∈ n.support",
"ppTerm": "?m.298",
"assigned": true,
"usedConstants": [
"Finsupp.instFunLike",
"Eq.mpr",
"Nat.instMulZeroClass",
"Finset",
"Finsupp.me... | [
"σ : Type u_1\nR : Type u_9\ninst✝ : CommSemiring R\nx : MvPowerSeries σ R\nn : σ →₀ ℕ\ns : σ\nh : ¬n s = 0\n⊢ ¬n s = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.EGauge | {
"line": 171,
"column": 65
} | {
"line": 171,
"column": 76
} | {
"line": 171,
"column": 77
} | [
{
"pp": "𝕜 : Type u_1\ninst✝³ : NormedDivisionRing 𝕜\nE : Type u_2\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\ns : Set E\ninst✝ : (𝓝[≠] 0).NeBot\nr : ℝ≥0∞\nhs₀ : 0 ∈ s\nh : ∀ (c : 𝕜), c ≠ 0 → 0 ∈ c • s → r ≤ ‖c‖ₑ\nhc : 0 ∈ 0 • s\nb : ℝ≥0∞\nhb : ‖0‖ₑ < b\n⊢ 0 < ?m.148",
"ppTerm": "?m.149",
"assig... | [
"𝕜 : Type u_1\ninst✝³ : NormedDivisionRing 𝕜\nE : Type u_2\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\ns : Set E\ninst✝ : (𝓝[≠] 0).NeBot\nr : ℝ≥0∞\nhs₀ : 0 ∈ s\nh : ∀ (c : 𝕜), c ≠ 0 → 0 ∈ c • s → r ≤ ‖c‖ₑ\nhc : 0 ∈ 0 • s\nb : ℝ≥0∞\nhb : ‖0‖ₑ < b\n⊢ 0 < ?m.148"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.EGauge | {
"line": 173,
"column": 17
} | {
"line": 173,
"column": 28
} | {
"line": 173,
"column": 29
} | [
{
"pp": "𝕜 : Type u_1\ninst✝³ : NormedDivisionRing 𝕜\nE : Type u_2\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\ns : Set E\ninst✝ : (𝓝[≠] 0).NeBot\nr : ℝ≥0∞\nhs₀ : 0 ∈ s\nh : ∀ (c : 𝕜), c ≠ 0 → 0 ∈ c • s → r ≤ ‖c‖ₑ\nhc : 0 ∈ 0 • s\nb : ℝ≥0∞\nhb : ‖0‖ₑ < b\nc : 𝕜\nhc₀ : c ∈ {0}ᶜ\nhcb : c ∈ eball 0 b\n⊢ c ... | [
"𝕜 : Type u_1\ninst✝³ : NormedDivisionRing 𝕜\nE : Type u_2\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\ns : Set E\ninst✝ : (𝓝[≠] 0).NeBot\nr : ℝ≥0∞\nhs₀ : 0 ∈ s\nh : ∀ (c : 𝕜), c ≠ 0 → 0 ∈ c • s → r ≤ ‖c‖ₑ\nhc : 0 ∈ 0 • s\nb : ℝ≥0∞\nhb : ‖0‖ₑ < b\nc : 𝕜\nhc₀ : c ∈ {0}ᶜ\nhcb : c ∈ eball 0 b\n⊢ ¬c = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.EGauge | {
"line": 173,
"column": 66
} | {
"line": 173,
"column": 77
} | {
"line": 173,
"column": 78
} | [
{
"pp": "𝕜 : Type u_1\ninst✝³ : NormedDivisionRing 𝕜\nE : Type u_2\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\ns : Set E\ninst✝ : (𝓝[≠] 0).NeBot\nr : ℝ≥0∞\nhs₀ : 0 ∈ s\nh : ∀ (c : 𝕜), c ≠ 0 → 0 ∈ c • s → r ≤ ‖c‖ₑ\nhc : 0 ∈ 0 • s\nb : ℝ≥0∞\nhb : ‖0‖ₑ < b\nc : 𝕜\nhc₀ : c ∈ {0}ᶜ\nhcb : c ∈ eball 0 b\n⊢ ‖c... | [
"𝕜 : Type u_1\ninst✝³ : NormedDivisionRing 𝕜\nE : Type u_2\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\ns : Set E\ninst✝ : (𝓝[≠] 0).NeBot\nr : ℝ≥0∞\nhs₀ : 0 ∈ s\nh : ∀ (c : 𝕜), c ≠ 0 → 0 ∈ c • s → r ≤ ‖c‖ₑ\nhc : 0 ∈ 0 • s\nb : ℝ≥0∞\nhb : ‖0‖ₑ < b\nc : 𝕜\nhc₀ : c ∈ {0}ᶜ\nhcb : c ∈ eball 0 b\n⊢ ‖c‖ₑ < b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.EGauge | {
"line": 206,
"column": 2
} | {
"line": 206,
"column": 52
} | {
"line": 207,
"column": 2
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NormedDivisionRing 𝕜\nE : Type u_2\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\nc : 𝕜\ns : Set E\nh : c = 0 → s.Nonempty\nx : E\n⊢ egauge 𝕜 s (c • x) = ‖c‖ₑ * egauge 𝕜 s x",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"instHSMul",
