module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.LinearAlgebra.Prod | {
"line": 478,
"column": 2
} | {
"line": 478,
"column": 20
} | {
"line": 478,
"column": 21
} | [
{
"pp": "R : Type u\nM : Type v\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\nM₂ : Type u_3\ninst✝³ : AddCommGroup M₂\ninst✝² : Module R M₂\nM₃ : Type u_4\ninst✝¹ : AddCommGroup M₃\ninst✝ : Module R M₃\nf : M →ₗ[R] M₃\ng : M₂ →ₗ[R] M₃\nhd : Disjoint f.range g.range\ny : M\nz : M₂\nh : 0 +... | [
"R : Type u\nM : Type v\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\nM₂ : Type u_3\ninst✝³ : AddCommGroup M₂\ninst✝² : Module R M₂\nM₃ : Type u_4\ninst✝¹ : AddCommGroup M₃\ninst✝ : Module R M₃\nf : M →ₗ[R] M₃\ng : M₂ →ₗ[R] M₃\nhd : Disjoint f.range g.range\ny : M\nz : M₂\nh : 0 + g z = 0\nth... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 157,
"column": 2
} | {
"line": 157,
"column": 31
} | {
"line": 157,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder 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",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoa... | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder 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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 160,
"column": 2
} | {
"line": 160,
"column": 31
} | {
"line": 160,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na b : α\nh : a < b\n⊢ insert b (Ioc a (b - 1)) = Ioc a b",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na b : α\nh : a < b\n⊢ insert b (Ioc a (b - 1)) = Ioc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 164,
"column": 2
} | {
"line": 164,
"column": 31
} | {
"line": 164,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder 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",
"ppTerm": "?m.31",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"u... | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder 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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Prod | {
"line": 487,
"column": 6
} | {
"line": 487,
"column": 88
} | {
"line": 487,
"column": 89
} | [
{
"pp": "R✝ : Type u\nK : Type u'\nM✝ : Type v\nV : Type v'\nM₂✝ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nM₅ : Type u_1\nM₆ : Type u_2\ninst✝¹³ : Semiring R✝\ninst✝¹² : AddCommMonoid M✝\ninst✝¹¹ : AddCommMonoid M₂✝\ninst✝¹⁰ : AddCommMonoid M₃\ninst✝⁹ : AddCommMonoid M₄\ninst✝⁸... | [
"R✝ : Type u\nK : Type u'\nM✝ : Type v\nV : Type v'\nM₂✝ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nM₅ : Type u_1\nM₆ : Type u_2\ninst✝¹³ : Semiring R✝\ninst✝¹² : AddCommMonoid M✝\ninst✝¹¹ : AddCommMonoid M₂✝\ninst✝¹⁰ : AddCommMonoid M₃\ninst✝⁹ : AddCommMonoid M₄\ninst✝⁸ : Module R✝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 167,
"column": 2
} | {
"line": 167,
"column": 31
} | {
"line": 167,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder 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",
"ppTerm": "?m.29",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder 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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 178,
"column": 2
} | {
"line": 178,
"column": 31
} | {
"line": 178,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : One α\ninst✝³ : LocallyFiniteOrder α\ninst✝² : Sub α\ninst✝¹ : PredSubOrder α\ninst✝ : NoMinOrder α\na b : α\n⊢ Icc a (b - 1) = Ico a b",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : One α\ninst✝³ : LocallyFiniteOrder α\ninst✝² : Sub α\ninst✝¹ : PredSubOrder α\ninst✝ : NoMinOrder α\na b : α\n⊢ Icc a (b - 1) = Ico a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 181,
"column": 2
} | {
"line": 181,
"column": 31
} | {
"line": 181,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : One α\ninst✝³ : LocallyFiniteOrder α\ninst✝² : Sub α\ninst✝¹ : PredSubOrder α\ninst✝ : NoMinOrder α\na b : α\n⊢ Ioc (a - 1) b = Icc a b",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : One α\ninst✝³ : LocallyFiniteOrder α\ninst✝² : Sub α\ninst✝¹ : PredSubOrder α\ninst✝ : NoMinOrder α\na b : α\n⊢ Ioc (a - 1) b = Icc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 184,
"column": 2
} | {
"line": 184,
"column": 31
} | {
"line": 184,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : One α\ninst✝³ : LocallyFiniteOrder α\ninst✝² : Sub α\ninst✝¹ : PredSubOrder α\ninst✝ : NoMinOrder α\na b : α\n⊢ Ioo (a - 1) b = Ico a b",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : One α\ninst✝³ : LocallyFiniteOrder α\ninst✝² : Sub α\ninst✝¹ : PredSubOrder α\ninst✝ : NoMinOrder α\na b : α\n⊢ Ioo (a - 1) b = Ico a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 187,
"column": 2
} | {
"line": 187,
"column": 31
} | {
