module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 771,
"column": 4
} | {
"line": 771,
"column": 33
} | {
"line": 771,
"column": 34
} | [
{
"pp": "R✝ : Type u_1\ninst✝⁵ : Semiring R✝\ninst✝⁴ : ValuativeRel R✝\nx✝¹ x' y y' z : R✝\nR : Type u_2\ninst✝³ : Ring R\ninst✝² : ValuativeRel R\nx : R\nS : Type u_3\nΓ : Type u_4\ninst✝¹ : Ring S\ninst✝ : LinearOrderedCommGroupWithZero Γ\nv : Valuation S Γ\nx✝ y✝ z✝ : S\nh0 : ¬v z✝ ≤ v 0\nh : v x✝ * v z✝ ≤ v... | [
"R✝ : Type u_1\ninst✝⁵ : Semiring R✝\ninst✝⁴ : ValuativeRel R✝\nx✝¹ x' y y' z : R✝\nR : Type u_2\ninst✝³ : Ring R\ninst✝² : ValuativeRel R\nx : R\nS : Type u_3\nΓ : Type u_4\ninst✝¹ : Ring S\ninst✝ : LinearOrderedCommGroupWithZero Γ\nv : Valuation S Γ\nx✝ y✝ z✝ : S\nh0 : ¬v z✝ ≤ v 0\nh : v x✝ * v z✝ ≤ v y✝ * v z✝\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 879,
"column": 24
} | {
"line": 879,
"column": 35
} | {
"line": 879,
"column": 36
} | [
{
"pp": "R : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nx x✝ : R\nh : x✝ ∈ {x | x ≤ᵥ 0}\n⊢ x • x✝ ∈ {x | x ≤ᵥ 0}",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"instHSMul",
"Semiring.toModule",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass... | [
"R : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nx x✝ : R\nh : x✝ ∈ {x | x ≤ᵥ 0}\n⊢ x * x✝ ≤ᵥ 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 882,
"column": 28
} | {
"line": 882,
"column": 46
} | {
"line": 882,
"column": 47
} | [
{
"pp": "R : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\na✝ x✝ : R\nh : a✝ ∈ supp R\n⊢ a✝ * x✝ ∈ supp R",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Submodule",
"Semiring.toModule",
"HMul.hMul",
"AddSubsemigroup.instSetLike",
"Ad... | [
"R : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\na✝ x✝ : R\nh : a✝ ∈ supp R\n⊢ a✝ * x✝ ≤ᵥ 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 890,
"column": 2
} | {
"line": 890,
"column": 13
} | {
"line": 890,
"column": 14
} | [
{
"pp": "R : Type u_2\ninst✝¹ : CommRing R\ninst✝ : ValuativeRel R\nx✝ : R\n⊢ x✝ ∈ supp R ↔ x✝ ∈ (valuation R).supp",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"Semiring.toModule",
"co... | [
"R : Type u_2\ninst✝¹ : CommRing R\ninst✝ : ValuativeRel R\nx✝ : R\n⊢ x✝ ≤ᵥ 0 ↔ (valuation R) x✝ = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 960,
"column": 2
} | {
"line": 960,
"column": 23
} | {
"line": 960,
"column": 24
} | [
{
"pp": "R : Type u_2\ninst✝¹ : Ring R\ninst✝ : ValuativeRel R\na : R\nha : a ≤ᵥ 1\nn m : ℕ\nhnm : n ≤ n + m\n⊢ a ^ (n + m) ≤ᵥ a ^ n",
"ppTerm": "?m.44",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"pow_add",
"id... | [
"R : Type u_2\ninst✝¹ : Ring R\ninst✝ : ValuativeRel R\na : R\nha : a ≤ᵥ 1\nn m : ℕ\nhnm : n ≤ n + m\n⊢ a ^ n * a ^ m ≤ᵥ a ^ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 966,
"column": 2
} | {
"line": 966,
"column": 23
} | {
"line": 966,
"column": 24
} | [
{
"pp": "R : Type u_2\ninst✝¹ : Ring R\ninst✝ : ValuativeRel R\na : R\nha : 1 ≤ᵥ a\nn m : ℕ\nhnm : n ≤ n + m\n⊢ a ^ n ≤ᵥ a ^ (n + m)",
"ppTerm": "?m.44",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"pow_add",
"id... | [
"R : Type u_2\ninst✝¹ : Ring R\ninst✝ : ValuativeRel R\na : R\nha : 1 ≤ᵥ a\nn m : ℕ\nhnm : n ≤ n + m\n⊢ a ^ n ≤ᵥ a ^ n * a ^ m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 1018,
"column": 2
} | {
"line": 1018,
"column": 13
} | {
"line": 1018,
"column": 14
} | [
{
"pp": "K : Type u_2\ninst✝¹ : DivisionRing K\ninst✝ : ValuativeRel K\nx : K\nhx : x ≠ 0\n⊢ 1 ≤ᵥ x⁻¹ ↔ x ≤ᵥ 1",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"K : Type u_2\ninst✝¹ : DivisionRing K\ninst✝ : ValuativeRel K\nx : K\nhx : x ≠ 0\n⊢ 1 ≤ᵥ x⁻¹ ↔ x ≤ᵥ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 1023,
"column": 2
} | {
"line": 1023,
"column": 13
} | {
"line": 1023,
"column": 14
} | [
{
"pp": "K : Type u_2\ninst✝¹ : DivisionRing K\ninst✝ : ValuativeRel K\nx : K\nhx : x ≠ 0\n⊢ x⁻¹ ≤ᵥ 1 ↔ 1 ≤ᵥ x",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"K : Type u_2\ninst✝¹ : DivisionRing K\ninst✝ : ValuativeRel K\nx : K\nhx : x ≠ 0\n⊢ x⁻¹ ≤ᵥ 1 ↔ 1 ≤ᵥ x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 1076,
"column": 32
} | {
"line": 1076,
"column": 43
} | {
"line": 1076,
"column": 44
} | [
{
"pp": "R : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\ns : (ValueGroupWithZero R)ˣ\nh : 1 ≠ s\n⊢ ↑s ≠ 1",
"ppTerm": "?m.104",
"assigned": true,
"usedConstants": [
"Units.val",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"congrArg",
"Units",
"id",
... | [
"R : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\ns : (ValueGroupWithZero R)ˣ\nh : 1 ≠ s\n⊢ ¬s = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 1077,
"column": 32
} | {
"line": 1077,
"column": 43
} | {
"line": 1077,
"column": 44
} | [
{
"pp": "R : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nr s : (ValueGroupWithZero R)ˣ\nh : r ≠ s\nhr : r ≠ 1\n⊢ ↑r ≠ 1",
"ppTerm": "?m.125",
"assigned": true,
"usedConstants": [
"Units.val",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"congrArg",
"Units",
... | [
"R : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nr s : (ValueGroupWithZero R)ˣ\nh : r ≠ s\nhr : r ≠ 1\n⊢ ¬r = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 1089,
"column": 28
} | {
"line": 1089,
"column": 82
} | {
"line": 1089,
"column": 83
} | [
{
"pp": "R : Type u_2\ninst✝³ : Ring R\ninst✝² : ValuativeRel R\nΓ₀ : Type u_3\ninst✝¹ : LinearOrderedCommMonoidWithZero Γ₀\nv : Valuation R Γ₀\ninst✝ : v.Compatible\nr : R\ns : ↥(posSubmonoid R)\nhr : ValueGroupWithZero.mk r s ≠ 0\nhr' : ValueGroupWithZero.mk r s ≠ 1\n⊢ v r ≠ 0",
"ppTerm": "?m.65",
"as... | [
"R : Type u_2\ninst✝³ : Ring R\ninst✝² : ValuativeRel R\nΓ₀ : Type u_3\ninst✝¹ : LinearOrderedCommMonoidWithZero Γ₀\nv : Valuation R Γ₀\ninst✝ : v.Compatible\nr : R\ns : ↥(posSubmonoid R)\nhr : ValueGroupWithZero.mk r s ≠ 0\nhr' : ValueGroupWithZero.mk r s ≠ 1\n⊢ ¬v r = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 1091,
"column": 6
} | {
"line": 1091,
"column": 60
} | {
"line": 1091,
"column": 61
} | [
{
"pp": "R : Type u_2\ninst✝³ : Ring R\ninst✝² : ValuativeRel R\nΓ₀ : Type u_3\ninst✝¹ : LinearOrderedCommMonoidWithZero Γ₀\nv : Valuation R Γ₀\ninst✝ : v.Compatible\nr : R\ns : ↥(posSubmonoid R)\nhr : ValueGroupWithZero.mk r s ≠ 0\nhr' : ValueGroupWithZero.mk r s ≠ 1\nhγ : v r ≠ 0\n⊢ v r ≤ v ↑s → v r < v ↑s",
... | [
"R : Type u_2\ninst✝³ : Ring R\ninst✝² : ValuativeRel R\nΓ₀ : Type u_3\ninst✝¹ : LinearOrderedCommMonoidWithZero Γ₀\nv : Valuation R Γ₀\ninst✝ : v.Compatible\nr : R\ns : ↥(posSubmonoid R)\nhr : ValueGroupWithZero.mk r s ≠ 0\nhr' : ValueGroupWithZero.mk r s ≠ 1\nhγ : v r ≠ 0\n⊢ v r ≤ v ↑s → v r < v ↑s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 1094,
"column": 19
} | {
"line": 1094,
"column": 30
} | {
"line": 1094,
"column": 31
} | [
{
"pp": "R : Type u_2\ninst✝³ : Ring R\ninst✝² : ValuativeRel R\nΓ₀ : Type u_3\ninst✝¹ : LinearOrderedCommMonoidWithZero Γ₀\nv : Valuation R Γ₀\ninst✝ : v.Compatible\nr : R\ns : ↥(posSubmonoid R)\nhr✝ : ValueGroupWithZero.mk r s ≠ 0\nhr' : ValueGroupWithZero.mk r s ≠ 1\nhγ : v r ≠ 0\nhγ' : v r ≤ v ↑s → v r < v ... | [
"R : Type u_2\ninst✝³ : Ring R\ninst✝² : ValuativeRel R\nΓ₀ : Type u_3\ninst✝¹ : LinearOrderedCommMonoidWithZero Γ₀\nv : Valuation R Γ₀\ninst✝ : v.Compatible\nr : R\ns : ↥(posSubmonoid R)\nhr✝ : ValueGroupWithZero.mk r s ≠ 0\nhr' : ValueGroupWithZero.mk r s ≠ 1\nhγ : v r ≠ 0\nhγ' : v r ≤ v ↑s → v r < v ↑s\nhr : ¬v ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 1094,
"column": 19
} | {
"line": 1094,
"column": 33
} | {
"line": 1094,
"column": 33
} | [
{
"pp": "R : Type u_2\ninst✝³ : Ring R\ninst✝² : ValuativeRel R\nΓ₀ : Type u_3\ninst✝¹ : LinearOrderedCommMonoidWithZero Γ₀\nv : Valuation R Γ₀\ninst✝ : v.Compatible\nr : R\ns : ↥(posSubmonoid R)\nhr✝ : ValueGroupWithZero.mk r s ≠ 0\nhr' : ValueGroupWithZero.mk r s ≠ 1\nhγ : v r ≠ 0\nhγ' : v r ≤ v ↑s → v r < v ... | [] | simpa using hγ | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 1094,
"column": 19
} | {
"line": 1094,
"column": 33
