module stringlengths 16 90 | startPos dict | endPos dict | goals listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 366
values | kind stringclasses 370
values |
|---|---|---|---|---|---|---|
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 829,
"column": 2
} | {
"line": 829,
"column": 65
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"Int.instAddCommMonoid",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"Multipli... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 832,
"column": 2
} | {
"line": 832,
"column": 65
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"Int.instAddCommMonoid",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 897,
"column": 59
} | {
"line": 897,
"column": 70
} | [
{
"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)",
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Algebra... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Order | {
"line": 359,
"column": 21
} | {
"line": 359,
"column": 32
} | [
{
"pp": "σ : Type u_1\nw : σ → ℕ\nR : Type u_3\ninst✝ : Ring R\nf : MvPowerSeries σ R\nh : weightedOrder w (-f) ≠ weightedOrder w f\n⊢ f = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Order | {
"line": 486,
"column": 4
} | {
"line": 486,
"column": 15
} | [
{
"pp": "case mp.h\nσ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nf : MvPowerSeries σ R\nh : 1 ≤ f.order\n⊢ ↑(degree 0) < f.order",
"usedConstants": [
"Finsupp.instAddZeroClass",
"Eq.mpr",
"Nat.instMulZeroClass",
"AddMonoidHom.instAddMonoidHomClass",
"instAddMonoidWithOneENat... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Order | {
"line": 490,
"column": 4
} | {
"line": 490,
"column": 42
} | [
{
"pp": "case mpr\nσ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nf : MvPowerSeries σ R\nh : constantCoeff f = 0\nd : σ →₀ ℕ\nhd : degree d = 0\n⊢ (coeff d) f = 0",
"usedConstants": [
"Finsupp.instAddZeroClass",
"Nat.instCanonicallyOrderedAdd",
"Nat.instMulZeroClass",
"Semiring.toMo... | simp [(degree_eq_zero_iff d).mp hd, h] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.RingTheory.MvPowerSeries.Order | {
"line": 499,
"column": 2
} | {
"line": 499,
"column": 13
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nf : MvPowerSeries σ R\nn : ℕ\nhf : constantCoeff f = 0\n⊢ ↑n ≤ n • f.order",
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"instAddMonoidWithOneENat",
"HMul.hMul",
"ENat.instNa... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Order | {
"line": 558,
"column": 2
} | {
"line": 558,
"column": 33
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nw : σ → ℕ\nf : MvPowerSeries σ R\np : ℕ\nhf : IsWeightedHomogeneous w f p\nd : σ →₀ ℕ\nhd : (weight w) d ≠ p\n⊢ (coeff d) f = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Trunc | {
"line": 153,
"column": 2
} | {
"line": 153,
"column": 13
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\ns : Finset (σ →₀ ℕ)\np : MvPowerSeries σ R\na✝ : σ →₀ ℕ\n⊢ a✝ ∉ s → a✝ ∉ ((truncFinset R s) p).support",
"usedConstants": [
"Eq.mpr",
"Nat.instMulZeroClass",
"Semiring.toModule",
"Classical.not_not._simp_1",
"AddMonoi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Trunc | {
"line": 157,
"column": 2
} | {
"line": 157,
"column": 40
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\ns : Finset (σ →₀ ℕ)\np : MvPowerSeries σ R\n⊢ ((truncFinset R s) p).totalDegree ≤ s.sup ⇑degree",
"usedConstants": [
"Finsupp.instAddZeroClass",
"Eq.mpr",
"Nat.instMulZeroClass",
"Nat.instLattice",
"Lattice.toSemilatt... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Trunc | {
"line": 183,
"column": 2
} | {
"line": 183,
"column": 13