"line": 187,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : One α\ninst✝³ : LocallyFiniteOrder α\ninst✝² : Sub α\ninst✝¹ : PredSubOrder α\ninst✝ : NoMinOrder α\na b : α\n⊢ Ioc (a - 1) (b - 1) = Ico a b",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"α : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : One α\ninst✝³ : LocallyFiniteOrder α\ninst✝² : Sub α\ninst✝¹ : PredSubOrder α\ninst✝ : NoMinOrder α\na b : α\n⊢ Ioc (a - 1) (b - 1) = Ico a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 192,
"column": 2
} | {
"line": 192,
"column": 31
} | {
"line": 192,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : One α\ninst✝³ : LocallyFiniteOrder 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",
"ppTerm": "?m.24",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"α : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : One α\ninst✝³ : LocallyFiniteOrder 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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 203,
"column": 2
} | {
"line": 203,
"column": 48
} | {
"line": 203,
"column": 49
} | [
{
"pp": "α : Type u_2\ninst✝⁷ : LinearOrder α\ninst✝⁶ : One α\ninst✝⁵ : LocallyFiniteOrder 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",
"ppTerm": "?m.27",
"assigned": false,
"usedConstants": [],
... | [
"α : Type u_2\ninst✝⁷ : LinearOrder α\ninst✝⁶ : One α\ninst✝⁵ : LocallyFiniteOrder 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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 217,
"column": 2
} | {
"line": 217,
"column": 31
} | {
"line": 217,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrderBot α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\nb : α\nhb : ¬IsMax b\n⊢ Iio (b + 1) = Iic b",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrderBot α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\nb : α\nhb : ¬IsMax b\n⊢ Iio (b + 1) = Iic b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 222,
"column": 2
} | {
"line": 222,
"column": 31
} | {
"line": 222,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : One α\ninst✝³ : LocallyFiniteOrderBot α\ninst✝² : Add α\ninst✝¹ : SuccAddOrder α\ninst✝ : NoMaxOrder α\nb : α\n⊢ Iio (b + 1) = Iic b",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : One α\ninst✝³ : LocallyFiniteOrderBot α\ninst✝² : Add α\ninst✝¹ : SuccAddOrder α\ninst✝ : NoMaxOrder α\nb : α\n⊢ Iio (b + 1) = Iic b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 230,
"column": 2
} | {
"line": 230,
"column": 31
} | {
"line": 230,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrderBot α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\nb : α\nhb : ¬IsMin b\n⊢ Iic (b - 1) = Iio b",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrderBot α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\nb : α\nhb : ¬IsMin b\n⊢ Iic (b - 1) = Iio b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 235,
"column": 2
} | {
"line": 235,
"column": 31
} | {
"line": 235,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : One α\ninst✝³ : LocallyFiniteOrderBot α\ninst✝² : Sub α\ninst✝¹ : PredSubOrder α\ninst✝ : NoMinOrder α\nb : α\n⊢ Iic (b - 1) = Iio b",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : One α\ninst✝³ : LocallyFiniteOrderBot α\ninst✝² : Sub α\ninst✝¹ : PredSubOrder α\ninst✝ : NoMinOrder α\nb : α\n⊢ Iic (b - 1) = Iio b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 249,
"column": 2
} | {
"line": 249,
"column": 31
} | {
"line": 249,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrderTop α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\na : α\nha : ¬IsMax a\n⊢ Ici (a + 1) = Ioi a",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrderTop α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\na : α\nha : ¬IsMax a\n⊢ Ici (a + 1) = Ioi a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 248,
"column": 80
} | {
"line": 249,
"column": 63
} | {
"line": 251,
"column": 0
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrderTop α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\na : α\nha : ¬IsMax a\n⊢ Ici (a + 1) = Ioi a",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Finset.Ici_succ_eq_Ioi_of_not_isMax",
"Order.suc... | [] | by
simpa [succ_eq_add_one] using Ici_succ_eq_Ioi_of_not_isMax ha | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 254,
"column": 2
} | {
"line": 254,
"column": 31
} | {
"line": 254,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : One α\ninst✝³ : LocallyFiniteOrderTop α\ninst✝² : Add α\ninst✝¹ : SuccAddOrder α\ninst✝ : NoMaxOrder α\na : α\n⊢ Ici (a + 1) = Ioi a",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : One α\ninst✝³ : LocallyFiniteOrderTop 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.Finset.SuccPred | {
"line": 262,
"column": 2
} | {
"line": 262,
"column": 31
} | {
"line": 262,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrderTop α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na : α\nha : ¬IsMin a\n⊢ Ioi (a - 1) = Ici a",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrderTop 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.Finset.SuccPred | {
"line": 267,
"column": 2
} | {
"line": 267,