"HMul.... | [
"𝕜 : Type u_1\ninst✝² : NormedDivisionRing 𝕜\nE : Type u_2\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\nc : 𝕜\ns : Set E\nh : c = 0 → s.Nonempty\nx : E\n⊢ egauge 𝕜 s (c • x) ≤ ‖c‖ₑ * egauge 𝕜 s x"
] | refine le_antisymm ?_ (le_egauge_smul_right c s x) | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.RingTheory.MvPowerSeries.Substitution | {
"line": 745,
"column": 4
} | {
"line": 745,
"column": 15
} | {
"line": 745,
"column": 16
} | [
{
"pp": "σ : Type u_1\nR : Type u_3\ninst✝ : CommRing R\na : σ → R\nf : MvPowerSeries σ R\nn : σ →₀ ℕ\nhn : n ∉ ⋯.toFinset\n⊢ (coeff n) f * (coeff n) (n.prod fun s e ↦ (a s • X s) ^ e) = 0",
"ppTerm": "?m.150",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"σ : Type u_1\nR : Type u_3\ninst✝ : CommRing R\na : σ → R\nf : MvPowerSeries σ R\nn : σ →₀ ℕ\nhn : n ∉ ⋯.toFinset\n⊢ (coeff n) f * (coeff n) (n.prod fun s e ↦ (a s • X s) ^ e) = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.EGauge | {
"line": 264,
"column": 64
} | {
"line": 264,
"column": 90
} | {
"line": 264,
"column": 91
} | [
{
"pp": "𝕜 : Type u_1\nι : Type u_2\nE : ι → Type u_3\ninst✝² : NormedDivisionRing 𝕜\ninst✝¹ : (i : ι) → AddCommGroup (E i)\ninst✝ : (i : ι) → Module 𝕜 (E i)\nU : (i : ι) → Set (E i)\nx : (i : ι) → E i\nr : ℝ≥0∞\nc : ι → 𝕜\nhr₀ : 0 < r\nhI : ∅.Finite\nhU : ∀ i ∈ ∅, Balanced 𝕜 (U i)\nhI₀ : ∅ = univ ∨ (∃ i ∈... | [
"𝕜 : Type u_1\nι : Type u_2\nE : ι → Type u_3\ninst✝² : NormedDivisionRing 𝕜\ninst✝¹ : (i : ι) → AddCommGroup (E i)\ninst✝ : (i : ι) → Module 𝕜 (E i)\nU : (i : ι) → Set (E i)\nx : (i : ι) → E i\nr : ℝ≥0∞\nc : ι → 𝕜\nhr₀ : 0 < r\nhI : ∅.Finite\nhU : ∀ i ∈ ∅, Balanced 𝕜 (U i)\nhI₀ : ∅ = univ ∨ (∃ i ∈ ∅, x i ≠ 0)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.EGauge | {
"line": 273,
"column": 54
} | {
"line": 273,
"column": 69
} | {
"line": 273,
"column": 70
} | [
{
"pp": "𝕜 : Type u_1\nι : Type u_2\nE : ι → Type u_3\ninst✝² : NormedDivisionRing 𝕜\ninst✝¹ : (i : ι) → AddCommGroup (E i)\ninst✝ : (i : ι) → Module 𝕜 (E i)\nI : Set ι\nhI : I.Finite\nU : (i : ι) → Set (E i)\nhU : ∀ i ∈ I, Balanced 𝕜 (U i)\nx : (i : ι) → E i\nhI₀ : I = univ ∨ (∃ i ∈ I, x i ≠ 0) ∨ (𝓝[≠] 0)... | [
"𝕜 : Type u_1\nι : Type u_2\nE : ι → Type u_3\ninst✝² : NormedDivisionRing 𝕜\ninst✝¹ : (i : ι) → AddCommGroup (E i)\ninst✝ : (i : ι) → Module 𝕜 (E i)\nI : Set ι\nhI : I.Finite\nU : (i : ι) → Set (E i)\nhU : ∀ i ∈ I, Balanced 𝕜 (U i)\nx : (i : ι) → E i\nhI₀ : I = univ ∨ (∃ i ∈ I, x i ≠ 0) ∨ (𝓝[≠] 0).NeBot\nr : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.EGauge | {
"line": 325,
"column": 2
} | {
"line": 325,
"column": 13
} | {
"line": 325,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NormedField 𝕜\nE : Type u_2\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : E\n⊢ ‖x‖ₑ ≤ egauge 𝕜 (closedBall 0 1) x",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"𝕜 : Type u_1\ninst✝² : NormedField 𝕜\nE : Type u_2\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : E\n⊢ ‖x‖ₑ ≤ egauge 𝕜 (closedBall 0 1) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.EGauge | {
