module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 237,
"column": 80
} | {
"line": 238,
"column": 63
} | {
"line": 240,
"column": 0
} | [
{
"pp": "α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\na : α\nha : ¬IsMax a\n⊢ Ici (a + 1) = Ioi a",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Set.Ioi",
"Order.succ",
"Set.Ici",
"Order.succ_eq_add_one",
"con... | [] | by
simpa [succ_eq_add_one] using Ici_succ_eq_Ioi_of_not_isMax ha | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 243,
"column": 2
} | {
"line": 243,
"column": 31
} | {
"line": 243,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : Add α\ninst✝¹ : SuccAddOrder α\ninst✝ : NoMaxOrder α\na : α\n⊢ Ici (a + 1) = Ioi a",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : Add α\ninst✝¹ : SuccAddOrder α\ninst✝ : NoMaxOrder α\na : α\n⊢ Ici (a + 1) = Ioi a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 251,
"column": 2
} | {
"line": 251,
"column": 31
} | {
"line": 251,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na : α\nha : ¬IsMin a\n⊢ Ioi (a - 1) = Ici a",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na : α\nha : ¬IsMin a\n⊢ Ioi (a - 1) = Ici a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 256,
"column": 2
} | {
"line": 256,
"column": 31
} | {
"line": 256,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : Sub α\ninst✝¹ : PredSubOrder α\ninst✝ : NoMinOrder α\na : α\n⊢ Ioi (a - 1) = Ici a",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : Sub α\ninst✝¹ : PredSubOrder α\ninst✝ : NoMinOrder α\na : α\n⊢ Ioi (a - 1) = Ici a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Basic | {
"line": 647,
"column": 2
} | {
"line": 647,
"column": 30
} | {
"line": 647,
"column": 31
} | [
{
"pp": "α : Type u_2\ninst✝² : AddCommGroup α\ninst✝¹ : PartialOrder α\ninst✝ : IsOrderedAddMonoid α\ns t : Interval α\n⊢ (s - t).length ≤ s.length + t.length",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"cov... | [
"α : Type u_2\ninst✝² : AddCommGroup α\ninst✝¹ : PartialOrder α\ninst✝ : IsOrderedAddMonoid α\ns t : Interval α\n⊢ (s + -t).length ≤ s.length + t.length"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Basic | {
"line": 508,
"column": 41
} | {
"line": 508,
"column": 52
} | {
"line": 508,
"column": 53
} | [
{
"pp": "Γ' : Type u_2\nR : Type u_3\ninst✝² : Zero R\ninst✝¹ : PartialOrder Γ'\nΓ : Type u_5\ninst✝ : LinearOrder Γ\nf : Γ ↪o Γ'\nx : R⟦Γ⟧\nhx : x ≠ 0\n⊢ x.orderTop ≠ ⊤",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"HahnSeries.orderTop_eq_top._sim... | [
"Γ' : Type u_2\nR : Type u_3\ninst✝² : Zero R\ninst✝¹ : PartialOrder Γ'\nΓ : Type u_5\ninst✝ : LinearOrder Γ\nf : Γ ↪o Γ'\nx : R⟦Γ⟧\nhx : x ≠ 0\n⊢ ¬x = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Basic | {
"line": 510,
"column": 4
} | {
"line": 510,
"column": 15
} | {
"line": 510,
"column": 16
} | [
{
"pp": "case inr.hg\nΓ' : Type u_2\nR : Type u_3\ninst✝² : Zero R\ninst✝¹ : PartialOrder Γ'\nΓ : Type u_5\ninst✝ : LinearOrder Γ\nf : Γ ↪o Γ'\nx : R⟦Γ⟧\nhx : x ≠ 0\n⊢ f (x.orderTop.untop ⋯) ∈ (embDomain f x).support",
"ppTerm": "?inr.hg",
"assigned": true,
"usedConstants": [
"HahnSeries.suppo... | [
"case inr.hg\nΓ' : Type u_2\nR : Type u_3\ninst✝² : Zero R\ninst✝¹ : PartialOrder Γ'\nΓ : Type u_5\ninst✝ : LinearOrder Γ\nf : Γ ↪o Γ'\nx : R⟦Γ⟧\nhx : x ≠ 0\n⊢ ¬x.coeff (x.orderTop.untop ⋯) = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Basic | {
"line": 516,
"column": 2
} | {
"line": 516,
"column": 13
} | {
"line": 516,
"column": 14
} | [
{
"pp": "case inr.hx\nΓ' : Type u_2\nR : Type u_3\ninst✝² : Zero R\ninst✝¹ : PartialOrder Γ'\nΓ : Type u_5\ninst✝ : LinearOrder Γ\nf : Γ ↪o Γ'\nx : R⟦Γ⟧\nhx : x ≠ 0\nz : Γ\nhz : z ∈ x.support\nhy : f z ∈ (embDomain f x).support\n⊢ x.coeff z ≠ 0",
"ppTerm": "?inr.hx",
"assigned": true,
"usedConstants... | [
"case inr.hx\nΓ' : Type u_2\nR : Type u_3\ninst✝² : Zero R\ninst✝¹ : PartialOrder Γ'\nΓ : Type u_5\ninst✝ : LinearOrder Γ\nf : Γ ↪o Γ'\nx : R⟦Γ⟧\nhx : x ≠ 0\nz : Γ\nhz : z ∈ x.support\nhy : f z ∈ (embDomain f x).support\n⊢ ¬x.coeff z = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Addition | {
"line": 231,
"column": 2
} | {
"line": 231,
"column": 52
} | {
"line": 231,
"column": 53
} | [
{
"pp": "R : Type u_3\ninst✝¹ : AddMonoid R\nΓ : Type u_8\ninst✝ : LinearOrder Γ\nx y : R⟦Γ⟧\nhxy : y.orderTop < x.orderTop\n⊢ (x + y).orderTop = y.orderTop",
"ppTerm": "?m.29",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_3\ninst✝¹ : AddMonoid R\nΓ : Type u_8\ninst✝ : LinearOrder Γ\nx y : R⟦Γ⟧\nhxy : y.orderTop < x.orderTop\n⊢ (x + y).orderTop = y.orderTop"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Addition | {
"line": 243,
"column": 50
} | {
"line": 243,
"column": 61
} | {
"line": 243,
"column": 62
} | [
{
"pp": "R : Type u_3\ninst✝¹ : AddMonoid R\nΓ : Type u_8\ninst✝ : LinearOrder Γ\nx y : R⟦Γ⟧\nhxy : x.orderTop < y.orderTop\nhx : x ≠ 0\nho : (x + y).orderTop = x.orderTop\nh : ¬x + y = 0\n⊢ ↑(x.orderTop.untop ⋯) < y.orderTop",
"ppTerm": "?m.123",
"assigned": true,
"usedConstants": [
"Iff.mpr"... | [
"R : Type u_3\ninst✝¹ : AddMonoid R\nΓ : Type u_8\ninst✝ : LinearOrder Γ\nx y : R⟦Γ⟧\nhxy : x.orderTop < y.orderTop\nhx : x ≠ 0\nho : (x + y).orderTop = x.orderTop\nh : ¬x + y = 0\n⊢ x.orderTop < y.orderTop"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Addition | {
"line": 247,
"column": 2
} | {
"line": 247,
"column": 52
} | {
"line": 247,
"column": 53
} | [
{
"pp": "R : Type u_3\ninst✝¹ : AddMonoid R\nΓ : Type u_8\ninst✝ : LinearOrder Γ\nx y : R⟦Γ⟧\nhxy : y.orderTop < x.orderTop\n⊢ (x + y).leadingCoeff = y.leadingCoeff",
"ppTerm": "?m.29",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_3\ninst✝¹ : AddMonoid R\nΓ : Type u_8\ninst✝ : LinearOrder Γ\nx y : R⟦Γ⟧\nhxy : y.orderTop < x.orderTop\n⊢ (x + y).leadingCoeff = y.leadingCoeff"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Addition | {
"line": 259,
"column": 2
} | {
"line": 259,
"column": 33
} | {
"line": 259,
"column": 34
} | [
{
"pp": "Γ : Type u_1\ninst✝² : PartialOrder Γ\nR : Type u_8\ninst✝¹ : AddCancelCommMonoid R\ninst✝ : Zero Γ\nx y : R⟦Γ⟧\nhxy : x = y + (single x.order) x.leadingCoeff\n⊢ y.coeff x.order = 0",
"ppTerm": "?m.37",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"Γ : Type u_1\ninst✝² : PartialOrder Γ\nR : Type u_8\ninst✝¹ : AddCancelCommMonoid R\ninst✝ : Zero Γ\nx y : R⟦Γ⟧\nhxy : x = y + (single x.order) x.leadingCoeff\n⊢ y.coeff x.order = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Addition | {
"line": 273,
"column": 4
} | {
"line": 273,
"column": 15
} | {
"line": 273,
"column": 16
} | [
{
"pp": "case inl\nR : Type u_8\nΓ : Type u_9\ninst✝² : LinearOrder Γ\ninst✝¹ : Zero Γ\ninst✝ : AddCancelCommMonoid R\nx y : R⟦Γ⟧\nhxy : x = y + (single x.order) x.leadingCoeff\nhy : y ≠ 0\nthis : x.order ≠ y.order\nhg : x.order ∈ y.support\n⊢ x.order ∈ x.support",
"ppTerm": "?inl",
"assigned": true,
... | [
"case inl\nR : Type u_8\nΓ : Type u_9\ninst✝² : LinearOrder Γ\ninst✝¹ : Zero Γ\ninst✝ : AddCancelCommMonoid R\nx y : R⟦Γ⟧\nhxy : x = y + (single x.order) x.leadingCoeff\nhy : y ≠ 0\nthis : x.order ≠ y.order\nhg : x.order ∈ y.support\n⊢ ¬x = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Addition | {
"line": 276,
"column": 4
} | {
"line": 276,
"column": 22
} | {
"line": 276,
"column": 23
} | [
{
"pp": "case inr\nR : Type u_8\nΓ : Type u_9\ninst✝² : LinearOrder Γ\ninst✝¹ : Zero Γ\ninst✝ : AddCancelCommMonoid R\nx y : R⟦Γ⟧\nhxy : x = y + (single x.order) x.leadingCoeff\nhy : y ≠ 0\nthis✝ : x.order ≠ y.order\ng : Γ\nhg : g ∈ y.support\nhgx : g ≠ x.order\nthis : x.coeff g = y.coeff g\n⊢ g ∈ x.support",
... | [
"case inr\nR : Type u_8\nΓ : Type u_9\ninst✝² : LinearOrder Γ\ninst✝¹ : Zero Γ\ninst✝ : AddCancelCommMonoid R\nx y : R⟦Γ⟧\nhxy : x = y + (single x.order) x.leadingCoeff\nhy : y ≠ 0\nthis✝ : x.order ≠ y.order\ng : Γ\nhg : g ∈ y.support\nhgx : g ≠ x.order\nthis : x.coeff g = y.coeff g\n⊢ ¬y.coeff g = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Addition | {
"line": 308,
"column": 2
} | {
"line": 308,
"column": 33
} | {
"line": 310,
"column": 0
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\ninst✝² : PartialOrder Γ\ninst✝¹ : AddMonoid R\ninst✝ : DecidableLT Γ\nc : Γ\nx y : R⟦Γ⟧\ni : Γ\n⊢ ((truncLT c) (x + y)).coeff i = ((truncLT c) x + (truncLT c) y).coeff i",