"column": 31
} | {
"line": 267,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : One α\ninst✝³ : LocallyFiniteOrderTop α\ninst✝² : Sub α\ninst✝¹ : PredSubOrder α\ninst✝ : NoMinOrder α\na : α\n⊢ Ioi (a - 1) = Ici a",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : One α\ninst✝³ : LocallyFiniteOrderTop 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.LinearAlgebra.Quotient.Basic | {
"line": 421,
"column": 73
} | {
"line": 421,
"column": 84
} | {
"line": 421,
"column": 85
} | [
{
"pp": "R : Type u_1\nM : Type u_2\nr : R\nx y : M\ninst✝² : Ring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\np p' P Q : Submodule R M\nhf : map (↑(LinearEquiv.refl R M)) P = Q\n⊢ P = Q",
"ppTerm": "?m.60",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_1\nM : Type u_2\nr : R\nx y : M\ninst✝² : Ring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\np p' P Q : Submodule R M\nhf : map (↑(LinearEquiv.refl R M)) P = Q\n⊢ P = Q"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fintype.Pigeonhole | {
"line": 76,
"column": 2
} | {
"line": 76,
"column": 35
} | {
"line": 76,
"column": 36
} | [
{
"pp": "α : Sort u_4\nβ : Sort u_5\ninst✝¹ : Infinite α\ninst✝ : Finite β\nf : α → β\n⊢ ∃ x y, x ≠ y ∧ f x = f y",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Exists",
"id",
"Ne",
"funext",
"And",
"_private.Mathlib.Da... | [
"α : Sort u_4\nβ : Sort u_5\ninst✝¹ : Infinite α\ninst✝ : Finite β\nf : α → β\n⊢ ∃ x y, f x = f y ∧ ¬x = y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.PartialSups | {
"line": 227,
"column": 13
} | {
"line": 227,
"column": 52
} | {
"line": 227,
"column": 53
} | [
{
"pp": "α : Type u_1\nι : Type u_3\ninst✝² : Preorder ι\ninst✝¹ : LocallyFiniteOrderBot ι\ninst✝ : ConditionallyCompleteLattice α\nf : ι → α\ni j : ι\nhj : j ∈ Iic i\n⊢ j ∈ Set.Iic i",
"ppTerm": "?m.40",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"_private.Mathlib.Order.PartialSups.... | [
"α : Type u_1\nι : Type u_3\ninst✝² : Preorder ι\ninst✝¹ : LocallyFiniteOrderBot ι\ninst✝ : ConditionallyCompleteLattice α\nf : ι → α\ni j : ι\nhj : j ∈ Iic i\n⊢ j ≤ i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.PartialSups | {
"line": 228,
"column": 47
} | {
"line": 228,
"column": 86
} | {
"line": 228,
"column": 87
} | [
{
"pp": "α : Type u_1\nι : Type u_3\ninst✝² : Preorder ι\ninst✝¹ : LocallyFiniteOrderBot ι\ninst✝ : ConditionallyCompleteLattice α\nf : ι → α\ni : ι\nx✝ : ↑(Set.Iic i)\nj : ι\nhj : j ∈ Set.Iic i\n⊢ ↑⟨j, hj⟩ ∈ Iic i",
"ppTerm": "?m.71",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Fins... | [
"α : Type u_1\nι : Type u_3\ninst✝² : Preorder ι\ninst✝¹ : LocallyFiniteOrderBot ι\ninst✝ : ConditionallyCompleteLattice α\nf : ι → α\ni : ι\nx✝ : ↑(Set.Iic i)\nj : ι\nhj : j ∈ Set.Iic i\n⊢ j ≤ i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.PartialSups | {
"line": 236,
"column": 6
} | {
"line": 236,
"column": 49
} | {
"line": 236,
"column": 50
} | [
{
"pp": "case pos.refine_1\nα : Type u_1\nι : Type u_3\ninst✝² : Preorder ι\ninst✝¹ : LocallyFiniteOrderBot ι\ninst✝ : ConditionallyCompleteLattice α\nf : ι → α\nh : BddAbove (Set.range f)\nhι : Nonempty ι\ni : ι\n⊢ (partialSups f) i ≤ ⨆ i, f i",
"ppTerm": "?pos.refine_1✝",
"assigned": true,
"usedCo... | [
"case pos.refine_1\nα : Type u_1\nι : Type u_3\ninst✝² : Preorder ι\ninst✝¹ : LocallyFiniteOrderBot ι\ninst✝ : ConditionallyCompleteLattice α\nf : ι → α\nh : BddAbove (Set.range f)\nhι : Nonempty ι\ni : ι\n⊢ ⨆ i_1, f ↑i_1 ≤ ⨆ i, f i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.PartialSups | {
"line": 274,
"column": 36
} | {
"line": 274,
"column": 60
} | {
"line": 274,
"column": 61
} | [
{
"pp": "α : Type u_1\nι : Type u_3\ninst✝² : Preorder ι\ninst✝¹ : LocallyFiniteOrderBot ι\ninst✝ : CompleteLattice α\nf g : ι → α\nh : partialSups f = partialSups g\n⊢ ⨆ i, (partialSups f) i = ⨆ i, g i",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.toSemila... | [
"α : Type u_1\nι : Type u_3\ninst✝² : Preorder ι\ninst✝¹ : LocallyFiniteOrderBot ι\ninst✝ : CompleteLattice α\nf g : ι → α\nh : partialSups f = partialSups g\n⊢ ⨆ i, (partialSups f) i = ⨆ i, (partialSups g) i"
] | ← iSup_partialSups_eq g, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.LinearAlgebra.Prod | {
"line": 629,
"column": 6
} | {
"line": 629,
"column": 17
} | {
"line": 629,
"column": 18
} | [
{
"pp": "R : Type u\nM : Type v\nM₂ : Type w\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid M₂\ninst✝¹ : Module R M\ninst✝ : Module R M₂\np₁ : Submodule R M\np₂ : Submodule R M₂\nq : Submodule R (M × M₂)\nhH : map (inl R M M₂) p₁ ≤ q\nhK : map (inr R M M₂) p₂ ≤ q\nx1 : M\nx2 : M₂\nh1 : (... | [
"R : Type u\nM : Type v\nM₂ : Type w\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid M₂\ninst✝¹ : Module R M\ninst✝ : Module R M₂\np₁ : Submodule R M\np₂ : Submodule R M₂\nq : Submodule R (M × M₂)\nhH : map (inl R M M₂) p₁ ≤ q\nhK : map (inr R M M₂) p₂ ≤ q\nx1 : M\nx2 : M₂\nh1 : (x1, x2).1 ∈ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Prod | {