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝¹ : DecidableEq σ\ninst✝ : CommSemiring R\nm n : σ →₀ ℕ\nφ : MvPowerSeries σ R\n⊢ MvPolynomial.coeff m ((trunc R n) φ) = if m < n then (coeff m) φ else 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Trunc | {
"line": 187,
"column": 22
} | {
"line": 187,
"column": 33
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝¹ : DecidableEq σ\ninst✝ : CommSemiring R\nn : σ →₀ ℕ\nhnn : n ≠ 0\n⊢ 0 ∈ Iio n",
"usedConstants": [
"Eq.mpr",
"Nat.instMulZeroClass",
"Preorder.toLT",
"LinearOrderedCommMonoidWithZero.toIsBotZeroClass",
"Finset",
"Finset.Iio",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Trunc | {
"line": 191,
"column": 20
} | {
"line": 191,
"column": 31
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝¹ : DecidableEq σ\ninst✝ : CommSemiring R\nn : σ →₀ ℕ\nhnn : n ≠ 0\na : R\n⊢ 0 ∈ Iio n",
"usedConstants": [
"Eq.mpr",
"Nat.instMulZeroClass",
"Preorder.toLT",
"LinearOrderedCommMonoidWithZero.toIsBotZeroClass",
"Finset",
"Finset.I... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Trunc | {
"line": 220,
"column": 2
} | {
"line": 220,
"column": 13
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝¹ : DecidableEq σ\ninst✝ : CommSemiring R\nm n : σ →₀ ℕ\nφ : MvPowerSeries σ R\n⊢ MvPolynomial.coeff m ((trunc' R n) φ) = if m ≤ n then (coeff m) φ else 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Trunc | {
"line": 262,
"column": 2
} | {
"line": 262,
"column": 49
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝¹ : DecidableEq σ\ninst✝ : CommSemiring R\nn : σ →₀ ℕ\nφ : MvPowerSeries σ R\n⊢ ((trunc' R n) φ).totalDegree ≤ degree n",
"usedConstants": [
"Finsupp.instAddZeroClass",
"Eq.mpr",
"Nat.instCanonicallyOrderedAdd",
"Nat.instMulZeroClass",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 70,
"column": 2
} | {
"line": 70,
"column": 13
} | [
{
"pp": "R : Type u_1\ninst✝ : Semiring R\nφ : R⟦X⟧\n⊢ φ.order = ⊤ ↔ φ = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 88,
"column": 4
} | {
"line": 88,
"column": 15
} | [
{
"pp": "R : Type u_1\ninst✝ : Semiring R\nφ : R⟦X⟧\nn : ℕ\nh : (coeff n) φ ≠ 0\n⊢ ↑(Nat.find ⋯) ≤ ↑n",
"usedConstants": [
"Eq.mpr",
"Nat.find_le_iff._simp_1",
"instDecidableNot",
"Semiring.toModule",
"instCharZeroENat",
"PowerSeries.order._proof_1",
"instAddMonoidW... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.PiTopology | {
"line": 152,
"column": 2
} | {
"line": 152,
"column": 30
} | [
{
"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",
"usedConstants": [
"Finsupp.instAddZer... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 117,
"column": 11
} | {
"line": 117,
"column": 22
} | [
{
"pp": "case top\nR : Type u_1\ninst✝ : Semiring R\nφ : R⟦X⟧\nh : ∀ (i : ℕ), ↑i < ⊤ → (coeff i) φ = 0\n⊢ ⊤ ≤ φ.order",
"usedConstants": [
"Eq.mpr",
"MvPowerSeries.instZero",
"instTopENat",
"instLinearOrderENat",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Semilatt... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 117,
"column": 31
} | {
"line": 117,
"column": 42
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"MvPowerSeries.instZero",
"Semiring.toModule",
"SemilinearMapClass.distribMulActionSemiHomClass",
"congrArg",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 120,
"column": 4
} | {
"line": 120,
"column": 15
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 118,
"column": 2
} | {
"line": 118,
"column": 12
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Semiring.toModule",
"instCharZeroENat",
"instAddMonoidWithOneENat",
"ENat.instNatCast",
"i... | | coe n => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | null |
Mathlib.RingTheory.MvPowerSeries.PiTopology | {
"line": 208,
"column": 4
} | {
"line": 208,
"column": 39
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 137,
"column": 2
} | {
"line": 137,
"column": 12
} | [
{