"line": 331,
"column": 2
} | {
"line": 331,
"column": 13
} | {
"line": 331,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NormedField 𝕜\nE : Type u_2\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : E\n⊢ ‖x‖ₑ ≤ egauge 𝕜 (ball 0 1) x",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"𝕜 : Type u_1\ninst✝² : NormedField 𝕜\nE : Type u_2\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : E\n⊢ ‖x‖ₑ ≤ egauge 𝕜 (ball 0 1) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.EGauge | {
"line": 342,
"column": 6
} | {
"line": 342,
"column": 17
} | {
"line": 342,
"column": 18
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NormedField 𝕜\nE : Type u_2\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nc : 𝕜\nx : E\nhc : 1 < ‖c‖\nthis : NontriviallyNormedField 𝕜 := { toNormedField := inst✝², non_trivial := ⋯ }\nh₀ : 0 ≠ 0 ∨ ‖x‖ ≠ 0\n⊢ ‖c‖ₑ ≠ 0",
"ppTerm": "?m.80",
"assigned": t... | [
"𝕜 : Type u_1\ninst✝² : NormedField 𝕜\nE : Type u_2\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nc : 𝕜\nx : E\nhc : 1 < ‖c‖\nthis : NontriviallyNormedField 𝕜 := { toNormedField := inst✝², non_trivial := ⋯ }\nh₀ : 0 ≠ 0 ∨ ‖x‖ ≠ 0\n⊢ ¬c = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.EGauge | {
"line": 343,
"column": 6
} | {
"line": 343,
"column": 47
} | {
"line": 343,
"column": 48
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NormedField 𝕜\nE : Type u_2\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nc : 𝕜\nx : E\nhc : 1 < ‖c‖\nthis : NontriviallyNormedField 𝕜 := { toNormedField := inst✝², non_trivial := ⋯ }\nh₀ : 0 ≠ 0 ∨ ‖x‖ ≠ 0\n⊢ ‖x‖ₑ ≠ 0",
"ppTerm": "?m.81",
"assigned": t... | [
"𝕜 : Type u_1\ninst✝² : NormedField 𝕜\nE : Type u_2\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nc : 𝕜\nx : E\nhc : 1 < ‖c‖\nthis : NontriviallyNormedField 𝕜 := { toNormedField := inst✝², non_trivial := ⋯ }\nh₀ : 0 ≠ 0 ∨ ‖x‖ ≠ 0\n⊢ ¬‖x‖ = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.EGauge | {
"line": 345,
"column": 32
} | {
"line": 345,
"column": 85
} | {
"line": 345,
"column": 86
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NormedField 𝕜\nE : Type u_2\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nc : 𝕜\nx : E\nr : ℝ≥0\nhc : 1 < ‖c‖\nh₀ : r ≠ 0 ∨ ‖x‖ ≠ 0\nthis : NontriviallyNormedField 𝕜 := { toNormedField := inst✝², non_trivial := ⋯ }\nhr : 0 < r\nhx : ‖x‖ = 0\n⊢ ‖x‖ₑ = 0",
"... | [
"𝕜 : Type u_1\ninst✝² : NormedField 𝕜\nE : Type u_2\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nc : 𝕜\nx : E\nr : ℝ≥0\nhc : 1 < ‖c‖\nh₀ : r ≠ 0 ∨ ‖x‖ ≠ 0\nthis : NontriviallyNormedField 𝕜 := { toNormedField := inst✝², non_trivial := ⋯ }\nhr : 0 < r\nhx : ‖x‖ = 0\n⊢ ‖x‖₊ = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.EGauge | {
"line": 358,
"column": 2
} | {
"line": 358,
"column": 13
} | {