"line": 632,
"column": 6
} | {
"line": 632,
"column": 17
} | {
"line": 632,
"column": 18
} | [
{
"pp": "R : Type u\nM : Type v\nM₂ : Type w\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid M₂\ninst✝¹ : Module R M\ninst✝ : Module R M₂\np₁ : Submodule R M\np₂ : Submodule R M₂\nq : Submodule R (M × M₂)\nhH : map (inl R M M₂) p₁ ≤ q\nhK : map (inr R M M₂) p₂ ≤ q\nx1 : M\nx2 : M₂\nh1 : (... | [
"R : Type u\nM : Type v\nM₂ : Type w\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid M₂\ninst✝¹ : Module R M\ninst✝ : Module R M₂\np₁ : Submodule R M\np₂ : Submodule R M₂\nq : Submodule R (M × M₂)\nhH : map (inl R M M₂) p₁ ≤ q\nhK : map (inr R M M₂) p₂ ≤ q\nx1 : M\nx2 : M₂\nh1 : (x1, x2).1 ∈ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Prod | {
"line": 632,
"column": 6
} | {
"line": 632,
"column": 20
} | {
"line": 633,
"column": 4
} | [
{
"pp": "R : Type u\nM : Type v\nM₂ : Type w\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid M₂\ninst✝¹ : Module R M\ninst✝ : Module R M₂\np₁ : Submodule R M\np₂ : Submodule R M₂\nq : Submodule R (M × M₂)\nhH : map (inl R M M₂) p₁ ≤ q\nhK : map (inr R M M₂) p₂ ≤ q\nx1 : M\nx2 : M₂\nh1 : (... | [] | simpa using h2 | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.LinearAlgebra.Prod | {
"line": 633,
"column": 4
} | {
"line": 633,
"column": 15
} | {
"line": 633,
"column": 16
} | [
{
"pp": "case mpr\nR : Type u\nM : Type v\nM₂ : Type w\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid M₂\ninst✝¹ : Module R M\ninst✝ : Module R M₂\np₁ : Submodule R M\np₂ : Submodule R M₂\nq : Submodule R (M × M₂)\nhH : map (inl R M M₂) p₁ ≤ q\nhK : map (inr R M M₂) p₂ ≤ q\nx1 : M\nx2 : ... | [
"case mpr\nR : Type u\nM : Type v\nM₂ : Type w\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid M₂\ninst✝¹ : Module R M\ninst✝ : Module R M₂\np₁ : Submodule R M\np₂ : Submodule R M₂\nq : Submodule R (M × M₂)\nhH : map (inl R M M₂) p₁ ≤ q\nhK : map (inr R M M₂) p₂ ≤ q\nx1 : M\nx2 : M₂\nh1 : (x1... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Disjointed | {
"line": 104,
"column": 13
} | {
"line": 104,
"column": 52
} | {
"line": 104,
"column": 53
} | [
{
"pp": "case empty\nα : Type u_1\nι : Type u_2\ninst✝² : GeneralizedBooleanAlgebra α\ninst✝¹ : Preorder ι\ninst✝ : LocallyFiniteOrderBot ι\nf : ι → α\np : α → Prop\nhdiff : ∀ ⦃t : α⦄ ⦃i : ι⦄, p t → p (t \\ f i)\ni : ι\nhpi : p (f i)\n⊢ p (f i \\ ∅.sup f)",
"ppTerm": "?empty",
"assigned": true,
"use... | [
"case empty\nα : Type u_1\nι : Type u_2\ninst✝² : GeneralizedBooleanAlgebra α\ninst✝¹ : Preorder ι\ninst✝ : LocallyFiniteOrderBot ι\nf : ι → α\np : α → Prop\nhdiff : ∀ ⦃t : α⦄ ⦃i : ι⦄, p t → p (t \\ f i)\ni : ι\nhpi : p (f i)\n⊢ p (f i)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Disjointed | {
"line": 138,
"column": 13
} | {
"line": 138,
"column": 24
} | {
"line": 138,
"column": 25
} | [
{
"pp": "α : Type u_1\nι : Type u_2\ninst✝² : GeneralizedBooleanAlgebra α\ninst✝¹ : PartialOrder ι\ninst✝ : LocallyFiniteOrderBot ι\nf : ι → α\nn : ℕ\nih : ∀ (i : ι), #(Iio i) ≤ n → (partialSups (disjointed f)) i = (partialSups f) i\ni : ι\nhi : #(Iio i) ≤ n + 1\nhn : #(Iio i) = n + 1\nr : ι\n⊢ r ∈ (Iio i).biUn... | [
"α : Type u_1\nι : Type u_2\ninst✝² : GeneralizedBooleanAlgebra α\ninst✝¹ : PartialOrder ι\ninst✝ : LocallyFiniteOrderBot ι\nf : ι → α\nn : ℕ\nih : ∀ (i : ι), #(Iio i) ≤ n → (partialSups (disjointed f)) i = (partialSups f) i\ni : ι\nhi : #(Iio i) ≤ n + 1\nhn : #(Iio i) = n + 1\nr : ι\n⊢ (∃ a < i, r ≤ a) ↔ r < i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Prod | {
"line": 941,
"column": 2
} | {
"line": 942,
"column": 69
} | {
"line": 942,
"column": 70
} | [
{
"pp": "case h\nR : Type u_3\nS : Type u_4\nG : Type u_5\nH : Type u_6\nI : Type u_7\ninst✝⁸ : Semiring R\ninst✝⁷ : Semiring S\nσ : R →+* S\ninst✝⁶ : RingHomSurjective σ\ninst✝⁵ : AddCommMonoid G\ninst✝⁴ : Module R G\ninst✝³ : AddCommMonoid H\ninst✝² : Module S H\ninst✝¹ : AddCommMonoid I\ninst✝ : Module S I\n... | [
"case h\nR : Type u_3\nS : Type u_4\nG : Type u_5\nH : Type u_6\nI : Type u_7\ninst✝⁸ : Semiring R\ninst✝⁷ : Semiring S\nσ : R →+* S\ninst✝⁶ : RingHomSurjective σ\ninst✝⁵ : AddCommMonoid G\ninst✝⁴ : Module R G\ninst✝³ : AddCommMonoid H\ninst✝² : Module S H\ninst✝¹ : AddCommMonoid I\ninst✝ : Module S I\nf : G →ₛₗ[σ]... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Prod | {
"line": 950,
"column": 2
} | {
"line": 950,
"column": 34
} | {
"line": 950,
"column": 35
} | [
{
"pp": "S : Type u_4\nH : Type u_6\nI : Type u_7\ninst✝⁴ : Semiring S\ninst✝³ : AddCommMonoid H\ninst✝² : Module S H\ninst✝¹ : AddCommMonoid I\ninst✝ : Module S I\nG : Submodule S (H × I)\nhf₁ : Bijective (Prod.fst ∘ ⇑G.subtype)\n⊢ ∃ f, G = f.graph",
"ppTerm": "?m.48",
"assigned": false,
"usedConst... | [