"ppTerm": "?m.46",
"assigned": true,
"usedConstants": [
"ZeroHom.funLike",
"Pre... | [] | by_cases h : i < c <;> simp [h] | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Algebra.Order.Module.PositiveLinearMap | {
"line": 61,
"column": 26
} | {
"line": 61,
"column": 37
} | {
"line": 61,
"column": 38
} | [
{
"pp": "F' : Type u_5\nE₁' : Type u_6\nE₂' : Type u_7\ninst✝⁷ : FunLike F' E₁' E₂'\ninst✝⁶ : AddGroup E₁'\ninst✝⁵ : LE E₁'\ninst✝⁴ : AddRightMono E₁'\ninst✝³ : AddGroup E₂'\ninst✝² : LE E₂'\ninst✝¹ : AddRightMono E₂'\ninst✝ : AddMonoidHomClass F' E₁' E₂'\nh : ∀ (f : F') (x : E₁'), 0 ≤ x → 0 ≤ f x\nf : F'\na b ... | [
"F' : Type u_5\nE₁' : Type u_6\nE₂' : Type u_7\ninst✝⁷ : FunLike F' E₁' E₂'\ninst✝⁶ : AddGroup E₁'\ninst✝⁵ : LE E₁'\ninst✝⁴ : AddRightMono E₁'\ninst✝³ : AddGroup E₂'\ninst✝² : LE E₂'\ninst✝¹ : AddRightMono E₂'\ninst✝ : AddMonoidHomClass F' E₁' E₂'\nh : ∀ (f : F') (x : E₁'), 0 ≤ x → 0 ≤ f x\nf : F'\na b : E₁'\nhab :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Module.PositiveLinearMap | {
"line": 170,
"column": 19
} | {
"line": 170,
"column": 42
} | {
"line": 170,
"column": 43
} | [
{
"pp": "case succ\nR : Type u_1\nE₁ : Type u_2\nE₂ : Type u_3\nE₃ : Type u_4\ninst✝¹⁰ : Semiring R\ninst✝⁹ : AddCommMonoid E₁\ninst✝⁸ : PartialOrder E₁\ninst✝⁷ : AddCommMonoid E₂\ninst✝⁶ : PartialOrder E₂\ninst✝⁵ : AddCommMonoid E₃\ninst✝⁴ : PartialOrder E₃\ninst✝³ : Module R E₁\ninst✝² : Module R E₂\ninst✝¹ :... | [
"case succ\nR : Type u_1\nE₁ : Type u_2\nE₂ : Type u_3\nE₃ : Type u_4\ninst✝¹⁰ : Semiring R\ninst✝⁹ : AddCommMonoid E₁\ninst✝⁸ : PartialOrder E₁\ninst✝⁷ : AddCommMonoid E₂\ninst✝⁶ : PartialOrder E₂\ninst✝⁵ : AddCommMonoid E₃\ninst✝⁴ : PartialOrder E₃\ninst✝³ : Module R E₁\ninst✝² : Module R E₂\ninst✝¹ : Module R E₃... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Module.PositiveLinearMap | {
"line": 203,
"column": 6
} | {
"line": 203,
"column": 17
} | {
"line": 203,
"column": 18
} | [
{
"pp": "R : Type u_1\nE₁ : Type u_2\nE₂ : Type u_3\ninst✝⁸ : Semiring R\ninst✝⁷ : AddCommGroup E₁\ninst✝⁶ : PartialOrder E₁\ninst✝⁵ : IsOrderedAddMonoid E₁\ninst✝⁴ : AddCommGroup E₂\ninst✝³ : PartialOrder E₂\ninst✝² : IsOrderedAddMonoid E₂\ninst✝¹ : Module R E₁\ninst✝ : Module R E₂\nf : E₁ →ₗ[R] E₂\nhf : ∀ (x ... | [
"R : Type u_1\nE₁ : Type u_2\nE₂ : Type u_3\ninst✝⁸ : Semiring R\ninst✝⁷ : AddCommGroup E₁\ninst✝⁶ : PartialOrder E₁\ninst✝⁵ : IsOrderedAddMonoid E₁\ninst✝⁴ : AddCommGroup E₂\ninst✝³ : PartialOrder E₂\ninst✝² : IsOrderedAddMonoid E₂\ninst✝¹ : Module R E₁\ninst✝ : Module R E₂\nf : E₁ →ₗ[R] E₂\nhf : ∀ (x : E₁), 0 ≤ x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder | {
"line": 52,
"column": 24
} | {
"line": 52,
"column": 35
} | {
"line": 52,
"column": 36
} | [
{
"pp": "M : Type u_1\ninst✝⁴ : CancelCommMonoid M\ninst✝³ : LinearOrder M\ninst✝² : IsOrderedMonoid M\ninst✝¹ : LocallyFiniteOrder M\ninst✝ : ExistsMulOfLE M\na b c d : M\nh₁ : a * c ≤ a * c * d\nh₂ : a * c * d < b * c\n⊢ a ≤ a * d",
"ppTerm": "?m.101",
"assigned": true,
"usedConstants": [
"l... | [
"M : Type u_1\ninst✝⁴ : CancelCommMonoid M\ninst✝³ : LinearOrder M\ninst✝² : IsOrderedMonoid M\ninst✝¹ : LocallyFiniteOrder M\ninst✝ : ExistsMulOfLE M\na b c d : M\nh₁ : a * c ≤ a * c * d\nh₂ : a * c * d < b * c\n⊢ 1 ≤ d"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder | {
"line": 52,
"column": 43
} | {
"line": 52,
"column": 77
} | {
"line": 52,
"column": 78
} | [
{
"pp": "M : Type u_1\ninst✝⁴ : CancelCommMonoid M\ninst✝³ : LinearOrder M\ninst✝² : IsOrderedMonoid M\ninst✝¹ : LocallyFiniteOrder M\ninst✝ : ExistsMulOfLE M\na b c d : M\nh₁ : a * c ≤ a * c * d\nh₂ : a * c * d < b * c\n⊢ a * d < b",
"ppTerm": "?m.102",
"assigned": false,
"usedConstants": [],
"... | [
"M : Type u_1\ninst✝⁴ : CancelCommMonoid M\ninst✝³ : LinearOrder M\ninst✝² : IsOrderedMonoid M\ninst✝¹ : LocallyFiniteOrder M\ninst✝ : ExistsMulOfLE M\na b c d : M\nh₁ : a * c ≤ a * c * d\nh₂ : a * c * d < b * c\n⊢ a * d < b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder | {
"line": 97,
"column": 30
} | {
"line": 97,
"column": 41
} | {
"line": 97,
"column": 42
} | [
{
"pp": "M : Type u_1\nG : Type u_2\ninst✝⁷ : AddCancelCommMonoid M\ninst✝⁶ : LinearOrder M\ninst✝⁵ : IsOrderedAddMonoid M\ninst✝⁴ : LocallyFiniteOrder M\ninst✝³ : AddCommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedAddMonoid G\ninst✝ : LocallyFiniteOrder G\na b : G\nhab : a ≤ b\nha : a ≤ 0\nhb : b ≤ 0\n⊢... | [
"M : Type u_1\nG : Type u_2\ninst✝⁷ : AddCancelCommMonoid M\ninst✝⁶ : LinearOrder M\ninst✝⁵ : IsOrderedAddMonoid M\ninst✝⁴ : LocallyFiniteOrder M\ninst✝³ : AddCommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedAddMonoid G\ninst✝ : LocallyFiniteOrder G\na b : G\nhab : a ≤ b\nha : a ≤ 0\nhb : b ≤ 0\n⊢ a + b ≤ 0"
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder | {
"line": 108,
"column": 30
} | {
"line": 108,
"column": 41
} | {
"line": 108,
"column": 42
} | [
{
"pp": "M : Type u_1\nG : Type u_2\ninst✝⁷ : AddCancelCommMonoid M\ninst✝⁶ : LinearOrder M\ninst✝⁵ : IsOrderedAddMonoid M\ninst✝⁴ : LocallyFiniteOrder M\ninst✝³ : AddCommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedAddMonoid G\ninst✝ : LocallyFiniteOrder G\na b : G\nhab : a ≤ (fun x ↦ a + x) b\n⊢ 0 ≤ b",... | [
"M : Type u_1\nG : Type u_2\ninst✝⁷ : AddCancelCommMonoid M\ninst✝⁶ : LinearOrder M\ninst✝⁵ : IsOrderedAddMonoid M\ninst✝⁴ : LocallyFiniteOrder M\ninst✝³ : AddCommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedAddMonoid G\ninst✝ : LocallyFiniteOrder G\na b : G\nhab : a ≤ (fun x ↦ a + x) b\n⊢ 0 ≤ b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 81,
"column": 50
} | {
"line": 81,
"column": 91
} | {
"line": 81,
"column": 92
} | [
{
"pp": "Γ : Type u_1\nR : Type u_2\ninst✝² : LinearOrder Γ\ninst✝¹ : Zero R\ninst✝ : LinearOrder R\nx : Lex R⟦Γ⟧\nhpos : 0 < (ofLex x).leadingCoeff\nhne : ofLex x ≠ 0\nhtop : (ofLex x).orderTop ≠ ⊤\n⊢ (ofLex 0).coeff ((ofLex x).orderTop.untop htop) < (ofLex x).coeff ((ofLex x).orderTop.untop htop)",
"ppTer... | [
"Γ : Type u_1\nR : Type u_2\ninst✝² : LinearOrder Γ\ninst✝¹ : Zero R\ninst✝ : LinearOrder R\nx : Lex R⟦Γ⟧\nhpos : 0 < (ofLex x).leadingCoeff\nhne : ofLex x ≠ 0\nhtop : (ofLex x).orderTop ≠ ⊤\n⊢ 0 < (ofLex x).leadingCoeff"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 83,
"column": 4
} | {
"line": 83,
"column": 15
} | {
"line": 83,
"column": 16
} | [
{
"pp": "case mp\nΓ : Type u_1\nR : Type u_2\ninst✝² : LinearOrder Γ\ninst✝¹ : Zero R\ninst✝ : LinearOrder R\nx : Lex R⟦Γ⟧\nhpos : 0 < (ofLex x).leadingCoeff\nhne : ofLex x ≠ 0\nhtop : (ofLex x).orderTop ≠ ⊤\nj : Γ\nhj : j < (ofLex x).orderTop.untop htop\n⊢ (ofLex 0).coeff j = (ofLex x).coeff j",
"ppTerm": ... | [
"case mp\nΓ : Type u_1\nR : Type u_2\ninst✝² : LinearOrder Γ\ninst✝¹ : Zero R\ninst✝ : LinearOrder R\nx : Lex R⟦Γ⟧\nhpos : 0 < (ofLex x).leadingCoeff\nhne : ofLex x ≠ 0\nhtop : (ofLex x).orderTop ≠ ⊤\nj : Γ\nhj : j < (ofLex x).orderTop.untop htop\n⊢ 0 = (ofLex x).coeff j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 87,
"column": 8
} | {
"line": 87,
"column": 19
} | {
"line": 87,
"column": 20
} | [
{
"pp": "case hg\nΓ : Type u_1\nR : Type u_2\ninst✝² : LinearOrder Γ\ninst✝¹ : Zero R\ninst✝ : LinearOrder R\nx : Lex R⟦Γ⟧\ni : Γ\nhj : ∀ j < i, (ofLex 0).coeff j = (ofLex x).coeff j\nhi : (ofLex 0).coeff i < (ofLex x).coeff i\n⊢ i ∈ (ofLex x).support",
"ppTerm": "?hg",
"assigned": true,
"usedConsta... | [
"case hg\nΓ : Type u_1\nR : Type u_2\ninst✝² : LinearOrder Γ\ninst✝¹ : Zero R\ninst✝ : LinearOrder R\nx : Lex R⟦Γ⟧\ni : Γ\nhj : ∀ j < i, (ofLex 0).coeff j = (ofLex x).coeff j\nhi : (ofLex 0).coeff i < (ofLex x).coeff i\n⊢ ¬(ofLex x).coeff i = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 90,
"column": 8
} | {
"line": 90,
"column": 19
} | {
"line": 90,
"column": 20
} | [
{
"pp": "case hx\nΓ : Type u_1\nR : Type u_2\ninst✝² : LinearOrder Γ\ninst✝¹ : Zero R\ninst✝ : LinearOrder R\nx : Lex R⟦Γ⟧\ni : Γ\nhj : ∀ j < i, (ofLex 0).coeff j = (ofLex x).coeff j\nhi : (ofLex 0).coeff i < (ofLex x).coeff i\ng : Γ\nhg : g < i\n⊢ g ∉ (ofLex x).support",
"ppTerm": "?hx",
"assigned": tr... | [
