module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Algebra.Module.ZLattice.Summable | {
"line": 252,
"column": 25
} | {
"line": 252,
"column": 50
} | {
"line": 252,
"column": 51
} | [
{
"pp": "E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : FiniteDimensional ℝ E\nL : Submodule ℤ E\ninst✝ : DiscreteTopology ↥L\nr : ℝ\nhr : r < -↑(finrank ℤ ↥L)\nx : E\nh✝ : Nontrivial ↥L\nH : IsClosed ↑L\nt : ↥L\nht : t ∈ {x_1 | (fun i ↦ ‖‖↑i - x‖ ^ r‖ ≤ (1 / 2) ^ r * ‖i‖ ^ r) x... | [
"E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : FiniteDimensional ℝ E\nL : Submodule ℤ E\ninst✝ : DiscreteTopology ↥L\nr : ℝ\nhr : r < -↑(finrank ℤ ↥L)\nx : E\nh✝ : Nontrivial ↥L\nH : IsClosed ↑L\nt : ↥L\nht : t ∈ {x_1 | (fun i ↦ ‖‖↑i - x‖ ^ r‖ ≤ (1 / 2) ^ r * ‖i‖ ^ r) x_1}ᶜ\nht₁ : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.ZLattice.Summable | {
"line": 252,
"column": 4
} | {
"line": 252,
"column": 70
} | {
"line": 252,
"column": 71
} | [
{
"pp": "case pos\nE : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : FiniteDimensional ℝ E\nL : Submodule ℤ E\ninst✝ : DiscreteTopology ↥L\nr : ℝ\nhr : r < -↑(finrank ℤ ↥L)\nx : E\nh✝ : Nontrivial ↥L\nH : IsClosed ↑L\nt : ↥L\nht : t ∈ {x_1 | (fun i ↦ ‖‖↑i - x‖ ^ r‖ ≤ (1 / 2) ^ r * ... | [
"case pos\nE : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : FiniteDimensional ℝ E\nL : Submodule ℤ E\ninst✝ : DiscreteTopology ↥L\nr : ℝ\nhr : r < -↑(finrank ℤ ↥L)\nx : E\nh✝ : Nontrivial ↥L\nH : IsClosed ↑L\nt : ↥L\nht : t ∈ {x_1 | (fun i ↦ ‖‖↑i - x‖ ^ r‖ ≤ (1 / 2) ^ r * ‖i‖ ^ r) x_1... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.ZLattice.Summable | {
"line": 256,
"column": 4
} | {
"line": 256,
"column": 85
} | {
"line": 256,
"column": 86
} | [
{
"pp": "E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : FiniteDimensional ℝ E\nL : Submodule ℤ E\ninst✝ : DiscreteTopology ↥L\nr : ℝ\nhr : r < -↑(finrank ℤ ↥L)\nx : E\nh✝ : Nontrivial ↥L\nH : IsClosed ↑L\nt : ↥L\nht : t ∈ {x_1 | (fun i ↦ ‖‖↑i - x‖ ^ r‖ ≤ (1 / 2) ^ r * ‖i‖ ^ r) x... | [
"E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : FiniteDimensional ℝ E\nL : Submodule ℤ E\ninst✝ : DiscreteTopology ↥L\nr : ℝ\nhr : r < -↑(finrank ℤ ↥L)\nx : E\nh✝ : Nontrivial ↥L\nH : IsClosed ↑L\nt : ↥L\nht : t ∈ {x_1 | (fun i ↦ ‖‖↑i - x‖ ^ r‖ ≤ (1 / 2) ^ r * ‖i‖ ^ r) x_1}ᶜ\nht₁ : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.ZLattice.Summable | {
"line": 259,
"column": 2
} | {
"line": 259,
"column": 13
} | {
"line": 259,
"column": 14
} | [
{
"pp": "case neg\nE : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : FiniteDimensional ℝ E\nL : Submodule ℤ E\ninst✝ : DiscreteTopology ↥L\nr : ℝ\nhr : r < -↑(finrank ℤ ↥L)\nx : E\nh✝ : Nontrivial ↥L\nH : IsClosed ↑L\nt : ↥L\nht : t ∈ {x_1 | (fun i ↦ ‖‖↑i - x‖ ^ r‖ ≤ (1 / 2) ^ r * ... | [
"case neg\nE : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : FiniteDimensional ℝ E\nL : Submodule ℤ E\ninst✝ : DiscreteTopology ↥L\nr : ℝ\nhr : r < -↑(finrank ℤ ↥L)\nx : E\nh✝ : Nontrivial ↥L\nH : IsClosed ↑L\nt : ↥L\nht : t ∈ {x_1 | (fun i ↦ ‖‖↑i - x‖ ^ r‖ ≤ (1 / 2) ^ r * ‖i‖ ^ r) x_1... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.ToFinsupp | {
"line": 103,
"column": 4
} | {
"line": 103,
"column": 39
} | {
"line": 104,
"column": 4
} | [
{
"pp": "case inl.h\nR : Type u_2\ninst✝³ : AddZeroClass R\nl₁ l₂ : List R\ninst✝² : DecidablePred fun x ↦ (l₁ ++ l₂).getD x 0 ≠ 0\ninst✝¹ : DecidablePred fun x ↦ l₁.getD x 0 ≠ 0\ninst✝ : DecidablePred fun x ↦ l₂.getD x 0 ≠ 0\nn : ℕ\nh : n < l₁.length\n⊢ n ∉ Set.range ⇑(addLeftEmbedding l₁.length)",
"ppTerm... | [
"case inl.h\nR : Type u_2\ninst✝³ : AddZeroClass R\nl₁ l₂ : List R\ninst✝² : DecidablePred fun x ↦ (l₁ ++ l₂).getD x 0 ≠ 0\ninst✝¹ : DecidablePred fun x ↦ l₁.getD x 0 ≠ 0\ninst✝ : DecidablePred fun x ↦ l₂.getD x 0 ≠ 0\nk : ℕ\nh : l₁.length + k < l₁.length\n⊢ False"
] | rintro ⟨k, rfl : length l₁ + k = n⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro | Lean.Parser.Tactic.rintro |
Mathlib.Algebra.Module.ZLattice.Summable | {
"line": 267,
"column": 2
} | {
"line": 267,
"column": 13
} | {
"line": 267,
"column": 14
} | [
{
"pp": "E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : FiniteDimensional ℝ E\nL : Submodule ℤ E\ninst✝ : DiscreteTopology ↥L\nn : ℤ\nhn : n < -↑(finrank ℤ ↥L)\n⊢ Summable fun z ↦ ‖z‖ ^ n",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Norm.norm",
... | [
"E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : FiniteDimensional ℝ E\nL : Submodule ℤ E\ninst✝ : DiscreteTopology ↥L\nn : ℤ\nhn : n < -↑(finrank ℤ ↥L)\n⊢ Summable fun z ↦ ‖↑z‖ ^ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.ZLattice.Summable | {
"line": 271,
"column": 2
} | {
"line": 271,
"column": 13
} | {
"line": 271,
"column": 14
} | [
{
"pp": "E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : FiniteDimensional ℝ E\nL : Submodule ℤ E\ninst✝ : DiscreteTopology ↥L\nn : ℕ\nhn : finrank ℤ ↥L < n\nx : E\n⊢ Summable fun z ↦ ‖↑z - x‖⁻¹ ^ n",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"Norm... | [
"E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : FiniteDimensional ℝ E\nL : Submodule ℤ E\ninst✝ : DiscreteTopology ↥L\nn : ℕ\nhn : finrank ℤ ↥L < n\nx : E\n⊢ Summable fun z ↦ (‖↑z - x‖ ^ n)⁻¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.ZLattice.Summable | {
"line": 275,
"column": 2
} | {
"line": 275,
"column": 13
} | {
"line": 275,
"column": 14
} | [
{
"pp": "E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : FiniteDimensional ℝ E\nL : Submodule ℤ E\ninst✝ : DiscreteTopology ↥L\nn : ℕ\nhn : finrank ℤ ↥L < n\n⊢ Summable fun z ↦ ‖z‖⁻¹ ^ n",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Norm.norm",
... | [
"E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : FiniteDimensional ℝ E\nL : Submodule ℤ E\ninst✝ : DiscreteTopology ↥L\nn : ℕ\nhn : finrank ℤ ↥L < n\n⊢ Summable fun z ↦ (‖↑z‖ ^ n)⁻¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Basic | {
"line": 771,
"column": 6
} | {
"line": 771,
"column": 69
} | {
"line": 771,
"column": 70
} | [
{
"pp": "ι : Type u\nE : Type v\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : Fintype ι\nl : IntegrationParams\ninst✝¹ : CompleteSpace E\nI : Box ι\nf : (ι → ℝ) → E\nhc : ContinuousOn f (Box.Icc I)\nμ : Measure (ι → ℝ)\ninst✝ : IsLocallyFiniteMeasure μ\nC : ℝ\nhC : f '' Box.Icc I ⊆ C • Metr... | [
"ι : Type u\nE : Type v\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : Fintype ι\nl : IntegrationParams\ninst✝¹ : CompleteSpace E\nI : Box ι\nf : (ι → ℝ) → E\nhc : ContinuousOn f (Box.Icc I)\nμ : Measure (ι → ℝ)\ninst✝ : IsLocallyFiniteMeasure μ\nC : ℝ\nhC : f '' Box.Icc I ⊆ C • Metric.closedBal... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Choose.Multinomial | {
"line": 155,
"column": 2
} | {
"line": 155,
"column": 57
} | {
"line": 155,
"column": 58
} | [
{
"pp": "α : Type u_1\nf : α → ℕ\na b : α\ninst✝ : DecidableEq α\nhab : a ≠ b\n⊢ (f a)! * (f b)! * multinomial {a, b} f = (f a + f b)!",
"ppTerm": "?m.22",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nf : α → ℕ\na b : α\ninst✝ : DecidableEq α\nhab : a ≠ b\n⊢ (f a)! * (f b)! * multinomial {a, b} f = (f a + f b)!"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.MvPolynomial.Division | {
"line": 231,
"column": 2
} | {
"line": 231,
"column": 13
} | {
"line": 231,
"column": 14
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝¹ : CommSemiring R\ninst✝ : IsLeftCancelAdd R\ni : σ\np q r : MvPolynomial σ R\nh : p = X i * q + r\nhr : ∀ n ∈ r.support, n i = 0\nn : σ →₀ ℕ\nhn : Finsupp.single i 1 + n ∈ r.support\n⊢ False",
"ppTerm": "?m.82",
"assigned": false,
"usedConstants": [],
... | [
"σ : Type u_1\nR : Type u_2\ninst✝¹ : CommSemiring R\ninst✝ : IsLeftCancelAdd R\ni : σ\np q r : MvPolynomial σ R\nh : p = X i * q + r\nhr : ∀ n ∈ r.support, n i = 0\nn : σ →₀ ℕ\nhn : Finsupp.single i 1 + n ∈ r.support\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.MvPolynomial.Division | {
"line": 239,
"column": 2
} | {
"line": 239,
"column": 13
} | {
"line": 239,
"column": 14
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝¹ : CommSemiring R\ninst✝ : IsLeftCancelAdd R\nf g h : MvPolynomial σ R\nH : (fun x ↦ f + x) g = (fun x ↦ f + x) h\nd : σ →₀ ℕ\n⊢ coeff d g = coeff d h",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
... | [
"σ : Type u_1\nR : Type u_2\ninst✝¹ : CommSemiring R\ninst✝ : IsLeftCancelAdd R\nf g h : MvPolynomial σ R\nH : (fun x ↦ f + x) g = (fun x ↦ f + x) h\nd : σ →₀ ℕ\n⊢ coeff d g = coeff d h"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.MvPolynomial.Division | {
"line": 291,
"column": 8
} | {
"line": 291,
"column": 46
} | {
"line": 291,
"column": 47
} | [
{
"pp": "case mp.inl.h\nσ : Type u_1\nR : Type u_3\ninst✝¹ : CommRing R\ni : σ\np q : MvPolynomial σ R\ninst✝ : IsCancelMulZero R\na✝ : Nontrivial R\nx✝ : NoZeroDivisors (MvPolynomial σ R)\nh : X i ∣ p * q\nhp : p.modMonomial (Finsupp.single i 1) + X i * p.divMonomial (Finsupp.single i 1) = p\nhq : q.modMonomia... | [
