module stringlengths 16 90 | startPos dict | endPos dict | goals listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 366
values | kind stringclasses 370
values |
|---|---|---|---|---|---|---|
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 68,
"column": 2
} | {
"line": 68,
"column": 31
} | [
{
"pp": "α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\na b : α\nh : a ≤ b\n⊢ insert a (Icc (a + 1) b) = Icc a b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 72,
"column": 2
} | {
"line": 72,
"column": 33
} | [
{
"pp": "α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\na b : α\nh : a ≤ b + 1\n⊢ insert (b + 1) (Icc a b) = Icc a (b + 1)",
"usedConstants": [
"Eq.mpr",
"Order.succ",
"congrArg",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartia... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 76,
"column": 2
} | {
"line": 76,
"column": 31
} | [
{
"pp": "α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\na b : α\nh : a ≤ b\nhb : ¬IsMax b\n⊢ insert b (Ico a b) = Ico a (b + 1)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 79,
"column": 2
} | {
"line": 79,
"column": 31
} | [
{
"pp": "α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\na b : α\nh : a < b\n⊢ insert a (Ico (a + 1) b) = Ico a b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 83,
"column": 2
} | {
"line": 83,
"column": 31
} | [
{
"pp": "α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\na b : α\nh : a ≤ b\nhb : ¬IsMax b\n⊢ insert (b + 1) (Ioc a b) = Ioc a (b + 1)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 86,
"column": 2
} | {
"line": 86,
"column": 31
} | [
{
"pp": "α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\na b : α\nh : a < b\n⊢ insert (a + 1) (Ioc (a + 1) b) = Ioc a b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 97,
"column": 2
} | {
"line": 97,
"column": 31
} | [
{
"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 b : α\n⊢ Icc (a + 1) b = Ioc a b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 100,
"column": 2
} | {
"line": 100,
"column": 31
} | [
{
"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 b : α\n⊢ Ico a (b + 1) = Icc a b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 103,
"column": 2
} | {
"line": 103,
"column": 31
} | [
{
"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 b : α\n⊢ Ioo a (b + 1) = Ioc a b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 106,
"column": 2
} | {
"line": 106,
"column": 31
} | [
{
"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 b : α\n⊢ Ico (a + 1) (b + 1) = Ioc a b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 111,
"column": 2
} | {
"line": 111,
"column": 31
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : Add α\ninst✝¹ : SuccAddOrder α\na b : α\ninst✝ : NoMaxOrder α\nh : a ≤ b\n⊢ insert b (Ico a b) = Ico a (b + 1)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 128,
"column": 2
} | {
"line": 128,
"column": 31
} | [
{
"pp": "α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na b : α\n⊢ Ioc a (b - 1) = Ioo a b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 131,
"column": 2
} | {
"line": 131,
"column": 31
} | [
{
"pp": "α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\nb : α\nhb : ¬IsMin b\na : α\n⊢ Icc a (b - 1) = Ico a b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 134,
"column": 2
} | {
"line": 134,
"column": 31
} | [
{
"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\nb : α\n⊢ Ioc (a - 1) b = Icc a b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 137,
"column": 2
} | {
"line": 137,
"column": 31
} | [
{
"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\nb : α\n⊢ Ioo (a - 1) b = Ico a b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 141,
"column": 2
} | {
"line": 141,
"column": 31
} | [
{
"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\nb : α\n⊢ Ioc (a - 1) (b - 1) = Ico a b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 146,
"column": 2
} | {
"line": 146,
"column": 31
} | [
{
"pp": "α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na b : α\nh : a ≤ b\n⊢ insert b (Icc a (b - 1)) = Icc a b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 150,