"case hx\nΓ : Type u_1\nR : Type u_2\ninst✝² : LinearOrder Γ\ninst✝¹ : Zero R\ninst✝ : LinearOrder R\nx : Lex R⟦Γ⟧\ni : Γ\nhj : ∀ j < i, (ofLex 0).coeff j = (ofLex x).coeff j\nhi : (ofLex 0).coeff i < (ofLex x).coeff i\ng : Γ\nhg : g < i\n⊢ (ofLex x).coeff g = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 95,
"column": 4
} | {
"line": 95,
"column": 15
} | {
"line": 95,
"column": 16
} | [
{
"pp": "case mpr\nΓ : Type u_1\nR : Type u_2\ninst✝² : LinearOrder Γ\ninst✝¹ : Zero R\ninst✝ : LinearOrder R\nx : Lex R⟦Γ⟧\ni : Γ\nhj : ∀ j < i, (ofLex 0).coeff j = (ofLex x).coeff j\nhi : (ofLex 0).coeff i < (ofLex x).coeff i\nhorder : (ofLex x).orderTop = ↑i\nhtop : (ofLex x).orderTop ≠ ⊤\nhne : ofLex x ≠ 0\... | [
"case mpr\nΓ : Type u_1\nR : Type u_2\ninst✝² : LinearOrder Γ\ninst✝¹ : Zero R\ninst✝ : LinearOrder R\nx : Lex R⟦Γ⟧\ni : Γ\nhj : ∀ j < i, (ofLex 0).coeff j = (ofLex x).coeff j\nhi : (ofLex 0).coeff i < (ofLex x).coeff i\nhorder : (ofLex x).orderTop = ↑i\nhtop : (ofLex x).orderTop ≠ ⊤\nhne : ofLex x ≠ 0\nhorder' : (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Unbundled.Units | {
"line": 25,
"column": 2
} | {
"line": 25,
"column": 13
} | {
"line": 25,
"column": 14
} | [
{
"pp": "M : Type u_1\ninst✝² : Monoid M\ninst✝¹ : LE M\ninst✝ : MulLeftMono M\nu : Mˣ\nx✝¹ x✝ : M\nh : ↑u * x✝¹ ≤ ↑u * x✝\n⊢ x✝¹ ≤ x✝",
"ppTerm": "?m.10",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"M : Type u_1\ninst✝² : Monoid M\ninst✝¹ : LE M\ninst✝ : MulLeftMono M\nu : Mˣ\nx✝¹ x✝ : M\nh : ↑u * x✝¹ ≤ ↑u * x✝\n⊢ x✝¹ ≤ x✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Unbundled.Units | {
"line": 61,
"column": 7
} | {
"line": 61,
"column": 18
} | {
"line": 61,
"column": 19
} | [
{
"pp": "M : Type u_1\ninst✝² : Monoid M\ninst✝¹ : LE M\ninst✝ : MulRightMono M\na b : M\nu : Mˣ\nx✝ : a * ↑u ≤ b * ↑u\n⊢ a ≤ b",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"M : Type u_1\ninst✝² : Monoid M\ninst✝¹ : LE M\ninst✝ : MulRightMono M\na b : M\nu : Mˣ\nx✝ : a * ↑u ≤ b * ↑u\n⊢ a ≤ b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 152,
"column": 36
} | {
"line": 152,
"column": 47
} | {
"line": 152,
"column": 48
} | [
{
"pp": "Γ : Type u_1\nR : Type u_2\ninst✝⁴ : LinearOrder Γ\ninst✝³ : LinearOrder R\ninst✝² : AddCommGroup R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Zero Γ\nx : Lex R⟦Γ⟧\nhne : x ≠ 0\nhne' : ofLex x ≠ 0\n⊢ ofLex |x| ≠ 0",
"ppTerm": "?m.62",
"assigned": true,
"usedConstants": [
"AddGroup.toSubt... | [
"Γ : Type u_1\nR : Type u_2\ninst✝⁴ : LinearOrder Γ\ninst✝³ : LinearOrder R\ninst✝² : AddCommGroup R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Zero Γ\nx : Lex R⟦Γ⟧\nhne : x ≠ 0\nhne' : ofLex x ≠ 0\n⊢ ¬x = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 171,
"column": 4
} | {
"line": 172,
"column": 11
} | {
"line": 172,
"column": 12
} | [
{
"pp": "case refine_2\nΓ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nh : (ofLex |y|).orderTop < (ofLex |x|).orderTop\n⊢ (ofLex |x|).coeff ((ofLex |y|).orderTop.untop ⋯) < (ofLex |y|).coeff ((ofLex |y|).orderTop... | [
"case refine_2\nΓ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nh : (ofLex |y|).orderTop < (ofLex |x|).orderTop\n⊢ ¬y = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 184,
"column": 24
} | {
"line": 184,
"column": 35
} | {
"line": 184,
"column": 36
} | [
{
"pp": "Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nh : (ofLex x).orderTop = (ofLex y).orderTop\nhy : y ≠ 0\n⊢ x ≠ 0",
"ppTerm": "?m.86",
"assigned": true,
"usedConstants": [
"Lex",
"S... | [
"Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nh : (ofLex x).orderTop = (ofLex y).orderTop\nhy : y ≠ 0\n⊢ ¬x = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 184,
"column": 83
} | {
"line": 184,
"column": 94
} | {
"line": 184,
"column": 95
} | [
{
"pp": "Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nh : (ofLex x).orderTop = (ofLex y).orderTop\nhy : y ≠ 0\n⊢ ofLex y ≠ 0",
"ppTerm": "?m.111",
"assigned": true,
"usedConstants": [
"Eq.mpr"... | [
"Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nh : (ofLex x).orderTop = (ofLex y).orderTop\nhy : y ≠ 0\n⊢ ¬y = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 185,
"column": 62
} | {
"line": 185,
"column": 73
} | {
"line": 185,
"column": 74
} | [
{
"pp": "Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nh : (ofLex x).orderTop = (ofLex y).orderTop\nhy : y ≠ 0\nhx : x ≠ 0\n⊢ (ofLex |x|).orderTop = (ofLex |y|).orderTop",
"ppTerm": "?m.138",
"assigned":... | [
"Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nh : (ofLex x).orderTop = (ofLex y).orderTop\nhy : y ≠ 0\nhx : x ≠ 0\n⊢ (ofLex x).orderTop = (ofLex y).orderTop"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 191,
"column": 51
} | {
"line": 191,
"column": 62
} | {
"line": 191,
"column": 63
} | [
{
"pp": "Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nh : (ofLex x).orderTop = (ofLex y).orderTop\nhy : y ≠ 0\nhx : x ≠ 0\nh' : (ofLex |x|).orderTop = (ofLex |y|).orderTop\nn : ℕ\nhn : |y| ≤ n • |x|\n⊢ 0 < |x|"... | [
"Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nh : (ofLex x).orderTop = (ofLex y).orderTop\nhy : y ≠ 0\nhx : x ≠ 0\nh' : (ofLex |x|).orderTop = (ofLex |y|).orderTop\nn : ℕ\nhn : |y| ≤ n • |x|\n⊢ ¬x = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 195,
"column": 36
} | {
"line": 195,
"column": 47
} | {
"line": 195,
"column": 48
} | [
{
"pp": "Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nh : (ofLex x).orderTop = (ofLex y).orderTop\nhy : y ≠ 0\nhx : x ≠ 0\nh' : (ofLex |x|).orderTop = (ofLex |y|).orderTop\nn : ℕ\nhn : |y| ≤ n • |x|\nhn' : |y| ... | [
"Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nh : (ofLex x).orderTop = (ofLex y).orderTop\nhy : y ≠ 0\nhx : x ≠ 0\nh' : (ofLex |x|).orderTop = (ofLex |y|).orderTop\nn : ℕ\nhn : |y| ≤ n • |x|\nhn' : |y| < (n + 1) • ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 195,
"column": 81
} | {
"line": 195,
"column": 92
} | {
"line": 195,
"column": 93
} | [
{
"pp": "Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nh : (ofLex x).orderTop = (ofLex y).orderTop\nhy : y ≠ 0\nhx : x ≠ 0\nh' : (ofLex |x|).orderTop = (ofLex |y|).orderTop\nn : ℕ\nhn : |y| ≤ n • |x|\nhn' : |y| ... | [
"Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nh : (ofLex x).orderTop = (ofLex y).orderTop\nhy : y ≠ 0\nhx : x ≠ 0\nh' : (ofLex |x|).orderTop = (ofLex |y|).orderTop\nn : ℕ\nhn : |y| ≤ n • |x|\nhn' : |y| < (n + 1) • ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 206,
"column": 41
} | {
"line": 206,
"column": 52
} | {
"line": 206,
"column": 53
} | [
{
"pp": "Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nh : (ofLex x).orderTop = (ofLex y).orderTop\nhy : y ≠ 0\nhx : x ≠ 0\nh' : (ofLex |x|).orderTop = (ofLex |y|).orderTop\nn : ℕ\nhn : |(ofLex y).leadingCoeff| ... | [
"Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nh : (ofLex x).orderTop = (ofLex y).orderTop\nhy : y ≠ 0\nhx : x ≠ 0\nh' : (ofLex |x|).orderTop = (ofLex |y|).orderTop\nn : ℕ\nhn : |(ofLex y).leadingCoeff| ≤ n • |(ofLe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 211,
"column": 8
} | {
"line": 211,
"column": 25
} | {
"line": 211,
"column": 26
} | [
{
"pp": "Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nh : (ofLex x).orderTop = (ofLex y).orderTop\nhy : y ≠ 0\nhx : x ≠ 0\nh' : (ofLex |x|).orderTop = (ofLex |y|).orderTop\nn : ℕ\nhn : |(ofLex y).leadingCoeff| ... | [
"Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nh : (ofLex x).orderTop = (ofLex y).orderTop\nhy : y ≠ 0\nhx : x ≠ 0\nh' : (ofLex |x|).orderTop = (ofLex |y|).orderTop\nn : ℕ\nhn : |(ofLex y).leadingCoeff| ≤ n • |(ofLe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 214,
"column": 8
} | {
"line": 214,
"column": 19
} | {
"line": 214,
"column": 20
} | [
{
"pp": "Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nh : (ofLex x).orderTop = (ofLex y).orderTop\nhy : y ≠ 0\nhx : x ≠ 0\nh' : (ofLex |x|).orderTop = (ofLex |y|).orderTop\nn : ℕ\nhn : |(ofLex y).leadingCoeff| ... | [
"Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nh : (ofLex x).orderTop = (ofLex y).orderTop\nhy : y ≠ 0\nhx : x ≠ 0\nh' : (ofLex |x|).orderTop = (ofLex |y|).orderTop\nn : ℕ\nhn : |(ofLex y).leadingCoeff| ≤ n • |(ofLe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 219,
"column": 38
} | {
"line": 219,
"column": 49
} | {
"line": 219,
"column": 50
} | [
{