"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",
"usedConstants": [
"Preorder.toLT",
"Semiring.toModule",
"instCharZeroENat",
"instAddMonoidWithOneENat",
"ENat.... | | coe n => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | null |
Mathlib.RingTheory.MvPowerSeries.PiTopology | {
"line": 248,
"column": 2
} | {
"line": 248,
"column": 13
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝¹ : TopologicalSpace R\ninst✝ : Semiring R\nf : MvPowerSeries σ R\nd : σ →₀ ℕ\n⊢ HasSum (fun i ↦ (monomial i) ((coeff i) f) d) (f d)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 177,
"column": 4
} | {
"line": 177,
"column": 41
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.PiTopology | {
"line": 271,
"column": 17
} | {
"line": 271,
"column": 28
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝¹ : TopologicalSpace R\ninst✝ : Semiring R\nι : Type u_3\nf : ι → MvPowerSeries σ R\na : (σ →₀ ℕ) → R\nh : ∀ (d : σ →₀ ℕ), HasSum (fun i ↦ (coeff d) (f i)) (a d)\n⊢ ∀ (d : σ →₀ ℕ), HasSum (fun i ↦ (coeff d) (f i)) ((coeff d) a)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 221,
"column": 4
} | {
"line": 221,
"column": 15
} | [
{
"pp": "case mp.h\nR : Type u_1\ninst✝ : Semiring R\nφ : R⟦X⟧\nh : 1 ≤ φ.order\n⊢ ↑0 < φ.order",
"usedConstants": [
"CharP.cast_eq_zero",
"Eq.mpr",
"instCharZeroENat",
"instAddMonoidWithOneENat",
"ENat.instNatCast",
"congrArg",
"AddMonoid.toAddZeroClass",
"Ad... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 234,
"column": 2
} | {
"line": 234,
"column": 13
} | [
{
"pp": "R : Type u_1\ninst✝ : Semiring R\nφ : R⟦X⟧\nn : ℕ\nhf : constantCoeff φ = 0\n⊢ ↑n ≤ n • φ.order",
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"instAddMonoidWithOneENat",
"HMul.hMul",
"ENat.instNatCast",
"congrArg",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.LinearTopology | {
"line": 306,
"column": 9
} | {
"line": 306,
"column": 20
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.PiTopology | {
"line": 302,
"column": 2
} | {
"line": 302,
"column": 28
} | [
{
"pp": "case h\nσ : 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 : m ≥ n + 1\n⊢ ↑m ≤ m • f.order",
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"instAddMon... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.PiTopology | {
"line": 153,
"column": 20
} | {
"line": 153,
"column": 31
} | [
{
"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))",
"usedConstants": [
"Eq.mpr",
"Semiring.toModule",
"congrA... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 286,
"column": 21
} | {
"line": 286,
"column": 32
} | [
{
"pp": "R : Type u_2\ninst✝ : Ring R\nφ : R⟦X⟧\nh : (-φ).order ≠ φ.order\n⊢ φ = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.PiTopology | {
"line": 168,
"column": 34
} | {
"line": 168,
"column": 45
} | [
{
"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 ≥ a, ↑n < (f b).order\ni : ι\nhi : ∀ b ≥ i, ↑n < (f b).order\nk : ι\nhk : i < k\n⊢ ↑n < (f k).order",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 325,
"column": 2
} | {
"line": 325,
"column": 34
} | [
{
"pp": "R : Type u_1\ninst✝ : Semiring R\nφ : R⟦X⟧\n⊢ X ^ φ.order.toNat ∣ φ",
"usedConstants": [
"Eq.mpr",
"Dvd.dvd",
"Semiring.toModule",
"_private.Mathlib.RingTheory.PowerSeries.Order.0.PowerSeries.X_pow_order_dvd._simp_1_1",
"semigroupDvd",
"LinearMap.instFunLike",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.LinearTopology | {
"line": 96,
"column": 22
} | {
"line": 96,
"column": 64
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"Nat.ins... | 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.PowerSeries.Order | {
"line": 334,
"column": 2
} | {
"line": 334,
"column": 12
} | [
{
"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",