} | {
"line": 1094,
"column": 33
} | [
{
"pp": "R : Type u_2\ninst✝³ : Ring R\ninst✝² : ValuativeRel R\nΓ₀ : Type u_3\ninst✝¹ : LinearOrderedCommMonoidWithZero Γ₀\nv : Valuation R Γ₀\ninst✝ : v.Compatible\nr : R\ns : ↥(posSubmonoid R)\nhr✝ : ValueGroupWithZero.mk r s ≠ 0\nhr' : ValueGroupWithZero.mk r s ≠ 1\nhγ : v r ≠ 0\nhγ' : v r ≤ v ↑s → v r < v ... | [] | simpa using hγ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 1094,
"column": 19
} | {
"line": 1094,
"column": 33
} | {
"line": 1094,
"column": 33
} | [
{
"pp": "R : Type u_2\ninst✝³ : Ring R\ninst✝² : ValuativeRel R\nΓ₀ : Type u_3\ninst✝¹ : LinearOrderedCommMonoidWithZero Γ₀\nv : Valuation R Γ₀\ninst✝ : v.Compatible\nr : R\ns : ↥(posSubmonoid R)\nhr✝ : ValueGroupWithZero.mk r s ≠ 0\nhr' : ValueGroupWithZero.mk r s ≠ 1\nhγ : v r ≠ 0\nhγ' : v r ≤ v ↑s → v r < v ... | [] | simpa using hγ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 1097,
"column": 9
} | {
"line": 1097,
"column": 66
} | {
"line": 1097,
"column": 67
} | [
{
"pp": "R : Type u_2\ninst✝³ : Ring R\ninst✝² : ValuativeRel R\nΓ₀ : Type u_3\ninst✝¹ : LinearOrderedCommMonoidWithZero Γ₀\nv : Valuation R Γ₀\ninst✝ : v.Compatible\nr : R\nhr : v r ≠ 0\nhr' : v r ≠ 1\n⊢ (valuation R) r ≠ 1",
"ppTerm": "?m.202",
"assigned": true,
"usedConstants": [
"LinearOrd... | [
"R : Type u_2\ninst✝³ : Ring R\ninst✝² : ValuativeRel R\nΓ₀ : Type u_3\ninst✝¹ : LinearOrderedCommMonoidWithZero Γ₀\nv : Valuation R Γ₀\ninst✝ : v.Compatible\nr : R\nhr : v r ≠ 0\nhr' : v r ≠ 1\n⊢ ¬(valuation R) r = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 1106,
"column": 25
} | {
"line": 1106,
"column": 53
} | {
"line": 1106,
"column": 53
} | [
{
"pp": "K : Type u_3\ninst✝¹ : DivisionRing K\ninst✝ : ValuativeRel K\nx : K\ny : ↥(posSubmonoid K)\n⊢ ValueGroupWithZero.mk x y = (valuation K) x / (valuation K) ↑y",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMo... | [
"K : Type u_3\ninst✝¹ : DivisionRing K\ninst✝ : ValuativeRel K\nx : K\ny : ↥(posSubmonoid K)\n⊢ (valuation K) x / (valuation K) ↑y = (valuation K) x / (valuation K) ↑y"
] | ValueGroupWithZero.mk_eq_div | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Topology.Algebra.Valued.ValuationTopology | {
"line": 301,
"column": 4
} | {
"line": 301,
"column": 15
} | {
"line": 301,
"column": 16
} | [
{
"pp": "case inl\nR : Type u\ninst✝¹ : Ring R\nΓ₀ : Type v\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\n_i : Valued R Γ₀\n⊢ IsClosed[_i.toTopologicalSpace] {x | v.restrict x = 0}",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"L... | [
"case inl\nR : Type u\ninst✝¹ : Ring R\nΓ₀ : Type v\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\n_i : Valued R Γ₀\n⊢ IsClosed[_i.toTopologicalSpace] {x | v x = 0}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 1154,
"column": 25
} | {
"line": 1156,
"column": 48
} | {
"line": 1158,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝³ : Semiring R\ninst✝² : ValuativeRel R\ninst✝¹ : IsDiscrete R\ninst✝ : IsNontrivial R\n⊢ 0 < uniformizer R",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"ValuativeRel.instLinearOrderValueGroupWithZero",
"Preorder.toLT",
"Par... | [] | by
obtain ⟨γ, hγ, hγ'⟩ := IsNontrivial.exists_lt_one (R := R)
exact hγ.trans_le (le_uniformizer_iff.mpr hγ') | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Topology.Algebra.UniformRing | {
"line": 134,
"column": 17
} | {
"line": 134,
"column": 70
} | {
"line": 135,
"column": 4
} | [
{
"pp": "α : Type u_1\ninst✝⁹ : Ring α\ninst✝⁸ : UniformSpace α\ninst✝⁷ : IsTopologicalRing α\ninst✝⁶ : IsUniformAddGroup α\nβ : Type u\ninst✝⁵ : UniformSpace β\ninst✝⁴ : Ring β\ninst✝³ : IsUniformAddGroup β\ninst✝² : IsTopologicalRing β\nf : α →+* β\nhf✝ : Continuous ⇑f\ninst✝¹ : CompleteSpace β\ninst✝ : T0Spa... | [] | by simp_rw [← coe_zero, extension_coe hf, f.map_zero] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 1264,
"column": 4
} | {
"line": 1264,
"column": 15
} | {
"line": 1264,
"column": 16
} | [
{
"pp": "R : Type u_2\nΓ : Type u_3\ninst✝³ : Ring R\ninst✝² : ValuativeRel R\ninst✝¹ : LinearOrderedCommGroupWithZero Γ\nv : Valuation R Γ\ninst✝ : v.Compatible\na : R\nr : ↥(posSubmonoid R)\nb : R\ns : ↥(posSubmonoid R)\nh : v (a * ↑s) < v (b * ↑r)\n⊢ (ofClass v) a * (ofClass v) ↑s < (ofClass v) b * (ofClass ... | [
"R : Type u_2\nΓ : Type u_3\ninst✝³ : Ring R\ninst✝² : ValuativeRel R\ninst✝¹ : LinearOrderedCommGroupWithZero Γ\nv : Valuation R Γ\ninst✝ : v.Compatible\na : R\nr : ↥(posSubmonoid R)\nb : R\ns : ↥(posSubmonoid R)\nh : v (a * ↑s) < v (b * ↑r)\n⊢ v a * v ↑s < v b * v ↑r"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 1353,
"column": 2
} | {
"line": 1353,
"column": 13
} | {
"line": 1353,
"column": 14
} | [
{
"pp": "R : Type u_2\nΓ : Type u_3\ninst✝³ : Ring R\ninst✝² : ValuativeRel R\ninst✝¹ : LinearOrderedCommGroupWithZero Γ\nv : Valuation R Γ\ninst✝ : v.Compatible\nγ : ValueGroupWithZero R\nx : R\n⊢ v.restrict x < (orderMonoidIso v) γ ↔ (valuation R) x < γ",
"ppTerm": "?m.31",
"assigned": false,
"use... | [
"R : Type u_2\nΓ : Type u_3\ninst✝³ : Ring R\ninst✝² : ValuativeRel R\ninst✝¹ : LinearOrderedCommGroupWithZero Γ\nv : Valuation R Γ\ninst✝ : v.Compatible\nγ : ValueGroupWithZero R\nx : R\n⊢ v.restrict x < (orderMonoidIso v) γ ↔ (valuation R) x < γ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 1393,
"column": 7
} | {
"line": 1393,
"column": 84
} | {
"line": 1393,
"column": 85
} | [
{
"pp": "A : Type u_1\nB : Type u_2\ninst✝⁵ : CommSemiring A\ninst✝⁴ : Semiring B\ninst✝³ : ValuativeRel A\ninst✝² : ValuativeRel B\ninst✝¹ : Algebra A B\ninst✝ : ValuativeExtension A B\nx✝ : ↥(posSubmonoid A)\na : A\nha : a ∈ posSubmonoid A\n⊢ (algebraMap A B) a ∈ posSubmonoid B",
"ppTerm": "?m.47",
"a... | [
"A : Type u_1\nB : Type u_2\ninst✝⁵ : CommSemiring A\ninst✝⁴ : Semiring B\ninst✝³ : ValuativeRel A\ninst✝² : ValuativeRel B\ninst✝¹ : Algebra A B\ninst✝ : ValuativeExtension A B\nx✝ : ↥(posSubmonoid A)\na : A\nha : a ∈ posSubmonoid A\n⊢ 0 <ᵥ a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.Discrete.Basic | {
"line": 125,
"column": 66
} | {
"line": 128,
"column": 39
} | {
"line": 130,
"column": 0
} | [
{
"pp": "Γ : Type u_1\ninst✝² : LinearOrderedCommGroupWithZero Γ\nA : Type u_2\ninst✝¹ : Ring A\nv : Valuation A Γ\ninst✝ : v.IsRankOneDiscrete\n⊢ zpowers (generator' v) = ⊤",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"Linea... | [] | by
rw [← map_subtype_inj, MonoidHom.map_zpowers,
subtype_apply, ← MonoidHom.range_eq_map, Subgroup.subtype_range]
apply generator_zpowers_eq_valueGroup | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.Valuation.Discrete.Basic | {
"line": 430,
"column": 2
} | {
"line": 430,
"column": 12
} | {
"line": 431,
"column": 2
} | [
{
"pp": "Γ : Type u_1\ninst✝³ : LinearOrderedCommGroupWithZero Γ\nK : Type u_2\ninst✝² : Field K\nv : Valuation K Γ\ninst✝¹ : IsCyclic ↥(MonoidWithZeroHom.ofClass v).valueGroup\ninst✝ : Nontrivial ↥(MonoidWithZeroHom.ofClass v).valueGroup\nI : Ideal ↥v.valuationSubring\n⊢ ∀ (P : Ideal ↥v.valuationSubring), P.Is... | [
"Γ : Type u_1\ninst✝³ : LinearOrderedCommGroupWithZero Γ\nK : Type u_2\ninst✝² : Field K\nv : Valuation K Γ\ninst✝¹ : IsCyclic ↥(MonoidWithZeroHom.ofClass v).valueGroup\ninst✝ : Nontrivial ↥(MonoidWithZeroHom.ofClass v).valueGroup\nI P : Ideal ↥v.valuationSubring\nhP : P.IsPrime\n⊢ Submodule.IsPrincipal P"
] | intro P hP | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.RingTheory.Valuation.Discrete.IsDiscreteValuationRing | {
"line": 44,
"column": 15
} | {
"line": 44,
"column": 65
} | {
"line": 44,
"column": 66
} | [
{
"pp": "A : Type u_1\nK : Type u_2\ninst✝⁵ : CommRing A\ninst✝⁴ : IsDomain A\ninst✝³ : IsDiscreteValuationRing A\ninst✝² : Field K\ninst✝¹ : Algebra A K\ninst✝ : IsFractionRing A K\n⊢ IsLocalRing.maximalIdeal A ≠ ⊥",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Sem... | [
"A : Type u_1\nK : Type u_2\ninst✝⁵ : CommRing A\ninst✝⁴ : IsDomain A\ninst✝³ : IsDiscreteValuationRing A\ninst✝² : Field K\ninst✝¹ : Algebra A K\ninst✝ : IsFractionRing A K\n⊢ ¬IsField A"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.Discrete.IsDiscreteValuationRing | {