"pp": "Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nh : (ofLex x).orderTop = (ofLex y).orderTop\nhy : y ≠ 0\nhx : x ≠ 0\nh' : (ofLex |x|).orderTop = (ofLex |y|).orderTop\nn : ℕ\nhn : |(ofLex y).leadingCoeff| ... | [
"Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nh : (ofLex x).orderTop = (ofLex y).orderTop\nhy : y ≠ 0\nhx : x ≠ 0\nh' : (ofLex |x|).orderTop = (ofLex |y|).orderTop\nn : ℕ\nhn : |(ofLex y).leadingCoeff| ≤ n • |(ofLe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 219,
"column": 83
} | {
"line": 219,
"column": 94
} | {
"line": 219,
"column": 95
} | [
{
"pp": "Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nh : (ofLex x).orderTop = (ofLex y).orderTop\nhy : y ≠ 0\nhx : x ≠ 0\nh' : (ofLex |x|).orderTop = (ofLex |y|).orderTop\nn : ℕ\nhn : |(ofLex y).leadingCoeff| ... | [
"Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nh : (ofLex x).orderTop = (ofLex y).orderTop\nhy : y ≠ 0\nhx : x ≠ 0\nh' : (ofLex |x|).orderTop = (ofLex |y|).orderTop\nn : ℕ\nhn : |(ofLex y).leadingCoeff| ≤ n • |(ofLe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 233,
"column": 4
} | {
"line": 233,
"column": 48
} | {
"line": 234,
"column": 6
} | [
{
"pp": "case inl\nΓ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nhlt : (ofLex x).orderTop < (ofLex y).orderTop\n⊢ ArchimedeanClass.mk x ≤ ArchimedeanClass.mk y ↔\n (ofLex x).orderTop < (ofLex y).orderTop ∨\n ... | [
"case inl\nΓ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nhlt : (ofLex x).orderTop < (ofLex y).orderTop\n⊢ ∃ n, |y| ≤ n • |x|"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 234,
"column": 13
} | {
"line": 234,
"column": 24
} | {
"line": 234,
"column": 25
} | [
{
"pp": "Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nhlt : (ofLex x).orderTop < (ofLex y).orderTop\n⊢ |y| ≤ 1 • |x|",
"ppTerm": "?m.122",
"assigned": true,
"usedConstants": [
"Lex.instAddMono... | [
"Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nhlt : (ofLex x).orderTop < (ofLex y).orderTop\n⊢ |y| ≤ |x|"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 237,
"column": 4
} | {
"line": 237,
"column": 21
} | {
"line": 237,
"column": 22
} | [
{
"pp": "case inr.inl\nΓ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nheq : (ofLex x).orderTop = (ofLex y).orderTop\n⊢ ArchimedeanClass.mk x ≤ ArchimedeanClass.mk y ↔\n (ofLex x).orderTop < (ofLex y).orderTop ... | [
"case inr.inl\nΓ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nheq : (ofLex x).orderTop = (ofLex y).orderTop\n⊢ ArchimedeanClass.mk x ≤ ArchimedeanClass.mk y ↔\n ArchimedeanClass.mk (ofLex x).leadingCoeff ≤ Archime... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 246,
"column": 4
} | {
"line": 246,
"column": 15
} | {
"line": 246,
"column": 16
} | [
{
"pp": "Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nhgt : (ofLex y).orderTop < (ofLex x).orderTop\nn : ℕ\nhn :\n (ofLex y).orderTop ≤ (ofLex x).orderTop ∧\n ((ofLex x).orderTop = (ofLex y).orderTop → ∀ (n... | [
"Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\nhgt : (ofLex y).orderTop < (ofLex x).orderTop\nn : ℕ\nhn :\n (ofLex y).orderTop ≤ (ofLex x).orderTop ∧\n ((ofLex x).orderTop = (ofLex y).orderTop → ∀ (n : ℕ), n • |... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 256,
"column": 4
} | {
"line": 256,
"column": 56
} | {
"line": 256,
"column": 57
} | [
{
"pp": "case mp\nΓ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\n⊢ ((ofLex x).orderTop < (ofLex y).orderTop ∨\n (ofLex x).orderTop = (ofLex y).orderTop ∧\n ArchimedeanClass.mk (ofLex x).leadingCoe... | [
"case mp\nΓ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx y : Lex R⟦Γ⟧\n⊢ (ofLex x).orderTop = (ofLex y).orderTop →\n ArchimedeanClass.mk (ofLex x).leadingCoeff ≤ ArchimedeanClass.mk (ofLex y).leadingCoeff →\n ArchimedeanCl... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Module.HahnEmbedding | {
"line": 94,
"column": 55
} | {
"line": 94,
"column": 66
} | {
"line": 94,
"column": 67
} | [
{
"pp": "K : Type u_1\ninst✝⁸ : DivisionRing K\ninst✝⁷ : LinearOrder K\ninst✝⁶ : IsOrderedRing K\ninst✝⁵ : Archimedean K\nM : Type u_2\ninst✝⁴ : AddCommGroup M\ninst✝³ : LinearOrder M\ninst✝² : IsOrderedAddMonoid M\ninst✝¹ : Module K M\ninst✝ : IsOrderedModule K M\nu : ArchimedeanStrata K M\nc : FiniteArchimede... | [
"K : Type u_1\ninst✝⁸ : DivisionRing K\ninst✝⁷ : LinearOrder K\ninst✝⁶ : IsOrderedRing K\ninst✝⁵ : Archimedean K\nM : Type u_2\ninst✝⁴ : AddCommGroup M\ninst✝³ : LinearOrder M\ninst✝² : IsOrderedAddMonoid M\ninst✝¹ : Module K M\ninst✝ : IsOrderedModule K M\nu : ArchimedeanStrata K M\nc : FiniteArchimedeanClass M\ne... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 274,
"column": 6
} | {
"line": 274,
"column": 17
} | {
"line": 274,
"column": 18
} | [
{
"pp": "Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx✝¹ x✝ : { a // a ≠ 0 }\na : Lex R⟦Γ⟧\nha : a ≠ 0\nb : Lex R⟦Γ⟧\nhb : b ≠ 0\nh : ArchimedeanClass.mk ↑⟨a, ha⟩ ≤ ArchimedeanClass.mk ↑⟨b, hb⟩\n⊢ (ofLex a).orderTop.untop ⋯ <... | [
"Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\nx✝¹ x✝ : { a // a ≠ 0 }\na : Lex R⟦Γ⟧\nha : a ≠ 0\nb : Lex R⟦Γ⟧\nhb : b ≠ 0\nh : ArchimedeanClass.mk ↑⟨a, ha⟩ ≤ ArchimedeanClass.mk ↑⟨b, hb⟩\n⊢ (ofLex a).orderTop < (ofLex b).orderTop ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Module.HahnEmbedding | {
"line": 115,
"column": 53
} | {
"line": 115,
"column": 64
} | {
"line": 115,
"column": 65
} | [
{
"pp": "K : Type u_1\ninst✝¹¹ : DivisionRing K\ninst✝¹⁰ : LinearOrder K\ninst✝⁹ : IsOrderedRing K\ninst✝⁸ : Archimedean K\nM : Type u_2\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : LinearOrder M\ninst✝⁵ : IsOrderedAddMonoid M\ninst✝⁴ : Module K M\ninst✝³ : IsOrderedModule K M\nR : Type u_3\ninst✝² : AddCommGroup R\ninst... | [
"K : Type u_1\ninst✝¹¹ : DivisionRing K\ninst✝¹⁰ : LinearOrder K\ninst✝⁹ : IsOrderedRing K\ninst✝⁸ : Archimedean K\nM : Type u_2\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : LinearOrder M\ninst✝⁵ : IsOrderedAddMonoid M\ninst✝⁴ : Module K M\ninst✝³ : IsOrderedModule K M\nR : Type u_3\ninst✝² : AddCommGroup R\ninst✝¹ : LinearO... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Module.HahnEmbedding | {
"line": 116,
"column": 53
} | {
"line": 116,
"column": 64
} | {
"line": 116,
"column": 65
} | [
{
"pp": "K : Type u_1\ninst✝¹¹ : DivisionRing K\ninst✝¹⁰ : LinearOrder K\ninst✝⁹ : IsOrderedRing K\ninst✝⁸ : Archimedean K\nM : Type u_2\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : LinearOrder M\ninst✝⁵ : IsOrderedAddMonoid M\ninst✝⁴ : Module K M\ninst✝³ : IsOrderedModule K M\nR : Type u_3\ninst✝² : AddCommGroup R\ninst... | [
"K : Type u_1\ninst✝¹¹ : DivisionRing K\ninst✝¹⁰ : LinearOrder K\ninst✝⁹ : IsOrderedRing K\ninst✝⁸ : Archimedean K\nM : Type u_2\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : LinearOrder M\ninst✝⁵ : IsOrderedAddMonoid M\ninst✝⁴ : Module K M\ninst✝³ : IsOrderedModule K M\nR : Type u_3\ninst✝² : AddCommGroup R\ninst✝¹ : LinearO... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Module.HahnEmbedding | {
"line": 132,
"column": 59
} | {
"line": 132,
"column": 70
} | {
"line": 132,
"column": 71
} | [
{
"pp": "K : Type u_1\ninst✝⁸ : DivisionRing K\ninst✝⁷ : LinearOrder K\ninst✝⁶ : IsOrderedRing K\ninst✝⁵ : Archimedean K\nM : Type u_2\ninst✝⁴ : AddCommGroup M\ninst✝³ : LinearOrder M\ninst✝² : IsOrderedAddMonoid M\ninst✝¹ : Module K M\ninst✝ : IsOrderedModule K M\nu : ArchimedeanStrata K M\nc : FiniteArchimede... | [
"K : Type u_1\ninst✝⁸ : DivisionRing K\ninst✝⁷ : LinearOrder K\ninst✝⁶ : IsOrderedRing K\ninst✝⁵ : Archimedean K\nM : Type u_2\ninst✝⁴ : AddCommGroup M\ninst✝³ : LinearOrder M\ninst✝² : IsOrderedAddMonoid M\ninst✝¹ : Module K M\ninst✝ : IsOrderedModule K M\nu : ArchimedeanStrata K M\nc : FiniteArchimedeanClass M\na... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Module.HahnEmbedding | {
"line": 133,
"column": 59
} | {
"line": 133,
"column": 70
} | {
"line": 133,
"column": 71
} | [
{
"pp": "K : Type u_1\ninst✝⁸ : DivisionRing K\ninst✝⁷ : LinearOrder K\ninst✝⁶ : IsOrderedRing K\ninst✝⁵ : Archimedean K\nM : Type u_2\ninst✝⁴ : AddCommGroup M\ninst✝³ : LinearOrder M\ninst✝² : IsOrderedAddMonoid M\ninst✝¹ : Module K M\ninst✝ : IsOrderedModule K M\nu : ArchimedeanStrata K M\nc : FiniteArchimede... | [