"usedConstants": [
"not_le",
"PowerSeries.coeff_mul_of_lt_order",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"False",
"Semigroup.t... | | coe n => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | null |
Mathlib.RingTheory.MvPowerSeries.LinearTopology | {
"line": 97,
"column": 6
} | {
"line": 97,
"column": 17
} | [
{
"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",
"usedConstants": [
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 361,
"column": 2
} | {
"line": 361,
"column": 13
} | [
{
"pp": "R : Type u_1\ninst✝¹ : Semiring R\ninst✝ : Nontrivial R\n⊢ order 1 = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Order | {
"line": 373,
"column": 2
} | {
"line": 373,
"column": 33
} | [
{
"pp": "R : Type u_1\ninst✝¹ : Semiring R\ninst✝ : Nontrivial R\n⊢ X.order = 1",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.LinearTopology | {
"line": 105,
"column": 6
} | {
"line": 105,
"column": 17
} | [
{
"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",
"usedCons... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.LinearTopology | {
"line": 131,
"column": 4
} | {
"line": 131,
"column": 49
} | [
{
"pp": "case refine_2\nσ : Type u_1\nR : Type u_2\ninst✝³ : Ring R\ninst✝² : TopologicalSpace R\ninst✝¹ : IsLinearTopology R R\ninst✝ : IsLinearTopology Rᵐᵒᵖ R\nI : TwoSidedIdeal R\nd : σ →₀ ℕ\nhI : ↑(I, d).1 ∈ 𝓝 0\n⊢ ((Iic d, I).1.pi fun x ↦ ↑(Iic d, I).2) ⊆ ↑(basis σ R (I, d))",
"usedConstants": [
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Evaluation | {
"line": 171,
"column": 4
} | {
"line": 171,
"column": 15
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.LinearTopology | {
"line": 158,
"column": 2
} | {
"line": 158,
"column": 28
} | [
{
"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, constantCoeff ((map (Ideal.Quotient.mk I)) f) ^ b = 0\nn : ℕ\nhn : n ≥ N + Finsupp.degree d\n⊢ (coeff ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.LinearTopology | {
"line": 171,
"column": 2
} | {
"line": 171,
"column": 28
} | [
{
"pp": "σ : Type u_1\nR : Type u_3\ninst✝² : CommRing R\ninst✝¹ : TopologicalSpace R\ninst✝ : IsLinearTopology R R\nf : MvPowerSeries σ R\nH : Tendsto (fun n ↦ constantCoeff (f ^ n)) atTop (𝓝 0)\n⊢ IsTopologicallyNilpotent (constantCoeff f)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Evaluation | {
"line": 175,
"column": 4
} | {
"line": 175,
"column": 84
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Evaluation | {
"line": 183,
"column": 4
} | {
"line": 183,
"column": 15
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Evaluation | {
"line": 248,
"column": 4
} | {
"line": 248,
"column": 43
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Substitution | {
"line": 102,
"column": 2
} | {
"line": 102,
"column": 56
} | [
{
"pp": "σ : Type u_1\nτ : Type u_4\nS : Type u_5\ninst✝ : CommRing S\nthis : UniformSpace S := ⊥\n⊢ HasSubst fun x ↦ 0",
"usedConstants": [
"Eq.mpr",
"MvPowerSeries.instZero",
"MvPowerSeries.WithPiTopology.instTopologicalSpace",
"CommSemiring.toSemiring",
"MvPowerSeries",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Substitution | {
"line": 127,
"column": 2
} | {
"line": 127,
"column": 56
} | [
{
"pp": "σ : Type u_1\nS : Type u_5\ninst✝ : CommRing S\nthis : UniformSpace S := ⊥\n⊢ HasSubst fun s ↦ X s",
"usedConstants": [
"Eq.mpr",
"MvPowerSeries.WithPiTopology.instTopologicalSpace",
"CommSemiring.toSemiring",
"MvPowerSeries",
"DiscreteUniformity.instDiscreteTopology",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Substitution | {
"line": 320,
"column": 6
} | {
"line": 320,
"column": 40
} | [
{
"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\nha' : ∀ (i : σ), constantCoeff (a i) = 0\nf : MvPowerSeries σ R\nhf : constantCoeff f = 0\nd : σ →₀ ℕ\nhd : ¬d = 0\ni : σ\nhi : d i ≠ 0\n⊢ c... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Substitution | {