"case mp.inl.h\nσ : Type u_1\nR : Type u_3\ninst✝¹ : CommRing R\ni : σ\np q : MvPolynomial σ R\ninst✝ : IsCancelMulZero R\na✝ : Nontrivial R\nx✝ : NoZeroDivisors (MvPolynomial σ R)\nh : X i ∣ p * q\nhp : p.modMonomial (Finsupp.single i 1) + X i * p.divMonomial (Finsupp.single i 1) = p\nhq : q.modMonomial (Finsupp.s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.MvPolynomial.Division | {
"line": 293,
"column": 8
} | {
"line": 293,
"column": 46
} | {
"line": 293,
"column": 47
} | [
{
"pp": "case mp.inr.h\nσ : Type u_1\nR : Type u_3\ninst✝¹ : CommRing R\ni : σ\np q : MvPolynomial σ R\ninst✝ : IsCancelMulZero R\na✝ : Nontrivial R\nx✝ : NoZeroDivisors (MvPolynomial σ R)\nh : X i ∣ p * q\nhp : p.modMonomial (Finsupp.single i 1) + X i * p.divMonomial (Finsupp.single i 1) = p\nhq : q.modMonomia... | [
"case mp.inr.h\nσ : Type u_1\nR : Type u_3\ninst✝¹ : CommRing R\ni : σ\np q : MvPolynomial σ R\ninst✝ : IsCancelMulZero R\na✝ : Nontrivial R\nx✝ : NoZeroDivisors (MvPolynomial σ R)\nh : X i ∣ p * q\nhp : p.modMonomial (Finsupp.single i 1) + X i * p.divMonomial (Finsupp.single i 1) = p\nhq : q.modMonomial (Finsupp.s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Choose.Multinomial | {
"line": 292,
"column": 10
} | {
"line": 292,
"column": 31
} | {
"line": 292,
"column": 32
} | [
{
"pp": "α : Type u_1\nR : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Semiring R\nf : α → R\na : α\ns : Finset α\nhas : a ∉ s\nih :\n ∀ (hc : (↑s).Pairwise (Commute on f)) (n : ℕ),\n (∑ i ∈ s, f i) ^ n = ∑ k ∈ s.piAntidiag n, ↑(multinomial s k) * s.noncommProd (fun i ↦ f i ^ k i) ⋯\nhc : (↑(cons a s has)).Pa... | [
"α : Type u_1\nR : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Semiring R\nf : α → R\na : α\ns : Finset α\nhas : a ∉ s\nih :\n ∀ (hc : (↑s).Pairwise (Commute on f)) (n : ℕ),\n (∑ i ∈ s, f i) ^ n = ∑ k ∈ s.piAntidiag n, ↑(multinomial s k) * s.noncommProd (fun i ↦ f i ^ k i) ⋯\nhc : (↑(cons a s has)).Pairwise (Comm... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.MvPolynomial.Division | {
"line": 325,
"column": 29
} | {
"line": 325,
"column": 50
} | {
"line": 325,
"column": 50
} | [
{
"pp": "case mp.g\nσ : Type u_1\nR : Type u_3\ninst✝¹ : CommRing R\ni : σ\np q : MvPolynomial σ R\ninst✝ : IsCancelMulZero R\nr : MvPolynomial σ R\nhp : X i * q = X i * (p.divMonomial (Finsupp.single i 1) * r)\nthis : X i ∣ p ∨ X i ∣ r\nhip : p.modMonomial (Finsupp.single i 1) = 0\n⊢ p.divMonomial (Finsupp.sin... | [
"case mp.g\nσ : Type u_1\nR : Type u_3\ninst✝¹ : CommRing R\ni : σ\np q : MvPolynomial σ R\ninst✝ : IsCancelMulZero R\nr : MvPolynomial σ R\nhp : q = p.divMonomial (Finsupp.single i 1) * r\nthis : X i ∣ p ∨ X i ∣ r\nhip : p.modMonomial (Finsupp.single i 1) = 0\n⊢ p.divMonomial (Finsupp.single i 1) ∣ q"
] | X_mul_cancel_left_iff | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.MvPolynomial.Nilpotent | {
"line": 50,
"column": 37
} | {
"line": 50,
"column": 48
} | {
"line": 50,
"column": 49
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝ : CommRing R\nn : ℕ\nP : MvPolynomial (Fin n) R\nf : Fin n ↪ σ\nH : ∀ (i : σ →₀ ℕ), IsNilpotent (coeff i ((rename ⇑f) P))\ni : Fin n →₀ ℕ\n⊢ IsNilpotent (coeff i P)",
"ppTerm": "?m.106",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"used... | [
"σ : Type u_1\nR : Type u_2\ninst✝ : CommRing R\nn : ℕ\nP : MvPolynomial (Fin n) R\nf : Fin n ↪ σ\nH : ∀ (i : σ →₀ ℕ), IsNilpotent (coeff i ((rename ⇑f) P))\ni : Fin n →₀ ℕ\n⊢ IsNilpotent (coeff i P)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.MvPolynomial.Nilpotent | {
"line": 62,
"column": 40
} | {
"line": 62,
"column": 69
} | {
"line": 62,
"column": 70
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝ : CommRing R\nP : MvPolynomial σ R\nH : IsUnit P\nn : σ →₀ ℕ\nhn : n ≠ 0\n⊢ ∃ i, n i ≠ 0",
"ppTerm": "?m.72",
"assigned": true,
"usedConstants": [
"Finsupp.instFunLike",
"Nat.instMulZeroClass",
"Exists",
"id",
"Ne",
"inst... | [
"σ : Type u_1\nR : Type u_2\ninst✝ : CommRing R\nP : MvPolynomial σ R\nH : IsUnit P\nn : σ →₀ ℕ\nhn : n ≠ 0\n⊢ ∃ i, ¬n i = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.MvPolynomial.Nilpotent | {
"line": 66,
"column": 4
} | {
"line": 66,
"column": 71
} | {
"line": 67,
"column": 4
} | [
{
"pp": "case refine_1\nσ : Type u_1\nR : Type u_2\ninst✝ : CommRing R\nP : MvPolynomial σ R\nH✝ : IsUnit P\nn : σ →₀ ℕ\nhn : n ≠ 0\ni : σ\nhi : n i ≠ 0\ne : Polynomial (MvPolynomial { b // b ≠ i } R) ≃ₐ[R] MvPolynomial σ R :=\n (optionEquivLeft R { b // b ≠ i }).symm.trans (renameEquiv R (Equiv.optionSubtypeN... | [
"σ : Type u_1\nR : Type u_2\ninst✝ : CommRing R\nP : MvPolynomial σ R\nH✝ : IsUnit P\nn : σ →₀ ℕ\nhn : n ≠ 0\ni : σ\nhi : n i ≠ 0\ne : Polynomial (MvPolynomial { b // b ≠ i } R) ≃ₐ[R] MvPolynomial σ R :=\n (optionEquivLeft R { b // b ≠ i }).symm.trans (renameEquiv R (Equiv.optionSubtypeNe i))\nH : ∀ (i_1 : { b // ... | convert! ← H (n.equivMapDomain (Equiv.optionSubtypeNe i).symm).some | Mathlib.Tactic._aux_Mathlib_Tactic_Convert___macroRules_Mathlib_Tactic_convert!_1 | Mathlib.Tactic.convert! |
Mathlib.Algebra.MvPolynomial.Nilpotent | {
"line": 72,
"column": 4
} | {
"line": 72,
"column": 15
} | {
"line": 72,
"column": 16
} | [
{
"pp": "case refine_2\nσ : Type u_1\nR : Type u_2\ninst✝ : CommRing R\nP : MvPolynomial σ R\nx✝ : IsUnit (coeff 0 P) ∧ ∀ (i : σ →₀ ℕ), i ≠ 0 → IsNilpotent (coeff i P)\nh₁ : IsUnit (coeff 0 P)\nh₂ : ∀ (i : σ →₀ ℕ), i ≠ 0 → IsNilpotent (coeff i P)\nthis : IsNilpotent (P - C (coeff 0 P))\n⊢ IsUnit P",
"ppTerm... | [
"case refine_2\nσ : Type u_1\nR : Type u_2\ninst✝ : CommRing R\nP : MvPolynomial σ R\nx✝ : IsUnit (coeff 0 P) ∧ ∀ (i : σ →₀ ℕ), i ≠ 0 → IsNilpotent (coeff i P)\nh₁ : IsUnit (coeff 0 P)\nh₂ : ∀ (i : σ →₀ ℕ), i ≠ 0 → IsNilpotent (coeff i P)\nthis : IsNilpotent (P - C (coeff 0 P))\n⊢ IsUnit P"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.MvPolynomial.Expand | {
"line": 169,
"column": 18
} | {
"line": 169,
"column": 26
} | {
"line": 169,
"column": 26
} | [
{
"pp": "σ : Type u_1\nR : Type u_3\ninst✝¹ : CommSemiring R\np : ℕ\nφ : MvPolynomial σ R\ninst✝ : DecidableEq σ\n| ((expand p) φ).support",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"Semiring.toModule",
"cong... | [
"σ : Type u_1\nR : Type u_3\ninst✝¹ : CommSemiring R\np : ℕ\nφ : MvPolynomial σ R\ninst✝ : DecidableEq σ\n| ((expand p) (∑ v ∈ φ.support, (monomial v) (coeff v φ))).support"
] | φ.as_sum | Lean.Elab.Tactic.Conv.evalRewrite | null |
Mathlib.Algebra.MvPolynomial.Division | {
"line": 374,
"column": 10
} | {
"line": 374,
"column": 29
} | {
"line": 374,
"column": 30
} | [
{
"pp": "case left\nσ : Type u_1\nR : Type u_3\ninst✝¹ : CommRing R\np q✝ : MvPolynomial σ R\ninst✝ : IsCancelMulZero R\nn✝ : σ →₀ ℕ\nhR : Nontrivial R\nd : ℕ\nhd :\n ∀ (n : σ →₀ ℕ),\n Finsupp.degree n = d →\n ∀ (p q : MvPolynomial σ R), p ∣ (monomial n) 1 * q ↔ ∃ m r, m ≤ n ∧ r ∣ q ∧ p = (monomial m) ... | [
"case left\nσ : Type u_1\nR : Type u_3\ninst✝¹ : CommRing R\np q✝ : MvPolynomial σ R\ninst✝ : IsCancelMulZero R\nn✝ : σ →₀ ℕ\nhR : Nontrivial R\nd : ℕ\nhd :\n ∀ (n : σ →₀ ℕ),\n Finsupp.degree n = d →\n ∀ (p q : MvPolynomial σ R), p ∣ (monomial n) 1 * q ↔ ∃ m r, m ≤ n ∧ r ∣ q ∧ p = (monomial m) 1 * r\nn : σ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.MvPolynomial.Funext | {
"line": 39,
"column": 4
} | {
"line": 39,
"column": 38
} | {
"line": 39,
"column": 39
} | [
{
"pp": "case zero\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np : MvPolynomial (Fin 0) R\ns : Fin 0 → Set R\nhs : ∀ (i : Fin 0), (s i).Infinite\nh : ∀ x ∈ Set.univ.pi s, (eval x) p = 0\n⊢ (isEmptyRingEquiv R (Fin 0)) p = (isEmptyRingEquiv R (Fin 0)) 0",
"ppTerm": "?zero",
"assigned": true,
... | [
"case zero\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np : MvPolynomial (Fin 0) R\ns : Fin 0 → Set R\nhs : ∀ (i : Fin 0), (s i).Infinite\nh : ∀ x ∈ Set.univ.pi s, (eval x) p = 0\n⊢ p.coeff 0 = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.MvPolynomial.Funext | {
"line": 48,
"column": 36
} | {
"line": 48,
"column": 56
} | {
"line": 48,
"column": 57
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nn : ℕ\nih :\n ∀ {p : MvPolynomial (Fin n) R} (s : Fin n → Set R),\n (∀ (i : Fin n), (s i).Infinite) → (∀ x ∈ Set.univ.pi s, (eval x) p = 0) → p = 0\np : MvPolynomial (Fin (n + 1)) R\ns : Fin (n + 1) → Set R\nhs : ∀ (i : Fin (n + 1)), (s i).Infi... | [
"R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nn : ℕ\nih :\n ∀ {p : MvPolynomial (Fin n) R} (s : Fin n → Set R),\n (∀ (i : Fin n), (s i).Infinite) → (∀ x ∈ Set.univ.pi s, (eval x) p = 0) → p = 0\np : MvPolynomial (Fin (n + 1)) R\ns : Fin (n + 1) → Set R\nhs : ∀ (i : Fin (n + 1)), (s i).Infinite\nh : ∀ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.MvPolynomial.Funext | {