"line": 60,
"column": 6
} | {
"line": 60,
"column": 22
} | {
"line": 60,
"column": 23
} | [
{
"pp": "case h.right\nA : Type u_1\nK : Type u_2\ninst✝⁵ : CommRing A\ninst✝⁴ : IsDomain A\ninst✝³ : IsDiscreteValuationRing A\ninst✝² : Field K\ninst✝¹ : Algebra A K\ninst✝ : IsFractionRing A K\nv : Valuation K (WithZero (Multiplicative ℤ)) := ⋯\nπ : K := ⋯\nhπ : v π = ↑(ofAdd (-1))\n⊢ Units.mk0 (v π) ⋯ ≠ 1",... | [
"case h.right\nA : Type u_1\nK : Type u_2\ninst✝⁵ : CommRing A\ninst✝⁴ : IsDomain A\ninst✝³ : IsDiscreteValuationRing A\ninst✝² : Field K\ninst✝¹ : Algebra A K\ninst✝ : IsFractionRing A K\nv : Valuation K (WithZero (Multiplicative ℤ)) := valuation K (maximalIdeal A)\nπ : K := ⋯.choose\nhπ : v π = ↑(ofAdd (-1))\n⊢ ¬... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Valued.ValuedField | {
"line": 80,
"column": 2
} | {
"line": 80,
"column": 52
} | {
"line": 81,
"column": 2
} | [
{
"pp": "K : Type u_1\ninst✝¹ : DivisionRing K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nv : Valuation K Γ₀\nx y r s : K\ny_ne : y ≠ 0\nhr : r ≠ 0\nhs : s ≠ 0\nh : v (x - y) < min (v s / v r * (v y * v y)) (v y)\nhr' : 0 < v r\n⊢ v (x⁻¹ - y⁻¹) * v r < v s",
"ppTerm": "?m.62",
"assigned"... | [
"K : Type u_1\ninst✝¹ : DivisionRing K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nv : Valuation K Γ₀\nx y r s : K\ny_ne : y ≠ 0\nhr : r ≠ 0\nhs : s ≠ 0\nh : v (x - y) < min (v s / v r * (v y * v y)) (v y)\nhr' : 0 < v r\nγ : Γ₀ˣ := Units.mk0 (v s / v r) ⋯\n⊢ v (x⁻¹ - y⁻¹) * v r < v s"
] | let γ : Γ₀ˣ := .mk0 (v s / v r) (by simp [hs, hr]) | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLet___1 | Lean.Parser.Tactic.tacticLet__ |
Mathlib.Topology.Algebra.Valued.ValuedField | {
"line": 115,
"column": 4
} | {
"line": 115,
"column": 15
} | {
"line": 115,
"column": 16
} | [
{
"pp": "K : Type u_1\ninst✝² : DivisionRing K\nΓ₀ : Type u_2\ninst✝¹ : LinearOrderedCommGroupWithZero Γ₀\ninst✝ : Valued K Γ₀\nx : K\nx_ne : x ≠ 0\nγ' : (ofClass v).ValueGroup₀ˣ := Units.mk0 ((restrict₀ (ofClass v)) x) ⋯\nhdef : γ' = Units.mk0 ((restrict₀ (ofClass v)) x) ⋯\ny : K\nhy : v y < (ofClass v) x\n⊢ y... | [
"K : Type u_1\ninst✝² : DivisionRing K\nΓ₀ : Type u_2\ninst✝¹ : LinearOrderedCommGroupWithZero Γ₀\ninst✝ : Valued K Γ₀\nx : K\nx_ne : x ≠ 0\nγ' : (ofClass v).ValueGroup₀ˣ := Units.mk0 ((restrict₀ (ofClass v)) x) ⋯\nhdef : γ' = Units.mk0 ((restrict₀ (ofClass v)) x) ⋯\ny : K\nhy : v y < (ofClass v) x\n⊢ v y < v x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Valued.WithVal | {
"line": 649,
"column": 4
} | {
"line": 649,
"column": 22
} | {
"line": 649,
"column": 23
} | [
{
"pp": "K : Type u_7\ninst✝¹ : DivisionRing K\nΓ₀ : Type u_8\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nv : Valuation K Γ₀\nγ : (ofClass v).ValueGroup₀ˣ\nr : K\nhr : (restrict₀ (ofClass v)) r = ↑γ\n⊢ v 0 < v r",
"ppTerm": "?m.90",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWi... | [
"K : Type u_7\ninst✝¹ : DivisionRing K\nΓ₀ : Type u_8\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nv : Valuation K Γ₀\nγ : (ofClass v).ValueGroup₀ˣ\nr : K\nhr : (restrict₀ (ofClass v)) r = ↑γ\n⊢ 0 < v r"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Valued.ValuedField | {
"line": 136,
"column": 35
} | {
"line": 136,
"column": 64
} | {
"line": 136,
"column": 65
} | [
{
"pp": "K : Type u_1\ninst✝¹ : DivisionRing K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\nx : K\nh : x ≠ 0\nv_ne : v.restrict x ≠ 0\n⊢ v x ≠ 0",
"ppTerm": "?m.172",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"L... | [
"K : Type u_1\ninst✝¹ : DivisionRing K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\nx : K\nh : x ≠ 0\nv_ne : v.restrict x ≠ 0\n⊢ ¬x = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Valued.ValuedField | {
"line": 152,
"column": 35
} | {
"line": 152,
"column": 46
} | {
"line": 152,
"column": 47
} | [
{
"pp": "K : Type u_1\ninst✝¹ : DivisionRing K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\nhsurj : Function.Surjective ⇑v\nx : K\nh : x ≠ 0\nh0 : v x ≠ 0\n⊢ v x ≠ 0",
"ppTerm": "?m.162",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMono... | [
"K : Type u_1\ninst✝¹ : DivisionRing K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\nhsurj : Function.Surjective ⇑v\nx : K\nh : x ≠ 0\nh0 : v x ≠ 0\n⊢ ¬x = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.DenselyOrdered | {
"line": 54,
"column": 2
} | {
"line": 54,
"column": 44
} | {
"line": 55,
"column": 2
} | [
{
"pp": "X : Type u_1\ninst✝¹ : LinearOrder X\ninst✝ : LocallyFiniteOrder X\ns : Set (WithBot X)\nH : DenselyOrdered ↑s\nx : X\nhx : ↑x ∈ s\ny : X\nhy : ↑y ∈ s\nhxy : x < y\nthis : ⟨↑x, hx⟩ < ⟨↑y, hy⟩\nz : { x // x ∈ s }\nhz : ⟨↑x, hx⟩ < z\nhz' : z < ⟨↑y, hy⟩\n⊢ ∃ a, (↑a ∈ s ∧ x < a) ∧ a < y",
"ppTerm": "?m... | [
"X : Type u_1\ninst✝¹ : LinearOrder X\ninst✝ : LocallyFiniteOrder X\ns : Set (WithBot X)\nH : DenselyOrdered ↑s\nx : X\nhx : ↑x ∈ s\ny : X\nhy : ↑y ∈ s\nhxy : x < y\nthis : ⟨↑x, hx⟩ < ⟨↑y, hy⟩\nz : { x // x ∈ s }\nhz : ↑x < ↑z\nhz' : ↑z < ↑y\n⊢ ∃ a, (↑a ∈ s ∧ x < a) ∧ a < y"
] | simp only [← Subtype.coe_lt_coe] at hz hz' | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.GroupTheory.ArchimedeanDensely | {
"line": 66,
"column": 2
} | {
"line": 66,
"column": 37
} | {
"line": 66,
"column": 38
} | [
{
"pp": "e : ℤ ≃+ ℤ\nhe : ¬IsOfFinAddOrder (e 1)\n⊢ AddSubgroup.zmultiples (e 1) = AddSubgroup.zmultiples 1",
"ppTerm": "?m.58",
"assigned": true,
"usedConstants": [
"Int.zmultiples_one",
"Eq.mpr",
"congrArg",
"id",
"Int",
"AddSubgroup",
"instOfNat",
"... | [
"e : ℤ ≃+ ℤ\nhe : ¬IsOfFinAddOrder (e 1)\n⊢ ⊤ = AddSubgroup.zmultiples (e 1)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.ArchimedeanDensely | {
"line": 115,
"column": 6
} | {
"line": 115,
"column": 54
} | {
"line": 115,
"column": 55
} | [
{
"pp": "case refine_1\nG : Type u_1\nG' : Type u_2\ninst✝⁵ : CommGroup G\ninst✝⁴ : LinearOrder G\ninst✝³ : IsOrderedMonoid G\ninst✝² : CommGroup G'\ninst✝¹ : LinearOrder G'\ninst✝ : IsOrderedMonoid G'\nx : G\ny : G'\nhxy : x = 1 ↔ y = 1\nhx : x = 1\na : G\nha : a ∈ closure {x}\n⊢ (fun x_1 ↦ ⟨1, ⋯⟩) ((fun x_1 ↦... | [
"case refine_1\nG : Type u_1\nG' : Type u_2\ninst✝⁵ : CommGroup G\ninst✝⁴ : LinearOrder G\ninst✝³ : IsOrderedMonoid G\ninst✝² : CommGroup G'\ninst✝¹ : LinearOrder G'\ninst✝ : IsOrderedMonoid G'\nx : G\ny : G'\nhxy : x = 1 ↔ y = 1\nhx : x = 1\na : G\nha : a ∈ closure {x}\n⊢ a = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.ArchimedeanDensely | {
"line": 117,
"column": 6
} | {
"line": 117,
"column": 61
} | {
"line": 117,
"column": 62
} | [
{
"pp": "case refine_2\nG : Type u_1\nG' : Type u_2\ninst✝⁵ : CommGroup G\ninst✝⁴ : LinearOrder G\ninst✝³ : IsOrderedMonoid G\ninst✝² : CommGroup G'\ninst✝¹ : LinearOrder G'\ninst✝ : IsOrderedMonoid G'\nx : G\ny : G'\nhxy : x = 1 ↔ y = 1\nhx : x = 1\na : G'\nha : a ∈ closure {y}\n⊢ (fun x_1 ↦ ⟨1, ⋯⟩) ((fun x_1 ... | [
"case refine_2\nG : Type u_1\nG' : Type u_2\ninst✝⁵ : CommGroup G\ninst✝⁴ : LinearOrder G\ninst✝³ : IsOrderedMonoid G\ninst✝² : CommGroup G'\ninst✝¹ : LinearOrder G'\ninst✝ : IsOrderedMonoid G'\nx : G\ny : G'\nhxy : x = 1 ↔ y = 1\nhx : x = 1\na : G'\nha : a ∈ closure {y}\n⊢ a = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.Discrete.IsDiscreteValuationRing | {
"line": 108,
"column": 49
} | {
"line": 118,
"column": 57
} | {
"line": 120,
"column": 0
} | [
{
"pp": "A : Type u_1\nK : Type u_2\ninst✝⁵ : CommRing A\ninst✝⁴ : IsDomain A\ninst✝³ : IsDiscreteValuationRing A\ninst✝² : Field K\ninst✝¹ : Algebra A K\ninst✝ : IsFractionRing A K\n⊢ MonoidHom.mker (valuation K (maximalIdeal A)) = Submonoid.map (algebraMap A K) (IsUnit.submonoid A)",
"ppTerm": "?m.37",
... | [] | by
ext a
simp only [MonoidHom.mem_mker, Submonoid.mem_map]
refine ⟨fun h ↦ ?_, fun h ↦ ?_⟩
· obtain ⟨b, rfl⟩ := IsDiscreteValuationRing.exists_lift_of_le_one h.le
rw [valuation_eq_one_iff_notMem] at h
simp only [IsDiscreteValuationRing.maximalIdeal, IsLocalRing.mem_maximalIdeal, mem_nonunits_iff,
... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.GroupTheory.ArchimedeanDensely | {
"line": 169,
"column": 34
} | {
"line": 169,
"column": 45
} | {
"line": 169,
"column": 46
} | [
{
"pp": "G : Type u_1\ninst✝³ : CommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedMonoid G\ninst✝ : MulArchimedean G\na b : G\nh : b = |a|ₘ ∧ 1 < b\nthis : ∀ {a : G}, b = |a|ₘ ∧ 1 < b → 1 ≤ a → IsLeast {y | y ∈ closure {a} ∧ 1 < y} b\nha : ¬1 ≤ a\n⊢ 1 ≤ a⁻¹",
"ppTerm": "?m.234",
"assigned": true,
... | [
"G : Type u_1\ninst✝³ : CommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedMonoid G\ninst✝ : MulArchimedean G\na b : G\nh : b = |a|ₘ ∧ 1 < b\nthis : ∀ {a : G}, b = |a|ₘ ∧ 1 < b → 1 ≤ a → IsLeast {y | y ∈ closure {a} ∧ 1 < y} b\nha : ¬1 ≤ a\n⊢ a ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.Reduction | {
"line": 174,
"column": 14
} | {
"line": 175,
"column": 11
} | {
"line": 175,
"column": 12
} | [
{
"pp": "case h.h₁\nR : Type u_1\ninst✝⁵ : CommRing R\nK : Type u_2\ninst✝⁴ : Field K\ninst✝³ : Algebra R K\ninst✝² : IsDomain R\ninst✝¹ : ValuationRing R\ninst✝ : IsFractionRing R K\nW : WeierstrassCurve K\nl₀ : List K := ⋯\nl : List (ValueGroup R K) := ⋯\nlmax : ValueGroup R K := ⋯\nhlmax_mem : lmax ∈ l\nhlma... | [
"case h.h₁\nR : Type u_1\ninst✝⁵ : CommRing R\nK : Type u_2\ninst✝⁴ : Field K\ninst✝³ : Algebra R K\ninst✝² : IsDomain R\ninst✝¹ : ValuationRing R\ninst✝ : IsFractionRing R K\nW : WeierstrassCurve K\nl₀ : List K := [W.a₁, W.a₂, W.a₃, W.a₄, W.a₆]\nl : List (ValueGroup R K) := List.map (fun a ↦ (valuation R K) a) l₀\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.Reduction | {
"line": 174,
"column": 14
} | {
"line": 175,
"column": 11
} | {
"line": 175,
"column": 12
} | [
{
"pp": "case h.h₂\nR : Type u_1\ninst✝⁵ : CommRing R\nK : Type u_2\ninst✝⁴ : Field K\ninst✝³ : Algebra R K\ninst✝² : IsDomain R\ninst✝¹ : ValuationRing R\ninst✝ : IsFractionRing R K\nW : WeierstrassCurve K\nl₀ : List K := ⋯\nl : List (ValueGroup R K) := ⋯\nlmax : ValueGroup R K := ⋯\nhlmax_mem : lmax ∈ l\nhlma... | [
"case h.h₂\nR : Type u_1\ninst✝⁵ : CommRing R\nK : Type u_2\ninst✝⁴ : Field K\ninst✝³ : Algebra R K\ninst✝² : IsDomain R\ninst✝¹ : ValuationRing R\ninst✝ : IsFractionRing R K\nW : WeierstrassCurve K\nl₀ : List K := [W.a₁, W.a₂, W.a₃, W.a₄, W.a₆]\nl : List (ValueGroup R K) := List.map (fun a ↦ (valuation R K) a) l₀\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.Reduction | {
"line": 174,
"column": 14
} | {
"line": 175,
"column": 11
} | {
"line": 175,
"column": 12
} | [
{
"pp": "case h.h₃\nR : Type u_1\ninst✝⁵ : CommRing R\nK : Type u_2\ninst✝⁴ : Field K\ninst✝³ : Algebra R K\ninst✝² : IsDomain R\ninst✝¹ : ValuationRing R\ninst✝ : IsFractionRing R K\nW : WeierstrassCurve K\nl₀ : List K := ⋯\nl : List (ValueGroup R K) := ⋯\nlmax : ValueGroup R K := ⋯\nhlmax_mem : lmax ∈ l\nhlma... | [
"case h.h₃\nR : Type u_1\ninst✝⁵ : CommRing R\nK : Type u_2\ninst✝⁴ : Field K\ninst✝³ : Algebra R K\ninst✝² : IsDomain R\ninst✝¹ : ValuationRing R\ninst✝ : IsFractionRing R K\nW : WeierstrassCurve K\nl₀ : List K := [W.a₁, W.a₂, W.a₃, W.a₄, W.a₆]\nl : List (ValueGroup R K) := List.map (fun a ↦ (valuation R K) a) l₀\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.Reduction | {
"line": 174,
"column": 14
} | {
"line": 175,
"column": 11
} | {
"line": 175,
"column": 12
} | [
{
"pp": "case h.h₄\nR : Type u_1\ninst✝⁵ : CommRing R\nK : Type u_2\ninst✝⁴ : Field K\ninst✝³ : Algebra R K\ninst✝² : IsDomain R\ninst✝¹ : ValuationRing R\ninst✝ : IsFractionRing R K\nW : WeierstrassCurve K\nl₀ : List K := ⋯\nl : List (ValueGroup R K) := ⋯\nlmax : ValueGroup R K := ⋯\nhlmax_mem : lmax ∈ l\nhlma... | [
"case h.h₄\nR : Type u_1\ninst✝⁵ : CommRing R\nK : Type u_2\ninst✝⁴ : Field K\ninst✝³ : Algebra R K\ninst✝² : IsDomain R\ninst✝¹ : ValuationRing R\ninst✝ : IsFractionRing R K\nW : WeierstrassCurve K\nl₀ : List K := [W.a₁, W.a₂, W.a₃, W.a₄, W.a₆]\nl : List (ValueGroup R K) := List.map (fun a ↦ (valuation R K) a) l₀\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.ArchimedeanDensely | {
"line": 190,
"column": 67
} | {
"line": 190,
"column": 78
} | {
"line": 190,
"column": 79
} | [
{
"pp": "G✝ : Type u_1\ninst✝⁷ : CommGroup G✝\ninst✝⁶ : LinearOrder G✝\ninst✝⁵ : IsOrderedMonoid G✝\ninst✝⁴ : MulArchimedean G✝\nG : Type u_2\ninst✝³ : AddCommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedAddMonoid G\ninst✝ : Archimedean G\nx : G\nh : IsLeast {y | 0 < y} x\n⊢ IsLeast {y | y ∈ ⊤ ∧ 0 < y} x"... | [
"G✝ : Type u_1\ninst✝⁷ : CommGroup G✝\ninst✝⁶ : LinearOrder G✝\ninst✝⁵ : IsOrderedMonoid G✝\ninst✝⁴ : MulArchimedean G✝\nG : Type u_2\ninst✝³ : AddCommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedAddMonoid G\ninst✝ : Archimedean G\nx : G\nh : IsLeast {y | 0 < y} x\n⊢ IsLeast {y | 0 < y} x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.Reduction | {
"line": 174,
"column": 14
} | {
"line": 175,
"column": 11
} | {
"line": 175,
"column": 12
} | [
{
"pp": "case h.h₆\nR : Type u_1\ninst✝⁵ : CommRing R\nK : Type u_2\ninst✝⁴ : Field K\ninst✝³ : Algebra R K\ninst✝² : IsDomain R\ninst✝¹ : ValuationRing R\ninst✝ : IsFractionRing R K\nW : WeierstrassCurve K\nl₀ : List K := ⋯\nl : List (ValueGroup R K) := ⋯\nlmax : ValueGroup R K := ⋯\nhlmax_mem : lmax ∈ l\nhlma... | [
"case h.h₆\nR : Type u_1\ninst✝⁵ : CommRing R\nK : Type u_2\ninst✝⁴ : Field K\ninst✝³ : Algebra R K\ninst✝² : IsDomain R\ninst✝¹ : ValuationRing R\ninst✝ : IsFractionRing R K\nW : WeierstrassCurve K\nl₀ : List K := [W.a₁, W.a₂, W.a₃, W.a₄, W.a₆]\nl : List (ValueGroup R K) := List.map (fun a ↦ (valuation R K) a) l₀\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.Reduction | {
"line": 182,
"column": 6
} | {
"line": 182,
"column": 28
} | {
"line": 182,
"column": 29
} | [
{
"pp": "case h\nR : Type u_1\ninst✝⁵ : CommRing R\nK : Type u_2\ninst✝⁴ : Field K\ninst✝³ : Algebra R K\ninst✝² : IsDomain R\ninst✝¹ : ValuationRing R\ninst✝ : IsFractionRing R K\nW : WeierstrassCurve K\nl₀ : List K := [W.a₁, W.a₂, W.a₃, W.a₄, W.a₆]\nl : List (ValueGroup R K) := List.map (fun a ↦ (valuation R ... | [
"case h\nR : Type u_1\ninst✝⁵ : CommRing R\nK : Type u_2\ninst✝⁴ : Field K\ninst✝³ : Algebra R K\ninst✝² : IsDomain R\ninst✝¹ : ValuationRing R\ninst✝ : IsFractionRing R K\nW : WeierstrassCurve K\nl₀ : List K := [W.a₁, W.a₂, W.a₃, W.a₄, W.a₆]\nl : List (ValueGroup R K) := List.map (fun a ↦ (valuation R K) a) l₀\nlm... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.ArchimedeanDensely | {
"line": 243,
"column": 6
} | {
"line": 243,
"column": 38
} | {
"line": 243,
"column": 39
} | [
{
"pp": "case neg.refine_2\nG : Type u_2\ninst✝³ : AddCommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedAddMonoid G\ninst✝ : Archimedean G\nx y : G\nH : ¬IsLeast {y | 0 < y} (y - x)\nhxy : x < y\nz : G\nhz : 0 < z ∧ z < y - x\n⊢ x + z < y",
"ppTerm": "?neg.refine_2✝",
"assigned": false,
"usedCo... | [
"case neg.refine_2\nG : Type u_2\ninst✝³ : AddCommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedAddMonoid G\ninst✝ : Archimedean G\nx y : G\nH : ¬IsLeast {y | 0 < y} (y - x)\nhxy : x < y\nz : G\nhz : 0 < z ∧ z < y - x\n⊢ x + z < y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.ArchimedeanDensely | {
"line": 254,
"column": 6
} | {
"line": 254,
"column": 26
} | {
"line": 254,
"column": 27
} | [
{
"pp": "case inl\nG : Type u_2\ninst✝³ : AddCommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedAddMonoid G\ninst✝ : Archimedean G\nthis : ∀ (x : G ≃+o ℤ), ¬DenselyOrdered G\nh : G ≃+o ℤ\n⊢ Nonempty (G ≃+o ℤ) ↔ ¬DenselyOrdered G",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Eq.... | [
"case inl\nG : Type u_2\ninst✝³ : AddCommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedAddMonoid G\ninst✝ : Archimedean G\nthis : ∀ (x : G ≃+o ℤ), ¬DenselyOrdered G\nh : G ≃+o ℤ\n⊢ Nonempty (G ≃+o ℤ)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.Reduction | {
"line": 241,
"column": 25
} | {
"line": 241,
"column": 36
} | {
"line": 241,
"column": 37
} | [
{