"line": 389,
"column": 2
} | {
"line": 391,
"column": 9
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Evaluation | {
"line": 205,
"column": 2
} | {
"line": 205,
"column": 46
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Substitution | {
"line": 407,
"column": 4
} | {
"line": 407,
"column": 15
} | [
{
"pp": "case pos.ha\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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Cardinal.Continuum | {
"line": 72,
"column": 34
} | {
"line": 72,
"column": 45
} | [
{
"pp": "⊢ ℶ_ 1 = 𝔠",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Cardinal.Continuum | {
"line": 182,
"column": 8
} | {
"line": 182,
"column": 32
} | [
{
"pp": "case a\nx : Cardinal.{u_1}\nh₁ : 2 ≤ x\nh₂ : x ≤ 𝔠\n⊢ x ^ ℵ₀ ≤ 𝔠",
"usedConstants": [
"Eq.mpr",
"Cardinal.instPowCardinal",
"Cardinal",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"id",
"Cardinal.aleph0",
"LE.le",
"Cardinal.c... | ← continuum_power_aleph0 | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.MvPowerSeries.Substitution | {
"line": 415,
"column": 6
} | {
"line": 415,
"column": 17
} | [
{
"pp": "case neg.ha.ha\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\nt : σ\nhs : d t ≠ 0 t\n⊢ IsNilpotent (constantCoeff (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Substitution | {
"line": 428,
"column": 4
} | {
"line": 428,
"column": 54
} | [
{
"pp": "σ : Type u_1\nτ : Type u_4\nS : Type u_5\ninst✝² : CommRing S\na : σ → MvPowerSeries τ S\nυ : Type u_7\nT : Type u_8\ninst✝¹ : CommRing T\ninst✝ : Algebra S T\nb : τ → MvPowerSeries υ T\nha : HasSubst a\nhb : HasSubst b\nthis✝ : UniformSpace S := ⋯\nthis : UniformSpace T := ⋯\n⊢ Filter.Tendsto (⇑(subst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Substitution | {
"line": 436,
"column": 2
} | {
"line": 436,
"column": 43
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Substitution | {
"line": 445,
"column": 2
} | {
"line": 445,
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Substitution | {
"line": 467,
"column": 2
} | {
"line": 467,
"column": 68
} | [
{
"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... | simp only [Finsupp.weight_apply, Finsupp.sum, Function.comp_apply] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.RingTheory.MvPowerSeries.Substitution | {
"line": 484,
"column": 4
} | {
"line": 484,
"column": 43
} | [
{
"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": 484,
"column": 4
} | {
"line": 484,
"column": 43
} | [
{
"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": 484,
"column": 4
} | {
"line": 484,
"column": 43
} | [
{
"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.NumberTheory.ArithmeticFunction.LFunction | {
"line": 105,
"column": 14
} | {
"line": 105,
"column": 25
} | [
{
"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 | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ArithmeticFunction.LFunction | {
"line": 105,
"column": 14
} | {
"line": 105,
"column": 40
} | [
{
"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": 560,
"column": 4
} | {
"line": 560,
"column": 15
} | [
{
"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",
"usedConstants": [
"Finsupp.instFunLike",
"Eq.mpr",
"Nat.instMulZeroClass",
"Finset",
"Finsupp.mem_support_iff._simp_1",
"Finsupp.support... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Real.Cardinality | {
"line": 75,
"column": 4
} | {
"line": 75,
"column": 20
} | [
{
"pp": "case true\nc : ℝ\nf : ℕ → Bool\nn : ℕ\nh : 0 ≤ c\nh' : f n = true\n⊢ 0 ≤ cantorFunctionAux c f n",
"usedConstants": [
"Eq.mpr",
"Real.instLE",
"Real",
"Real.instZero",
"congrArg",
"id",