"line": 358,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NormedField 𝕜\nE : Type u_2\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nc : 𝕜\nhc : 1 < ‖c‖\nx : E\n⊢ egauge 𝕜 (ball 0 1) x ≤ ‖c‖ₑ * ‖x‖ₑ",
"ppTerm": "?m.28",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"𝕜 : Type u_1\ninst✝² : NormedField 𝕜\nE : Type u_2\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nc : 𝕜\nhc : 1 < ‖c‖\nx : E\n⊢ egauge 𝕜 (ball 0 1) x ≤ ‖c‖ₑ * ‖x‖ₑ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.TangentCone.DimOne | {
"line": 33,
"column": 4
} | {
"line": 33,
"column": 45
} | {
"line": 33,
"column": 46
} | [
{
"pp": "case hds\n𝕜 : Type u_1\ninst✝ : NormedDivisionRing 𝕜\ns : Set 𝕜\nx : 𝕜\nhx : AccPt x (𝓟 s)\ny : 𝕜\n⊢ ∃ᶠ (n : 𝕜) in 𝓝[≠] x, x + (n - x) ∈ s",
"ppTerm": "?hds",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"AddGroupWithOne.toAddGroup",
"congrArg",
"AddCommGro... | [
"case hds\n𝕜 : Type u_1\ninst✝ : NormedDivisionRing 𝕜\ns : Set 𝕜\nx : 𝕜\nhx : AccPt x (𝓟 s)\ny : 𝕜\n⊢ ∃ᶠ (n : 𝕜) in 𝓝[≠] x, n ∈ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.TangentCone.DimOne | {
"line": 36,
"column": 27
} | {
"line": 36,
"column": 52
} | {
"line": 36,
"column": 53
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NormedDivisionRing 𝕜\ns : Set 𝕜\nx : 𝕜\nhx : AccPt x (𝓟 s)\ny z : 𝕜\nhz : z ∈ {x}ᶜ\n⊢ z - x ≠ 0",
"ppTerm": "?m.121",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"AddGroupWithOne.toAddGroup",
"congrArg",
"HSub.hSub",
"NormedDivisi... | [
"𝕜 : Type u_1\ninst✝ : NormedDivisionRing 𝕜\ns : Set 𝕜\nx : 𝕜\nhx : AccPt x (𝓟 s)\ny z : 𝕜\nhz : z ∈ {x}ᶜ\n⊢ ¬z = x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.TangentCone.Basic | {
"line": 86,
"column": 2
} | {
"line": 86,
"column": 13
} | {
"line": 86,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝³ : AddCommGroup E\ninst✝² : SMul 𝕜 E\ninst✝¹ : TopologicalSpace E\ns : Set E\nx : E\ninst✝ : ContinuousAdd E\ny : E\nhy : y ∈ tangentConeAt 𝕜 s x\nι : Type (max u_1 u_2)\nl : Filter ι\nhl : l.NeBot\nd : ι → E\nhd : Tendsto d l (𝓝 0)\nhds : ∀ᶠ (n : ι) in l, x + d n ... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝³ : AddCommGroup E\ninst✝² : SMul 𝕜 E\ninst✝¹ : TopologicalSpace E\ns : Set E\nx : E\ninst✝ : ContinuousAdd E\ny : E\nhy : y ∈ tangentConeAt 𝕜 s x\nι : Type (max u_1 u_2)\nl : Filter ι\nhl : l.NeBot\nd : ι → E\nhd : Tendsto d l (𝓝 0)\nhds : ∀ᶠ (n : ι) in l, x + d n ∈ s\n⊢ Tends... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Substitution | {
"line": 543,
"column": 48
} | {
"line": 543,
"column": 59
} | {
"line": 543,
"column": 60
} | [
{
"pp": "R : Type u_2\ninst✝¹ : CommRing R\nP : R⟦X⟧\nhP : constantCoeff P = 0\ninst✝ : Invertible ((coeff 1) P)\n⊢ Invertible ((coeff 1) P.substInv)",
"ppTerm": "?m.50",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Semiring.toModule",
"congrArg",
"CommSemiring.toSemiring"... | [
"R : Type u_2\ninst✝¹ : CommRing R\nP : R⟦X⟧\nhP : constantCoeff P = 0\ninst✝ : Invertible ((coeff 1) P)\n⊢ Invertible ⅟((coeff 1) P)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.TangentCone.Basic | {