"column": 2
} | {
"line": 150,
"column": 33
} | [
{
"pp": "α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na b : α\nh : a - 1 ≤ b\n⊢ insert (a - 1) (Icc a b) = Icc (a - 1) b",
"usedConstants": [
"Eq.mpr",
"PredSubOrder.toPredOrder",
"congrArg",
"PartialOrder.toPreorder",
"HSub.hSub... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 154,
"column": 2
} | {
"line": 154,
"column": 31
} | [
{
"pp": "α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na b : α\nh : a ≤ b\nha : ¬IsMin a\n⊢ insert a (Ioc a b) = Ioc (a - 1) b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 157,
"column": 2
} | {
"line": 157,
"column": 31
} | [
{
"pp": "α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na b : α\nh : a < b\n⊢ insert b (Ioc a (b - 1)) = Ioc a b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 161,
"column": 2
} | {
"line": 161,
"column": 31
} | [
{
"pp": "α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na b : α\nh : a ≤ b\nha : ¬IsMin a\n⊢ insert (a - 1) (Ico a b) = Ico (a - 1) b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 164,
"column": 2
} | {
"line": 164,
"column": 31
} | [
{
"pp": "α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na b : α\nh : a < b\n⊢ insert (b - 1) (Ico a (b - 1)) = Ico a b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 175,
"column": 2
} | {
"line": 175,
"column": 31
} | [
{
"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 b : α\n⊢ Icc a (b - 1) = Ico a b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 178,
"column": 2
} | {
"line": 178,
"column": 31
} | [
{
"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 b : α\n⊢ Ioc (a - 1) b = Icc a b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 181,
"column": 2
} | {
"line": 181,
"column": 31
} | [
{
"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 b : α\n⊢ Ioo (a - 1) b = Ico a b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 184,
"column": 2
} | {
"line": 184,
"column": 31
} | [
{
"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 b : α\n⊢ Ioc (a - 1) (b - 1) = Ico a b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 189,
"column": 2
} | {
"line": 189,
"column": 31
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : Sub α\ninst✝¹ : PredSubOrder α\na b : α\ninst✝ : NoMinOrder α\nh : a ≤ b\n⊢ insert a (Ioc a b) = Ioc (a - 1) b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 200,
"column": 2
} | {
"line": 200,
"column": 48
} | [
{
"pp": "α : Type u_2\ninst✝⁶ : LinearOrder α\ninst✝⁵ : One α\ninst✝⁴ : Add α\ninst✝³ : Sub α\ninst✝² : SuccAddOrder α\ninst✝¹ : PredSubOrder α\ninst✝ : Nontrivial α\na b : α\n⊢ Icc (a + 1) (b - 1) = Ioo a b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 210,
"column": 2
} | {
"line": 210,
"column": 31
} | [
{
"pp": "α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\nb : α\nhb : ¬IsMax b\n⊢ Iio (b + 1) = Iic b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 215,
"column": 2
} | {
"line": 215,
"column": 31
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : Add α\ninst✝¹ : SuccAddOrder α\ninst✝ : NoMaxOrder α\nb : α\n⊢ Iio (b + 1) = Iic b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 223,
"column": 2
} | {
"line": 223,
"column": 31
} | [
{
"pp": "α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\nb : α\nhb : ¬IsMin b\n⊢ Iic (b - 1) = Iio b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 228,
"column": 2
} | {
"line": 228,
"column": 31
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : Sub α\ninst✝¹ : PredSubOrder α\ninst✝ : NoMinOrder α\nb : α\n⊢ Iic (b - 1) = Iio b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 238,
"column": 2
} | {
"line": 238,
"column": 31
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 237,
"column": 80
} | {
"line": 238,
"column": 63
} | [
{
"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",
"usedConstants": [
"Set.Ioi",
"Order.succ",
"Set.Ici",
"Order.succ_eq_add_one",
"congrArg",
"PartialOrder.toPreorder",
... | 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