"line": 48,
"column": 65
} | {
"line": 48,
"column": 76
} | {
"line": 48,
"column": 77
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nn : ℕ\nih :\n ∀ {p : MvPolynomial (Fin n) R} (s : Fin n → Set R),\n (∀ (i : Fin n), (s i).Infinite) → (∀ x ∈ Set.univ.pi s, (eval x) p = 0) → p = 0\np : MvPolynomial (Fin (n + 1)) R\ns : Fin (n + 1) → Set R\nhs : ∀ (i : Fin (n + 1)), (s i).Infi... | [
"R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nn : ℕ\nih :\n ∀ {p : MvPolynomial (Fin n) R} (s : Fin n → Set R),\n (∀ (i : Fin n), (s i).Infinite) → (∀ x ∈ Set.univ.pi s, (eval x) p = 0) → p = 0\np : MvPolynomial (Fin (n + 1)) R\ns : Fin (n + 1) → Set R\nhs : ∀ (i : Fin (n + 1)), (s i).Infinite\nh : ∀ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.MvPolynomial.Funext | {
"line": 71,
"column": 4
} | {
"line": 71,
"column": 39
} | {
"line": 72,
"column": 2
} | [
{
"pp": "case inl\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nσ : Type u_2\np✝ q : MvPolynomial σ R\ns : σ → Set R\nhs : ∀ (i : σ), (s i).Infinite\nh✝ : ∀ x ∈ Set.univ.pi s, (eval x) p✝ = (eval x) q\nn : ℕ\nf : Fin n → σ\nhf : Function.Injective f\np : MvPolynomial (Fin n) R\nh : ∀ x ∈ Set.univ.pi s... | [] | rw [hf.extend_apply]; exact hx _ ⟨⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.MvPolynomial.Funext | {
"line": 71,
"column": 4
} | {
"line": 71,
"column": 39
} | {
"line": 72,
"column": 2
} | [
{
"pp": "case inl\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nσ : Type u_2\np✝ q : MvPolynomial σ R\ns : σ → Set R\nhs : ∀ (i : σ), (s i).Infinite\nh✝ : ∀ x ∈ Set.univ.pi s, (eval x) p✝ = (eval x) q\nn : ℕ\nf : Fin n → σ\nhf : Function.Injective f\np : MvPolynomial (Fin n) R\nh : ∀ x ∈ Set.univ.pi s... | [] | rw [hf.extend_apply]; exact hx _ ⟨⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Nat.Choose.Multinomial | {
"line": 402,
"column": 34
} | {
"line": 402,
"column": 49
} | {
"line": 402,
"column": 50
} | [
{
"pp": "n : ℕ\nα : Type u_1\ninst✝ : DecidableEq α\nm : Fin (n + 1)\ns : Sym α (n - ↑m)\nx : α\nhx : x ∉ ↑s\nj : α\nhj : j ∈ ↑s\nh : x = j\n⊢ x ∈ ↑s",
"ppTerm": "?m.107",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"HSub.hSub",
"Membership.mem",
"Multise... | [
"n : ℕ\nα : Type u_1\ninst✝ : DecidableEq α\nm : Fin (n + 1)\ns : Sym α (n - ↑m)\nx : α\nhx : x ∉ ↑s\nj : α\nhj : j ∈ ↑s\nh : x = j\n⊢ j ∈ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.GameAdd | {
"line": 215,
"column": 8
} | {
"line": 215,
"column": 40
} | {
"line": 215,
"column": 41
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nrα : α → α → Prop\nrβ : β → β → Prop\na✝ : α\nb✝ : β\nC : α → α → Sort u_3\nhr : WellFounded rα\nIH : (a₁ b₁ : α) → ((a₂ b₂ : α) → GameAdd rα s(a₂, b₂) s(a₁, b₁) → C a₂ b₂) → C a₁ b₁\na b : α\n⊢ WellFounded fun x y ↦ Prod.GameAdd rα rα x y ∨ Prod.GameAdd rα rα x.swap y",
... | [
"α : Type u_1\nβ : Type u_2\nrα : α → α → Prop\nrβ : β → β → Prop\na✝ : α\nb✝ : β\nC : α → α → Sort u_3\nhr : WellFounded rα\nIH : (a₁ b₁ : α) → ((a₂ b₂ : α) → GameAdd rα s(a₂, b₂) s(a₁, b₁) → C a₂ b₂) → C a₁ b₁\na b : α\n⊢ WellFounded fun x y ↦ GameAdd rα s(x.1, x.2) s(y.1, y.2)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finsupp.WellFounded | {
"line": 44,
"column": 4
} | {
"line": 44,
"column": 41
} | {
"line": 44,
"column": 42
} | [
{
"pp": "α : Type u_1\nN : Type u_2\ninst✝ : Zero N\nr : α → α → Prop\ns : N → N → Prop\nhbot : ∀ ⦃n : N⦄, ¬s n 0\nhs : WellFounded s\nx : α →₀ N\nh : ∀ a ∈ x.support, Acc (rᶜ ⊓ fun x1 x2 ↦ x1 ≠ x2) a\n⊢ ∀ i ∈ x.toDFinsupp.support, Acc (rᶜ ⊓ fun x1 x2 ↦ x1 ≠ x2) i",
"ppTerm": "?m.50",
"assigned": true,
... | [
"α : Type u_1\nN : Type u_2\ninst✝ : Zero N\nr : α → α → Prop\ns : N → N → Prop\nhbot : ∀ ⦃n : N⦄, ¬s n 0\nhs : WellFounded s\nx : α →₀ N\nh : ∀ a ∈ x.support, Acc (rᶜ ⊓ fun x1 x2 ↦ x1 ≠ x2) a\n⊢ ∀ i ∈ x.support, Acc (rᶜ ⊓ fun x1 x2 ↦ x1 ≠ x2) i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Choose.Multinomial | {
"line": 461,
"column": 50
} | {
"line": 461,
"column": 70
} | {
"line": 461,
"column": 70
} | [
{
"pp": "case swap\nm : Multiset ℕ\nl✝ l' : List ℕ\nx y : ℕ\nl : List ℕ\n⊢ (y + (x + l.sum)).choose (y + (x + l.sum) - y) * (x + l.sum).choose x * l.multinomial =\n (x + (y + l.sum)).choose x * (y + l.sum).choose y * l.multinomial",
"ppTerm": "?swap",
"assigned": true,
"usedConstants": [
"E... | [
"case swap\nm : Multiset ℕ\nl✝ l' : List ℕ\nx y : ℕ\nl : List ℕ\n⊢ (y + (x + l.sum)).choose (x + l.sum) * (x + l.sum).choose x * l.multinomial =\n (x + (y + l.sum)).choose x * (y + l.sum).choose y * l.multinomial"
] | add_tsub_cancel_left | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Nat.Choose.Multinomial | {
"line": 462,
"column": 62
} | {
"line": 462,
"column": 82
} | {
"line": 462,
"column": 82
} | [
{
"pp": "case swap\nm : Multiset ℕ\nl✝ l' : List ℕ\nx y : ℕ\nl : List ℕ\n⊢ (x + (y + l.sum)).choose x * (x + (y + l.sum) - x).choose (x + l.sum - x) * l.multinomial =\n (x + (y + l.sum)).choose x * (y + l.sum).choose y * l.multinomial",
"ppTerm": "?swap",
"assigned": true,
"usedConstants": [
... | [
"case swap\nm : Multiset ℕ\nl✝ l' : List ℕ\nx y : ℕ\nl : List ℕ\n⊢ (x + (y + l.sum)).choose x * (y + l.sum).choose (x + l.sum - x) * l.multinomial =\n (x + (y + l.sum)).choose x * (y + l.sum).choose y * l.multinomial"
] | add_tsub_cancel_left | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Finsupp.MonomialOrder | {
"line": 147,
"column": 32
} | {
"line": 147,
"column": 43
} | {
"line": 147,
"column": 44
} | [
{
"pp": "α : Type u_1\nN : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : AddCommMonoid N\ninst✝¹ : PartialOrder N\ninst✝ : IsOrderedCancelAddMonoid N\na b : Lex (α →₀ N)\nh : a ≤ b\nc : Lex (α →₀ N)\n⊢ a + c ≤ b + c",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preord... | [
"α : Type u_1\nN : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : AddCommMonoid N\ninst✝¹ : PartialOrder N\ninst✝ : IsOrderedCancelAddMonoid N\na b : Lex (α →₀ N)\nh : a ≤ b\nc : Lex (α →₀ N)\n⊢ a ≤ b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finsupp.MonomialOrder | {
"line": 146,
"column": 38
} | {
"line": 146,
"column": 76
} | {
"line": 146,
"column": 77
} | [
{
"pp": "α : Type u_1\nN : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : AddCommMonoid N\ninst✝¹ : PartialOrder N\ninst✝ : IsOrderedCancelAddMonoid N\na b c : Lex (α →₀ N)\nh : a + b ≤ a + c\n⊢ b ≤ c",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"α : Type u_1\nN : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : AddCommMonoid N\ninst✝¹ : PartialOrder N\ninst✝ : IsOrderedCancelAddMonoid N\na b c : Lex (α →₀ N)\nh : a + b ≤ a + c\n⊢ b ≤ c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Basic | {
"line": 884,
"column": 26
} | {
"line": 884,
"column": 60
} | {
"line": 884,
"column": 61
} | [
{
"pp": "ι : Type u\nE : Type v\nF : Type w\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\nI : Box ι\ninst✝ : Fintype ι\nl : IntegrationParams\nf : (ι → ℝ) → E\nvol : ι →ᵇᵃ[⊤] E →L[ℝ] F\nhl : l ≤ Henstock\nB : ι →ᵇᵃ[↑I] ℝ\nhB0 : ∀ (J : Box ι), ... | [
"ι : Type u\nE : Type v\nF : Type w\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\nI : Box ι\ninst✝ : Fintype ι\nl : IntegrationParams\nf : (ι → ℝ) → E\nvol : ι →ᵇᵃ[⊤] E →L[ℝ] F\nhl : l ≤ Henstock\nB : ι →ᵇᵃ[↑I] ℝ\nhB0 : ∀ (J : Box ι), 0 ≤ B J\ng :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.DFinsupp.WellFounded | {
"line": 100,
"column": 8
} | {
"line": 100,
"column": 24
} | {
"line": 100,
"column": 25
} | [
{
"pp": "case pos.hnc\nι : Type u_1\nα : ι → Type u_2\ninst✝¹ : (i : ι) → Zero (α i)\nr : ι → ι → Prop\ns : (i : ι) → α i → α i → Prop\ninst✝ : (i : ι) → (s : Set ι) → Decidable (i ∈ s)\np : Set ι\nx₁ x₂ x : Π₀ (i : ι), α i\ni : ι\nhr : ∀ (j : ι), r j i → x j = if j ∈ p then x₁ j else x₂ j\nhp : i ∉ p\nhs : s i... | [
"case pos.hnc\nι : Type u_1\nα : ι → Type u_2\ninst✝¹ : (i : ι) → Zero (α i)\nr : ι → ι → Prop\ns : (i : ι) → α i → α i → Prop\ninst✝ : (i : ι) → (s : Set ι) → Decidable (i ∈ s)\np : Set ι\nx₁ x₂ x : Π₀ (i : ι), α i\ni : ι\nhr : ∀ (j : ι), r j i → x j = if j ∈ p then x₁ j else x₂ j\nhp : i ∉ p\nhs : s i (x i) (x₂ i... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Basic | {
"line": 904,
"column": 4
} | {
"line": 904,
"column": 93
} | {
"line": 904,
"column": 94
} | [
{
"pp": "ι : Type u\nE : Type v\nF : Type w\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\nI : Box ι\ninst✝ : Fintype ι\nf : (ι → ℝ) → E\nvol : ι →ᵇᵃ[⊤] E →L[ℝ] F\nB : ι →ᵇᵃ[↑I] ℝ\nhB0 : ∀ (J : Box ι), 0 ≤ B J\ng : ι →ᵇᵃ[↑I] F\nH :\n ∀ (x : ℝ≥... | [
"ι : Type u\nE : Type v\nF : Type w\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\nI : Box ι\ninst✝ : Fintype ι\nf : (ι → ℝ) → E\nvol : ι →ᵇᵃ[⊤] E →L[ℝ] F\nB : ι →ᵇᵃ[↑I] ℝ\nhB0 : ∀ (J : Box ι), 0 ≤ B J\ng : ι →ᵇᵃ[↑I] F\nH :\n ∀ (x : ℝ≥0),\n ∀ x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.DFinsupp.WellFounded | {