"pp": "R : Type u_1\ninst✝⁶ : CommRing R\ninst✝⁵ : IsDomain R\ninst✝⁴ : IsDiscreteValuationRing R\nK : Type u_2\ninst✝³ : Field K\ninst✝² : Algebra R K\ninst✝¹ : IsFractionRing R K\nW : WeierstrassCurve K\ninst✝ : IsMinimal R W\n⊢ IsIntegral R W",
"ppTerm": "?m.20",
"assigned": false,
"usedConstan... | [
"R : Type u_1\ninst✝⁶ : CommRing R\ninst✝⁵ : IsDomain R\ninst✝⁴ : IsDiscreteValuationRing R\nK : Type u_2\ninst✝³ : Field K\ninst✝² : Algebra R K\ninst✝¹ : IsFractionRing R K\nW : WeierstrassCurve K\ninst✝ : IsMinimal R W\n⊢ IsIntegral R W"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.Reduction | {
"line": 295,
"column": 2
} | {
"line": 295,
"column": 18
} | {
"line": 295,
"column": 19
} | [
{
"pp": "R : Type u_1\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDomain R\ninst✝³ : IsDiscreteValuationRing R\nK : Type u_2\ninst✝² : Field K\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\nW : WeierstrassCurve K\nhW : IsMinimal R W\nh :\n ¬(valuation K (IsDiscreteValuationRing.maximalIdeal R)) ((algebraMap R K) (int... | [
"R : Type u_1\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDomain R\ninst✝³ : IsDiscreteValuationRing R\nK : Type u_2\ninst✝² : Field K\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\nW : WeierstrassCurve K\nhW : IsMinimal R W\nh :\n ¬(valuation K (IsDiscreteValuationRing.maximalIdeal R)) ((algebraMap R K) (integralModel R... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Valued.ValuedField | {
"line": 393,
"column": 26
} | {
"line": 393,
"column": 61
} | {
"line": 393,
"column": 62
} | [
{
"pp": "K : Type u_1\ninst✝¹ : Field K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\nγ : Γ₀ˣ\nx : hat K\nγ₀' : (ofClass v).ValueGroup₀ := extension x\nhγ₀'_def : γ₀' = extension x\nγ₀ : Γ₀ := extensionValuation x\nhγ₀_def : γ₀ = extensionValuation x\nheq : γ₀ = embedding γ₀'\nh :... | [
"K : Type u_1\ninst✝¹ : Field K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\nγ : Γ₀ˣ\nx : hat K\nγ₀' : (ofClass v).ValueGroup₀ := extension x\nhγ₀'_def : γ₀' = extension x\nγ₀ : Γ₀ := extensionValuation x\nhγ₀_def : γ₀ = extensionValuation x\nheq : γ₀ = embedding γ₀'\nh : γ₀ ≠ 0\n⊢ γ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Valued.ValuedField | {
"line": 403,
"column": 6
} | {
"line": 403,
"column": 23
} | {
"line": 403,
"column": 24
} | [
{
"pp": "K : Type u_1\ninst✝¹ : Field K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\nγ : Γ₀ˣ\nx : hat K\nγ₀' : (ofClass v).ValueGroup₀ := extension x\nhγ₀'_def : γ₀' = extension x\nγ₀ : Γ₀ := extensionValuation x\nhγ₀_def : γ₀ = extensionValuation x\nheq : γ₀ = embedding γ₀'\nh :... | [
"K : Type u_1\ninst✝¹ : Field K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\nγ : Γ₀ˣ\nx : hat K\nγ₀' : (ofClass v).ValueGroup₀ := extension x\nhγ₀'_def : γ₀' = extension x\nγ₀ : Γ₀ := extensionValuation x\nhγ₀_def : γ₀ = extensionValuation x\nheq : γ₀ = embedding γ₀'\nh : γ₀ ≠ 0\nh' ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Valued.ValuedField | {
"line": 409,
"column": 6
} | {
"line": 409,
"column": 23
} | {
"line": 409,
"column": 24
} | [
{
"pp": "K : Type u_1\ninst✝¹ : Field K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\nγ : Γ₀ˣ\nx : hat K\nγ₀' : (ofClass v).ValueGroup₀ := extension x\nhγ₀'_def : γ₀' = extension x\nγ₀ : Γ₀ := extensionValuation x\nhγ₀_def : γ₀ = extensionValuation x\nheq : γ₀ = embedding γ₀'\nh :... | [
"K : Type u_1\ninst✝¹ : Field K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\nγ : Γ₀ˣ\nx : hat K\nγ₀' : (ofClass v).ValueGroup₀ := extension x\nhγ₀'_def : γ₀' = extension x\nγ₀ : Γ₀ := extensionValuation x\nhγ₀_def : γ₀ = extensionValuation x\nheq : γ₀ = embedding γ₀'\nh : γ₀ ≠ 0\nh' ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Valued.ValuedField | {
"line": 429,
"column": 4
} | {
"line": 429,
"column": 15
} | {
"line": 429,
"column": 16
} | [
{
"pp": "K : Type u_1\ninst✝¹ : Field K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\n⊢ embedding (extensionValuation.restrict ↑⋯.choose) = embedding 1",
"ppTerm": "?m.75",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
... | [
"K : Type u_1\ninst✝¹ : Field K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\n⊢ v ⋯.choose = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 116,
"column": 2
} | {
"line": 116,
"column": 43
} | {
"line": 117,
"column": 2
} | [
{
"pp": "case pos\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDedekindDomain R\nv : HeightOneSpectrum R\nx y : R\nhx : x = 0\n⊢ (if x * y = 0 then 0 else exp (-↑((Associates.mk v.asIdeal).count (Associates.mk (Ideal.span {x * y})).factors))) =\n (if x = 0 then 0 else exp (-↑((Associates.mk v.asIdeal).count... | [
"case neg\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDedekindDomain R\nv : HeightOneSpectrum R\nx y : R\nhx : ¬x = 0\n⊢ (if x * y = 0 then 0 else exp (-↑((Associates.mk v.asIdeal).count (Associates.mk (Ideal.span {x * y})).factors))) =\n (if x = 0 then 0 else exp (-↑((Associates.mk v.asIdeal).count (Associate... | · rw [hx, zero_mul, if_pos rfl, zero_mul] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Topology.Algebra.Valued.ValuedField | {
"line": 447,
"column": 6
} | {
"line": 447,
"column": 29
} | {
"line": 447,
"column": 30
} | [
{
"pp": "case pos\nK : Type u_1\ninst✝¹ : Field K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\na b : (ofClass v).ValueGroup₀\nx : K := ⋯.choose\nhx_def : x = ⋯.choose\ny : K := ⋯.choose\nhy_def : y = ⋯.choose\nxy : K := ⋯.choose\nhxy_def : xy = ⋯.choose\nhxy : v xy = embedding a ... | [
"case pos\nK : Type u_1\ninst✝¹ : Field K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\na b : (ofClass v).ValueGroup₀\nx : K := ⋯.choose\nhx_def : x = ⋯.choose\ny : K := ⋯.choose\nhy_def : y = ⋯.choose\nxy : K := ⋯.choose\nhxy_def : xy = ⋯.choose\nhxy : v xy = embedding a * embedding ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Valued.ValuedField | {
"line": 449,
"column": 8
} | {
"line": 449,
"column": 31
} | {
"line": 449,
"column": 32
} | [
{
"pp": "case pos\nK : Type u_1\ninst✝¹ : Field K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\na b : (ofClass v).ValueGroup₀\nx : K := ⋯.choose\nhx_def : x = ⋯.choose\ny : K := ⋯.choose\nhy_def : y = ⋯.choose\nxy : K := ⋯.choose\nhxy_def : xy = ⋯.choose\nhxy : v xy = embedding a ... | [
"case pos\nK : Type u_1\ninst✝¹ : Field K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\na b : (ofClass v).ValueGroup₀\nx : K := ⋯.choose\nhx_def : x = ⋯.choose\ny : K := ⋯.choose\nhy_def : y = ⋯.choose\nxy : K := ⋯.choose\nhxy_def : xy = ⋯.choose\nhxy : v xy = embedding a * embedding ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Basic | {
"line": 139,
"column": 2
} | {
"line": 139,
"column": 24
} | {
"line": 140,
"column": 4
} | [
{
"pp": "R : Type u_1\ninst✝ : Semiring R\nm n : ℕ\na b : R\n⊢ (monomial m) a * (monomial n) b = (monomial (m + n)) (a * b)",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Unit.unit",
"Nat.instMulZeroClass",
"Semiring.toModule",
"HMul.hMul",
"... | [
"R : Type u_1\ninst✝ : Semiring R\nm n : ℕ\na b : R\n⊢ (MvPowerSeries.monomial (single () m)) a * (MvPowerSeries.monomial (single () n)) b =\n (MvPowerSeries.monomial (single () m + single () n)) (a * b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Basic | {
"line": 230,
"column": 2
} | {
"line": 230,
"column": 55
} | {
"line": 230,
"column": 56
} | [
{
"pp": "R : Type u_1\ninst✝¹ : Semiring R\ninst✝ : Nontrivial R\nH : X = 0\n⊢ False",
"ppTerm": "?m.7",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_1\ninst✝¹ : Semiring R\ninst✝ : Nontrivial R\nH : X = 0\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Basic | {
"line": 254,
"column": 34
} | {
"line": 254,
"column": 54
} | {
"line": 254,
"column": 54
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nm n : σ →₀ ℕ\nφ : MvPowerSeries σ R\na : R\n⊢ a * (coeff (m + n - m)) φ = a * (coeff n) φ",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.instCanonicallyOrderedAdd",
"Nat.instMulZeroClass",
"Fin... | [