"K : Type u_1\ninst✝⁸ : DivisionRing K\ninst✝⁷ : LinearOrder K\ninst✝⁶ : IsOrderedRing K\ninst✝⁵ : Archimedean K\nM : Type u_2\ninst✝⁴ : AddCommGroup M\ninst✝³ : LinearOrder M\ninst✝² : IsOrderedAddMonoid M\ninst✝¹ : Module K M\ninst✝ : IsOrderedModule K M\nu : ArchimedeanStrata K M\nc : FiniteArchimedeanClass M\na... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Module.HahnEmbedding | {
"line": 136,
"column": 10
} | {
"line": 136,
"column": 21
} | {
"line": 136,
"column": 22
} | [
{
"pp": "K : Type u_1\ninst✝⁸ : DivisionRing K\ninst✝⁷ : LinearOrder K\ninst✝⁶ : IsOrderedRing K\ninst✝⁵ : Archimedean K\nM : Type u_2\ninst✝⁴ : AddCommGroup M\ninst✝³ : LinearOrder M\ninst✝² : IsOrderedAddMonoid M\ninst✝¹ : Module K M\ninst✝ : IsOrderedModule K M\nu : ArchimedeanStrata K M\nc : FiniteArchimede... | [
"K : Type u_1\ninst✝⁸ : DivisionRing K\ninst✝⁷ : LinearOrder K\ninst✝⁶ : IsOrderedRing K\ninst✝⁵ : Archimedean K\nM : Type u_2\ninst✝⁴ : AddCommGroup M\ninst✝³ : LinearOrder M\ninst✝² : IsOrderedAddMonoid M\ninst✝¹ : Module K M\ninst✝ : IsOrderedModule K M\nu : ArchimedeanStrata K M\nc : FiniteArchimedeanClass M\na... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Multiplication | {
"line": 438,
"column": 4
} | {
"line": 438,
"column": 33
} | {
"line": 439,
"column": 4
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nS : Type u_4\nV : Type u_5\ninst✝³ : AddCommMonoid Γ\ninst✝² : PartialOrder Γ\ninst✝¹ : IsOrderedCancelAddMonoid Γ\ninst✝ : NonUnitalNonAssocSemiring R\nx y z : R⟦Γ⟧\n⊢ (HahnModule.of R).symm ((x + y) • (HahnModule.of R) z) =\n (HahnModule.of R).symm (x • (... | [
"Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nS : Type u_4\nV : Type u_5\ninst✝³ : AddCommMonoid Γ\ninst✝² : PartialOrder Γ\ninst✝¹ : IsOrderedCancelAddMonoid Γ\ninst✝ : NonUnitalNonAssocSemiring R\nx y z : R⟦Γ⟧\n⊢ ∀ (r s u : R), (r + s) • u = r • u + s • u"
] | refine HahnModule.add_smul ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 401,
"column": 45
} | {
"line": 401,
"column": 56
} | {
"line": 401,
"column": 57
} | [
{
"pp": "Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : PartialOrder R\nΓ' : Type u_3\ninst✝¹ : LinearOrder Γ'\nf : Γ ↪o Γ'\ninst✝ : Zero R\na b : Lex R⟦Γ⟧\nk : Γ\nhj : ∀ j < f k, (embDomain f (ofLex a)).coeff j = (embDomain f (ofLex b)).coeff j\nhi : (embDomain f (ofLex a)).coeff (f k) < (embDoma... | [
"Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : PartialOrder R\nΓ' : Type u_3\ninst✝¹ : LinearOrder Γ'\nf : Γ ↪o Γ'\ninst✝ : Zero R\na b : Lex R⟦Γ⟧\nk : Γ\nhj : ∀ j < f k, (embDomain f (ofLex a)).coeff j = (embDomain f (ofLex b)).coeff j\nhi : (embDomain f (ofLex a)).coeff (f k) < (embDomain f (ofLex ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Module.HahnEmbedding | {
"line": 142,
"column": 4
} | {
"line": 142,
"column": 51
} | {
"line": 142,
"column": 52
} | [
{
"pp": "case pos\nK : Type u_1\ninst✝⁸ : DivisionRing K\ninst✝⁷ : LinearOrder K\ninst✝⁶ : IsOrderedRing K\ninst✝⁵ : Archimedean K\nM : Type u_2\ninst✝⁴ : AddCommGroup M\ninst✝³ : LinearOrder M\ninst✝² : IsOrderedAddMonoid M\ninst✝¹ : Module K M\ninst✝ : IsOrderedModule K M\nu : ArchimedeanStrata K M\nc : Finit... | [
"case pos\nK : Type u_1\ninst✝⁸ : DivisionRing K\ninst✝⁷ : LinearOrder K\ninst✝⁶ : IsOrderedRing K\ninst✝⁵ : Archimedean K\nM : Type u_2\ninst✝⁴ : AddCommGroup M\ninst✝³ : LinearOrder M\ninst✝² : IsOrderedAddMonoid M\ninst✝¹ : Module K M\ninst✝ : IsOrderedModule K M\nu : ArchimedeanStrata K M\nc : FiniteArchimedean... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 402,
"column": 8
} | {
"line": 402,
"column": 19
} | {
"line": 402,
"column": 20
} | [
{
"pp": "case mp.inl\nΓ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : PartialOrder R\nΓ' : Type u_3\ninst✝¹ : LinearOrder Γ'\nf : Γ ↪o Γ'\ninst✝ : Zero R\na b : Lex R⟦Γ⟧\nk : Γ\nhj : ∀ j < f k, (embDomain f (ofLex a)).coeff j = (embDomain f (ofLex b)).coeff j\nhi : (embDomain f (ofLex a)).coeff (f ... | [
"case mp.inl\nΓ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : PartialOrder R\nΓ' : Type u_3\ninst✝¹ : LinearOrder Γ'\nf : Γ ↪o Γ'\ninst✝ : Zero R\na b : Lex R⟦Γ⟧\nk : Γ\nhj : ∀ j < f k, (embDomain f (ofLex a)).coeff j = (embDomain f (ofLex b)).coeff j\nhi : (embDomain f (ofLex a)).coeff (f k) < (embDom... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 405,
"column": 47
} | {
"line": 405,
"column": 58
} | {
"line": 405,
"column": 59
} | [
{
"pp": "Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : PartialOrder R\nΓ' : Type u_3\ninst✝¹ : LinearOrder Γ'\nf : Γ ↪o Γ'\ninst✝ : Zero R\na b : Lex R⟦Γ⟧\ni : Γ\nhj : ∀ j < i, (ofLex a).coeff j = (ofLex b).coeff j\nhi : (ofLex a).coeff i < (ofLex b).coeff i\n⊢ (embDomain f (ofLex a)).coeff (f i)... | [
"Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : PartialOrder R\nΓ' : Type u_3\ninst✝¹ : LinearOrder Γ'\nf : Γ ↪o Γ'\ninst✝ : Zero R\na b : Lex R⟦Γ⟧\ni : Γ\nhj : ∀ j < i, (ofLex a).coeff j = (ofLex b).coeff j\nhi : (ofLex a).coeff i < (ofLex b).coeff i\n⊢ (ofLex a).coeff i < (ofLex b).coeff i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Module.HahnEmbedding | {
"line": 145,
"column": 4
} | {
"line": 145,
"column": 15
} | {
"line": 145,
"column": 16
} | [
{
"pp": "case neg\nK : Type u_1\ninst✝⁸ : DivisionRing K\ninst✝⁷ : LinearOrder K\ninst✝⁶ : IsOrderedRing K\ninst✝⁵ : Archimedean K\nM : Type u_2\ninst✝⁴ : AddCommGroup M\ninst✝³ : LinearOrder M\ninst✝² : IsOrderedAddMonoid M\ninst✝¹ : Module K M\ninst✝ : IsOrderedModule K M\nu : ArchimedeanStrata K M\nc : Finit... | [
"case neg\nK : Type u_1\ninst✝⁸ : DivisionRing K\ninst✝⁷ : LinearOrder K\ninst✝⁶ : IsOrderedRing K\ninst✝⁵ : Archimedean K\nM : Type u_2\ninst✝⁴ : AddCommGroup M\ninst✝³ : LinearOrder M\ninst✝² : IsOrderedAddMonoid M\ninst✝¹ : Module K M\ninst✝ : IsOrderedModule K M\nu : ArchimedeanStrata K M\nc : FiniteArchimedean... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Archimedean | {
"line": 120,
"column": 2
} | {
"line": 120,
"column": 71
} | {
"line": 120,
"column": 72
} | [
{
"pp": "case mk.mk\nR : Type u_1\ninst✝² : LinearOrder R\ninst✝¹ : CommRing R\ninst✝ : IsStrictOrderedRing R\nx : R\nhx : x ≠ 0\ny z : R\nhyz : (fun x_1 ↦ mk x + x_1) (mk y) = (fun x_1 ↦ mk x + x_1) (mk z)\n⊢ mk y = mk z",
"ppTerm": "?mk.mk",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"case mk.mk\nR : Type u_1\ninst✝² : LinearOrder R\ninst✝¹ : CommRing R\ninst✝ : IsStrictOrderedRing R\nx : R\nhx : x ≠ 0\ny z : R\nhyz : (fun x_1 ↦ mk x + x_1) (mk y) = (fun x_1 ↦ mk x + x_1) (mk z)\n⊢ (∃ m, |z| ≤ ↑m * |y|) ∧ ∃ n, |y| ≤ ↑n * |z|"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 408,
"column": 10
} | {
"line": 408,
"column": 21
} | {
"line": 408,
"column": 22
} | [
{
"pp": "case pos\nΓ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : PartialOrder R\nΓ' : Type u_3\ninst✝¹ : LinearOrder Γ'\nf : Γ ↪o Γ'\ninst✝ : Zero R\na b : Lex R⟦Γ⟧\ni : Γ\nhj : ∀ j < i, (ofLex a).coeff j = (ofLex b).coeff j\nhi : (ofLex a).coeff i < (ofLex b).coeff i\nj' : Γ\nhki : f j' < f i\n⊢... | [
"case pos\nΓ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : PartialOrder R\nΓ' : Type u_3\ninst✝¹ : LinearOrder Γ'\nf : Γ ↪o Γ'\ninst✝ : Zero R\na b : Lex R⟦Γ⟧\ni : Γ\nhj : ∀ j < i, (ofLex a).coeff j = (ofLex b).coeff j\nhi : (ofLex a).coeff i < (ofLex b).coeff i\nj' : Γ\nhki : f j' < f i\n⊢ (ofLex a).c... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Multiplication | {
"line": 475,
"column": 2
} | {
"line": 475,
"column": 13
} | {
"line": 475,
"column": 14
} | [
{
"pp": "Γ' : Type u_2\nR : Type u_3\ninst✝³ : NonUnitalNonAssocSemiring R\ninst✝² : PartialOrder Γ'\ninst✝¹ : AddCommGroup Γ'\ninst✝ : IsOrderedAddMonoid Γ'\nr : R\nx : R⟦Γ'⟧\na b : Γ'\n⊢ ((single b) r * x).coeff a = r * x.coeff (a - b)",
"ppTerm": "?m.33",
"assigned": false,
"usedConstants": [],
... | [
"Γ' : Type u_2\nR : Type u_3\ninst✝³ : NonUnitalNonAssocSemiring R\ninst✝² : PartialOrder Γ'\ninst✝¹ : AddCommGroup Γ'\ninst✝ : IsOrderedAddMonoid Γ'\nr : R\nx : R⟦Γ'⟧\na b : Γ'\n⊢ ((single b) r * x).coeff a = r * x.coeff (a - b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Multiplication | {
"line": 480,
"column": 2
} | {
"line": 480,
"column": 13
} | {
"line": 480,
"column": 14
} | [
{