"line": 128,
"column": 45
} | {
"line": 128,
"column": 67
} | {
"line": 128,
"column": 67
} | [
{
"pp": "ι : Type u_1\nα : ι → Type u_2\ninst✝² : (i : ι) → Zero (α i)\nr : ι → ι → Prop\ns : (i : ι) → α i → α i → Prop\nhbot : ∀ ⦃i : ι⦄ ⦃a : α i⦄, ¬s i a 0\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → (x : α i) → Decidable (x ≠ 0)\nb : ι\nt : Finset ι\nhb : b ∉ t\nih :\n ∀ (x : Π₀ (i : ι), α i), x.support = t... | [
"ι : Type u_1\nα : ι → Type u_2\ninst✝² : (i : ι) → Zero (α i)\nr : ι → ι → Prop\ns : (i : ι) → α i → α i → Prop\nhbot : ∀ ⦃i : ι⦄ ⦃a : α i⦄, ¬s i a 0\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → (x : α i) → Decidable (x ≠ 0)\nb : ι\nt : Finset ι\nhb : b ∉ t\nih :\n ∀ (x : Π₀ (i : ι), α i), x.support = t → (∀ i ∈ t,... | Finset.erase_insert hb | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.DFinsupp.WellFounded | {
"line": 140,
"column": 6
} | {
"line": 140,
"column": 18
} | {
"line": 140,
"column": 18
} | [
{
"pp": "case intro\nι : Type u_1\nα : ι → Type u_2\ninst✝¹ : (i : ι) → Zero (α i)\nr : ι → ι → Prop\ns : (i : ι) → α i → α i → Prop\nhbot : ∀ ⦃i : ι⦄ ⦃a : α i⦄, ¬s i a 0\nhs✝ : ∀ (i : ι), WellFounded (s i)\ninst✝ : DecidableEq ι\ni✝ i : ι\nh✝ : ∀ (y : ι), (rᶜ ⊓ fun x1 x2 ↦ x1 ≠ x2) y i → Acc (rᶜ ⊓ fun x1 x2 ↦ ... | [
"case intro\nι : Type u_1\nα : ι → Type u_2\ninst✝¹ : (i : ι) → Zero (α i)\nr : ι → ι → Prop\ns : (i : ι) → α i → α i → Prop\nhbot : ∀ ⦃i : ι⦄ ⦃a : α i⦄, ¬s i a 0\nhs✝ : ∀ (i : ι), WellFounded (s i)\ninst✝ : DecidableEq ι\ni✝ i : ι\nh✝ : ∀ (y : ι), (rᶜ ⊓ fun x1 x2 ↦ x1 ≠ x2) y i → Acc (rᶜ ⊓ fun x1 x2 ↦ x1 ≠ x2) y\n... | single_apply | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Finsupp.MonomialOrder.DegLex | {
"line": 151,
"column": 4
} | {
"line": 151,
"column": 39
} | {
"line": 151,
"column": 40
} | [
{
"pp": "α : Type u_1\ninst✝ : LinearOrder α\na b : DegLex (α →₀ ℕ)\nh :\n degree (ofDegLex a) < degree (ofDegLex b) ∨\n degree (ofDegLex a) = degree (ofDegLex b) ∧ toLex (ofDegLex a) ≤ toLex (ofDegLex b)\nc : DegLex (α →₀ ℕ)\n⊢ degree (ofDegLex (a + c)) < degree (ofDegLex (b + c)) ∨\n degree (ofDegLex (... | [
"α : Type u_1\ninst✝ : LinearOrder α\na b : DegLex (α →₀ ℕ)\nh :\n degree (ofDegLex a) < degree (ofDegLex b) ∨\n degree (ofDegLex a) = degree (ofDegLex b) ∧ toLex (ofDegLex a) ≤ toLex (ofDegLex b)\nc : DegLex (α →₀ ℕ)\n⊢ degree (ofDegLex a) < degree (ofDegLex b) ∨\n degree (ofDegLex a) = degree (ofDegLex b) ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finsupp.MonomialOrder.DegLex | {
"line": 147,
"column": 4
} | {
"line": 148,
"column": 32
} | {
"line": 148,
"column": 33
} | [
{
"pp": "α : Type u_1\ninst✝ : LinearOrder α\na b c : DegLex (α →₀ ℕ)\nh :\n degree (ofDegLex (a + b)) < degree (ofDegLex (a + c)) ∨\n degree (ofDegLex (a + b)) = degree (ofDegLex (a + c)) ∧ toLex (ofDegLex (a + b)) ≤ toLex (ofDegLex (a + c))\n⊢ degree (ofDegLex b) < degree (ofDegLex c) ∨\n degree (ofDeg... | [
"α : Type u_1\ninst✝ : LinearOrder α\na b c : DegLex (α →₀ ℕ)\nh :\n degree (ofDegLex (a + b)) < degree (ofDegLex (a + c)) ∨\n degree (ofDegLex (a + b)) = degree (ofDegLex (a + c)) ∧ toLex (ofDegLex (a + b)) ≤ toLex (ofDegLex (a + c))\n⊢ degree (ofDegLex b) < degree (ofDegLex c) ∨\n degree (ofDegLex b) = deg... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.MvPolynomial.NoZeroDivisors | {
"line": 102,
"column": 6
} | {
"line": 102,
"column": 17
} | {
"line": 102,
"column": 18
} | [
{
"pp": "R : Type u_1\nσ : Type u_2\ninst✝¹ : CommSemiring R\ninst✝ : NoZeroDivisors R\nf : MvPolynomial σ R\na : R\nha : a ≠ 0\nhf : ∀ (i : σ →₀ ℕ), coeff 0 f ∣ coeff i (C a)\nthis : f = C (coeff 0 f)\n⊢ coeff 0 f ∣ a",
"ppTerm": "?m.81",
"assigned": false,
"usedConstants": [],
"usedFVars": [],... | [
"R : Type u_1\nσ : Type u_2\ninst✝¹ : CommSemiring R\ninst✝ : NoZeroDivisors R\nf : MvPolynomial σ R\na : R\nha : a ≠ 0\nhf : ∀ (i : σ →₀ ℕ), coeff 0 f ∣ coeff i (C a)\nthis : f = C (coeff 0 f)\n⊢ coeff 0 f ∣ a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.MvPolynomial.NoZeroDivisors | {
"line": 104,
"column": 4
} | {
"line": 104,
"column": 15
} | {
"line": 104,
"column": 16
} | [
{
"pp": "case h\nR : Type u_1\nσ : Type u_2\ninst✝¹ : CommSemiring R\ninst✝ : NoZeroDivisors R\nf : MvPolynomial σ R\na : R\nha : a ≠ 0\nhf : f ∣ C a\n⊢ f.totalDegree ≤ 0",
"ppTerm": "?h",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.instMulZeroClass",
"LinearOrderedCommMono... | [
"case h\nR : Type u_1\nσ : Type u_2\ninst✝¹ : CommSemiring R\ninst✝ : NoZeroDivisors R\nf : MvPolynomial σ R\na : R\nha : a ≠ 0\nhf : f ∣ C a\n⊢ f.totalDegree = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.MvPolynomial.NoZeroDivisors | {
"line": 123,
"column": 59
} | {
"line": 123,
"column": 70
} | {
"line": 123,
"column": 71
} | [
{
"pp": "R : Type u_1\nσ : Type u_2\ninst✝ : CommSemiring R\np : MvPolynomial σ R\nj : σ\nc : R\nhc : c ∈ R⁰\nhp : ¬p = 0\nh : ((optionEquivLeft R { b // b ≠ j }) ((rename ⇑(optionSubtypeNe j).symm) p)).leadingCoeff = 0\n⊢ (rename ⇑?m.78) p = (rename ⇑?m.78) 0",
"ppTerm": "?m.81",
"assigned": true,
... | [
"R : Type u_1\nσ : Type u_2\ninst✝ : CommSemiring R\np : MvPolynomial σ R\nj : σ\nc : R\nhc : c ∈ R⁰\nhp : ¬p = 0\nh : ((optionEquivLeft R { b // b ≠ j }) ((rename ⇑(optionSubtypeNe j).symm) p)).leadingCoeff = 0\n⊢ (rename ⇑?m.78) p = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.MvPolynomial.NoZeroDivisors | {
"line": 129,
"column": 4
} | {
"line": 129,
"column": 15
} | {
"line": 129,
"column": 16
} | [
{
"pp": "case neg\nR : Type u_1\nσ : Type u_2\ninst✝ : CommSemiring R\np : MvPolynomial σ R\nj : σ\nc : R\nhc : c ∈ R⁰\nhp : ¬p = 0\nhp' : C c * ((optionEquivLeft R { b // ¬b = j }) ((rename ⇑(optionSubtypeNe j).symm) p)).leadingCoeff = 0\nm : { b // b ≠ j } →₀ ℕ\n⊢ c * coeff m ((optionEquivLeft R { b // b ≠ j ... | [
"case neg\nR : Type u_1\nσ : Type u_2\ninst✝ : CommSemiring R\np : MvPolynomial σ R\nj : σ\nc : R\nhc : c ∈ R⁰\nhp : ¬p = 0\nhp' : C c * ((optionEquivLeft R { b // ¬b = j }) ((rename ⇑(optionSubtypeNe j).symm) p)).leadingCoeff = 0\nm : { b // b ≠ j } →₀ ℕ\n⊢ c * coeff m ((optionEquivLeft R { b // ¬b = j }) ((rename... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPolynomial.MonomialOrder | {
"line": 336,
"column": 4
} | {
"line": 336,
"column": 63
} | {
"line": 336,
"column": 64
} | [
{
"pp": "case neg\nσ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommSemiring R\nf g : MvPolynomial σ R\nb : σ →₀ ℕ\nhb : b ∈ (f + g).support\nhf : coeff b f = 0\n⊢ b ∈ g.support",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.instMulZeroClass",
... | [
"case neg\nσ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommSemiring R\nf g : MvPolynomial σ R\nb : σ →₀ ℕ\nhb : b ∈ (f + g).support\nhf : coeff b f = 0\n⊢ coeff b g ≠ 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Antidiag.FinsuppEquiv | {
"line": 49,
"column": 4
} | {
"line": 49,
"column": 66
} | {
"line": 49,
"column": 67
} | [
{
"pp": "ι : Type u_1\nμ : Type u_2\nμ' : Type u_3\ninst✝³ : DecidableEq ι\ninst✝² : AddCommMonoid μ\ninst✝¹ : HasAntidiagonal μ\ninst✝ : DecidableEq μ\ns : Finset ι\nn : μ\nf : ↥(s.finsuppAntidiag n)\nhf : ((↑f).sum fun x x_1 ↦ x_1) = n ∧ (↑f).support ⊆ s\n⊢ ((subtypeDomain (fun x ↦ x ∈ s) ↑f).sum fun x ↦ id) ... | [
"ι : Type u_1\nμ : Type u_2\nμ' : Type u_3\ninst✝³ : DecidableEq ι\ninst✝² : AddCommMonoid μ\ninst✝¹ : HasAntidiagonal μ\ninst✝ : DecidableEq μ\ns : Finset ι\nn : μ\nf : ↥(s.finsuppAntidiag n)\nhf : ((↑f).sum fun x x_1 ↦ x_1) = n ∧ (↑f).support ⊆ s\n⊢ ∑ x ∈ (↑f).support, ↑f x = n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Antidiag.FinsuppEquiv | {
"line": 51,
"column": 8
} | {
"line": 51,
"column": 25
} | {
"line": 51,
"column": 26
} | [
{
"pp": "ι : Type u_1\nμ : Type u_2\nμ' : Type u_3\ninst✝³ : DecidableEq ι\ninst✝² : AddCommMonoid μ\ninst✝¹ : HasAntidiagonal μ\ninst✝ : DecidableEq μ\ns : Finset ι\nn : μ\nf : { P // (P.sum fun x ↦ id) = n }\n⊢ ((↑f).extendDomain.sum fun x x_1 ↦ x_1) = n",
"ppTerm": "?m.98",
"assigned": true,
"use... | [
"ι : Type u_1\nμ : Type u_2\nμ' : Type u_3\ninst✝³ : DecidableEq ι\ninst✝² : AddCommMonoid μ\ninst✝¹ : HasAntidiagonal μ\ninst✝ : DecidableEq μ\ns : Finset ι\nn : μ\nf : { P // (P.sum fun x ↦ id) = n }\n⊢ ∑ x ∈ (↑f).support, ↑f x = n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Sym.Card | {
"line": 135,
"column": 12
} | {
"line": 135,
"column": 33
} | {
"line": 135,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\ns : Finset α\na b : α\nha : a ∈ s\nhb : b ∈ s\nhab : a ≠ b ∨ b ≠ a\n⊢ (a, b) ∉ {(b, a)}",
"ppTerm": "?m.75",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"and_self",