"S : Type u_4\nH : Type u_6\nI : Type u_7\ninst✝⁴ : Semiring S\ninst✝³ : AddCommMonoid H\ninst✝² : Module S H\ninst✝¹ : AddCommMonoid I\ninst✝ : Module S I\nG : Submodule S (H × I)\nhf₁ : Bijective (Prod.fst ∘ ⇑G.subtype)\n⊢ ∃ f, G = f.graph"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.SuccPred.LinearLocallyFinite | {
"line": 174,
"column": 6
} | {
"line": 174,
"column": 50
} | {
"line": 174,
"column": 51
} | [
{
"pp": "case inr\nι : Type u_1\ninst✝² : LinearOrder ι\ninst✝¹ : LocallyFiniteOrder ι\ninst✝ : SuccOrder ι\ni j : ι\nhij : i = j\n⊢ succ^[0] i = j",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"Order.succ",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
... | [
"case inr\nι : Type u_1\ninst✝² : LinearOrder ι\ninst✝¹ : LocallyFiniteOrder ι\ninst✝ : SuccOrder ι\ni j : ι\nhij : i = j\n⊢ i = j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.SuccPred.LinearLocallyFinite | {
"line": 178,
"column": 16
} | {
"line": 178,
"column": 60
} | {
"line": 178,
"column": 61
} | [
{
"pp": "case zero\nι : Type u_1\ninst✝² : LinearOrder ι\ninst✝¹ : LocallyFiniteOrder ι\ninst✝ : SuccOrder ι\ni j : ι\nhij : i < j\nh : ∀ (n : ℕ), succ^[n] i ≠ j\n⊢ succ^[0] i < j",
"ppTerm": "?zero",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"Order.succ",
"PartialOrder... | [
"case zero\nι : Type u_1\ninst✝² : LinearOrder ι\ninst✝¹ : LocallyFiniteOrder ι\ninst✝ : SuccOrder ι\ni j : ι\nhij : i < j\nh : ∀ (n : ℕ), succ^[n] i ≠ j\n⊢ i < j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Disjointed | {
"line": 150,
"column": 8
} | {
"line": 150,
"column": 53
} | {
"line": 150,
"column": 54
} | [
{
"pp": "case succ.inr.hab\nα : Type u_1\nι : Type u_2\ninst✝² : GeneralizedBooleanAlgebra α\ninst✝¹ : PartialOrder ι\ninst✝ : LocallyFiniteOrderBot ι\nf : ι → α\nn : ℕ\ni : ι\nhi : #(Iio i) ≤ n + 1\nhn : #(Iio i) = n + 1\nhun : (Iio i).biUnion Iic = Iio i\nih : ∀ (i : ι), #(Iio i) ≤ n → (Iic i).sup (disjointed... | [
"case succ.inr.hab\nα : Type u_1\nι : Type u_2\ninst✝² : GeneralizedBooleanAlgebra α\ninst✝¹ : PartialOrder ι\ninst✝ : LocallyFiniteOrderBot ι\nf : ι → α\nn : ℕ\ni : ι\nhi : #(Iio i) ≤ n + 1\nhn : #(Iio i) = n + 1\nhun : (Iio i).biUnion Iic = Iio i\nih : ∀ (i : ι), #(Iio i) ≤ n → (Iic i).sup (disjointed f) = (Iic i... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Prod | {
"line": 985,
"column": 2
} | {
"line": 985,
"column": 34
} | {
"line": 985,
"column": 35
} | [
{
"pp": "S : Type u_4\nH : Type u_6\nI : Type u_7\ninst✝⁴ : Semiring S\ninst✝³ : AddCommMonoid H\ninst✝² : Module S H\ninst✝¹ : AddCommMonoid I\ninst✝ : Module S I\nG : Submodule S (H × I)\nhG₁ : Bijective (Prod.fst ∘ ⇑G.subtype)\nhG₂ : Bijective (Prod.snd ∘ ⇑G.subtype)\n⊢ ∃ e, G = (↑e).graph",
"ppTerm": "?... | [
"S : Type u_4\nH : Type u_6\nI : Type u_7\ninst✝⁴ : Semiring S\ninst✝³ : AddCommMonoid H\ninst✝² : Module S H\ninst✝¹ : AddCommMonoid I\ninst✝ : Module S I\nG : Submodule S (H × I)\nhG₁ : Bijective (Prod.fst ∘ ⇑G.subtype)\nhG₂ : Bijective (Prod.snd ∘ ⇑G.subtype)\n⊢ ∃ e, G = (↑e).graph"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.SuccPred.LinearLocallyFinite | {
"line": 189,
"column": 50
} | {
"line": 189,
"column": 88
} | {
"line": 189,
"column": 89
} | [
{
"pp": "ι : Type u_1\ninst✝² : LinearOrder ι\ninst✝¹ : LocallyFiniteOrder ι\ninst✝ : SuccOrder ι\ni j : ι\nhij : i < j\nh : ∀ (n : ℕ), succ^[n] i ≠ j\nh_lt : ∀ (n : ℕ), succ^[n] i < j\nh_mem : ∀ (n : ℕ), succ^[n] i ∈ Finset.Icc i j\nf : ℕ → ↥(Finset.Icc i j) := fun n ↦ ⟨succ^[n] i, ⋯⟩\nn m : ℕ\nhnm_ne : n ≠ m\... | [
"ι : Type u_1\ninst✝² : LinearOrder ι\ninst✝¹ : LocallyFiniteOrder ι\ninst✝ : SuccOrder ι\ni j : ι\nhij : i < j\nh : ∀ (n : ℕ), succ^[n] i ≠ j\nh_lt : ∀ (n : ℕ), succ^[n] i < j\nh_mem : ∀ (n : ℕ), succ^[n] i ∈ Finset.Icc i j\nf : ℕ → ↥(Finset.Icc i j) := fun n ↦ ⟨succ^[n] i, ⋯⟩\nn m : ℕ\nhnm_ne : n ≠ m\nhfnm : f n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Disjointed | {
"line": 159,
"column": 11
} | {
"line": 159,
"column": 80
} | {
"line": 159,
"column": 81
} | [
{
"pp": "α : Type u_1\nι : Type u_2\ninst✝³ : GeneralizedBooleanAlgebra α\ninst✝² : PartialOrder ι\ninst✝¹ : LocallyFiniteOrderBot ι\ninst✝ : Fintype ι\nf : ι → α\nr : ι\n⊢ r ∈ univ.biUnion Iic ↔ r ∈ univ",
"ppTerm": "?m.40",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.univ",
... | [
"α : Type u_1\nι : Type u_2\ninst✝³ : GeneralizedBooleanAlgebra α\ninst✝² : PartialOrder ι\ninst✝¹ : LocallyFiniteOrderBot ι\ninst✝ : Fintype ι\nf : ι → α\nr : ι\n⊢ ∃ a, r ≤ a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Disjointed | {
"line": 175,
"column": 2
} | {
"line": 175,
"column": 50
} | {
"line": 176,
"column": 4
} | [
{
"pp": "case e_a.e_s\nα : Type u_1\nι : Type u_2\ninst✝² : GeneralizedBooleanAlgebra α\ninst✝¹ : PartialOrder ι\ninst✝ : LocallyFiniteOrderBot ι\nf : ι → α\ni : ι\nstep1 : f i \\ (Iio i).sup f = (partialSups f) i \\ (Iio i).sup f\nr : ι\n⊢ r ∈ (Iio i).biUnion Iic ↔ r ∈ Iio i",
"ppTerm": "?e_a.e_s✝",
"a... | [