"LE.le",
"Cardinal.cantorFunctionAux_true",
"Monoid.toPow",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Substitution | {
"line": 615,
"column": 4
} | {
"line": 615,
"column": 15
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Cardinality | {
"line": 34,
"column": 2
} | {
"line": 34,
"column": 14
} | [
{
"pp": "⊢ ℵ₀ < 𝔠",
"usedConstants": [
"Cardinal.aleph0",
"Cardinal.cantor"
]
}
] | apply cantor | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.LinearAlgebra.Complex.FiniteDimensional | {
"line": 68,
"column": 2
} | {
"line": 68,
"column": 23
} | [
{
"pp": "⊢ lift.{0, 0} #ℚ < lift.{0, 0} #ℝ",
"usedConstants": [
"Eq.mpr",
"Real",
"Preorder.toLT",
"NoMinOrder.infinite",
"Cardinal",
"congrArg",
"Rat.nontrivial",
"Rat",
"PartialOrder.toPreorder",
"Cardinal.lift",
"Cardinal.mk",
"id",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Complex.FiniteDimensional | {
"line": 74,
"column": 2
} | {
"line": 74,
"column": 13
} | [
{
"pp": "⊢ Cardinal.lift.{0, 0} #ℚ < Cardinal.lift.{0, 0} #ℂ",
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"NoMinOrder.infinite",
"Cardinal",
"congrArg",
"Rat.nontrivial",
"Rat",
"PartialOrder.toPreorder",
"Cardinal.lift",
"Cardinal.mk",
"i... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.LSeries.Basic | {
"line": 122,
"column": 2
} | {
"line": 122,
"column": 26
} | [
{
"pp": "f g : ℕ → ℂ\ns : ℂ\nn : ℕ\nh : ‖f n‖ ≤ ‖g n‖\n⊢ ‖term f s n‖ ≤ ‖term g s n‖",
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"Real.instPow",
"Real.instLE",
"Real",
"instHDiv",
"Real.instZero",
"congrArg",
"Real.instDivInvMonoid",
"Complex.instN... | 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
} | [
{
"pp": "f : ℕ → ℂ\ns s' : ℂ\nh : s.re ≤ s'.re\nn : ℕ\n⊢ ‖term f s' n‖ ≤ ‖term f s n‖",
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"Real.instPow",
"Real.instLE",
"Real",
"instHDiv",
"Real.instZero",
"congrArg",
"Real.instDivInvMonoid",
"Complex.inst... | simp only [norm_term_eq] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.NumberTheory.LSeries.Basic | {
"line": 144,
"column": 2
} | {
"line": 144,
"column": 39
} | [
{
"pp": "a : ℕ → ℂ\nn : ℕ\nhn : n ≠ 0\nh : 0 < a n\nx : ℝ\n⊢ 0 < term a (↑x) n",
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"instHDiv",
"congrArg",
"PartialOrder.toPreorder",
"Complex.instZero",
"LSeries.term_of_ne_zero",
"Complex.instPow",
"Complex.i... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.LSeries.Basic | {
"line": 345,
"column": 55
} | {
"line": 345,
"column": 66
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.LSeries.Basic | {
"line": 358,
"column": 4
} | {
"line": 358,
"column": 43
} | [
{
"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))‖",
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"NormedCommRing.toSem... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.LSeries.Basic | {
"line": 363,
"column": 2
} | {
"line": 363,
"column": 13
} | [
{
"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)",
"usedConstants": [
"neg_add_rev"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.EGauge | {
"line": 128,
"column": 19
} | {
"line": 128,
"column": 38
} | [
{
"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\nx : E\nhs : Balanced 𝕜 s\nhc : egauge 𝕜 s x < ‖c‖ₑ\na : 𝕜\nhxa : x ∈ a • s\nha : ‖a‖ₑ < ‖c‖ₑ\n⊢ ‖a‖ ≤ ‖c‖",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.EGauge | {
"line": 149,
"column": 2
} | {
"line": 149,
"column": 13
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.EGauge | {
"line": 155,
"column": 2
} | {
"line": 155,
"column": 13
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.EGauge | {
"line": 171,
"column": 65
} | {
"line": 171,
"column": 76
} | [
{