"_private.Mathlib.Data.Sym.Card.0.Sym2.two_mul_car... | [
"α : Type u_1\ninst✝ : DecidableEq α\ns : Finset α\na b : α\nha : a ∈ s\nhb : b ∈ s\nhab : a ≠ b ∨ b ≠ a\n⊢ ¬a = b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPolynomial.MonomialOrder | {
"line": 396,
"column": 4
} | {
"line": 396,
"column": 43
} | {
"line": 397,
"column": 2
} | [
{
"pp": "case pos\nσ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommSemiring R\nf g : MvPolynomial σ R\nc : σ →₀ ℕ\nhc : m.toSyn (m.degree f + m.degree g) < m.toSyn c\nd e : σ →₀ ℕ\nhde : d + e = c\nhd : m.toSyn (m.degree f) < m.toSyn d\n⊢ coeff d f * coeff e g = 0",
"ppTerm": "?pos✝",
"assi... | [] | rw [m.coeff_eq_zero_of_lt hd, zero_mul] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.RingTheory.MvPolynomial.MonomialOrder | {
"line": 396,
"column": 4
} | {
"line": 396,
"column": 43
} | {
"line": 397,
"column": 2
} | [
{
"pp": "case pos\nσ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommSemiring R\nf g : MvPolynomial σ R\nc : σ →₀ ℕ\nhc : m.toSyn (m.degree f + m.degree g) < m.toSyn c\nd e : σ →₀ ℕ\nhde : d + e = c\nhd : m.toSyn (m.degree f) < m.toSyn d\n⊢ coeff d f * coeff e g = 0",
"ppTerm": "?pos✝",
"assi... | [] | rw [m.coeff_eq_zero_of_lt hd, zero_mul] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.MvPolynomial.MonomialOrder | {
"line": 396,
"column": 4
} | {
"line": 396,
"column": 43
} | {
"line": 397,
"column": 2
} | [
{
"pp": "case pos\nσ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommSemiring R\nf g : MvPolynomial σ R\nc : σ →₀ ℕ\nhc : m.toSyn (m.degree f + m.degree g) < m.toSyn c\nd e : σ →₀ ℕ\nhde : d + e = c\nhd : m.toSyn (m.degree f) < m.toSyn d\n⊢ coeff d f * coeff e g = 0",
"ppTerm": "?pos✝",
"assi... | [] | rw [m.coeff_eq_zero_of_lt hd, zero_mul] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.UniqueFactorizationDomain.Nat | {
"line": 37,
"column": 4
} | {
"line": 37,
"column": 46
} | {
"line": 38,
"column": 4
} | [
{
"pp": "case succ.succ\na n✝ : ℕ\nh : DvdNotUnit (a + 1) (n✝ + 1)\n⊢ (if a + 1 = 0 then ⊤ else ↑(a + 1)) < if n✝ + 1 = 0 then ⊤ else ↑(n✝ + 1)",
"ppTerm": "?succ.succ",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Dvd.dvd",
"ENat.instNatCast",
"instTopENat",
"Nat.i... | [
"case succ.succ\na n✝ : ℕ\nh : DvdNotUnit (a + 1) (n✝ + 1)\nh1 : a + 1 ∣ n✝ + 1\nh2 : ¬n✝ + 1 ∣ a + 1\n⊢ (if a + 1 = 0 then ⊤ else ↑(a + 1)) < if n✝ + 1 = 0 then ⊤ else ↑(n✝ + 1)"
] | obtain ⟨h1, h2⟩ := dvd_and_not_dvd_iff.2 h | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.RingTheory.MvPolynomial.MonomialOrder | {
"line": 421,
"column": 8
} | {
"line": 421,
"column": 41
} | {
"line": 421,
"column": 42
} | [
{
"pp": "σ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommSemiring R\nf g : MvPolynomial σ R\na b : σ →₀ ℕ\nha : m.toSyn (m.degree f) ≤ m.toSyn a\nhb : m.toSyn (m.degree g) ≤ m.toSyn b\nc d : σ →₀ ℕ\nh : (c, d) ≠ (a, b)\nhcd : c + d = a + b\nhf : m.toSyn c ≤ m.toSyn (m.degree f)\nhf' : m.toSyn d ≤ m... | [
"σ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommSemiring R\nf g : MvPolynomial σ R\na b : σ →₀ ℕ\nha : m.toSyn (m.degree f) ≤ m.toSyn a\nhb : m.toSyn (m.degree g) ≤ m.toSyn b\nc d : σ →₀ ℕ\nh : (c, d) ≠ (a, b)\nhcd : c + d = a + b\nhf : m.toSyn c ≤ m.toSyn (m.degree f)\nhf' : m.toSyn d ≤ m.toSyn (m.de... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPolynomial.MonomialOrder | {
"line": 489,
"column": 68
} | {
"line": 492,
"column": 89
} | {
"line": 494,
"column": 0
} | [
{
"pp": "σ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommSemiring R\nf g : MvPolynomial σ R\nhf : IsRegular (m.leadingCoeff f)\n⊢ m.leadingCoeff (f * g) = m.leadingCoeff f * m.leadingCoeff g",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Nat.instMulZeroClass",
"A... | [] | by
by_cases hg : g = 0
· simp [hg]
· simp only [leadingCoeff, degree_mul_of_isRegular_left hf hg, coeff_mul_of_degree_add] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.MvPolynomial.MonomialOrder | {
"line": 632,
"column": 2
} | {
"line": 637,
"column": 31
} | {
"line": 639,
"column": 0
} | [
{
"pp": "σ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommSemiring R\nι : Type u_3\nP : ι → MvPolynomial σ R\ns : Finset ι\n⊢ coeff (∑ i ∈ s, m.degree (P i)) (∏ i ∈ s, P i) = ∏ i ∈ s, m.leadingCoeff (P i)",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Mo... | [] | induction s using Finset.induction_on with
| empty => simp
| insert a s has hrec =>
simp only [Finset.prod_insert has, Finset.sum_insert has]
rw [coeff_mul_of_add_of_degree_le (le_of_eq rfl) degree_prod_le]
exact congr_arg₂ _ rfl hrec | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | Lean.Parser.Tactic.induction |
Mathlib.RingTheory.MvPolynomial.MonomialOrder | {
"line": 632,
"column": 2
} | {
"line": 637,
"column": 31
} | {
"line": 639,
"column": 0
} | [
{
"pp": "σ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommSemiring R\nι : Type u_3\nP : ι → MvPolynomial σ R\ns : Finset ι\n⊢ coeff (∑ i ∈ s, m.degree (P i)) (∏ i ∈ s, P i) = ∏ i ∈ s, m.leadingCoeff (P i)",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Mo... | [] | induction s using Finset.induction_on with
| empty => simp
| insert a s has hrec =>
simp only [Finset.prod_insert has, Finset.sum_insert has]
rw [coeff_mul_of_add_of_degree_le (le_of_eq rfl) degree_prod_le]
exact congr_arg₂ _ rfl hrec | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.MvPolynomial.MonomialOrder | {
"line": 632,
"column": 2
} | {
"line": 637,
"column": 31
} | {
"line": 639,
"column": 0
} | [
{
"pp": "σ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommSemiring R\nι : Type u_3\nP : ι → MvPolynomial σ R\ns : Finset ι\n⊢ coeff (∑ i ∈ s, m.degree (P i)) (∏ i ∈ s, P i) = ∏ i ∈ s, m.leadingCoeff (P i)",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Mo... | [] | induction s using Finset.induction_on with
| empty => simp
| insert a s has hrec =>
simp only [Finset.prod_insert has, Finset.sum_insert has]
rw [coeff_mul_of_add_of_degree_le (le_of_eq rfl) degree_prod_le]
exact congr_arg₂ _ rfl hrec | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.MvPolynomial.MonomialOrder | {
"line": 630,
"column": 86
} | {
"line": 637,
"column": 31
} | {
"line": 639,
"column": 0
} | [
{
"pp": "σ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommSemiring R\nι : Type u_3\nP : ι → MvPolynomial σ R\ns : Finset ι\n⊢ coeff (∑ i ∈ s, m.degree (P i)) (∏ i ∈ s, P i) = ∏ i ∈ s, m.leadingCoeff (P i)",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Mo... | [] | by
classical
induction s using Finset.induction_on with
| empty => simp
| insert a s has hrec =>
simp only [Finset.prod_insert has, Finset.sum_insert has]
rw [coeff_mul_of_add_of_degree_le (le_of_eq rfl) degree_prod_le]
exact congr_arg₂ _ rfl hrec | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.MvPolynomial.MonomialOrder | {
"line": 691,
"column": 69
} | {
"line": 692,
"column": 75
} | {
"line": 694,
"column": 0
} | [
{
"pp": "σ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommSemiring R\nι : Type u_3\nP : ι → MvPolynomial σ R\ns : Finset ι\nH : ∀ i ∈ s, IsRegular (m.leadingCoeff (P i))\n⊢ m.leadingCoeff (∏ i ∈ s, P i) = ∏ i ∈ s, m.leadingCoeff (P i)",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants... | [] | by
simp only [leadingCoeff, degree_prod_of_regular H, coeff_prod_sum_degree] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Nat.Squarefree | {
"line": 59,
"column": 4
} | {
"line": 59,
"column": 50
} | {
"line": 60,
"column": 2
} | [
{
"pp": "case pos\nn p : ℕ\nhn : ∀ (x : ℕ), emultiplicity x n ≤ 1 ∨ IsUnit x\nhn' : n ≠ 0\nhp : Prime p\nthis : emultiplicity p n ≤ 1\n⊢ multiplicity p n ≤ 1",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Nat.instMonoid",
"multiplicity_le_of_emultiplicity_le",
"instOfNa... | [] | exact multiplicity_le_of_emultiplicity_le this | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.RingTheory.MvPolynomial.MonomialOrder | {
"line": 737,
"column": 2
} | {
"line": 737,
"column": 86
} | {
"line": 738,
"column": 2
} | [
{
"pp": "σ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommSemiring R\nf : MvPolynomial σ R\n⊢ m.degree (m.leadingTerm f) = m.degree f",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MonomialOrder.degree_monomial",
"Nat.instMulZeroClass",
"AddM... | [
"σ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommSemiring R\nf : MvPolynomial σ R\n⊢ f = 0 → 0 = m.degree f"
] | simp only [leadingTerm, degree_monomial, leadingCoeff_eq_zero_iff, ite_eq_right_iff] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.RingTheory.MvPolynomial.MonomialOrder | {
"line": 780,
"column": 2
} | {
"line": 780,
"column": 34
} | {
"line": 780,
"column": 35
} | [
{