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 251,
"column": 2
} | {
"line": 251,
"column": 31
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 256,
"column": 2
} | {
"line": 256,
"column": 31
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Module.Archimedean | {
"line": 32,
"column": 56
} | {
"line": 32,
"column": 67
} | [
{
"pp": "M : Type u_1\ninst✝⁸ : AddCommGroup M\ninst✝⁷ : LinearOrder M\ninst✝⁶ : IsOrderedAddMonoid M\nK : Type u_2\ninst✝⁵ : Ring K\ninst✝⁴ : LinearOrder K\ninst✝³ : IsOrderedRing K\ninst✝² : Archimedean K\ninst✝¹ : Module K M\ninst✝ : PosSMulMono K M\na : M\nk : K\nh : k ≠ 0\nthis : Nontrivial K\n⊢ 0 < |k|",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Module.Archimedean | {
"line": 58,
"column": 4
} | {
"line": 58,
"column": 40
} | [
{
"pp": "case inr\nM : Type u_1\ninst✝⁸ : AddCommGroup M\ninst✝⁷ : LinearOrder M\ninst✝⁶ : IsOrderedAddMonoid M\nK : Type u_2\ninst✝⁵ : Ring K\ninst✝⁴ : LinearOrder K\ninst✝³ : IsOrderedRing K\ninst✝² : Archimedean K\ninst✝¹ : Module K M\ninst✝ : PosSMulMono K M\ns : UpperSet (ArchimedeanClass M)\nk : K\na : M\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Module.Archimedean | {
"line": 107,
"column": 2
} | {
"line": 107,
"column": 13
} | [
{
"pp": "case inr\nM : Type u_1\ninst✝⁸ : AddCommGroup M\ninst✝⁷ : LinearOrder M\ninst✝⁶ : IsOrderedAddMonoid M\nK : Type u_2\ninst✝⁵ : Ring K\ninst✝⁴ : LinearOrder K\ninst✝³ : IsOrderedRing K\ninst✝² : Archimedean K\ninst✝¹ : Module K M\ninst✝ : PosSMulMono K M\nc : ArchimedeanClass M\nhc : c ≠ ⊤\na : M\nha : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Basic | {
"line": 647,
"column": 2
} | {
"line": 647,
"column": 30
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"covariant_swap_add_of_covariant_add",
"Add... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Basic | {
"line": 163,
"column": 24
} | {
"line": 163,
"column": 65
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nS : Type u_4\ninst✝² : PartialOrder Γ\ninst✝¹ : Zero R\ninst✝ : PartialOrder Γ'\nx : R⟦Γ'⟧⟦Γ⟧\na : Γ\n⊢ {y | toLex (a, y) ∈ Function.support fun g ↦ (x.coeff g.1).coeff g.2}.IsPWO",
"usedConstants": [
"Set.IsPWO",
"Eq.mpr",
"Equiv.instEqu... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Basic | {
"line": 163,
"column": 24
} | {
"line": 163,
"column": 92
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nS : Type u_4\ninst✝² : PartialOrder Γ\ninst✝¹ : Zero R\ninst✝ : PartialOrder Γ'\nx : R⟦Γ'⟧⟦Γ⟧\na : Γ\n⊢ {y | toLex (a, y) ∈ Function.support fun g ↦ (x.coeff g.1).coeff g.2}.IsPWO",
"usedConstants": [
"Set.IsPWO",
"Eq.mpr",
"Equiv.instEqu... | simpa [Function.mem_support, ne_eq] using (x.coeff a).isPWO_support' | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.RingTheory.HahnSeries.Basic | {
"line": 163,
"column": 24
} | {
"line": 163,
"column": 92
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nS : Type u_4\ninst✝² : PartialOrder Γ\ninst✝¹ : Zero R\ninst✝ : PartialOrder Γ'\nx : R⟦Γ'⟧⟦Γ⟧\na : Γ\n⊢ {y | toLex (a, y) ∈ Function.support fun g ↦ (x.coeff g.1).coeff g.2}.IsPWO",
"usedConstants": [
"Set.IsPWO",
"Eq.mpr",
"Equiv.instEqu... | simpa [Function.mem_support, ne_eq] using (x.coeff a).isPWO_support' | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.HahnSeries.Basic | {
"line": 163,
"column": 24
} | {
"line": 163,
"column": 92
} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nS : Type u_4\ninst✝² : PartialOrder Γ\ninst✝¹ : Zero R\ninst✝ : PartialOrder Γ'\nx : R⟦Γ'⟧⟦Γ⟧\na : Γ\n⊢ {y | toLex (a, y) ∈ Function.support fun g ↦ (x.coeff g.1).coeff g.2}.IsPWO",
"usedConstants": [
"Set.IsPWO",
"Eq.mpr",
"Equiv.instEqu... | simpa [Function.mem_support, ne_eq] using (x.coeff a).isPWO_support' | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.HahnSeries.Basic | {
"line": 509,
"column": 41
} | {
"line": 509,
"column": 52
} | [
{
"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 ≠ ⊤",
"usedConstants": [
"Eq.mpr",
"congrArg",
"HahnSeries.orderTop_eq_top._simp_1",
"HahnSeries.orderTop",
"Sem... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Basic | {