"line": 169,
"column": 4
} | {
"line": 169,
"column": 15
} | {
"line": 169,
"column": 16
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Semiring 𝕜\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : ContinuousAdd E\ns : Set E\nx : E\ninst✝ : T2Space E\nhx : ¬AccPt x (𝓟 s)\ny : E\nhy : y ∈ tangentConeAt 𝕜 s x\nι : Type (max u_1 u_2)\nl : Filter ι\nhl : l.NeBot\nc... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Semiring 𝕜\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : ContinuousAdd E\ns : Set E\nx : E\ninst✝ : T2Space E\nhx : ¬AccPt x (𝓟 s)\ny : E\nhy : y ∈ tangentConeAt 𝕜 s x\nι : Type (max u_1 u_2)\nl : Filter ι\nhl : l.NeBot\nc : ι → 𝕜\nd... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.TangentCone.Basic | {
"line": 172,
"column": 4
} | {
"line": 172,
"column": 15
} | {
"line": 172,
"column": 16
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Semiring 𝕜\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : ContinuousAdd E\ns : Set E\nx : E\ninst✝ : T2Space E\ny : E\nhy : y ∈ tangentConeAt 𝕜 s x\nι : Type (max u_1 u_2)\nl : Filter ι\nhl : l.NeBot\nc : ι → 𝕜\nd : ι → E\n... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Semiring 𝕜\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : ContinuousAdd E\ns : Set E\nx : E\ninst✝ : T2Space E\ny : E\nhy : y ∈ tangentConeAt 𝕜 s x\nι : Type (max u_1 u_2)\nl : Filter ι\nhl : l.NeBot\nc : ι → 𝕜\nd : ι → E\nhd₀ : Tendst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.TangentCone.Basic | {
"line": 174,
"column": 2
} | {
"line": 174,
"column": 13
} | {
"line": 174,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Semiring 𝕜\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : ContinuousAdd E\ns : Set E\nx : E\ninst✝ : T2Space E\nhx : ¬AccPt x (𝓟 s)\ny : E\nhy : y ∈ tangentConeAt 𝕜 s x\nι : Type (max u_1 u_2)\nl : Filter ι\nhl : l.NeBot\nc... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Semiring 𝕜\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : ContinuousAdd E\ns : Set E\nx : E\ninst✝ : T2Space E\nhx : ¬AccPt x (𝓟 s)\ny : E\nhy : y ∈ tangentConeAt 𝕜 s x\nι : Type (max u_1 u_2)\nl : Filter ι\nhl : l.NeBot\nc : ι → 𝕜\nd... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.TangentCone.Basic | {
"line": 200,
"column": 4
} | {
"line": 200,
"column": 15
} | {
"line": 200,
"column": 16
} | [
{
"pp": "case refine_1\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁶ : DivisionSemiring 𝕜\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : TopologicalSpace 𝕜\ninst✝² : TopologicalSpace E\ninst✝¹ : ContinuousSMul 𝕜 E\ns : Set E\nx y : E\nα : Type u_3\nl : Filter α\ninst✝ : l.NeBot\nc : α → 𝕜\nhc₀ : Tendsto c ... | [
"case refine_1\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁶ : DivisionSemiring 𝕜\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : TopologicalSpace 𝕜\ninst✝² : TopologicalSpace E\ninst✝¹ : ContinuousSMul 𝕜 E\ns : Set E\nx y : E\nα : Type u_3\nl : Filter α\ninst✝ : l.NeBot\nc : α → 𝕜\nhc₀ : Tendsto c l (𝓝 0) ∧ ∀... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.TangentCone.Basic | {