"pp": "σ✝ : Type u_1\nm✝ : MonomialOrder σ✝\nR✝ : Type u_2\ninst✝² : CommSemiring R✝\nσ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝¹ : CommSemiring R\ninst✝ : NoZeroDivisors R\np p' q : MvPolynomial σ R\nhp : p ≠ 0\nhq : q ≠ 0\nh : m.toSyn (m.degree (p * q)) < m.toSyn (m.degree p' + m.degree q)\n⊢ m.... | [
"σ✝ : Type u_1\nm✝ : MonomialOrder σ✝\nR✝ : Type u_2\ninst✝² : CommSemiring R✝\nσ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝¹ : CommSemiring R\ninst✝ : NoZeroDivisors R\np p' q : MvPolynomial σ R\nhp : p ≠ 0\nhq : q ≠ 0\nh : m.toSyn (m.degree (p * q)) < m.toSyn (m.degree p' + m.degree q)\n⊢ m.toSyn (m.deg... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPolynomial.MonomialOrder | {
"line": 787,
"column": 2
} | {
"line": 787,
"column": 92
} | {
"line": 787,
"column": 93
} | [
{
"pp": "σ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝¹ : CommSemiring R\ninst✝ : NoZeroDivisors R\np p' q : MvPolynomial σ R\nhp : p ≠ 0\nhq : q ≠ 0\nh : m.toSyn (m.degree p) < m.toSyn (m.degree p')\n⊢ m.toSyn (m.degree (p * q)) < m.toSyn (m.degree (p' * q))",
"ppTerm": "?m.55",
"assigned": tr... | [
"σ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝¹ : CommSemiring R\ninst✝ : NoZeroDivisors R\np p' q : MvPolynomial σ R\nhp : p ≠ 0\nhq : q ≠ 0\nh : m.toSyn (m.degree p) < m.toSyn (m.degree p')\n⊢ m.toSyn (m.degree p) < m.toSyn (m.degree p')"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPolynomial.MonomialOrder | {
"line": 1002,
"column": 2
} | {
"line": 1002,
"column": 17
} | {
"line": 1002,
"column": 18
} | [
{
"pp": "σ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommRing R\nf g : MvPolynomial σ R\nh : m.degree f = m.degree g\nhs : m.sPolynomial f g ≠ 0\n⊢ m.toSyn (m.degree (m.sPolynomial f g)) < m.toSyn (m.degree f)",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"σ : Type u_1\nm : MonomialOrder σ\nR : Type u_2\ninst✝ : CommRing R\nf g : MvPolynomial σ R\nh : m.degree f = m.degree g\nhs : m.sPolynomial f g ≠ 0\n⊢ m.toSyn (m.degree (m.sPolynomial f g)) < m.toSyn (m.degree g)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.MvPolynomial.SchwartzZippel | {
"line": 164,
"column": 12
} | {
"line": 164,
"column": 23
} | {
"line": 164,
"column": 24
} | [
{
"pp": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : DecidableEq R\nn : ℕ\np : MvPolynomial (Fin (n + 1)) R\nhp : p ≠ 0\nS : Fin (n + 1) → Finset R\np' : Polynomial (MvPolynomial (Fin n) R) := (finSuccEquiv R n) p\nhp' : p' = (finSuccEquiv R n) p\nk : ℕ := p'.natDegree\nhk : k = p'.natDegree... | [
"R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : DecidableEq R\nn : ℕ\np : MvPolynomial (Fin (n + 1)) R\nhp : p ≠ 0\nS : Fin (n + 1) → Finset R\np' : Polynomial (MvPolynomial (Fin n) R) := (finSuccEquiv R n) p\nhp' : p' = (finSuccEquiv R n) p\nk : ℕ := p'.natDegree\nhk : k = p'.natDegree\npₖ : MvPol... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ArithmeticFunction.Defs | {
"line": 409,
"column": 48
} | {
"line": 409,
"column": 59
} | {
"line": 409,
"column": 60
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nf : ArithmeticFunction R\nthis : Invertible (f 1) → Invertible f\n⊢ IsUnit (f 1) → IsUnit f",
"ppTerm": "?m.86",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_1\ninst✝ : CommRing R\nf : ArithmeticFunction R\nthis : Invertible (f 1) → Invertible f\n⊢ IsUnit (f 1) → IsUnit f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ArithmeticFunction.Defs | {
"line": 409,
"column": 4
} | {
"line": 410,
"column": 86
} | {
"line": 412,
"column": 0
} | [
{
"pp": "case mpr\nR : Type u_1\ninst✝ : CommRing R\nf : ArithmeticFunction R\n⊢ IsUnit (f 1) → IsUnit f",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"ArithmeticFunction.instFunLikeNat",
"ArithmeticFunction.instMul",
"Monoid.toMulOneClass",
"... | [] | suffices Invertible (f 1) → Invertible f by simpa using Nonempty.map this
exact fun hf ↦ ⟨_, dirichletInverse_mul_self f hf, self_mul_dirichletInverse f hf⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.ArithmeticFunction.Defs | {
"line": 409,
"column": 4
} | {
"line": 410,
"column": 86
} | {
"line": 412,
"column": 0
} | [
{
"pp": "case mpr\nR : Type u_1\ninst✝ : CommRing R\nf : ArithmeticFunction R\n⊢ IsUnit (f 1) → IsUnit f",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"ArithmeticFunction.instFunLikeNat",
"ArithmeticFunction.instMul",
"Monoid.toMulOneClass",
"... | [] | suffices Invertible (f 1) → Invertible f by simpa using Nonempty.map this
exact fun hf ↦ ⟨_, dirichletInverse_mul_self f hf, self_mul_dirichletInverse f hf⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Nat.Squarefree | {
"line": 362,
"column": 2
} | {
"line": 362,
"column": 49
} | {
"line": 363,
"column": 4
} | [
{
"pp": "m n : ℕ\nhm : Squarefree m\nhn : n ≠ 0\nthis : (m / m.gcd n).Coprime (m.gcd n)\n⊢ (m / m.gcd n).Coprime n",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"m n : ℕ\nhm : Squarefree m\nhn : n ≠ 0\nthis : (m / m.gcd n).Coprime (m.gcd n)\n⊢ (m / m.gcd n).Coprime n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Factorization.PrimePow | {
"line": 133,
"column": 4
} | {
"line": 133,
"column": 15
} | {
"line": 133,
"column": 16
} | [
{
"pp": "a b : ℕ\nhab : a.Coprime b\nha : a ≠ 0\nhb : b ≠ 0\np k : ℕ\nhp : Prime p\nleft✝ : 0 < k\nhn : IsPrimePow (p ^ k)\nt : p ∈ a.factorization.support ∩ b.factorization.support\n⊢ False",
"ppTerm": "?m.168",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"a b : ℕ\nhab : a.Coprime b\nha : a ≠ 0\nhb : b ≠ 0\np k : ℕ\nhp : Prime p\nleft✝ : 0 < k\nhn : IsPrimePow (p ^ k)\nt : p ∈ a.factorization.support ∩ b.factorization.support\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ArithmeticFunction.Misc | {
"line": 197,
"column": 13
} | {
"line": 197,
"column": 27
} | {
"line": 197,
"column": 27
} | [
{
"pp": "k x✝ : ℕ\n⊢ (ζ * pow k) x✝ = { toFun := fun n ↦ ∑ d ∈ n.divisors, d ^ k, map_zero' := ⋯ } x✝",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.instMulZeroClass",
"HMul.hMul",
"ArithmeticFunction.instFunLikeNat",
"ArithmeticFunction.instMu... | [
"k x✝ : ℕ\n⊢ ∑ i ∈ x✝.divisors, (pow k) i = { toFun := fun n ↦ ∑ d ∈ n.divisors, d ^ k, map_zero' := ⋯ } x✝"
] | zeta_mul_apply | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Nat.Factorization.PrimePow | {
"line": 192,
"column": 2
} | {
"line": 192,
"column": 13
} | {
"line": 192,
"column": 14
} | [
{
"pp": "p a m n : ℕ\nhp : Prime p\nh : p ^ m = a ^ n\nthis : Finsupp.single p m = n • a.factorization\n⊢ m = n * a.factorization p",
"ppTerm": "?m.38",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"p a m n : ℕ\nhp : Prime p\nh : p ^ m = a ^ n\nthis : Finsupp.single p m = n • a.factorization\n⊢ m = n * a.factorization p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ArithmeticFunction.Misc | {
"line": 216,
"column": 2
} | {
"line": 216,
"column": 32
} | {
"line": 216,
"column": 33
} | [
{
"pp": "k n : ℕ\n⊢ ∑ i ∈ n.divisors, n ^ k ≤ n * n ^ k",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"instPowNat",
"Eq.mpr",
"HMul.hMul",
"congrArg",
"Preorder.toLE",
"id",
"instMulNat",
"LE.le",
"instNatPowNat",
"Nat.divisors"... | [
"k n : ℕ\n⊢ #n.divisors * n ^ k ≤ n * n ^ k"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ArithmeticFunction.Defs | {
"line": 504,
"column": 26
} | {
"line": 504,
"column": 82
} | {
"line": 504,
"column": 83
} | [
{
"pp": "R : Type u_1\ninst✝ : CommSemiring R\nf g : ArithmeticFunction R\nhf : f.IsMultiplicative\nhg : g.IsMultiplicative\na1 a2 b1 b2 : ℕ\nha : ((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 ≠ 0\ncop : (((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2).Coprime (((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2... | [
"R : Type u_1\ninst✝ : CommSemiring R\nf g : ArithmeticFunction R\nhf : f.IsMultiplicative\nhg : g.IsMultiplicative\na1 a2 b1 b2 : ℕ\nha : ((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 ≠ 0\ncop : (((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2).Coprime (((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2)\nhb : ((a1... | cop.coprime_mul_left.coprime_mul_right_right.gcd_eq_one, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.ArithmeticFunction.Defs | {
"line": 505,
"column": 23
} | {
"line": 505,
"column": 32
} | {
"line": 505,
"column": 32
} | [
{
"pp": "R : Type u_1\ninst✝ : CommSemiring R\nf g : ArithmeticFunction R\nhf : f.IsMultiplicative\nhg : g.IsMultiplicative\na1 a2 b1 b2 : ℕ\nha : ((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 ≠ 0\nhb : ((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2 ≠ 0\nc1 c2 d1 d2 : ℕ\ncop : (((c1, c2), d1, d2).1.1 * ((c1,... | [
"R : Type u_1\ninst✝ : CommSemiring R\nf g : ArithmeticFunction R\nhf : f.IsMultiplicative\nhg : g.IsMultiplicative\na1 a2 b1 b2 : ℕ\nha : ((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 ≠ 0\nhb : ((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2 ≠ 0\nc1 c2 d1 d2 : ℕ\ncop : (((c1, c2), d1, d2).1.1 * ((c1, c2), d1, d2... | ← hcd.2.1 | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.ArithmeticFunction.Misc | {