"line": 511,
"column": 4
} | {
"line": 511,
"column": 15
} | [
{
"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",
"usedConstants": [
"HahnSeries.support",
"Eq.mpr",
"HahnSeries.embDomai... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Basic | {
"line": 517,
"column": 2
} | {
"line": 517,
"column": 13
} | [
{
"pp": "case inr.hx.h\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",
"usedConstants": [
"SemilatticeInf.toPartialOrder",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Addition | {
"line": 230,
"column": 2
} | {
"line": 230,
"column": 52
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Addition | {
"line": 242,
"column": 50
} | {
"line": 242,
"column": 61
} | [
{
"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",
"usedConstants": [
"Iff.mpr",
"Eq.mpr",
"HahnSeries.orderTop_n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Addition | {
"line": 246,
"column": 2
} | {
"line": 246,
"column": 52
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Addition | {
"line": 258,
"column": 2
} | {
"line": 258,
"column": 33
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Addition | {
"line": 272,
"column": 4
} | {
"line": 272,
"column": 15
} | [
{
"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",
"usedConstants": [
"HahnSeries.suppo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Addition | {
"line": 275,
"column": 4
} | {
"line": 275,
"column": 22
} | [
{
"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",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Addition | {
"line": 307,
"column": 2
} | {
"line": 307,
"column": 33
} | [
{
"pp": "case coeff.h\nΓ : 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",
"usedConstants": [
"ZeroHom.funLike",
"Preorder.toLT",
"eq_false",
... | 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": 62,
"column": 26
} | {
"line": 62,
"column": 37
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Module.PositiveLinearMap | {
"line": 146,
"column": 19
} | {
"line": 146,
"column": 42
} | [
{
"pp": "case succ\nR : Type u_1\nE₁ : Type u_2\nE₂ : Type u_3\ninst✝⁷ : Semiring R\ninst✝⁶ : AddCommMonoid E₁\ninst✝⁵ : PartialOrder E₁\ninst✝⁴ : AddCommMonoid E₂\ninst✝³ : PartialOrder E₂\ninst✝² : Module R E₁\ninst✝¹ : Module R E₂\ninst✝ : IsOrderedAddMonoid E₂\nf : E₁ →ₚ[R] E₂\nx y : E₁\nh : x ≤ y\nn : ℕ\ni... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Module.PositiveLinearMap | {
"line": 179,
"column": 6
} | {
"line": 179,
"column": 17
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder | {
"line": 52,
"column": 24
} | {
"line": 52,
"column": 35
} | [
{
"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",
"usedConstants": [
"le_mul_iff_one_le_right'._simp_2",
"IsLef... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder | {
"line": 52,
"column": 43
} | {
"line": 52,
"column": 77
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder | {
"line": 97,
"column": 30
} | {
"line": 97,
"column": 41
} | [
{
"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⊢... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder | {
"line": 108,
"column": 30
} | {
"line": 108,
"column": 41
} | [
{
"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",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder | {
"line": 133,
"column": 78
} | {
"line": 133,
"column": 89
} | [
{
"pp": "G : Type u_2\ninst✝⁴ : AddCommGroup G\ninst✝³ : LinearOrder G\ninst✝² : IsOrderedAddMonoid G\ninst✝¹ : LocallyFiniteOrder G\ninst✝ : Nontrivial G\na : G\nha : 0 < a\n⊢ 0 ∈ Icc 0 a",
"usedConstants": [
"Eq.mpr",
"instReflLe",
"congrArg",
"Finset",
"PartialOrder.toPreord... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder | {
"line": 134,
"column": 34
} | {
"line": 134,
"column": 45
} | [
{
"pp": "G : Type u_2\ninst✝⁴ : AddCommGroup G\ninst✝³ : LinearOrder G\ninst✝² : IsOrderedAddMonoid G\ninst✝¹ : LocallyFiniteOrder G\ninst✝ : Nontrivial G\na : G\nha : 0 < a\nH : IsMax ⟨0, ⋯⟩\n⊢ a ∈ Icc 0 a",
"usedConstants": [
"Eq.mpr",
"and_true",
"instReflLe",
"congrArg",
"F... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder | {
"line": 145,
"column": 28
} | {
"line": 145,
"column": 44
} | [
{
"pp": "G : Type u_2\ninst✝⁴ : AddCommGroup G\ninst✝³ : LinearOrder G\ninst✝² : IsOrderedAddMonoid G\ninst✝¹ : LocallyFiniteOrder G\ninst✝ : Nontrivial G\na : G\nha : 0 < a\nb : ↥(Icc 0 a)\nhb : ⟨0, ⋯⟩ ⋖ b\nthis✝ : 0 ≤ ↑b\nx : G\nh₁ : 0 ≤ x\nh₂ : x < ↑b\nhx' : ¬x = 0\nthis : 0 ≤ ↑b ∧ ↑b ≤ a\n⊢ x ∈ Icc 0 a",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder | {
"line": 146,
"column": 29
} | {
"line": 146,
"column": 40
} | [
{
"pp": "G : Type u_2\ninst✝⁴ : AddCommGroup G\ninst✝³ : LinearOrder G\ninst✝² : IsOrderedAddMonoid G\ninst✝¹ : LocallyFiniteOrder G\ninst✝ : Nontrivial G\na : G\nha : 0 < a\nb : ↥(Icc 0 a)\nhb : ⟨0, ⋯⟩ ⋖ b\nthis✝ : 0 ≤ ↑b\nx : G\nh₁ : 0 ≤ x\nh₂ : x < ↑b\nhx' : ¬x = 0\nthis : 0 ≤ ↑b ∧ ↑b ≤ a\n⊢ ⟨0, ⋯⟩ ≠ ⟨x, ⋯⟩"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder | {
"line": 148,
"column": 4
} | {
"line": 148,
"column": 15
} | [
{
"pp": "case h.h.mpr\nG : Type u_2\ninst✝⁴ : AddCommGroup G\ninst✝³ : LinearOrder G\ninst✝² : IsOrderedAddMonoid G\ninst✝¹ : LocallyFiniteOrder G\ninst✝ : Nontrivial G\na : G\nha : 0 < a\nb : ↥(Icc 0 a)\nhb : ⟨0, ⋯⟩ ⋖ b\nthis : 0 ≤ ↑b\n⊢ 0 ≤ 0 ∧ 0 < ↑b",
"usedConstants": [
"Eq.mpr",
"Preorder.t... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder | {
"line": 147,
"column": 4
} | {
"line": 148,
"column": 20
} | [
{
"pp": "case h.h.mpr\nG : Type u_2\ninst✝⁴ : AddCommGroup G\ninst✝³ : LinearOrder G\ninst✝² : IsOrderedAddMonoid G\ninst✝¹ : LocallyFiniteOrder G\ninst✝ : Nontrivial G\na : G\nha : 0 < a\nb : ↥(Icc 0 a)\nhb : ⟨0, ⋯⟩ ⋖ b\nthis : 0 ≤ ↑b\nx : G\n⊢ x = 0 → 0 ≤ x ∧ x < ↑b",
"usedConstants": [
"Eq.mpr",
... | rintro rfl
simpa using hb.1 | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Monoid.LocallyFiniteOrder | {
"line": 147,
"column": 4
} | {
"line": 148,
"column": 20
} | [
{
"pp": "case h.h.mpr\nG : Type u_2\ninst✝⁴ : AddCommGroup G\ninst✝³ : LinearOrder G\ninst✝² : IsOrderedAddMonoid G\ninst✝¹ : LocallyFiniteOrder G\ninst✝ : Nontrivial G\na : G\nha : 0 < a\nb : ↥(Icc 0 a)\nhb : ⟨0, ⋯⟩ ⋖ b\nthis : 0 ≤ ↑b\nx : G\n⊢ x = 0 → 0 ≤ x ∧ x < ↑b",
"usedConstants": [
"Eq.mpr",
... | rintro rfl
simpa using hb.1 | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 81,
"column": 50
} | {
"line": 81,
"column": 91
} | [
{
"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)",
"usedC... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 83,
"column": 4
} | {
"line": 83,
"column": 15
} | [
{
"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",
"usedConst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 87,
"column": 8
} | {
"line": 87,
"column": 19
} | [
{
"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",
"usedConstants": [
"HahnSeries.support",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 90,
"column": 8
} | {
"line": 90,
"column": 19
} | [
{
"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",
"usedConstants": [
"HahnSerie... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Unbundled.Units | {
"line": 25,
"column": 2
} | {
"line": 25,
"column": 13
} | [
{
"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✝",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Unbundled.Units | {
"line": 61,
"column": 7
} | {
"line": 61,
"column": 18
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 95,
"column": 4
} | {
"line": 95,
"column": 15
} | [
{
"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\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 154,
"column": 36
} | {
"line": 154,
"column": 47
} | [
{
"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",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Equiv.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 174,
"column": 4
} | {
"line": 175,
"column": 11
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 187,
"column": 24
} | {
"line": 187,
"column": 35
} | [
{
"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",
"usedConstants": [
"Lex",
"SemilatticeInf.toPartialOrder",
"Distrib... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 187,
"column": 83
} | {