"line": 289,
"column": 2
} | {
"line": 289,
"column": 31
} | {
"line": 289,
"column": 32
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁷ : DivisionSemiring 𝕜\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module 𝕜 E\ninst✝⁴ : TopologicalSpace E\ninst✝³ : TopologicalSpace 𝕜\ninst✝² : (𝓝[≠] 0).NeBot\ninst✝¹ : ContinuousSMul 𝕜 E\nx : E\ns : Set E\ninst✝ : ContinuousAdd E\nh : s ∈ 𝓝 x\n⊢ UniqueDiffWithinAt 𝕜 s... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝⁷ : DivisionSemiring 𝕜\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module 𝕜 E\ninst✝⁴ : TopologicalSpace E\ninst✝³ : TopologicalSpace 𝕜\ninst✝² : (𝓝[≠] 0).NeBot\ninst✝¹ : ContinuousSMul 𝕜 E\nx : E\ns : Set E\ninst✝ : ContinuousAdd E\nh : s ∈ 𝓝 x\n⊢ UniqueDiffWithinAt 𝕜 s x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Congr | {
"line": 49,
"column": 6
} | {
"line": 50,
"column": 13
} | {
"line": 50,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : TopologicalSpace E\nF : Type u_3\ninst✝² : AddCommGroup F\ninst✝¹ : Module 𝕜 F\ninst✝ : TopologicalSpace F\nf : E → F\nf' : E →L[𝕜] F\nx : E\ns t : Set E\nh : s =ᶠ[𝓝[≠] x] t\n⊢ �... | [
"𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : TopologicalSpace E\nF : Type u_3\ninst✝² : AddCommGroup F\ninst✝¹ : Module 𝕜 F\ninst✝ : TopologicalSpace F\nf : E → F\nf' : E →L[𝕜] F\nx : E\ns t : Set E\nh : s =ᶠ[𝓝[≠] x] t\n⊢ 𝓝[s ∩ {x}ᶜ] ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Asymptotics.TVS | {
"line": 223,
"column": 2
} | {
"line": 223,
"column": 13
} | {
"line": 223,
"column": 14
} | [
{
"pp": "case right\nα : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : TopologicalSpace E\ninst✝³ : Module 𝕜 E\ninst✝² : AddCommGroup F\ninst✝¹ : TopologicalSpace F\ninst✝ : Module 𝕜 F\nl : Filter α\nf : α → E\ng : α → F\nh : f =o[�... | [
"case right\nα : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : TopologicalSpace E\ninst✝³ : Module 𝕜 E\ninst✝² : AddCommGroup F\ninst✝¹ : TopologicalSpace F\ninst✝ : Module 𝕜 F\nl : Filter α\nf : α → E\ng : α → F\nh : f =o[𝕜; l] g\nU :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Basic | {
"line": 147,
"column": 14
} | {
"line": 147,
"column": 25
} | {
"line": 147,
"column": 26
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁹ : AddCommGroup E\ninst✝⁸ : Module 𝕜 E\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : ContinuousAdd E\ninst✝⁵ : ContinuousSMul 𝕜 E\nF : Type u_3\ninst✝⁴ : AddCommGroup F\ninst✝³ : Module 𝕜 F\ninst✝² : TopologicalSpace F\ninst✝¹ : Conti... | [
"𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁹ : AddCommGroup E\ninst✝⁸ : Module 𝕜 E\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : ContinuousAdd E\ninst✝⁵ : ContinuousSMul 𝕜 E\nF : Type u_3\ninst✝⁴ : AddCommGroup F\ninst✝³ : Module 𝕜 F\ninst✝² : TopologicalSpace F\ninst✝¹ : ContinuousAdd F\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Basic | {