"line": 400,
"column": 4
} | {
"line": 400,
"column": 64
} | {
"line": 401,
"column": 2
} | [
{
"pp": "R : Type u_2\ninst✝ : Semiring R\nf g : ArithmeticFunction R\nN n : ℕ\nhn : 0 < n ∧ n ≤ N\n⊢ ∑ x ∈ n.divisorsAntidiagonal, f x.1 * g x.2 = ∑ x ∈ Ioc 0 N ×ˢ Ioc 0 N with x.1 * x.2 = n, f x.1 * g x.2",
"ppTerm": "?m.148",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.to... | [] | rw [divisorsAntidiagonal_eq_prod_filter_of_le hn.1.ne' hn.2] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.NumberTheory.ArithmeticFunction.Defs | {
"line": 506,
"column": 42
} | {
"line": 506,
"column": 98
} | {
"line": 507,
"column": 10
} | [
{
"pp": "R : Type u_1\ninst✝ : CommSemiring R\nf g : ArithmeticFunction R\nhf : f.IsMultiplicative\nhg : g.IsMultiplicative\na1 a2 b1 b2 : ℕ\nha : ((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 ≠ 0\nhb : ((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2 ≠ 0\nc1 c2 d1 d2 : ℕ\ncop : (((c1, c2), d1, d2).1.1 * ((c1,... | [
"R : Type u_1\ninst✝ : CommSemiring R\nf g : ArithmeticFunction R\nhf : f.IsMultiplicative\nhg : g.IsMultiplicative\na1 a2 b1 b2 : ℕ\nha : ((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 ≠ 0\nhb : ((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2 ≠ 0\nc1 c2 d1 d2 : ℕ\ncop : (((c1, c2), d1, d2).1.1 * ((c1, c2), d1, d2... | cop.coprime_mul_left.coprime_mul_right_right.gcd_eq_one, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.ArithmeticFunction.Misc | {
"line": 396,
"column": 2
} | {
"line": 403,
"column": 47
} | {
"line": 405,
"column": 0
} | [
{
"pp": "R : Type u_2\ninst✝ : Semiring R\nf g : ArithmeticFunction R\nN : ℕ\n⊢ ∑ n ∈ Ioc 0 N, (f * g) n = ∑ x ∈ Ioc 0 N ×ˢ Ioc 0 N with x.1 * x.2 ≤ N, f x.1 * g x.2",
"ppTerm": "?m.69",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.instMulZeroClass",
"Preorder.toLT",
"... | [] | simp only [mul_apply]
trans ∑ n ∈ Ioc 0 N, ∑ x ∈ Ioc 0 N ×ˢ Ioc 0 N with x.1 * x.2 = n, f x.1 * g x.2
· refine sum_congr rfl fun n hn ↦ ?_
simp only [mem_Ioc] at hn
rw [divisorsAntidiagonal_eq_prod_filter_of_le hn.1.ne' hn.2]
· simp_rw [sum_filter]
rw [sum_comm]
exact sum_congr rfl fun _ _ ↦ (by s... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.ArithmeticFunction.Misc | {
"line": 396,
"column": 2
} | {
"line": 403,
"column": 47
} | {
"line": 405,
"column": 0
} | [
{
"pp": "R : Type u_2\ninst✝ : Semiring R\nf g : ArithmeticFunction R\nN : ℕ\n⊢ ∑ n ∈ Ioc 0 N, (f * g) n = ∑ x ∈ Ioc 0 N ×ˢ Ioc 0 N with x.1 * x.2 ≤ N, f x.1 * g x.2",
"ppTerm": "?m.69",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.instMulZeroClass",
"Preorder.toLT",
"... | [] | simp only [mul_apply]
trans ∑ n ∈ Ioc 0 N, ∑ x ∈ Ioc 0 N ×ˢ Ioc 0 N with x.1 * x.2 = n, f x.1 * g x.2
· refine sum_congr rfl fun n hn ↦ ?_
simp only [mem_Ioc] at hn
rw [divisorsAntidiagonal_eq_prod_filter_of_le hn.1.ne' hn.2]
· simp_rw [sum_filter]
rw [sum_comm]
exact sum_congr rfl fun _ _ ↦ (by s... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.ArithmeticFunction.Misc | {
"line": 434,
"column": 2
} | {
"line": 434,
"column": 13
} | {
"line": 434,
"column": 14
} | [
{
"pp": "case e'_3\nN : ℕ\n⊢ ∑ n ∈ Ioc 0 N, N / n = ∑ n ∈ Ioc 0 N, zeta n * ↑(N / n)",
"ppTerm": "?e'_3",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.instMulZeroClass",
"instHDiv",
"HMul.hMul",
"ArithmeticFunction... | [
"case e'_3\nN : ℕ\n⊢ ∑ n ∈ Ioc 0 N, N / n = ∑ x ∈ Ioc 0 N, if x = 0 then 0 else N / x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Antidiag.Tendsto | {
"line": 36,
"column": 35
} | {
"line": 36,
"column": 46
} | {
"line": 36,
"column": 47
} | [
{
"pp": "M : Type u_1\nR : Type u_2\ninst✝² : AddMonoid M\ninst✝¹ : HasAntidiagonal M\nf : M × M → R\ninst✝ : LinearOrder R\nF : Filter R\nhf : Tendsto f cofinite F\nU : Set R\nhU : U ∈ F\nx : M\nhx : (antidiagonal x).sup' ⋯ f ∉ U\ni : M × M\nhi : i ∈ antidiagonal x\ne : (antidiagonal x).sup' ⋯ f = f i\n⊢ i.1 +... | [
"M : Type u_1\nR : Type u_2\ninst✝² : AddMonoid M\ninst✝¹ : HasAntidiagonal M\nf : M × M → R\ninst✝ : LinearOrder R\nF : Filter R\nhf : Tendsto f cofinite F\nU : Set R\nhU : U ∈ F\nx : M\nhx : (antidiagonal x).sup' ⋯ f ∉ U\ni : M × M\nhi : i ∈ antidiagonal x\ne : (antidiagonal x).sup' ⋯ f = f i\n⊢ i.1 + i.2 = x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Antidiag.Tendsto | {
"line": 37,
"column": 28
} | {
"line": 37,
"column": 39
} | {
"line": 37,
"column": 40
} | [
{
"pp": "M : Type u_1\nR : Type u_2\ninst✝² : AddMonoid M\ninst✝¹ : HasAntidiagonal M\nf : M × M → R\ninst✝ : LinearOrder R\nF : Filter R\nhf : Tendsto f cofinite F\nU : Set R\nhU : U ∈ F\ni : M × M\nhx : (antidiagonal (i.1 + i.2)).sup' ⋯ f ∉ U\nhi : i ∈ antidiagonal (i.1 + i.2)\ne : (antidiagonal (i.1 + i.2)).... | [
"M : Type u_1\nR : Type u_2\ninst✝² : AddMonoid M\ninst✝¹ : HasAntidiagonal M\nf : M × M → R\ninst✝ : LinearOrder R\nF : Filter R\nhf : Tendsto f cofinite F\nU : Set R\nhU : U ∈ F\ni : M × M\nhx : (antidiagonal (i.1 + i.2)).sup' ⋯ f ∉ U\nhi : i ∈ antidiagonal (i.1 + i.2)\ne : (antidiagonal (i.1 + i.2)).sup' ⋯ f = f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Antidiag.Tendsto | {
"line": 37,
"column": 59
} | {
"line": 37,
"column": 70
} | {
"line": 37,
"column": 71
} | [
{
"pp": "M : Type u_1\nR : Type u_2\ninst✝² : AddMonoid M\ninst✝¹ : HasAntidiagonal M\nf : M × M → R\ninst✝ : LinearOrder R\nF : Filter R\nhf : Tendsto f cofinite F\nU : Set R\nhU : U ∈ F\ni : M × M\nhx : (antidiagonal (i.1 + i.2)).sup' ⋯ f ∉ U\nhi : i ∈ antidiagonal (i.1 + i.2)\ne : (antidiagonal (i.1 + i.2)).... | [
"M : Type u_1\nR : Type u_2\ninst✝² : AddMonoid M\ninst✝¹ : HasAntidiagonal M\nf : M × M → R\ninst✝ : LinearOrder R\nF : Filter R\nhf : Tendsto f cofinite F\nU : Set R\nhU : U ∈ F\ni : M × M\nhx : (antidiagonal (i.1 + i.2)).sup' ⋯ f ∉ U\nhi : i ∈ antidiagonal (i.1 + i.2)\ne : (antidiagonal (i.1 + i.2)).sup' ⋯ f = f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ArithmeticFunction.Defs | {
"line": 511,
"column": 23
} | {
"line": 511,
"column": 32
} | {
"line": 511,
"column": 32
} | [
{
"pp": "R : Type u_1\ninst✝ : CommSemiring R\nf g : ArithmeticFunction R\nhf : f.IsMultiplicative\nhg : g.IsMultiplicative\na1 a2 b1 b2 : ℕ\nha : ((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 ≠ 0\nhb : ((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2 ≠ 0\nc1 c2 d1 d2 : ℕ\ncop : (((c1, c2), d1, d2).1.1 * ((c1,... | [
"R : Type u_1\ninst✝ : CommSemiring R\nf g : ArithmeticFunction R\nhf : f.IsMultiplicative\nhg : g.IsMultiplicative\na1 a2 b1 b2 : ℕ\nha : ((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 ≠ 0\nhb : ((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2 ≠ 0\nc1 c2 d1 d2 : ℕ\ncop : (((c1, c2), d1, d2).1.1 * ((c1, c2), d1, d2... | ← hcd.2.1 | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Antidiag.Nat | {
"line": 275,
"column": 4
} | {
"line": 275,
"column": 22
} | {
"line": 276,
"column": 4
} | [
{
"pp": "n : ℕ\na : Fin 3 → ℕ\nha : a ∈ finMulAntidiag 3 n\nb : Fin 3 → ℕ\nhb : b ∈ finMulAntidiag 3 n\nhfab : f a ha = f b hb\nhfab1 : a 0 * a 1 = b 0 * b 1\nhfab2 : a 0 * a 2 = b 0 * b 2\nhprods : a 0 * a 1 * a 2 = a 0 * a 1 * b 2\nhab2 : a 2 = b 2\n⊢ a 0 = b 0",
"ppTerm": "?m.110",
"assigned": true,
... | [
"n : ℕ\na : Fin 3 → ℕ\nha : a ∈ finMulAntidiag 3 n\nb : Fin 3 → ℕ\nhb : b ∈ finMulAntidiag 3 n\nhfab : f a ha = f b hb\nhfab1 : a 0 * a 1 = b 0 * b 1\nhfab2 : a 0 * b 2 = b 0 * b 2\nhprods : a 0 * a 1 * a 2 = a 0 * a 1 * b 2\nhab2 : a 2 = b 2\n⊢ a 0 = b 0"
] | rw [hab2] at hfab2 | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Order.Antidiag.Nat | {
"line": 297,
"column": 2
} | {
"line": 297,
"column": 52
} | {
"line": 298,
"column": 4
} | [
{
"pp": "case h\nn : ℕ\nhn : n ≠ 0\nb : ℕ × ℕ\nhb : b ∈ {x ∈ n.divisors ×ˢ n.divisors | x.1.lcm x.2 = n}\ng : ℕ := ⋯\na : Fin (succ 0).succ.succ → ℕ := ⋯\nha : a ∈ finMulAntidiag 3 n\n⊢ f a ha = b",
"ppTerm": "?h",
"assigned": true,
"usedConstants": [
"id",
"Prod.fst",
"Prod.ext",
... | [
"case h.fst\nn : ℕ\nhn : n ≠ 0\nb : ℕ × ℕ\nhb : b ∈ {x ∈ n.divisors ×ˢ n.divisors | x.1.lcm x.2 = n}\ng : ℕ := b.1.gcd b.2\na : Fin (succ 0).succ.succ → ℕ := ![g, b.1 / g, b.2 / g]\nha : a ∈ finMulAntidiag 3 n\n⊢ g * (b.1 / g) = b.1",
"case h.snd\nn : ℕ\nhn : n ≠ 0\nb : ℕ × ℕ\nhb : b ∈ {x ∈ n.divisors ×ˢ n.diviso... | apply Prod.ext <;> dsimp only [a, Matrix.cons_val] | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.NumberTheory.ArithmeticFunction.Defs | {
"line": 517,
"column": 23
} | {
"line": 517,
"column": 32
} | {
"line": 517,
"column": 32
} | [
{
"pp": "R : Type u_1\ninst✝ : CommSemiring R\nf g : ArithmeticFunction R\nhf : f.IsMultiplicative\nhg : g.IsMultiplicative\na1 a2 b1 b2 : ℕ\nha : ((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 ≠ 0\nhb : ((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2 ≠ 0\nc1 c2 d1 d2 : ℕ\ncop : (((c1, c2), d1, d2).1.1 * ((c1,... | [