"pp": "Γ' : Type u_2\nR : Type u_3\ninst✝³ : NonUnitalNonAssocSemiring R\ninst✝² : PartialOrder Γ'\ninst✝¹ : AddCommGroup Γ'\ninst✝ : IsOrderedAddMonoid Γ'\nr : R\nx : R⟦Γ'⟧\na b : Γ'\n⊢ (x * (single b) r).coeff a = x.coeff (a - b) * r",
"ppTerm": "?m.33",
"assigned": false,
"usedConstants": [],
... | [
"Γ' : Type u_2\nR : Type u_3\ninst✝³ : NonUnitalNonAssocSemiring R\ninst✝² : PartialOrder Γ'\ninst✝¹ : AddCommGroup Γ'\ninst✝ : IsOrderedAddMonoid Γ'\nr : R\nx : R⟦Γ'⟧\na b : Γ'\n⊢ (x * (single b) r).coeff a = x.coeff (a - b) * r"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Cone | {
"line": 68,
"column": 39
} | {
"line": 68,
"column": 50
} | {
"line": 68,
"column": 51
} | [
{
"pp": "T : Type u_1\ninst✝² : Ring T\ninst✝¹ : PartialOrder T\ninst✝ : IsOrderedRing T\na✝ a : T\n⊢ a ∈ (Subsemiring.nonneg T).carrier → -a ∈ (Subsemiring.nonneg T).carrier → a = 0",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
... | [
"T : Type u_1\ninst✝² : Ring T\ninst✝¹ : PartialOrder T\ninst✝ : IsOrderedRing T\na✝ a : T\n⊢ 0 ≤ a → a ≤ 0 → a = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Cone | {
"line": 90,
"column": 49
} | {
"line": 90,
"column": 60
} | {
"line": 90,
"column": 61
} | [
{
"pp": "S : Type u_1\nR : Type u_2\ninst✝² : Ring R\ninst✝¹ : SetLike S R\nC : S\ninst✝ : RingConeClass S R\nx✝ : PartialOrder R := PartialOrder.mkOfAddGroupCone C\nthis✝ : IsOrderedAddMonoid R\nthis : ZeroLEOneClass R\nx y : R\nxnn : 0 ≤ x\nynn : 0 ≤ y\n⊢ x * y - 0 ∈ C",
"ppTerm": "?m.49",
"assigned":... | [
"S : Type u_1\nR : Type u_2\ninst✝² : Ring R\ninst✝¹ : SetLike S R\nC : S\ninst✝ : RingConeClass S R\nx✝ : PartialOrder R := PartialOrder.mkOfAddGroupCone C\nthis✝ : IsOrderedAddMonoid R\nthis : ZeroLEOneClass R\nx y : R\nxnn : 0 ≤ x\nynn : 0 ≤ y\n⊢ x * y ∈ C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Archimedean | {
"line": 155,
"column": 2
} | {
"line": 155,
"column": 13
} | {
"line": 155,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝⁶ : LinearOrder R\ninst✝⁵ : CommRing R\ninst✝⁴ : IsStrictOrderedRing R\nS : Type u_3\ninst✝³ : LinearOrder S\ninst✝² : CommRing S\ninst✝¹ : IsStrictOrderedRing S\ninst✝ : Archimedean S\nf : S →+*o R\nx : S\nh : x ≠ 0\n⊢ mk (f x) = 0",
"ppTerm": "?m.22",
"assigned": false,
... | [
"R : Type u_1\ninst✝⁶ : LinearOrder R\ninst✝⁵ : CommRing R\ninst✝⁴ : IsStrictOrderedRing R\nS : Type u_3\ninst✝³ : LinearOrder S\ninst✝² : CommRing S\ninst✝¹ : IsStrictOrderedRing S\ninst✝ : Archimedean S\nf : S →+*o R\nx : S\nh : x ≠ 0\n⊢ mk (f x) = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Archimedean | {
"line": 169,
"column": 2
} | {
"line": 169,
"column": 13
} | {
"line": 169,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝⁶ : LinearOrder R\ninst✝⁵ : CommRing R\ninst✝⁴ : IsStrictOrderedRing R\nS : Type u_3\ninst✝³ : LinearOrder S\ninst✝² : CommRing S\ninst✝¹ : IsStrictOrderedRing S\ninst✝ : Archimedean S\nf : S →+*o R\ny : S\n⊢ 0 ≤ mk (f y)",
"ppTerm": "?m.20",
"assigned": false,
"usedConst... | [
"R : Type u_1\ninst✝⁶ : LinearOrder R\ninst✝⁵ : CommRing R\ninst✝⁴ : IsStrictOrderedRing R\nS : Type u_3\ninst✝³ : LinearOrder S\ninst✝² : CommRing S\ninst✝¹ : IsStrictOrderedRing S\ninst✝ : Archimedean S\nf : S →+*o R\ny : S\n⊢ 0 ≤ mk (f y)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Archimedean | {
"line": 175,
"column": 4
} | {
"line": 175,
"column": 15
} | {
"line": 175,
"column": 16
} | [
{
"pp": "case hpos\nR : Type u_1\ninst✝⁶ : LinearOrder R\ninst✝⁵ : CommRing R\ninst✝⁴ : IsStrictOrderedRing R\nS : Type u_3\ninst✝³ : LinearOrder S\ninst✝² : CommRing S\ninst✝¹ : IsStrictOrderedRing S\ninst✝ : Archimedean S\nf : S →+*o R\nx : R\nhx : 0 < mk x\ny : S\nhy : 0 < y\n⊢ 0 ≤ f y",
"ppTerm": "?hpos... | [
"case hpos\nR : Type u_1\ninst✝⁶ : LinearOrder R\ninst✝⁵ : CommRing R\ninst✝⁴ : IsStrictOrderedRing R\nS : Type u_3\ninst✝³ : LinearOrder S\ninst✝² : CommRing S\ninst✝¹ : IsStrictOrderedRing S\ninst✝ : Archimedean S\nf : S →+*o R\nx : R\nhx : 0 < mk x\ny : S\nhy : 0 < y\n⊢ 0 ≤ f y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Archimedean | {
"line": 181,
"column": 4
} | {
"line": 181,
"column": 15
} | {
"line": 181,
"column": 16
} | [
{
"pp": "case hneg\nR : Type u_1\ninst✝⁶ : LinearOrder R\ninst✝⁵ : CommRing R\ninst✝⁴ : IsStrictOrderedRing R\nS : Type u_3\ninst✝³ : LinearOrder S\ninst✝² : CommRing S\ninst✝¹ : IsStrictOrderedRing S\ninst✝ : Archimedean S\nf : S →+*o R\nx : R\nhx : 0 < mk x\ny : S\nhy : y < 0\n⊢ f y ≤ 0",
"ppTerm": "?hneg... | [
"case hneg\nR : Type u_1\ninst✝⁶ : LinearOrder R\ninst✝⁵ : CommRing R\ninst✝⁴ : IsStrictOrderedRing R\nS : Type u_3\ninst✝³ : LinearOrder S\ninst✝² : CommRing S\ninst✝¹ : IsStrictOrderedRing S\ninst✝ : Archimedean S\nf : S →+*o R\nx : R\nhx : 0 < mk x\ny : S\nhy : y < 0\n⊢ f y ≤ 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Archimedean | {
"line": 208,
"column": 2
} | {
"line": 208,
"column": 13
} | {
"line": 208,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝² : LinearOrder R\ninst✝¹ : CommRing R\ninst✝ : IsStrictOrderedRing R\nx : R\nn : ℕ\nhn : |ArchimedeanOrder.val (ArchimedeanOrder.of x)| ≤ n • |ArchimedeanOrder.val (ArchimedeanOrder.of 1)|\n⊢ |x| ≤ ↑n",
"ppTerm": "?m.33",
"assigned": false,
"usedConstants": [],
"used... | [
"R : Type u_1\ninst✝² : LinearOrder R\ninst✝¹ : CommRing R\ninst✝ : IsStrictOrderedRing R\nx : R\nn : ℕ\nhn : |ArchimedeanOrder.val (ArchimedeanOrder.of x)| ≤ n • |ArchimedeanOrder.val (ArchimedeanOrder.of 1)|\n⊢ |x| ≤ ↑n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Archimedean | {
"line": 255,
"column": 37
} | {
"line": 255,
"column": 48
} | {
"line": 255,
"column": 49
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝⁷ : LinearOrder R\ninst✝⁶ : LinearOrder S\ninst✝⁵ : CommRing R\ninst✝⁴ : IsStrictOrderedRing R\ninst✝³ : Ring S\ninst✝² : IsStrictOrderedRing S\ninst✝¹ : DenselyOrdered R\ninst✝ : Archimedean R\nx y : S\nf : R →+* S\nhf : StrictMono ⇑f\nq : R\n⊢ 0 < f q ↔ 0 < q",
"p... | [
"R : Type u_1\nS : Type u_2\ninst✝⁷ : LinearOrder R\ninst✝⁶ : LinearOrder S\ninst✝⁵ : CommRing R\ninst✝⁴ : IsStrictOrderedRing R\ninst✝³ : Ring S\ninst✝² : IsStrictOrderedRing S\ninst✝¹ : DenselyOrdered R\ninst✝ : Archimedean R\nx y : S\nf : R →+* S\nhf : StrictMono ⇑f\nq : R\n⊢ 0 < f q ↔ 0 < q"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.IsNonarchimedean | {
"line": 125,
"column": 4
} | {
"line": 125,
"column": 36
} | {
"line": 125,
"column": 37
} | [
{
"pp": "case inr\nα : Type u_2\nS : Type u_3\ninst✝¹ : LinearOrder S\ninst✝ : AddCommGroup α\nf : α → S\nfna : IsNonarchimedean f\nNeg : ∀ (a : α), f a = f (-a)\na b : α\nhne : f a ≠ f b\nH : ∀ {a b : α}, f a ≠ f b → f a > f b → f (a + b) = max (f a) (f b)\nhab : ¬f a > f b\n⊢ f (a + b) = max (f a) (f b)",
... | [
"case inr\nα : Type u_2\nS : Type u_3\ninst✝¹ : LinearOrder S\ninst✝ : AddCommGroup α\nf : α → S\nfna : IsNonarchimedean f\nNeg : ∀ (a : α), f a = f (-a)\na b : α\nhne : f a ≠ f b\nH : ∀ {a b : α}, f a ≠ f b → f a > f b → f (a + b) = max (f a) (f b)\nhab : ¬f a > f b\n⊢ f (a + b) = max (f a) (f b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.IsNonarchimedean | {
"line": 128,
"column": 4
} | {
"line": 128,
"column": 44
} | {
"line": 128,
"column": 45
} | [
{
"pp": "case inl\nα : Type u_2\nS : Type u_3\ninst✝¹ : LinearOrder S\ninst✝ : AddCommGroup α\nf : α → S\nfna : IsNonarchimedean f\nNeg : ∀ (a : α), f a = f (-a)\na b : α\nhne : f a ≠ f b\nhab : f a > f b\nh : f (a + b + -b) ≤ f (a + b)\n⊢ max (f a) (f b) ≤ f (a + b)",
"ppTerm": "?inl",
"assigned": true... | [
"case inl\nα : Type u_2\nS : Type u_3\ninst✝¹ : LinearOrder S\ninst✝ : AddCommGroup α\nf : α → S\nfna : IsNonarchimedean f\nNeg : ∀ (a : α), f a = f (-a)\na b : α\nhne : f a ≠ f b\nhab : f a > f b\nh : f (a + b + -b) ≤ f (a + b)\n⊢ f a ≤ f (a + b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.IsNonarchimedean | {
"line": 129,
"column": 35
} | {
"line": 129,
"column": 54
} | {
"line": 129,
"column": 55
} | [
{
"pp": "α : Type u_2\nS : Type u_3\ninst✝¹ : LinearOrder S\ninst✝ : AddCommGroup α\nf : α → S\nfna : IsNonarchimedean f\nNeg : ∀ (a : α), f a = f (-a)\na b : α\nhne : f a ≠ f b\nhab : f a > f b\nh : f (a + b + -b) ≤ f (-b)\n⊢ f (-b) < f (a + b + -b)",
"ppTerm": "?m.119",
"assigned": true,
"usedCons... | [