"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.146",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.EGauge | {
"line": 173,
"column": 17
} | {
"line": 173,
"column": 28
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.EGauge | {
"line": 173,
"column": 66
} | {
"line": 173,
"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\nc : 𝕜\nhc₀ : c ∈ {0}ᶜ\nhcb : c ∈ eball 0 b\n⊢ ‖c... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.EGauge | {
"line": 206,
"column": 2
} | {
"line": 206,
"column": 52
} | [
{
"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",
"usedConstants": [
"instHSMul",
"HMul.hMul",
"CommSemiring.toSemiring",
... | refine le_antisymm ?_ (le_egauge_smul_right c s x) | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.Convex.EGauge | {
"line": 264,
"column": 64
} | {
"line": 264,
"column": 90
} | [
{
"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 ∈... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.EGauge | {
"line": 272,
"column": 38
} | {
"line": 272,
"column": 57
} | [
{
"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)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Substitution | {
"line": 62,
"column": 61
} | {
"line": 63,
"column": 21
} | [
{
"pp": "τ : Type u_3\nS : Type u_4\ninst✝ : CommRing S\na : MvPowerSeries τ S\nha : MvPowerSeries.constantCoeff a = 0\n⊢ HasSubst a",
"usedConstants": [
"congrArg",
"CommSemiring.toSemiring",
"IsNilpotent.zero._simp_1",
"MvPowerSeries",
"RingHom",
"MvPowerSeries.constant... | by
simp [HasSubst, ha] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.Convex.EGauge | {
"line": 273,
"column": 54
} | {
"line": 273,
"column": 69
} | [
{
"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)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Substitution | {
"line": 186,
"column": 2
} | {
"line": 186,
"column": 27
} | [
{
"pp": "case H\nR : Type u_2\ninst✝⁶ : CommRing R\nτ : Type u_3\nS : Type u_4\ninst✝⁵ : CommRing S\ninst✝⁴ : Algebra R S\na : MvPowerSeries τ S\ninst✝³ : UniformSpace R\ninst✝² : DiscreteUniformity R\ninst✝¹ : UniformSpace S\ninst✝ : DiscreteUniformity S\nha : HasSubst a\nf : R⟦X⟧\n⊢ (substAlgHom ha) f = (aeva... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.EGauge | {
"line": 325,
"column": 2
} | {
"line": 325,
"column": 13
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.EGauge | {
"line": 331,
"column": 2
} | {
"line": 331,
"column": 13
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.EGauge | {
"line": 342,
"column": 6
} | {
"line": 342,
"column": 17
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.EGauge | {
"line": 343,
"column": 6
} | {
"line": 343,
"column": 47
} | [
{
"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",
"usedConstants": [
"Norm.norm"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.EGauge | {
"line": 345,
"column": 32
} | {
"line": 345,
"column": 85
} | [
{
"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",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.EGauge | {
"line": 358,
"column": 2
} | {
"line": 358,
"column": 13
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Substitution | {
"line": 377,
"column": 2
} | {
"line": 377,
"column": 61
} | [
{
"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 = ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.TangentCone.Basic | {
"line": 86,
"column": 2
} | {
"line": 86,
"column": 13
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.TangentCone.Basic | {
"line": 169,
"column": 4
} | {
"line": 169,
"column": 15
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.TangentCone.Basic | {
"line": 172,
"column": 4
} | {
"line": 172,
"column": 15
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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