"case e_a.e_s\nα : Type u_1\nι : Type u_2\ninst✝² : GeneralizedBooleanAlgebra α\ninst✝¹ : PartialOrder ι\ninst✝ : LocallyFiniteOrderBot ι\nf : ι → α\ni : ι\nstep1 : f i \\ (Iio i).sup f = (partialSups f) i \\ (Iio i).sup f\nr : ι\n⊢ (∃ a < i, r ≤ a) ↔ r < i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.Basic | {
"line": 56,
"column": 2
} | {
"line": 56,
"column": 37
} | {
"line": 58,
"column": 0
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : AddCommMonoid α\ninst✝³ : PartialOrder α\ninst✝² : IsOrderedCancelAddMonoid α\ninst✝¹ : ExistsAddOfLE α\ninst✝ : LocallyFiniteOrder α\na b c : α\n⊢ ⇑(addRightEmbedding c) '' Set.Ioc a b = Set.Ioc (a + c) (b + c)",
"ppTerm": "?m.47",
"assigned": true,
"usedConstants": ... | [] | exact Set.image_add_const_Ioc _ _ _ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Order.Disjointed | {
"line": 229,
"column": 2
} | {
"line": 229,
"column": 37
} | {
"line": 229,
"column": 38
} | [
{
"pp": "case e_a.e_s\nα : Type u_1\nι : Type u_2\ninst✝³ : GeneralizedBooleanAlgebra α\ninst✝² : LinearOrder ι\ninst✝¹ : LocallyFiniteOrderBot ι\ninst✝ : SuccOrder ι\nf : ι → α\ni : ι\nhi : ¬IsMax i\nm : ι\n⊢ m ∈ Iio (succ i) ↔ m ∈ Iic i",
"ppTerm": "?e_a.e_s✝",
"assigned": true,
"usedConstants": [... | [
"case e_a.e_s\nα : Type u_1\nι : Type u_2\ninst✝³ : GeneralizedBooleanAlgebra α\ninst✝² : LinearOrder ι\ninst✝¹ : LocallyFiniteOrderBot ι\ninst✝ : SuccOrder ι\nf : ι → α\ni : ι\nhi : ¬IsMax i\nm : ι\n⊢ m < succ i ↔ m ≤ i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Disjointed | {
"line": 239,
"column": 4
} | {
"line": 239,
"column": 60
} | {
"line": 239,
"column": 61
} | [
{
"pp": "case pos\nα : Type u_1\nι : Type u_2\ninst✝³ : GeneralizedBooleanAlgebra α\ninst✝² : LinearOrder ι\ninst✝¹ : LocallyFiniteOrderBot ι\ninst✝ : SuccOrder ι\nf : ι → α\nhf : Monotone f\ni : ι\nh : IsMax i\n⊢ disjointed f (succ i) ⊔ f i = f (succ i)",
"ppTerm": "?pos✝",
"assigned": true,
"usedC... | [
"case pos\nα : Type u_1\nι : Type u_2\ninst✝³ : GeneralizedBooleanAlgebra α\ninst✝² : LinearOrder ι\ninst✝¹ : LocallyFiniteOrderBot ι\ninst✝ : SuccOrder ι\nf : ι → α\nhf : Monotone f\ni : ι\nh : IsMax i\n⊢ disjointed f i ≤ f i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.Basic | {
"line": 80,
"column": 2
} | {
"line": 80,
"column": 77
} | {
"line": 82,
"column": 0
} | [
{
"pp": "α : Type u_2\ninst✝⁵ : AddCommMonoid α\ninst✝⁴ : PartialOrder α\ninst✝³ : IsOrderedCancelAddMonoid α\ninst✝² : ExistsAddOfLE α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : DecidableEq α\na b c : α\n⊢ image (fun x ↦ c + x) (Ioo a b) = Ioo (c + a) (c + b)",
"ppTerm": "?m.29",
"assigned": true,
"us... | [] | rw [← map_add_left_Ioo, map_eq_image, addLeftEmbedding, Embedding.coeFn_mk] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Order.Interval.Finset.Basic | {
"line": 80,
"column": 2
} | {
"line": 80,
"column": 77
} | {
"line": 82,
"column": 0
} | [
{
"pp": "α : Type u_2\ninst✝⁵ : AddCommMonoid α\ninst✝⁴ : PartialOrder α\ninst✝³ : IsOrderedCancelAddMonoid α\ninst✝² : ExistsAddOfLE α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : DecidableEq α\na b c : α\n⊢ image (fun x ↦ c + x) (Ioo a b) = Ioo (c + a) (c + b)",
"ppTerm": "?m.29",
"assigned": true,
"us... | [] | rw [← map_add_left_Ioo, map_eq_image, addLeftEmbedding, Embedding.coeFn_mk] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Interval.Finset.Basic | {
"line": 80,
"column": 2
} | {
"line": 80,
"column": 77
} | {
"line": 82,
"column": 0
} | [
{
"pp": "α : Type u_2\ninst✝⁵ : AddCommMonoid α\ninst✝⁴ : PartialOrder α\ninst✝³ : IsOrderedCancelAddMonoid α\ninst✝² : ExistsAddOfLE α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : DecidableEq α\na b c : α\n⊢ image (fun x ↦ c + x) (Ioo a b) = Ioo (c + a) (c + b)",
"ppTerm": "?m.29",
"assigned": true,
"us... | [] | rw [← map_add_left_Ioo, map_eq_image, addLeftEmbedding, Embedding.coeFn_mk] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Disjointed | {
"line": 258,
"column": 6
} | {
"line": 258,
"column": 51
} | {
"line": 258,
"column": 52
} | [
{
"pp": "case pos\nα : Type u_1\ninst✝³ : GeneralizedBooleanAlgebra α\nι : Type u_3\ninst✝² : LinearOrder ι\ninst✝¹ : LocallyFiniteOrder ι\ninst✝ : OrderBot ι\nf : ι → α\nhf : Monotone f\nm✝ n : ι\nthis : SuccOrder ι := LinearLocallyFiniteOrder.succOrder ι\nm : ι\nhm : n ≤ m\nih : (Ioc n m).sup (disjointed f) =... | [
"case pos\nα : Type u_1\ninst✝³ : GeneralizedBooleanAlgebra α\nι : Type u_3\ninst✝² : LinearOrder ι\ninst✝¹ : LocallyFiniteOrder ι\ninst✝ : OrderBot ι\nf : ι → α\nhf : Monotone f\nm✝ n : ι\nthis : SuccOrder ι := LinearLocallyFiniteOrder.succOrder ι\nm : ι\nhm : n ≤ m\nih : (Ioc n m).sup (disjointed f) = f m \\ f n\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.BigOperators.Intervals | {
"line": 96,
"column": 2
} | {
"line": 96,
"column": 35
} | {
"line": 96,
"column": 36
} | [
{