"line": 150,
"column": 6
} | {
"line": 150,
"column": 28
} | {
"line": 150,
"column": 29
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁹ : AddCommGroup E\ninst✝⁸ : Module 𝕜 E\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : ContinuousAdd E\ninst✝⁵ : ContinuousSMul 𝕜 E\nF : Type u_3\ninst✝⁴ : AddCommGroup F\ninst✝³ : Module 𝕜 F\ninst✝² : TopologicalSpace F\ninst✝¹ : Conti... | [
"𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁹ : AddCommGroup E\ninst✝⁸ : Module 𝕜 E\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : ContinuousAdd E\ninst✝⁵ : ContinuousSMul 𝕜 E\nF : Type u_3\ninst✝⁴ : AddCommGroup F\ninst✝³ : Module 𝕜 F\ninst✝² : TopologicalSpace F\ninst✝¹ : ContinuousAdd F\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Basic | {
"line": 153,
"column": 2
} | {
"line": 153,
"column": 13
} | {
"line": 153,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁹ : AddCommGroup E\ninst✝⁸ : Module 𝕜 E\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : ContinuousAdd E\ninst✝⁵ : ContinuousSMul 𝕜 E\nF : Type u_3\ninst✝⁴ : AddCommGroup F\ninst✝³ : Module 𝕜 F\ninst✝² : TopologicalSpace F\ninst✝¹ : Conti... | [
"𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁹ : AddCommGroup E\ninst✝⁸ : Module 𝕜 E\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : ContinuousAdd E\ninst✝⁵ : ContinuousSMul 𝕜 E\nF : Type u_3\ninst✝⁴ : AddCommGroup F\ninst✝³ : Module 𝕜 F\ninst✝² : TopologicalSpace F\ninst✝¹ : ContinuousAdd F\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Basic | {
"line": 546,
"column": 4
} | {
"line": 546,
"column": 15
} | {
"line": 546,
"column": 16
} | [
{
"pp": "case pos\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : ℝ → E\nx : ℝ\nH : DifferentiableWithinAt ℝ f (Ioi x) x\nA : HasDerivWithinAt f (derivWithin f (Ioi x) x) (Ici x) x\nB : HasDerivWithinAt f (derivWithin f (Ici x) x) (Ici x) x\n⊢ derivWithin f (Ioi x) x = derivWithin f (... | [
"case pos\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : ℝ → E\nx : ℝ\nH : DifferentiableWithinAt ℝ f (Ioi x) x\nA : HasDerivWithinAt f (derivWithin f (Ioi x) x) (Ici x) x\nB : HasDerivWithinAt f (derivWithin f (Ici x) x) (Ici x) x\n⊢ derivWithin f (Ioi x) x = derivWithin f (Ici x) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Basic | {
"line": 175,
"column": 2
} | {
"line": 175,
"column": 42
} | {
"line": 176,
"column": 2
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹¹ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹⁰ : AddCommGroup E\ninst✝⁹ : Module 𝕜 E\ninst✝⁸ : TopologicalSpace E\ninst✝⁷ : ContinuousAdd E\ninst✝⁶ : ContinuousSMul 𝕜 E\nF : Type u_3\ninst✝⁵ : AddCommGroup F\ninst✝⁴ : Module 𝕜 F\ninst✝³ : TopologicalSpace F\ninst✝² : Cont... | [
"𝕜 : Type u_1\ninst✝¹¹ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹⁰ : AddCommGroup E\ninst✝⁹ : Module 𝕜 E\ninst✝⁸ : TopologicalSpace E\ninst✝⁷ : ContinuousAdd E\ninst✝⁶ : ContinuousSMul 𝕜 E\nF : Type u_3\ninst✝⁵ : AddCommGroup F\ninst✝⁴ : Module 𝕜 F\ninst✝³ : TopologicalSpace F\ninst✝² : ContinuousAdd F\... | rw [HasFDerivAt, ← nhdsWithin_univ] at * | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.Calculus.Deriv.Basic | {