"R : Type u_1\ninst✝ : CommSemiring R\nf g : ArithmeticFunction R\nhf : f.IsMultiplicative\nhg : g.IsMultiplicative\na1 a2 b1 b2 : ℕ\nha : ((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 ≠ 0\nhb : ((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2 ≠ 0\nc1 c2 d1 d2 : ℕ\ncop : (((c1, c2), d1, d2).1.1 * ((c1, c2), d1, d2... | ← hcd.2.1 | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.ArithmeticFunction.Defs | {
"line": 522,
"column": 23
} | {
"line": 522,
"column": 32
} | {
"line": 522,
"column": 32
} | [
{
"pp": "R : Type u_1\ninst✝ : CommSemiring R\nf g : ArithmeticFunction R\nhf : f.IsMultiplicative\nhg : g.IsMultiplicative\na1 a2 b1 b2 : ℕ\nha : ((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 ≠ 0\nhb : ((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2 ≠ 0\nc1 c2 d1 d2 : ℕ\ncop : (((c1, c2), d1, d2).1.1 * ((c1,... | [
"R : Type u_1\ninst✝ : CommSemiring R\nf g : ArithmeticFunction R\nhf : f.IsMultiplicative\nhg : g.IsMultiplicative\na1 a2 b1 b2 : ℕ\nha : ((a1, a2), b1, b2).1.1 * ((a1, a2), b1, b2).1.2 ≠ 0\nhb : ((a1, a2), b1, b2).2.1 * ((a1, a2), b1, b2).2.2 ≠ 0\nc1 c2 d1 d2 : ℕ\ncop : (((c1, c2), d1, d2).1.1 * ((c1, c2), d1, d2... | ← hcd.2.1 | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Disjointed | {
"line": 35,
"column": 2
} | {
"line": 35,
"column": 36
} | {
"line": 35,
"column": 37
} | [
{
"pp": "α : Type u_1\nι : Type u_2\ninst✝⁶ : GeneralizedBooleanAlgebra α\ninst✝⁵ : LinearOrder ι\ninst✝⁴ : LocallyFiniteOrderBot ι\ninst✝³ : Add ι\ninst✝² : One ι\ninst✝¹ : SuccAddOrder ι\ninst✝ : NoMaxOrder ι\nf : ι → α\ni : ι\n⊢ disjointed f (i + 1) = f (i + 1) \\ (partialSups f) i",
"ppTerm": "?m.32",
... | [
"α : Type u_1\nι : Type u_2\ninst✝⁶ : GeneralizedBooleanAlgebra α\ninst✝⁵ : LinearOrder ι\ninst✝⁴ : LocallyFiniteOrderBot ι\ninst✝³ : Add ι\ninst✝² : One ι\ninst✝¹ : SuccAddOrder ι\ninst✝ : NoMaxOrder ι\nf : ι → α\ni : ι\n⊢ disjointed f (i + 1) = f (i + 1) \\ (partialSups f) i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Disjointed | {
"line": 52,
"column": 2
} | {
"line": 52,
"column": 38
} | {
"line": 52,
"column": 39
} | [
{
"pp": "α : Type u_1\nι : Type u_2\ninst✝⁵ : GeneralizedBooleanAlgebra α\ninst✝⁴ : LinearOrder ι\ninst✝³ : LocallyFiniteOrderBot ι\ninst✝² : Add ι\ninst✝¹ : One ι\ninst✝ : SuccAddOrder ι\nf : ι → α\nhf : Monotone f\ni : ι\n⊢ disjointed f (i + 1) ⊔ f i = f (i + 1)",
"ppTerm": "?m.29",
"assigned": false,... | [
"α : Type u_1\nι : Type u_2\ninst✝⁵ : GeneralizedBooleanAlgebra α\ninst✝⁴ : LinearOrder ι\ninst✝³ : LocallyFiniteOrderBot ι\ninst✝² : Add ι\ninst✝¹ : One ι\ninst✝ : SuccAddOrder ι\nf : ι → α\nhf : Monotone f\ni : ι\n⊢ disjointed f (i + 1) ⊔ f i = f (i + 1)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Disjointed | {
"line": 76,
"column": 19
} | {
"line": 76,
"column": 77
} | {
"line": 76,
"column": 78
} | [
{
"pp": "case succ\nα : Type u_1\nι : Type u_2\ninst✝ : GeneralizedBooleanAlgebra α\nf : ℕ → α\np : α → Sort u_3\nhdiff : ⦃t : α⦄ → ⦃i : ℕ⦄ → p t → p (t \\ f i)\nn : ℕ\nh : p (f (n + 1))\nk : ℕ\nih : p (f (n + 1) \\ (partialSups f) k)\n⊢ p (f (n + 1) \\ (partialSups f) (k + 1))",
"ppTerm": "?succ",
"ass... | [
"case succ\nα : Type u_1\nι : Type u_2\ninst✝ : GeneralizedBooleanAlgebra α\nf : ℕ → α\np : α → Sort u_3\nhdiff : ⦃t : α⦄ → ⦃i : ℕ⦄ → p t → p (t \\ f i)\nn : ℕ\nh : p (f (n + 1))\nk : ℕ\nih : p (f (n + 1) \\ (partialSups f) k)\n⊢ p ((f (n + 1) \\ (partialSups f) k) \\ f (k + 1))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Field.GeomSum | {
"line": 60,
"column": 4
} | {
"line": 60,
"column": 15
} | {
"line": 60,
"column": 16
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\ninst✝¹ : LinearOrder K\ninst✝ : IsStrictOrderedRing K\nx : K\nm n : ℕ\nhx : 0 ≤ x\nh'x : x < 1\nhmn : m ≤ n\n⊢ x ^ m - x ^ n ≤ x ^ m",
"ppTerm": "?m.82",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"AddLeftCancelSemigroup.toIsLeftCancelAdd",
... | [
"K : Type u_1\ninst✝² : Field K\ninst✝¹ : LinearOrder K\ninst✝ : IsStrictOrderedRing K\nx : K\nm n : ℕ\nhx : 0 ≤ x\nh'x : x < 1\nhmn : m ≤ n\n⊢ 0 ≤ x ^ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Field.GeomSum | {
"line": 63,
"column": 6
} | {
"line": 63,
"column": 17
} | {
"line": 63,
"column": 18
} | [
{
"pp": "case inr\nK : Type u_1\ninst✝² : Field K\ninst✝¹ : LinearOrder K\ninst✝ : IsStrictOrderedRing K\nx : K\nm n : ℕ\nhx : 0 ≤ x\nh'x : x < 1\nhmn : n < m\n⊢ 0 ≤ 1 - x",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"AddGroup... | [
"case inr\nK : Type u_1\ninst✝² : Field K\ninst✝¹ : LinearOrder K\ninst✝ : IsStrictOrderedRing K\nx : K\nm n : ℕ\nhx : 0 ≤ x\nh'x : x < 1\nhmn : n < m\n⊢ x ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Field.GeomSum | {
"line": 64,
"column": 6
} | {
"line": 64,
"column": 17
} | {
"line": 64,
"column": 18
} | [
{
"pp": "case inr\nK : Type u_1\ninst✝² : Field K\ninst✝¹ : LinearOrder K\ninst✝ : IsStrictOrderedRing K\nx : K\nm n : ℕ\nhx : 0 ≤ x\nh'x : x < 1\nhmn : n < m\n⊢ ¬m < n",
"ppTerm": "?inr✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"PartialOrder.toPreorder",
... | [
"case inr\nK : Type u_1\ninst✝² : Field K\ninst✝¹ : LinearOrder K\ninst✝ : IsStrictOrderedRing K\nx : K\nm n : ℕ\nhx : 0 ≤ x\nh'x : x < 1\nhmn : n < m\n⊢ n ≤ m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 141,
"column": 6
} | {
"line": 141,
"column": 17
} | {
"line": 141,
"column": 18
} | [
{
"pp": "M✝ : Type u_1\ninst✝⁴ : Group M✝\ninst✝³ : Lattice M✝\nM : Type u_2\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na✝ b✝ : M\na b : MulArchimedeanOrder M\nthis : (∀ (n : ℕ), |val b|ₘ ^ n < |val a|ₘ) → ∃ n, |val b|ₘ ≤ |val a|ₘ ^ n\n⊢ (∀ (n : ℕ), |val b|ₘ ^ n < |val a|ₘ) ↔ (∃ n... | [
"M✝ : Type u_1\ninst✝⁴ : Group M✝\ninst✝³ : Lattice M✝\nM : Type u_2\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na✝ b✝ : M\na b : MulArchimedeanOrder M\nthis : (∀ (n : ℕ), |val b|ₘ ^ n < |val a|ₘ) → ∃ n, |val b|ₘ ≤ |val a|ₘ ^ n\n⊢ (∀ (n : ℕ), |val b|ₘ ^ n < |val a|ₘ) → ∃ n, |val b|ₘ ≤ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 144,
"column": 17
} | {
"line": 144,
"column": 28
} | {
"line": 144,
"column": 29
} | [
{
"pp": "M✝ : Type u_1\ninst✝⁴ : Group M✝\ninst✝³ : Lattice M✝\nM : Type u_2\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na✝ b✝ : M\na b : MulArchimedeanOrder M\nh✝ : ∀ (n : ℕ), |val b|ₘ ^ n < |val a|ₘ\nh : |val b|ₘ ^ 1 ≤ |val a|ₘ\n⊢ |val b|ₘ ≤ |val a|ₘ ^ 1",
"ppTerm": "?m.176",... | [
"M✝ : Type u_1\ninst✝⁴ : Group M✝\ninst✝³ : Lattice M✝\nM : Type u_2\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na✝ b✝ : M\na b : MulArchimedeanOrder M\nh✝ : ∀ (n : ℕ), |val b|ₘ ^ n < |val a|ₘ\nh : |val b|ₘ ^ 1 ≤ |val a|ₘ\n⊢ |val b|ₘ ≤ |val a|ₘ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 150,
"column": 24
} | {
"line": 150,
"column": 35
} | {
"line": 150,
"column": 36
} | [
{
"pp": "M✝ : Type u_1\ninst✝⁴ : Group M✝\ninst✝³ : Lattice M✝\nM : Type u_2\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na✝ b✝ : M\na b : MulArchimedeanOrder M\nhab : |val a|ₘ ≤ |val b|ₘ\n⊢ |val a|ₘ ≤ |val b|ₘ ^ 1",
"ppTerm": "?m.45",
"assigned": true,
"usedConstants": ... | [
"M✝ : Type u_1\ninst✝⁴ : Group M✝\ninst✝³ : Lattice M✝\nM : Type u_2\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na✝ b✝ : M\na b : MulArchimedeanOrder M\nhab : |val a|ₘ ≤ |val b|ₘ\n⊢ |val a|ₘ ≤ |val b|ₘ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 151,
"column": 24
} | {
"line": 151,
"column": 35
} | {
"line": 151,
"column": 36
} | [
{
"pp": "M✝ : Type u_1\ninst✝⁴ : Group M✝\ninst✝³ : Lattice M✝\nM : Type u_2\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na✝ b✝ : M\na b : MulArchimedeanOrder M\nhab : |val b|ₘ ≤ |val a|ₘ\n⊢ |val b|ₘ ≤ |val a|ₘ ^ 1",
"ppTerm": "?m.58",
"assigned": true,
"usedConstants": ... | [
"M✝ : Type u_1\ninst✝⁴ : Group M✝\ninst✝³ : Lattice M✝\nM : Type u_2\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na✝ b✝ : M\na b : MulArchimedeanOrder M\nhab : |val b|ₘ ≤ |val a|ₘ\n⊢ |val b|ₘ ≤ |val a|ₘ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 325,
"column": 2
} | {
"line": 325,
"column": 13
} | {
"line": 325,
"column": 14
} | [
{
"pp": "M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na : M\nha : a ∈ Set.Ici 1\nb : M\nhb : b ∈ Set.Ici 1\nhab : ∀ (n : ℕ), |b|ₘ ^ n < |a|ₘ\nh : b ^ 1 < a\n⊢ b < a",
"ppTerm": "?m.67",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGo... | [
"M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na : M\nha : a ∈ Set.Ici 1\nb : M\nhb : b ∈ Set.Ici 1\nhab : ∀ (n : ℕ), |b|ₘ ^ n < |a|ₘ\nh : b ^ 1 < a\n⊢ b < a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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