"σ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nm n : σ →₀ ℕ\nφ : MvPowerSeries σ R\na : R\n⊢ a * (coeff n) φ = a * (coeff n) φ",
"case hc\nσ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nm n : σ →₀ ℕ\nφ : MvPowerSeries σ R\na : R\n⊢ m ≤ m + n"
] | add_tsub_cancel_left | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.PowerSeries.Basic | {
"line": 293,
"column": 2
} | {
"line": 293,
"column": 13
} | {
"line": 293,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝ : Semiring R\nφ ψ : R⟦X⟧\nh : ∀ (n : ℕ), (coeff n) (φ * X) = (coeff n) (ψ * X)\nn : ℕ\n⊢ (coeff n) φ = (coeff n) ψ",
"ppTerm": "?m.33",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_1\ninst✝ : Semiring R\nφ ψ : R⟦X⟧\nh : ∀ (n : ℕ), (coeff n) (φ * X) = (coeff n) (ψ * X)\nn : ℕ\n⊢ (coeff n) φ = (coeff n) ψ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Basic | {
"line": 304,
"column": 2
} | {
"line": 304,
"column": 13
} | {
"line": 304,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝ : Semiring R\nφ ψ : R⟦X⟧\nh : ∀ (n : ℕ), (coeff n) (X * φ) = (coeff n) (X * ψ)\nn : ℕ\n⊢ (coeff n) φ = (coeff n) ψ",
"ppTerm": "?m.33",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_1\ninst✝ : Semiring R\nφ ψ : R⟦X⟧\nh : ∀ (n : ℕ), (coeff n) (X * φ) = (coeff n) (X * ψ)\nn : ℕ\n⊢ (coeff n) φ = (coeff n) ψ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Basic | {
"line": 308,
"column": 6
} | {
"line": 308,
"column": 44
} | {
"line": 309,
"column": 8
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\nφ ψ : MvPowerSeries σ R\nn : σ →₀ ℕ\n⊢ (coeff n) (φ * ψ) = (coeff n) (ψ * φ)",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Finsupp.instHasAntidiagonal",
"Eq.mpr",
"Nat.instMulZeroClass",
"Semigroup.toMu... | [
"σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\nφ ψ : MvPowerSeries σ R\nn : σ →₀ ℕ\n⊢ ∑ p ∈ antidiagonal n, (coeff p.1) φ * (coeff p.2) ψ = ∑ p ∈ antidiagonal n, (coeff p.1) ψ * (coeff p.2) φ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Basic | {
"line": 381,
"column": 2
} | {
"line": 381,
"column": 13
} | {
"line": 381,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝ : Semiring R\nk : ℕ\nφ ψ : R⟦X⟧\nh : ∀ (n : ℕ), (coeff n) (φ * X ^ k) = (coeff n) (ψ * X ^ k)\nn : ℕ\n⊢ (coeff n) φ = (coeff n) ψ",
"ppTerm": "?m.47",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_1\ninst✝ : Semiring R\nk : ℕ\nφ ψ : R⟦X⟧\nh : ∀ (n : ℕ), (coeff n) (φ * X ^ k) = (coeff n) (ψ * X ^ k)\nn : ℕ\n⊢ (coeff n) φ = (coeff n) ψ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Basic | {
"line": 394,
"column": 2
} | {
"line": 394,
"column": 13
} | {
"line": 394,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝ : Semiring R\nk : ℕ\nφ ψ : R⟦X⟧\nh : ∀ (n : ℕ), (coeff n) (X ^ k * φ) = (coeff n) (X ^ k * ψ)\nn : ℕ\n⊢ (coeff n) φ = (coeff n) ψ",
"ppTerm": "?m.47",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_1\ninst✝ : Semiring R\nk : ℕ\nφ ψ : R⟦X⟧\nh : ∀ (n : ℕ), (coeff n) (X ^ k * φ) = (coeff n) (X ^ k * ψ)\nn : ℕ\n⊢ (coeff n) φ = (coeff n) ψ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 154,
"column": 10
} | {
"line": 154,
"column": 33
} | {
"line": 155,
"column": 10
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDedekindDomain R\nv : HeightOneSpectrum R\nx y : R\nhx : ¬x = 0\nhy : ¬y = 0\nhxy : ¬x + y = 0\nnmin : ℕ :=\n min ((Associates.mk v.asIdeal).count (Associates.mk (Ideal.span {x})).factors)\n ((Associates.mk v.asIdeal).count (Associates.mk (Ideal.span {y}... | [
"R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDedekindDomain R\nv : HeightOneSpectrum R\nx y : R\nhx : ¬x = 0\nhy : ¬y = 0\nhxy : ¬x + y = 0\nnmin : ℕ :=\n min ((Associates.mk v.asIdeal).count (Associates.mk (Ideal.span {x})).factors)\n ((Associates.mk v.asIdeal).count (Associates.mk (Ideal.span {y})).factors)\... | · exact min_le_left _ _ | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.RingTheory.MvPowerSeries.Basic | {
"line": 361,
"column": 33
} | {
"line": 361,
"column": 56
} | {
"line": 361,
"column": 57
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝¹ : Semiring R\nm : ℕ\ninst✝ : NeZero m\nn : σ →₀ ℕ\na : R\ni : σ\nH : n + single i m = 0\n⊢ False",
"ppTerm": "?m.27",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"σ : Type u_1\nR : Type u_2\ninst✝¹ : Semiring R\nm : ℕ\ninst✝ : NeZero m\nn : σ →₀ ℕ\na : R\ni : σ\nH : n + single i m = 0\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Basic | {
"line": 421,
"column": 44
} | {
"line": 421,
"column": 55
} | {
"line": 421,
"column": 56
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nn : σ →₀ ℕ\nφ : MvPowerSeries σ R\na : R\n⊢ (coeff n) (φ * C a) = (coeff n) φ * a",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"σ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nn : σ →₀ ℕ\nφ : MvPowerSeries σ R\na : R\n⊢ (coeff n) (φ * C a) = (coeff n) φ * a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Basic | {
"line": 425,
"column": 44
} | {
"line": 425,
"column": 55
} | {
"line": 425,
"column": 56
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nn : σ →₀ ℕ\nφ : MvPowerSeries σ R\na : R\n⊢ (coeff n) (C a * φ) = a * (coeff n) φ",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"σ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nn : σ →₀ ℕ\nφ : MvPowerSeries σ R\na : R\n⊢ (coeff n) (C a * φ) = a * (coeff n) φ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Basic | {
"line": 428,
"column": 40
} | {
"line": 428,
"column": 51
} | {
"line": 428,
"column": 52
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nφ : MvPowerSeries σ R\ns : σ\nh : single s 1 ≤ 0\n⊢ False",
"ppTerm": "?m.32",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"σ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nφ : MvPowerSeries σ R\ns : σ\nh : single s 1 ≤ 0\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Basic | {
"line": 503,
"column": 4
} | {
"line": 503,
"column": 45
} | {
"line": 503,
"column": 46
} | [
{
"pp": "case e'_2.mpr\nR : Type u_1\ninst✝ : Semiring R\nn : ℕ\nφ : R⟦X⟧\nh : ∀ (m : Unit →₀ ℕ), m () < n → (MvPowerSeries.coeff m) φ = 0\nm : ℕ\nhm : m < n\n⊢ (single () m) () < n",
"ppTerm": "?e'_2.mpr",
"assigned": true,
"usedConstants": [
"Finsupp.instFunLike",
"Eq.mpr",
"Unit... | [
"case e'_2.mpr\nR : Type u_1\ninst✝ : Semiring R\nn : ℕ\nφ : R⟦X⟧\nh : ∀ (m : Unit →₀ ℕ), m () < n → (MvPowerSeries.coeff m) φ = 0\nm : ℕ\nhm : m < n\n⊢ m < n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Valued.ValuedField | {
"line": 481,
"column": 8
} | {
"line": 481,
"column": 61
} | {
"line": 481,
"column": 62
} | [
{
"pp": "K : Type u_1\ninst✝¹ : Field K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\na b : (ofClass v).ValueGroup₀\nhab : extensionValuation.restrict ↑⋯.choose = extensionValuation.restrict ↑⋯.choose\nx : K := ⋯.choose\nhx_def : x = ⋯.choose\ny : K := ⋯.choose\nhy_def : y = ⋯.cho... | [
"K : Type u_1\ninst✝¹ : Field K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\na b : (ofClass v).ValueGroup₀\nhab : extensionValuation.restrict ↑⋯.choose = extensionValuation.restrict ↑⋯.choose\nx : K := ⋯.choose\nhx_def : x = ⋯.choose\ny : K := ⋯.choose\nhy_def : y = ⋯.choose\nhx : v ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Basic | {
"line": 628,
"column": 2
} | {
"line": 628,
"column": 50
} | {
"line": 629,
"column": 4
} | [
{
"pp": "R : Type u_2\ninst✝ : CommSemiring R\nι : Type u_3\nf : ι → ℕ\ng : ι → R\ns : Finset ι\n⊢ ∏ i ∈ s, (monomial (f i)) (g i) = (monomial (∑ i ∈ s, f i)) (∏ i ∈ s, g i)",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Unit.unit",
"Nat.instMulZeroClass",
... | [
"R : Type u_2\ninst✝ : CommSemiring R\nι : Type u_3\nf : ι → ℕ\ng : ι → R\ns : Finset ι\n⊢ ∏ x ∈ s, (MvPowerSeries.monomial (single () (f x))) (g x) =\n (MvPowerSeries.monomial (∑ b ∈ s, single () (f b))) (∏ i ∈ s, g i)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.PowerSeries.Basic | {
"line": 632,
"column": 2
} | {
"line": 632,
"column": 24
} | {
"line": 632,
"column": 25
} | [
{