"pp": "δ : Type u_4\ninst✝ : CommGroup δ\nf : ℕ → δ\nm n : ℕ\nh : m ≤ n\n⊢ ∏ k ∈ Ico m n, f k = (∏ k ∈ range n, f k) / ∏ k ∈ range m, f k",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"instHDiv",
"HMul.hMul",
"Monoid.toMulOn... | [
"δ : Type u_4\ninst✝ : CommGroup δ\nf : ℕ → δ\nm n : ℕ\nh : m ≤ n\n⊢ ∏ k ∈ Ico m n, f k = (∏ k ∈ range n, f k) * (∏ k ∈ range m, f k)⁻¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.BigOperators.Intervals | {
"line": 111,
"column": 2
} | {
"line": 111,
"column": 43
} | {
"line": 112,
"column": 2
} | [
{
"pp": "M : Type u_4\ninst✝ : AddCommMonoid M\na b : ℕ\nf : ℕ → ℕ → M\n⊢ ∑ i ∈ Ico a b, ∑ j ∈ Ico i b, f i j = ∑ j ∈ Ico a b, ∑ i ∈ Ico a (j + 1), f i j",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Nat.instLocallyFiniteOrder",
"Finset.sigm... | [
"M : Type u_4\ninst✝ : AddCommMonoid M\na b : ℕ\nf : ℕ → ℕ → M\n⊢ ∑ x ∈ (Ico a b).sigma fun i ↦ Ico i b, f x.fst x.snd = ∑ x ∈ (Ico a b).sigma fun j ↦ Ico a (j + 1), f x.snd x.fst"
] | rw [Finset.sum_sigma', Finset.sum_sigma'] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.BigOperators.Intervals | {
"line": 121,
"column": 2
} | {
"line": 121,
"column": 43
} | {
"line": 122,
"column": 2
} | [
{
"pp": "M : Type u_4\ninst✝ : AddCommMonoid M\na b : ℕ\nf : ℕ → ℕ → M\n⊢ ∑ i ∈ Ico a b, ∑ j ∈ Ico (i + 1) b, f i j = ∑ j ∈ Ico a b, ∑ i ∈ Ico a j, f i j",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Nat.instLocallyFiniteOrder",
"Finset.sigm... | [
"M : Type u_4\ninst✝ : AddCommMonoid M\na b : ℕ\nf : ℕ → ℕ → M\n⊢ ∑ x ∈ (Ico a b).sigma fun i ↦ Ico (i + 1) b, f x.fst x.snd = ∑ x ∈ (Ico a b).sigma (Ico a), f x.snd x.fst"
] | rw [Finset.sum_sigma', Finset.sum_sigma'] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Finset.NatAntidiagonal | {
"line": 130,
"column": 2
} | {
"line": 130,
"column": 13
} | {
"line": 130,
"column": 14
} | [
{
"pp": "n k : ℕ\nh : k ≤ n\naux₁ : (fun a ↦ a.1 ≤ k) = (fun a ↦ a.2 ≤ k) ∘ ⇑(Equiv.prodComm ℕ ℕ).symm\naux₂ : ∀ (i j : ℕ), (∃ a b, a + b = k ∧ b = i ∧ a + (n - k) = j) ↔ ∃ a b, a + b = k ∧ a = i ∧ b + (n - k) = j\ni j : ℕ\n⊢ (i, j) ∈\n map\n (({ toFun := fun x ↦ x + (n - k), inj' := ⋯ }.prodMap (Em... | [
"n k : ℕ\nh : k ≤ n\naux₁ : (fun a ↦ a.1 ≤ k) = (fun a ↦ a.2 ≤ k) ∘ ⇑(Equiv.prodComm ℕ ℕ).symm\naux₂ : ∀ (i j : ℕ), (∃ a b, a + b = k ∧ b = i ∧ a + (n - k) = j) ↔ ∃ a b, a + b = k ∧ a = i ∧ b + (n - k) = j\ni j : ℕ\n⊢ (∃ a, a + i = k ∧ a + (n - k) = j) ↔ ∃ b, i + b = k ∧ b + (n - k) = j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Ideal.Defs | {
"line": 96,
"column": 22
} | {
"line": 96,
"column": 44
} | {
"line": 96,
"column": 45
} | [
{
"pp": "α : Type u\nβ : Type v\nF : Type w\nR : Type ?u.7\nM : Type ?u.9\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nm m' : M\na✝ b✝ : R\nh : a✝ ∈ {r | r • m = r • m'}\nh' : b✝ ∈ {r | r • m = r • m'}\n⊢ a✝ + b✝ ∈ {r | r • m = r • m'}",
"ppTerm": "?m.32",
"assigned": true,
"u... | [
"α : Type u\nβ : Type v\nF : Type w\nR : Type ?u.7\nM : Type ?u.9\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nm m' : M\na✝ b✝ : R\nh : a✝ ∈ {r | r • m = r • m'}\nh' : b✝ ∈ {r | r • m = r • m'}\n⊢ a✝ • m + b✝ • m = a✝ • m' + b✝ • m'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Ideal.Lattice | {
"line": 115,
"column": 2
} | {
"line": 115,
"column": 21
} | {
"line": 115,
"column": 22
} | [
{
"pp": "case neg\nK : Type u\ninst✝ : DivisionSemiring K\nI : Ideal K\nh1 : 1 ∉ I\nr : K\nhr : r ∈ I\nH : ¬r = 0\n⊢ r ∈ ⊥",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Submodule",
"False",
"Semiring.toModule",
"eq_false",
"OrderBot.toBot",
... | [
"case neg\nK : Type u\ninst✝ : DivisionSemiring K\nI : Ideal K\nh1 : 1 ∉ I\nr : K\nhr : r ∈ I\nH : ¬r = 0\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Ideal.Defs | {
"line": 98,
"column": 24
} | {
"line": 98,
"column": 46
} | {
"line": 98,
"column": 47
} | [
{
"pp": "α : Type u\nβ : Type v\nF : Type w\nR : Type ?u.7\nM : Type ?u.9\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nm m' : M\nx✝¹ x✝ : R\nh : x✝ ∈ {r | r • m = r • m'}\n⊢ x✝¹ • x✝ ∈ {r | r • m = r • m'}",
"ppTerm": "?m.53",
"assigned": true,
"usedConstants": [
"Eq.mpr... | [
"α : Type u\nβ : Type v\nF : Type w\nR : Type ?u.7\nM : Type ?u.9\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nm m' : M\nx✝¹ x✝ : R\nh : x✝ ∈ {r | r • m = r • m'}\n⊢ x✝¹ • x✝ • m = x✝¹ • x✝ • m'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Ideal.Defs | {
"line": 119,
"column": 55
} | {
"line": 120,
"column": 52
} | {
"line": 122,
"column": 0
} | [
{
"pp": "α : Type u\na b : α\ninst✝ : CommSemiring α\nI : Ideal α\nhab : a ∣ b\nha : a ∈ I\n⊢ b ∈ I",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Semigroup.toMul",
"Dvd.dvd",
"Semiring.toModule",
"HMul.hMul",
"CommSemiring.toNonUnitalCommSemiring",
"C... | [] | by
obtain ⟨c, rfl⟩ := hab; exact I.mul_mem_right _ ha | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.Ideal.Defs | {
"line": 147,
"column": 2
} | {
"line": 147,
"column": 62
} | {
"line": 149,
"column": 0
} | [
{