"line": 187,
"column": 94
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"Equiv.instEquivLike",
"congrArg... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 188,
"column": 62
} | {
"line": 188,
"column": 73
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 194,
"column": 51
} | {
"line": 194,
"column": 62
} | [
{
"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|"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 198,
"column": 36
} | {
"line": 198,
"column": 47
} | [
{
"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| ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 198,
"column": 81
} | {
"line": 198,
"column": 92
} | [
{
"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| ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 209,
"column": 41
} | {
"line": 209,
"column": 52
} | [
{
"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| ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 214,
"column": 8
} | {
"line": 214,
"column": 25
} | [
{
"pp": "case hi\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 x).orderTop = (ofLex y).orderTop\nhy : y ≠ 0\nhx : x ≠ 0\nh' : (ofLex |x|).orderTop = (ofLex |y|).orderTop\nn : ℕ\nhn : |(ofLex y).leadi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 217,
"column": 8
} | {
"line": 217,
"column": 19
} | [
{
"pp": "case hi\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 x).orderTop = (ofLex y).orderTop\nhy : y ≠ 0\nhx : x ≠ 0\nh' : (ofLex |x|).orderTop = (ofLex |y|).orderTop\nn : ℕ\nhn : |(ofLex y).leadi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 222,
"column": 38
} | {
"line": 222,
"column": 49
} | [
{
"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| ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 222,
"column": 83
} | {
"line": 222,
"column": 94
} | [
{
"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| ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 236,
"column": 4
} | {
"line": 236,
"column": 48
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 237,
"column": 13
} | {
"line": 237,
"column": 24
} | [
{
"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|",
"usedConstants": [
"Eq.mpr",
"instHSMul",
"abs",
"congrArg",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 240,
"column": 4
} | {
"line": 240,
"column": 21
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 249,
"column": 4
} | {
"line": 249,
"column": 15
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 260,
"column": 4
} | {
"line": 260,
"column": 56
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 279,
"column": 6
} | {
"line": 279,
"column": 17
} | [
{
"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 ⋯ <... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 288,
"column": 6
} | {
"line": 288,
"column": 17
} | [
{
"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 : Lex (Γ × FiniteArchimedeanClass R)\na : { a // a ≠ 0 }\n⊢ toLex ((single (ofLex x).1) ↑a) ≠ 0",
"usedConstants": [
"Eq.mpr",
"ZeroHom.funLike",
"E... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 291,
"column": 6
} | {
"line": 291,
"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 : Lex (Γ × FiniteArchimedeanClass R)\nx✝¹ x✝ : { a // a ≠ 0 }\na : R\nha : a ≠ 0\nb : R\nhb : b ≠ 0\nh : FiniteArchimedeanClass.mk ↑⟨a, ha⟩ ⋯ ≤ FiniteArchimedeanClass.mk ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 298,
"column": 21
} | {
"line": 298,
"column": 41
} | [
{
"pp": "Γ : Type u_1\nR : Type u_2\ninst✝³ : LinearOrder Γ\ninst✝² : LinearOrder R\ninst✝¹ : AddCommGroup R\ninst✝ : IsOrderedAddMonoid R\na✝ b✝ : Lex (Γ × FiniteArchimedeanClass R)\nx✝¹ : Γ × FiniteArchimedeanClass R\nao : Γ\nx✝ : Γ × FiniteArchimedeanClass R\nbo : Γ\na : R\nha : a ≠ 0\nb : R\nhb : b ≠ 0\nh✝ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 414,
"column": 45
} | {
"line": 414,
"column": 56
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.HahnSeries.Lex | {
"line": 415,
"column": 8
} | {
"line": 415,
"column": 19
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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