"pp": "R : Type u_2\ninst✝ : CommSemiring R\nm : ℕ\na : R\nn : ℕ\n⊢ (monomial m) a ^ n = (monomial (n * m)) (a ^ n)",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Semiring.toModule",
"HMul.hMul",
"CommSemiring.toSemiring",
"LinearMap.instFunLike",
"id",
... | [
"R : Type u_2\ninst✝ : CommSemiring R\nm : ℕ\na : R\nn : ℕ\n⊢ (MvPowerSeries.monomial (single () m)) a ^ n = (MvPowerSeries.monomial (single () (n * m))) (a ^ n)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Valued.ValuedField | {
"line": 495,
"column": 10
} | {
"line": 495,
"column": 37
} | {
"line": 495,
"column": 38
} | [
{
"pp": "K : Type u_1\ninst✝¹ : Field K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\na b : (ofClass v).ValueGroup₀\nx : K := ⋯.choose\nhx_def : x = ⋯.choose\ny : K := ⋯.choose\nhy_def : y = ⋯.choose\nhx : v x = embedding a\nhy : v y = embedding b\nthis : failed to pretty print ex... | [
"K : Type u_1\ninst✝¹ : Field K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\na b : (ofClass v).ValueGroup₀\nx : K := ⋯.choose\nhx_def : x = ⋯.choose\ny : K := ⋯.choose\nhy_def : y = ⋯.choose\nhx : v x = embedding a\nhy : v y = embedding b\nthis : failed to pretty print expression (us... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Basic | {
"line": 627,
"column": 10
} | {
"line": 632,
"column": 42
} | {
"line": 633,
"column": 8
} | [
{
"pp": "case pos\nσ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\ns : σ\nn : ℕ\nφ : MvPowerSeries σ R\nh : ∀ (m : σ →₀ ℕ), m s < n → (coeff m) φ = 0\nm : σ →₀ ℕ\nH : m - single s n + single s n = m\ni j : σ →₀ ℕ\nhij : (i, j).1 + (i, j).2 = m\nhne : (i, j) ≠ (single s n, m - single s n)\nhi : (i, j).1 = single... | [] | exfalso
apply hne
rw [← hij, ← hi, Prod.mk_inj]
refine ⟨rfl, ?_⟩
ext t
simp only [add_tsub_cancel_left] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.MvPowerSeries.Basic | {
"line": 627,
"column": 10
} | {
"line": 632,
"column": 42
} | {
"line": 633,
"column": 8
} | [
{
"pp": "case pos\nσ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\ns : σ\nn : ℕ\nφ : MvPowerSeries σ R\nh : ∀ (m : σ →₀ ℕ), m s < n → (coeff m) φ = 0\nm : σ →₀ ℕ\nH : m - single s n + single s n = m\ni j : σ →₀ ℕ\nhij : (i, j).1 + (i, j).2 = m\nhne : (i, j) ≠ (single s n, m - single s n)\nhi : (i, j).1 = single... | [] | exfalso
apply hne
rw [← hij, ← hi, Prod.mk_inj]
refine ⟨rfl, ?_⟩
ext t
simp only [add_tsub_cancel_left] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Algebra.Valued.ValuedField | {
"line": 510,
"column": 4
} | {
"line": 511,
"column": 39
} | {
"line": 511,
"column": 40
} | [
{
"pp": "case h\nK : Type u_1\ninst✝¹ : Field K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\nx : (ofClass extensionValuation).ValueGroup₀\nk' : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)\nhk' : (restrict₀ (ofClass extensionValua... | [
"case h\nK : Type u_1\ninst✝¹ : Field K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\nx : (ofClass extensionValuation).ValueGroup₀\nk' : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)\nhk' : (restrict₀ (ofClass extensionValuation)) k' = ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 282,
"column": 2
} | {
"line": 282,
"column": 53
} | {
"line": 283,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDedekindDomain R\nv : HeightOneSpectrum R\nhv : Irreducible (Associates.mk v.asIdeal)\nhlt : v.asIdeal ^ 2 < v.asIdeal\n⊢ ∃ π, v.intValuation π = exp (-1)",
"ppTerm": "?m.50",
"assigned": true,
"usedConstants": [
"Int.instAddCommMonoid",
... | [
"R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDedekindDomain R\nv : HeightOneSpectrum R\nhv : Irreducible (Associates.mk v.asIdeal)\nhlt : v.asIdeal ^ 2 < v.asIdeal\nπ : R\nmem : π ∈ v.asIdeal\nnotMem : π ∉ v.asIdeal ^ 2\n⊢ ∃ π, v.intValuation π = exp (-1)"
] | obtain ⟨π, mem, notMem⟩ := SetLike.exists_of_lt hlt | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 304,
"column": 2
} | {
"line": 305,
"column": 9
} | {
"line": 305,
"column": 10
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDedekindDomain R\nv : HeightOneSpectrum R\nπ : v.intValuation.Uniformizer\n⊢ v.intValuation ↑π.val = exp (-1)",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"Multiplicative.group",
"AddGroup.toSubtractionMonoid",
"Uni... | [
"R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDedekindDomain R\nv : HeightOneSpectrum R\nπ : v.intValuation.Uniformizer\n⊢ ↑(Valuation.IsRankOneDiscrete.generator v.intValuation) = (exp 1)⁻¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Order | {
"line": 136,
"column": 2
} | {
"line": 136,
"column": 13
} | {
"line": 136,
"column": 14
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nw : σ → ℕ\nf : MvPowerSeries σ R\n⊢ f ≠ 0 ↔ ∃ n d, (coeff d) f ≠ 0 ∧ (weight w) d = n",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Finsupp.instAddZeroClass",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
... | [
"σ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nw : σ → ℕ\nf : MvPowerSeries σ R\n⊢ ¬f = 0 ↔ ∃ d, ¬(coeff d) f = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Basic | {
"line": 652,
"column": 10
} | {
"line": 653,
"column": 46
} | {
"line": 654,
"column": 8
} | [
{
"pp": "case pos\nσ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\ns : σ\nn : ℕ\nφ : MvPowerSeries σ R\nh : ∀ (m : σ →₀ ℕ), m s < n → (coeff m) φ = 0\nm : σ →₀ ℕ\nH : n ≤ m s\nt : σ\nhst : s = t\n⊢ (m - single s n + single s n) t = m t",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
... | [] | subst t
simpa using! tsub_add_cancel_of_le H | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.MvPowerSeries.Basic | {
"line": 652,
"column": 10
} | {
"line": 653,
"column": 46
} | {
"line": 654,
"column": 8
} | [
{
"pp": "case pos\nσ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\ns : σ\nn : ℕ\nφ : MvPowerSeries σ R\nh : ∀ (m : σ →₀ ℕ), m s < n → (coeff m) φ = 0\nm : σ →₀ ℕ\nH : n ≤ m s\nt : σ\nhst : s = t\n⊢ (m - single s n + single s n) t = m t",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
... | [] | subst t
simpa using! tsub_add_cancel_of_le H | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.MvPowerSeries.Order | {
"line": 202,
"column": 4
} | {
"line": 202,
"column": 52
} | {
"line": 202,
"column": 53
} | [
{
"pp": "case coe\nσ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nw : σ → ℕ\nf : MvPowerSeries σ R\na✝ : ℕ\nh : ∀ (d : σ →₀ ℕ), ↑((weight w) d) < ↑a✝ → (coeff d) f = 0\n⊢ ∀ (d : σ →₀ ℕ), (weight w) d < a✝ → (coeff d) f = 0",
"ppTerm": "?coe",
"assigned": false,
"usedConstants": [],
"usedFVars":... | [
"case coe\nσ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nw : σ → ℕ\nf : MvPowerSeries σ R\na✝ : ℕ\nh : ∀ (d : σ →₀ ℕ), ↑((weight w) d) < ↑a✝ → (coeff d) f = 0\n⊢ ∀ (d : σ →₀ ℕ), (weight w) d < a✝ → (coeff d) f = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 447,
"column": 2
} | {
"line": 447,
"column": 13
} | {
"line": 447,
"column": 14
} | [
{
"pp": "case inr\nR : Type u_1\ninst✝⁴ : CommRing R\ninst✝³ : IsDedekindDomain R\nK : Type u_2\ninst✝² : Field K\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\nn d : R\nhd : d ∈ nonZeroDivisors R\nhx : IsLocalization.mk' K n ⟨d, hd⟩ * (algebraMap R K) ↑(n, ⟨d, hd⟩).2 = (algebraMap R K) (n, ⟨d, hd⟩).1\nhn0 ... | [
"case inr\nR : Type u_1\ninst✝⁴ : CommRing R\ninst✝³ : IsDedekindDomain R\nK : Type u_2\ninst✝² : Field K\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\nn d : R\nhd : d ∈ nonZeroDivisors R\nhx : IsLocalization.mk' K n ⟨d, hd⟩ * (algebraMap R K) ↑(n, ⟨d, hd⟩).2 = (algebraMap R K) (n, ⟨d, hd⟩).1\nhn0 : n ≠ 0\nhd0... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Order | {
"line": 212,
"column": 18
} | {
"line": 212,
"column": 54
} | {
"line": 212,
"column": 55
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nw : σ → ℕ\nf : MvPowerSeries σ R\nn : ℕ\nh : weightedOrder w f = ↑n\nd : σ →₀ ℕ\nhd : (coeff d) f ≠ 0 ∧ ↑((weight w) d) = weightedOrder w f\n⊢ (coeff d) f ≠ 0 ∧ (weight w) d = n",
"ppTerm": "?m.68",
"assigned": true,
"usedConstants": [
"... | [