"α : Type u_2\nS : Type u_3\ninst✝¹ : LinearOrder S\ninst✝ : AddCommGroup α\nf : α → S\nfna : IsNonarchimedean f\nNeg : ∀ (a : α), f a = f (-a)\na b : α\nhne : f a ≠ f b\nhab : f a > f b\nh : f (a + b + -b) ≤ f (-b)\n⊢ f (-b) < f a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Archimedean | {
"line": 261,
"column": 6
} | {
"line": 261,
"column": 31
} | {
"line": 261,
"column": 32
} | [
{
"pp": "case mp.succ\nR : Type u_1\nS : Type u_2\ninst✝⁷ : LinearOrder R\ninst✝⁶ : LinearOrder S\ninst✝⁵ : CommRing R\ninst✝⁴ : IsStrictOrderedRing R\ninst✝³ : Ring S\ninst✝² : IsStrictOrderedRing S\ninst✝¹ : DenselyOrdered R\ninst✝ : Archimedean R\nx y : S\nf : R →+* S\nhf : StrictMono ⇑f\nH : ∀ {q : R}, 0 < ... | [
"case mp.succ\nR : Type u_1\nS : Type u_2\ninst✝⁷ : LinearOrder R\ninst✝⁶ : LinearOrder S\ninst✝⁵ : CommRing R\ninst✝⁴ : IsStrictOrderedRing R\ninst✝³ : Ring S\ninst✝² : IsStrictOrderedRing S\ninst✝¹ : DenselyOrdered R\ninst✝ : Archimedean R\nx y : S\nf : R →+* S\nhf : StrictMono ⇑f\nH : ∀ {q : R}, 0 < f q ↔ 0 < q\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Archimedean | {
"line": 269,
"column": 4
} | {
"line": 269,
"column": 37
} | {
"line": 269,
"column": 38
} | [
{
"pp": "case mpr\nR : Type u_1\nS : Type u_2\ninst✝⁷ : LinearOrder R\ninst✝⁶ : LinearOrder S\ninst✝⁵ : CommRing R\ninst✝⁴ : IsStrictOrderedRing R\ninst✝³ : Ring S\ninst✝² : IsStrictOrderedRing S\ninst✝¹ : DenselyOrdered R\ninst✝ : Archimedean R\nx y : S\nf : R →+* S\nhf : StrictMono ⇑f\nH : ∀ {q : R}, 0 < f q ... | [
"case mpr\nR : Type u_1\nS : Type u_2\ninst✝⁷ : LinearOrder R\ninst✝⁶ : LinearOrder S\ninst✝⁵ : CommRing R\ninst✝⁴ : IsStrictOrderedRing R\ninst✝³ : Ring S\ninst✝² : IsStrictOrderedRing S\ninst✝¹ : DenselyOrdered R\ninst✝ : Archimedean R\nx y : S\nf : R →+* S\nhf : StrictMono ⇑f\nH : ∀ {q : R}, 0 < f q ↔ 0 < q\nq :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Archimedean | {
"line": 283,
"column": 30
} | {
"line": 283,
"column": 41
} | {
"line": 283,
"column": 42
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝³ : LinearOrder R\ninst✝² : LinearOrder S\ninst✝¹ : Field R\ninst✝ : IsOrderedRing R\nx y : R\nh : mk x = mk y\nhx : x ≠ 0\nhy : y ≠ 0\n⊢ mk x ≠ ⊤",
"ppTerm": "?m.82",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"ArchimedeanC... | [
"R : Type u_1\nS : Type u_2\ninst✝³ : LinearOrder R\ninst✝² : LinearOrder S\ninst✝¹ : Field R\ninst✝ : IsOrderedRing R\nx y : R\nh : mk x = mk y\nhx : x ≠ 0\nhy : y ≠ 0\n⊢ ¬x = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.IsNonarchimedean | {
"line": 173,
"column": 2
} | {
"line": 173,
"column": 34
} | {
"line": 173,
"column": 35
} | [
{
"pp": "R : Type u_1\ninst✝¹ : LinearOrder R\nα : Type u_2\nβ : Type u_3\ninst✝ : AddCommMonoid α\nf : α → R\nhna : IsNonarchimedean f\ng : β → α\nt : Finset β\nht : t.Nonempty\n⊢ ∃ b ∈ t, f (t.sum g) ≤ f (g b)",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"u... | [
"R : Type u_1\ninst✝¹ : LinearOrder R\nα : Type u_2\nβ : Type u_3\ninst✝ : AddCommMonoid α\nf : α → R\nhna : IsNonarchimedean f\ng : β → α\nt : Finset β\nht : t.Nonempty\n⊢ ∃ b ∈ t, f (t.sum g) ≤ f (g b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Archimedean | {
"line": 322,
"column": 2
} | {
"line": 322,
"column": 13
} | {
"line": 322,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝² : LinearOrder R\ninst✝¹ : Field R\ninst✝ : IsOrderedRing R\nq : ℚ\nh : q ≠ 0\n⊢ mk ↑q = 0",
"ppTerm": "?m.13",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_1\ninst✝² : LinearOrder R\ninst✝¹ : Field R\ninst✝ : IsOrderedRing R\nq : ℚ\nh : q ≠ 0\n⊢ mk ↑q = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Archimedean | {
"line": 321,
"column": 59
} | {
"line": 322,
"column": 87
} | {
"line": 324,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝² : LinearOrder R\ninst✝¹ : Field R\ninst✝ : IsOrderedRing R\nq : ℚ\nh : q ≠ 0\n⊢ mk ↑q = 0",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"RingHom.instRingHomClass",
"IsDomain.to_noZeroDivisors",
"OrderAddMonoidHom.mk",
"DivisionRing.to... | [] | by
simpa using mk_map_of_archimedean ⟨(Rat.castHom R).toAddMonoidHom, fun _ ↦ by simp⟩ h | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Order.Ring.Archimedean | {
"line": 330,
"column": 2
} | {
"line": 330,
"column": 13
} | {
"line": 330,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝² : LinearOrder R\ninst✝¹ : Field R\ninst✝ : IsOrderedRing R\nx y : R\n⊢ mk x ≤ mk y ↔ ∃ q, 0 < q ∧ ↑q * |y| ≤ |x|",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_1\ninst✝² : LinearOrder R\ninst✝¹ : Field R\ninst✝ : IsOrderedRing R\nx y : R\n⊢ mk x ≤ mk y ↔ ∃ q, 0 < q ∧ ↑q * |y| ≤ |x|"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Ordering.Defs | {
"line": 159,
"column": 13
} | {
"line": 159,
"column": 49
} | {
"line": 159,
"column": 50
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nP : RingPreordering R\nx✝ : P.HasIdealSupport\n⊢ ∀ (x a : R), a ∈ P → -a ∈ P → x * a ∈ P ∧ -(x * a) ∈ P",
"ppTerm": "?m.31",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_1\ninst✝ : CommRing R\nP : RingPreordering R\nx✝ : P.HasIdealSupport\n⊢ ∀ (x a : R), a ∈ P → -a ∈ P → x * a ∈ P ∧ -(x * a) ∈ P"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Ordering.Defs | {
"line": 165,
"column": 21
} | {
"line": 165,
"column": 32
} | {
"line": 165,
"column": 33
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nP : RingPreordering R\ninst✝ : HasMemOrNegMem P\nx a : R\nha : a ∈ P.supportAddSubgroup\nhx : x ∈ P\n⊢ x * a ∈ ↑P",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SetLike.mem_coe._simp_1",
"HMul.hMul",
"CommSemir... | [
"R : Type u_1\ninst✝¹ : CommRing R\nP : RingPreordering R\ninst✝ : HasMemOrNegMem P\nx a : R\nha : a ∈ P.supportAddSubgroup\nhx : x ∈ P\n⊢ x * a ∈ P"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Ordering.Defs | {
"line": 165,
"column": 53
} | {
"line": 165,
"column": 64
} | {
"line": 165,
"column": 65
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nP : RingPreordering R\ninst✝ : HasMemOrNegMem P\nx a : R\nha : a ∈ P.supportAddSubgroup\nhx : x ∈ P\n⊢ x * a ∈ -↑P",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SetLike.mem_coe._simp_1",
"NonUnitalCommRing.toNonUnit... | [
"R : Type u_1\ninst✝¹ : CommRing R\nP : RingPreordering R\ninst✝ : HasMemOrNegMem P\nx a : R\nha : a ∈ P.supportAddSubgroup\nhx : x ∈ P\n⊢ -(x * a) ∈ P"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Ordering.Defs | {
"line": 166,
"column": 21
} | {
"line": 166,
"column": 32
} | {
"line": 166,
"column": 33
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nP : RingPreordering R\ninst✝ : HasMemOrNegMem P\nx a : R\nha : a ∈ P.supportAddSubgroup\nhx : -x ∈ P\n⊢ x * a ∈ ↑P",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SetLike.mem_coe._simp_1",
"HMul.hMul",
"CommSemi... | [
"R : Type u_1\ninst✝¹ : CommRing R\nP : RingPreordering R\ninst✝ : HasMemOrNegMem P\nx a : R\nha : a ∈ P.supportAddSubgroup\nhx : -x ∈ P\n⊢ x * a ∈ P"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Ordering.Defs | {
"line": 166,
"column": 53
} | {
"line": 166,
"column": 64
} | {
"line": 166,
"column": 65
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nP : RingPreordering R\ninst✝ : HasMemOrNegMem P\nx a : R\nha : a ∈ P.supportAddSubgroup\nhx : -x ∈ P\n⊢ x * a ∈ -↑P",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SetLike.mem_coe._simp_1",
"NonUnitalCommRing.toNonUni... | [
"R : Type u_1\ninst✝¹ : CommRing R\nP : RingPreordering R\ninst✝ : HasMemOrNegMem P\nx a : R\nha : a ∈ P.supportAddSubgroup\nhx : -x ∈ P\n⊢ -(x * a) ∈ P"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Ordering.Defs | {
"line": 179,
"column": 18
} | {
"line": 179,
"column": 29
} | {
"line": 179,
"column": 30
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nP : RingPreordering R\ninst✝ : P.HasIdealSupport\n⊢ ∀ (c : R) {x : R}, x ∈ P.supportAddSubgroup.carrier → c • x ∈ P.supportAddSubgroup.carrier",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHSMul",
"Semiring.toMo... | [
"R : Type u_1\ninst✝¹ : CommRing R\nP : RingPreordering R\ninst✝ : P.HasIdealSupport\n⊢ ∀ (c : R) {x : R}, x ∈ P.supportAddSubgroup → c * x ∈ P.supportAddSubgroup"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Multiplication | {
"line": 701,
"column": 8
} | {