"line": 876,
"column": 2
} | {
"line": 876,
"column": 13
} | {
"line": 876,
"column": 14
} | [
{
"pp": "𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\nf' : F\nx₀ : 𝕜\nhf : HasDerivAt f f' x₀\nC : ℝ\nhC₀ : 0 ≤ C\nhlip : ∀ᶠ (x : 𝕜) in 𝓝 x₀, ‖f x - f x₀‖ ≤ C * ‖x - x₀‖\n⊢ ‖f'‖ ≤ C",
"ppTerm": "?m.40",
"assigned": ... | [
"𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\nf' : F\nx₀ : 𝕜\nhf : HasDerivAt f f' x₀\nC : ℝ\nhC₀ : 0 ≤ C\nhlip : ∀ᶠ (x : 𝕜) in 𝓝 x₀, ‖f x - f x₀‖ ≤ C * ‖x - x₀‖\n⊢ ‖f'‖ ≤ C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Basic | {
"line": 882,
"column": 2
} | {
"line": 882,
"column": 13
} | {
"line": 882,
"column": 14
} | [
{
"pp": "𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\nf' : F\nx₀ : 𝕜\nhf : HasDerivAt f f' x₀\ns : Set 𝕜\nhs : s ∈ 𝓝 x₀\nC : ℝ≥0\nhlip : LipschitzOnWith C f s\n⊢ ‖f'‖ ≤ ↑C",
"ppTerm": "?m.23",
"assigned": false,
... | [
"𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\nf' : F\nx₀ : 𝕜\nhf : HasDerivAt f f' x₀\ns : Set 𝕜\nhs : s ∈ 𝓝 x₀\nC : ℝ≥0\nhlip : LipschitzOnWith C f s\n⊢ ‖f'‖ ≤ ↑C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Basic | {
"line": 888,
"column": 2
} | {
"line": 888,
"column": 13
} | {
"line": 888,
"column": 14
} | [
{
"pp": "𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\nf' : F\nx₀ : 𝕜\nhf : HasDerivAt f f' x₀\nC : ℝ≥0\nhlip : LipschitzWith C f\n⊢ ‖f'‖ ≤ ↑C",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedF... | [
"𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\nf' : F\nx₀ : 𝕜\nhf : HasDerivAt f f' x₀\nC : ℝ≥0\nhlip : LipschitzWith C f\n⊢ ‖f'‖ ≤ ↑C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Basic | {
"line": 896,
"column": 2
} | {
"line": 896,
"column": 41
} | {
"line": 896,
"column": 42
} | [
{
"pp": "𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\nx₀ : 𝕜\nC : ℝ\nhC₀ : 0 ≤ C\nhlip : ∀ᶠ (x : 𝕜) in 𝓝 x₀, ‖f x - f x₀‖ ≤ C * ‖x - x₀‖\n⊢ ‖deriv f x₀‖ ≤ C",
"ppTerm": "?m.39",
"assigned": true,
"usedConstants"... | [
"𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\nx₀ : 𝕜\nC : ℝ\nhC₀ : 0 ≤ C\nhlip : ∀ᶠ (x : 𝕜) in 𝓝 x₀, ‖f x - f x₀‖ ≤ C * ‖x - x₀‖\n⊢ ‖fderiv 𝕜 f x₀‖ ≤ C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Basic | {
"line": 903,
"column": 2
} | {
"line": 903,
"column": 41
} | {
"line": 903,
"column": 42
} | [
{
"pp": "𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\nx₀ : 𝕜\ns : Set 𝕜\nhs : s ∈ 𝓝 x₀\nC : ℝ≥0\nhlip : LipschitzOnWith C f s\n⊢ ‖deriv f x₀‖ ≤ ↑C",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
... | [
"𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : 𝕜 → F\nx₀ : 𝕜\ns : Set 𝕜\nhs : s ∈ 𝓝 x₀\nC : ℝ≥0\nhlip : LipschitzOnWith C f s\n⊢ ‖fderiv 𝕜 f x₀‖ ≤ ↑C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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