"σ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nw : σ → ℕ\nf : MvPowerSeries σ R\nn : ℕ\nh : weightedOrder w f = ↑n\nd : σ →₀ ℕ\nhd : (coeff d) f ≠ 0 ∧ ↑((weight w) d) = weightedOrder w f\n⊢ ¬(coeff d) f = 0 ∧ (weight w) d = n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 474,
"column": 7
} | {
"line": 474,
"column": 45
} | {
"line": 474,
"column": 46
} | [
{
"pp": "R : Type u_1\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDedekindDomain R\nK : Type u_2\nS : Type u_3\ninst✝³ : Field K\ninst✝² : CommSemiring S\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\nv : HeightOneSpectrum R\nx : K\n⊢ x ∈ (subalgebra.ofField K v.asIdeal.primeCompl ⋯).toSubring ∨\n x⁻¹ ∈ (subalgebra... | [
"R : Type u_1\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDedekindDomain R\nK : Type u_2\nS : Type u_3\ninst✝³ : Field K\ninst✝² : CommSemiring S\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\nv : HeightOneSpectrum R\nx : K\n⊢ x ∈ subalgebra.ofField K v.asIdeal.primeCompl ⋯ ∨ x⁻¹ ∈ subalgebra.ofField K v.asIdeal.primeComp... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Basic | {
"line": 703,
"column": 8
} | {
"line": 703,
"column": 67
} | {
"line": 703,
"column": 68
} | [
{
"pp": "σ : Type u_1\nR : Type u_3\ninst✝² : CommSemiring R\nι : Type u_4\ninst✝¹ : DecidableEq ι\ninst✝ : DecidableEq σ\nf : ι → MvPowerSeries σ R\na : ι\ns : Finset ι\nha : a ∉ s\nih : ∀ (d : σ →₀ ℕ), (coeff d) (∏ j ∈ s, f j) = ∑ l ∈ s.finsuppAntidiag d, ∏ i ∈ s, (coeff (l i)) (f i)\nu v u' v' : σ →₀ ℕ\nhuv ... | [
"σ : Type u_1\nR : Type u_3\ninst✝² : CommSemiring R\nι : Type u_4\ninst✝¹ : DecidableEq ι\ninst✝ : DecidableEq σ\nf : ι → MvPowerSeries σ R\na : ι\ns : Finset ι\nha : a ∉ s\nih : ∀ (d : σ →₀ ℕ), (coeff d) (∏ j ∈ s, f j) = ∑ l ∈ s.finsuppAntidiag d, ∏ i ∈ s, (coeff (l i)) (f i)\nu v u' v' : σ →₀ ℕ\nhuv : u' + v' = ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Valued.ValuedField | {
"line": 584,
"column": 19
} | {
"line": 584,
"column": 30
} | {
"line": 584,
"column": 31
} | [
{
"pp": "K : Type u_1\ninst✝¹ : Field K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\nh : Function.Surjective ⇑v\nγ : Γ₀\na✝ : K\nha : v ↑a✝ = γ\n⊢ v ?m.243 = γ",
"ppTerm": "?m.244",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"K : Type u_1\ninst✝¹ : Field K\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nhv : Valued K Γ₀\nh : Function.Surjective ⇑v\nγ : Γ₀\na✝ : K\nha : v ↑a✝ = γ\n⊢ v ?m.243 = γ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 544,
"column": 2
} | {
"line": 546,
"column": 27
} | {
"line": 547,
"column": 2
} | [
{
"pp": "case pos\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDedekindDomain R\nv : HeightOneSpectrum R\na b : R\nhv : v.intValuation b ≤ v.intValuation a\nγ : Multiplicative ℤ\nha : a = 0\n⊢ ∃ y, v.intValuation (b - y * a) < ↑γ",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Int.... | [
"case neg\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDedekindDomain R\nv : HeightOneSpectrum R\na b : R\nhv : v.intValuation b ≤ v.intValuation a\nγ : Multiplicative ℤ\nha : ¬a = 0\n⊢ ∃ y, v.intValuation (b - y * a) < ↑γ"
] | · subst ha
rw [map_zero, le_zero_iff] at hv
exact ⟨0, by simp [hv]⟩ | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 562,
"column": 4
} | {
"line": 563,
"column": 90
} | {
"line": 563,
"column": 91
} | [
{
"pp": "case neg\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDedekindDomain R\nv : HeightOneSpectrum R\na b : R\nhv : v.intValuation b ≤ v.intValuation a\nγ : Multiplicative ℤ\nha : ¬a = 0\nhvaz : v.intValuation a ≠ 0\nhγz : ↑γ ≠ 0\nn : ℕ\nhna : exp (-↑n) < v.intValuation a\nhnγ : exp (-↑n) < ↑γ\nhvn : emult... | [
"case neg\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDedekindDomain R\nv : HeightOneSpectrum R\na b : R\nhv : v.intValuation b ≤ v.intValuation a\nγ : Multiplicative ℤ\nha : ¬a = 0\nhvaz : v.intValuation a ≠ 0\nhγz : ↑γ ≠ 0\nn : ℕ\nhna : exp (-↑n) < v.intValuation a\nhnγ : exp (-↑n) < ↑γ\nhvn : emultiplicity v.a... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Order | {
"line": 359,
"column": 21
} | {
"line": 359,
"column": 32
} | {
"line": 359,
"column": 33
} | [
{
"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",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Order | {
"line": 486,
"column": 4
} | {
"line": 486,
"column": 15
} | {
"line": 486,
"column": 16
} | [
{
"pp": "case mp\nσ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nf : MvPowerSeries σ R\nh : 1 ≤ f.order\n⊢ ↑(degree 0) < f.order",
"ppTerm": "?mp",
"assigned": true,
"usedConstants": [
"Finsupp.instAddZeroClass",
"Eq.mpr",
"Nat.instMulZeroClass",
"AddMonoidHom.instAddMonoidH... | [
"case mp\nσ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nf : MvPowerSeries σ R\nh : 1 ≤ f.order\n⊢ 0 < f.order"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Order | {
"line": 490,
"column": 4
} | {
"line": 490,
"column": 42
} | {
"line": 492,
"column": 0
} | [
{
"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",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"Finsupp.instAddZeroClass",
"Nat.instCanonicallyOrderedAdd",
... | [] | simp [(degree_eq_zero_iff d).mp hd, h] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.RingTheory.DedekindDomain.AdicValuation | {
"line": 722,
"column": 6
} | {
"line": 722,
"column": 90
} | {
"line": 722,
"column": 91
} | [
{
"pp": "case refine_1\nR : Type u_1\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDedekindDomain R\nK : Type u_2\nS : Type u_3\ninst✝³ : Field K\ninst✝² : CommSemiring S\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\nv : HeightOneSpectrum R\ns : Set (adicCompletion K v)\nx✝ : ∃ t ∈ 𝓝 0, toCompletion ⁻¹' t ⊆ s\nt : Set... | [
"case refine_1\nR : Type u_1\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDedekindDomain R\nK : Type u_2\nS : Type u_3\ninst✝³ : Field K\ninst✝² : CommSemiring S\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\nv : HeightOneSpectrum R\ns : Set (adicCompletion K v)\nx✝ : ∃ t ∈ 𝓝 0, toCompletion ⁻¹' t ⊆ s\nt : Set (HeightOneS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Order | {
"line": 499,
"column": 2
} | {
"line": 499,
"column": 13
} | {
"line": 499,
"column": 14
} | [
{
"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",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"instAddMonoidWithOn... | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Trunc | {
"line": 163,
"column": 2
} | {
"line": 163,
"column": 13
} | {
"line": 163,
"column": 14
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\ns : Finset (σ →₀ ℕ)\np : MvPowerSeries σ R\nx✝ : σ →₀ ℕ\n⊢ x✝ ∉ s → x✝ ∉ ((truncFinset R s) p).support",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.instMulZeroClass",
"Semiring.toModule",
... | [
"σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\ns : Finset (σ →₀ ℕ)\np : MvPowerSeries σ R\nx✝ : σ →₀ ℕ\n⊢ x✝ ∉ s → MvPolynomial.coeff x✝ ((truncFinset R s) p) = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Trunc | {
"line": 197,
"column": 22
} | {
"line": 197,
"column": 33
} | {
"line": 197,
"column": 34
} | [
{
"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",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.instMulZeroClass",
"Preorder.toLT",
"LinearOrderedCommMonoidWithZero.toIsBotZeroC... | [
"σ : Type u_1\nR : Type u_2\ninst✝¹ : DecidableEq σ\ninst✝ : CommSemiring R\nn : σ →₀ ℕ\nhnn : n ≠ 0\n⊢ 0 < n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Trunc | {
"line": 201,
"column": 20
} | {
"line": 201,
"column": 31
} | {
"line": 201,
"column": 32
} | [
{
"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",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.instMulZeroClass",
"Preorder.toLT",
"LinearOrderedCommMonoidWithZero.toIsB... | [
"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 < n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPowerSeries.Order | {
"line": 558,
"column": 2
} | {
"line": 558,
"column": 33
} | {
"line": 558,
"column": 34
} | [
{
"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",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.