"line": 701,
"column": 39
} | {
"line": 701,
"column": 40
} | [
{
"pp": "case inr.refine_1\nΓ✝ : Type u_1\nΓ' : Type u_2\nR✝ : Type u_3\nS : Type u_4\nV : Type u_5\nΓ : Type ?u.9\nR : Type ?u.15\ninst✝³ : LinearOrder Γ\ninst✝² : AddCommMonoid Γ\ninst✝¹ : IsOrderedCancelAddMonoid Γ\ninst✝ : CommRing R\ny : R⟦Γ⟧ˣ\nh : y ∈ {x | 0 < (↑x - 1).orderTop}\nh✝ : Nontrivial R\nthis :... | [
"case inr.refine_1\nΓ✝ : Type u_1\nΓ' : Type u_2\nR✝ : Type u_3\nS : Type u_4\nV : Type u_5\nΓ : Type ?u.9\nR : Type ?u.15\ninst✝³ : LinearOrder Γ\ninst✝² : AddCommMonoid Γ\ninst✝¹ : IsOrderedCancelAddMonoid Γ\ninst✝ : CommRing R\ny : R⟦Γ⟧ˣ\nh : y ∈ {x | 0 < (↑x - 1).orderTop}\nh✝ : Nontrivial R\nthis : (↑y).orderT... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Multiplication | {
"line": 702,
"column": 8
} | {
"line": 702,
"column": 39
} | {
"line": 702,
"column": 40
} | [
{
"pp": "case inr.refine_2\nΓ✝ : Type u_1\nΓ' : Type u_2\nR✝ : Type u_3\nS : Type u_4\nV : Type u_5\nΓ : Type ?u.9\nR : Type ?u.15\ninst✝³ : LinearOrder Γ\ninst✝² : AddCommMonoid Γ\ninst✝¹ : IsOrderedCancelAddMonoid Γ\ninst✝ : CommRing R\ny : R⟦Γ⟧ˣ\nh : y ∈ {x | 0 < (↑x - 1).orderTop}\nh✝ : Nontrivial R\nthis :... | [
"case inr.refine_2\nΓ✝ : Type u_1\nΓ' : Type u_2\nR✝ : Type u_3\nS : Type u_4\nV : Type u_5\nΓ : Type ?u.9\nR : Type ?u.15\ninst✝³ : LinearOrder Γ\ninst✝² : AddCommMonoid Γ\ninst✝¹ : IsOrderedCancelAddMonoid Γ\ninst✝ : CommRing R\ny : R⟦Γ⟧ˣ\nh : y ∈ {x | 0 < (↑x - 1).orderTop}\nh✝ : Nontrivial R\nthis : (↑y).orderT... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Ordering.Basic | {
"line": 81,
"column": 23
} | {
"line": 81,
"column": 34
} | {
"line": 81,
"column": 35
} | [
{
"pp": "R✝¹ : Type u_1\ninst✝² : CommRing R✝¹\nP✝¹ : RingPreordering R✝¹\nR✝ : Type u_2\ninst✝¹ : CommRing R✝\nP✝ : Set R✝\nadd✝ : ?m.2\nmul✝ : ?m.3\nsq✝ : ?m.4\nneg_one✝ : ?m.5\nR : Type u_3\ninst✝ : CommRing R\nP : Set R\nadd : ∀ {x y : R}, x ∈ P → y ∈ P → x + y ∈ P\nmul : ∀ {x y : R}, x ∈ P → y ∈ P → x * y ... | [
"R✝¹ : Type u_1\ninst✝² : CommRing R✝¹\nP✝¹ : RingPreordering R✝¹\nR✝ : Type u_2\ninst✝¹ : CommRing R✝\nP✝ : Set R✝\nadd✝ : ?m.2\nmul✝ : ?m.3\nsq✝ : ?m.4\nneg_one✝ : ?m.5\nR : Type u_3\ninst✝ : CommRing R\nP : Set R\nadd : ∀ {x y : R}, x ∈ P → y ∈ P → x + y ∈ P\nmul : ∀ {x y : R}, x ∈ P → y ∈ P → x * y ∈ P\nsq : ∀ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Ordering.Basic | {
"line": 83,
"column": 17
} | {
"line": 83,
"column": 28
} | {
"line": 83,
"column": 29
} | [
{
"pp": "R✝¹ : Type u_1\ninst✝² : CommRing R✝¹\nP✝¹ : RingPreordering R✝¹\nR✝ : Type u_2\ninst✝¹ : CommRing R✝\nP✝ : Set R✝\nadd✝ : ?m.2\nmul✝ : ?m.3\nsq✝ : ?m.4\nneg_one✝ : ?m.5\nR : Type u_3\ninst✝ : CommRing R\nP : Set R\nadd : ∀ {x y : R}, x ∈ P → y ∈ P → x + y ∈ P\nmul : ∀ {x y : R}, x ∈ P → y ∈ P → x * y ... | [
"R✝¹ : Type u_1\ninst✝² : CommRing R✝¹\nP✝¹ : RingPreordering R✝¹\nR✝ : Type u_2\ninst✝¹ : CommRing R✝\nP✝ : Set R✝\nadd✝ : ?m.2\nmul✝ : ?m.3\nsq✝ : ?m.4\nneg_one✝ : ?m.5\nR : Type u_3\ninst✝ : CommRing R\nP : Set R\nadd : ∀ {x y : R}, x ∈ P → y ∈ P → x + y ∈ P\nmul : ∀ {x y : R}, x ∈ P → y ∈ P → x * y ∈ P\nsq : ∀ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Ordering.Basic | {
"line": 80,
"column": 23
} | {
"line": 80,
"column": 34
} | {
"line": 80,
"column": 35
} | [
{
"pp": "R✝¹ : Type u_1\ninst✝² : CommRing R✝¹\nP✝¹ : RingPreordering R✝¹\nR✝ : Type u_2\ninst✝¹ : CommRing R✝\nP✝ : Set R✝\nadd✝ : ?m.2\nmul✝ : ?m.3\nsq✝ : ?m.4\nneg_one✝ : ?m.5\nR : Type u_3\ninst✝ : CommRing R\nP : Set R\nadd : ∀ {x y : R}, x ∈ P → y ∈ P → x + y ∈ P\nmul : ∀ {x y : R}, x ∈ P → y ∈ P → x * y ... | [
"R✝¹ : Type u_1\ninst✝² : CommRing R✝¹\nP✝¹ : RingPreordering R✝¹\nR✝ : Type u_2\ninst✝¹ : CommRing R✝\nP✝ : Set R✝\nadd✝ : ?m.2\nmul✝ : ?m.3\nsq✝ : ?m.4\nneg_one✝ : ?m.5\nR : Type u_3\ninst✝ : CommRing R\nP : Set R\nadd : ∀ {x y : R}, x ∈ P → y ∈ P → x + y ∈ P\nmul : ∀ {x y : R}, x ∈ P → y ∈ P → x * y ∈ P\nsq : ∀ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Ordering.Basic | {
"line": 82,
"column": 18
} | {
"line": 82,
"column": 29
} | {
"line": 82,
"column": 30
} | [
{
"pp": "R✝¹ : Type u_1\ninst✝² : CommRing R✝¹\nP✝¹ : RingPreordering R✝¹\nR✝ : Type u_2\ninst✝¹ : CommRing R✝\nP✝ : Set R✝\nadd✝ : ?m.2\nmul✝ : ?m.3\nsq✝ : ?m.4\nneg_one✝ : ?m.5\nR : Type u_3\ninst✝ : CommRing R\nP : Set R\nadd : ∀ {x y : R}, x ∈ P → y ∈ P → x + y ∈ P\nmul : ∀ {x y : R}, x ∈ P → y ∈ P → x * y ... | [
"R✝¹ : Type u_1\ninst✝² : CommRing R✝¹\nP✝¹ : RingPreordering R✝¹\nR✝ : Type u_2\ninst✝¹ : CommRing R✝\nP✝ : Set R✝\nadd✝ : ?m.2\nmul✝ : ?m.3\nsq✝ : ?m.4\nneg_one✝ : ?m.5\nR : Type u_3\ninst✝ : CommRing R\nP : Set R\nadd : ∀ {x y : R}, x ∈ P → y ∈ P → x + y ∈ P\nmul : ∀ {x y : R}, x ∈ P → y ∈ P → x * y ∈ P\nsq : ∀ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Ordering.Basic | {
"line": 102,
"column": 2
} | {
"line": 102,
"column": 13
} | {
"line": 102,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nP : RingPreordering R\ninst✝ : P.HasIdealSupport\n⊢ 1 ∉ P.support",
"ppTerm": "?m.12",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_1\ninst✝¹ : CommRing R\nP : RingPreordering R\ninst✝ : P.HasIdealSupport\n⊢ 1 ∉ P.support"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Ordering.Basic | {
"line": 109,
"column": 2
} | {
"line": 109,
"column": 13
} | {
"line": 109,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nP : RingPreordering R\ninst✝ : P.HasIdealSupport\n⊢ Submodule.toAddSubgroup P.support ≠ Submodule.toAddSubgroup ⊤",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Submodule",
"Semiring.toModule",
"congrArg",
... | [
"R : Type u_1\ninst✝¹ : CommRing R\nP : RingPreordering R\ninst✝ : P.HasIdealSupport\n⊢ ¬P.support = ⊤"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Ordering.Basic | {
"line": 165,
"column": 2
} | {
"line": 165,
"column": 45
} | {
"line": 165,
"column": 46
} | [
{
"pp": "F : Type u_2\ninst✝ : Field F\nP : RingPreordering F\n⊢ P.support = ⊥",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"AddSubgroup.instBot",
"Semiring.toModule",
"CommSemiring.toSemiring",
"_private.Mathlib.Algebra.Order.Ring.Ordering.Basic.0... | [
"F : Type u_2\ninst✝ : Field F\nP : RingPreordering F\n⊢ Submodule.toAddSubgroup P.support = ⊥"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Ordering.Basic | {
"line": 167,
"column": 35
} | {
"line": 167,
"column": 46
} | {
"line": 167,
"column": 47
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nP✝ : RingPreordering R\nF : Type u_2\ninst✝ : Field F\nP : RingPreordering F\n⊢ P.support.IsPrime",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Semiring.toModule",
"congrArg",
"CommSemiring.toSemiring",
"... | [
"R : Type u_1\ninst✝¹ : CommRing R\nP✝ : RingPreordering R\nF : Type u_2\ninst✝ : Field F\nP : RingPreordering F\n⊢ ⊥.IsPrime"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Module.HahnEmbedding | {
"line": 329,
"column": 34
} | {
"line": 329,
"column": 45
} | {
"line": 329,
"column": 46
} | [
{
"pp": "K : Type u_1\ninst✝¹² : DivisionRing K\ninst✝¹¹ : LinearOrder K\ninst✝¹⁰ : IsOrderedRing K\ninst✝⁹ : Archimedean K\nM : Type u_2\ninst✝⁸ : AddCommGroup M\ninst✝⁷ : LinearOrder M\ninst✝⁶ : IsOrderedAddMonoid M\ninst✝⁵ : Module K M\ninst✝⁴ : IsOrderedModule K M\nR : Type u_3\ninst✝³ : AddCommGroup R\nins... | [
"K : Type u_1\ninst✝¹² : DivisionRing K\ninst✝¹¹ : LinearOrder K\ninst✝¹⁰ : IsOrderedRing K\ninst✝⁹ : Archimedean K\nM : Type u_2\ninst✝⁸ : AddCommGroup M\ninst✝⁷ : LinearOrder M\ninst✝⁶ : IsOrderedAddMonoid M\ninst✝⁵ : Module K M\ninst✝⁴ : IsOrderedModule K M\nR : Type u_3\ninst✝³ : AddCommGroup R\ninst✝² : Linear... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Ordering.Basic | {
"line": 175,
"column": 27
} | {
"line": 175,
"column": 38
} | {
"line": 175,
"column": 39
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nP : RingPreordering R\nx✝¹ : P.IsOrdering\na b : R\nx✝ : -(a * b) ∈ P\nthis : ¬(a ∈ P ∨ b ∈ P)\n⊢ a * b ∈ P",
"ppTerm": "?m.42",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_1\ninst✝ : CommRing R\nP : RingPreordering R\nx✝¹ : P.IsOrdering\na b : R\nx✝ : -(a * b) ∈ P\nthis : ¬(a ∈ P ∨ b ∈ P)\n⊢ a * b ∈ P"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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