"pp": "α : Type u\ninst✝¹ : Ring α\nI : Ideal α\na b c d : α\ninst✝ : I.IsTwoSided\nh1 : a - b ∈ I\nh2 : c - d ∈ I\n⊢ (a - b) * c + b * (c - d) ∈ I",
"ppTerm": "?m.81",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"AddGroupWithOne.toAddGroup",
"HSub.hSub",
"Ideal.add_m... | [] | exact I.add_mem (I.mul_mem_right _ h1) (I.mul_mem_left _ h2) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Data.Finset.NatAntidiagonal | {
"line": 154,
"column": 2
} | {
"line": 154,
"column": 13
} | {
"line": 154,
"column": 14
} | [
{
"pp": "n k : ℕ\nh : k ≤ n\naux₁ : (fun a ↦ k ≤ a.2) = (fun a ↦ k ≤ a.1) ∘ ⇑(Equiv.prodComm ℕ ℕ).symm\naux₂ : ∀ (i j : ℕ), (∃ a b, a + b = n - k ∧ b = i ∧ a + k = j) ↔ ∃ a b, a + b = n - k ∧ a = i ∧ b + k = j\ni j : ℕ\n⊢ (i, j) ∈\n map (({ toFun := fun x ↦ x + k, inj' := ⋯ }.prodMap (Embedding.refl ℕ)).tr... | [
"n k : ℕ\nh : k ≤ n\naux₁ : (fun a ↦ k ≤ a.2) = (fun a ↦ k ≤ a.1) ∘ ⇑(Equiv.prodComm ℕ ℕ).symm\naux₂ : ∀ (i j : ℕ), (∃ a b, a + b = n - k ∧ b = i ∧ a + k = j) ↔ ∃ a b, a + b = n - k ∧ a = i ∧ b + k = j\ni j : ℕ\n⊢ (∃ a, a + i = n - k ∧ a + k = j) ↔ ∃ b, i + b = n - k ∧ b + k = j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Ideal.Prime | {
"line": 93,
"column": 23
} | {
"line": 93,
"column": 59
} | {
"line": 93,
"column": 60
} | [
{
"pp": "α : Type u\nβ : Type v\nF : Type w\ninst✝² : Semiring α\nI : Ideal α\na b : α\ninst✝¹ : Nontrivial α\ninst✝ : NoZeroDivisors α\nx✝ y✝ : α\nh : x✝ * y✝ ∈ ⊥\n⊢ x✝ * y✝ = 0",
"ppTerm": "?m.26",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\nβ : Type v\nF : Type w\ninst✝² : Semiring α\nI : Ideal α\na b : α\ninst✝¹ : Nontrivial α\ninst✝ : NoZeroDivisors α\nx✝ y✝ : α\nh : x✝ * y✝ ∈ ⊥\n⊢ x✝ * y✝ = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Idempotent | {
"line": 68,
"column": 20
} | {
"line": 68,
"column": 32
} | {
"line": 68,
"column": 33
} | [
{
"pp": "R : Type u_1\ninst✝ : Semiring R\na b : R\nmul : a * b = 0\nadd : a + b = 1\n| a",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"HMul.hMul",
"congrArg",
"MulOne.toMul",
"MulZeroOneClass.toMulOneClass",
"instMulZeroOneClassOfSemi... | [
"R : Type u_1\ninst✝ : Semiring R\na b : R\nmul : a * b = 0\nadd : a + b = 1\n| a * 1"
] | ← mul_one a, | Lean.Elab.Tactic.Conv.evalRewrite | null |
Mathlib.Algebra.Ring.Idempotent | {
"line": 106,
"column": 2
} | {
"line": 106,
"column": 46
} | {
"line": 106,
"column": 47
} | [
{
"pp": "R : Type u_1\ninst✝¹ : NonUnitalNonAssocSemiring R\ninst✝ : IsCancelAdd R\na b : R\nha : IsIdempotentElem a\nhb : IsIdempotentElem b\nh : IsIdempotentElem (a + b)\n⊢ a + b * a + (a * b + b) = a + (0 + b)",
"ppTerm": "?m.67",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.h... | [
"R : Type u_1\ninst✝¹ : NonUnitalNonAssocSemiring R\ninst✝ : IsCancelAdd R\na b : R\nha : IsIdempotentElem a\nhb : IsIdempotentElem b\nh : IsIdempotentElem (a + b)\n⊢ a + b * a + (a * b + b) = a + b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Choose.Sum | {
"line": 96,
"column": 2
} | {
"line": 96,
"column": 34
} | {
"line": 96,
"column": 35
} | [
{
"pp": "n : ℕ\nthis : ∑ m ∈ range (n + 1), 1 ^ m * 1 ^ (n - m) * ↑(n.choose m) = (1 + 1) ^ n\n⊢ ∑ m ∈ range (n + 1), n.choose m = 2 ^ n",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"n : ℕ\nthis : ∑ m ∈ range (n + 1), 1 ^ m * 1 ^ (n - m) * ↑(n.choose m) = (1 + 1) ^ n\n⊢ ∑ m ∈ range (n + 1), n.choose m = 2 ^ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Choose.Sum | {
"line": 119,
"column": 2
} | {
"line": 119,
"column": 42
} | {
"line": 119,
"column": 43
} | [
{
"pp": "n : ℕ\nt : (2 * n + 1).choose n ≤ ∑ i ∈ range (n + 1), (2 * n + 1).choose i\n⊢ (2 * n + 1).choose n ≤ 4 ^ n",
"ppTerm": "?m.73",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.choose",
"HMul.hMul",
"Nat.instMonoid",
"id",
"instMulNat",
"instOfN... | [
"n : ℕ\nt : (2 * n + 1).choose n ≤ ∑ i ∈ range (n + 1), (2 * n + 1).choose i\n⊢ (2 * n + 1).choose n ≤ 4 ^ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Ideal.Span | {
"line": 85,
"column": 2
} | {
"line": 85,
"column": 41
} | {
"line": 85,
"column": 42
} | [
{
"pp": "α : Type u\ninst✝ : Semiring α\n⊢ IsCompactElement ⊤",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Semiring.toModule",
"congrArg",
"_private.Mathlib.RingTheory.Ideal.Span.0.Ideal.isCompactElement_... | [
"α : Type u\ninst✝ : Semiring α\n⊢ IsCompactElement (span {1})"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Choose.Sum | {
"line": 180,
"column": 12
} | {
"line": 180,
"column": 41
} | {
"line": 181,
"column": 2
} | [
{
"pp": "case zero\nn : ℕ\n⊢ ∑ i ∈ range (n + 1), multichoose 0 i = (n + 0).choose 0",
"ppTerm": "?zero",
"assigned": true,
"usedConstants": [
"Nat.choose",
"congrArg",
"Finset",
"AddMonoid.toAddZeroClass",
"Nat.instAddMonoid",
"Membership.mem",
"AddZeroClas... | [] | simp [Finset.sum_range_succ'] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Nat.Choose.Sum | {
"line": 180,
"column": 12
} | {
"line": 180,
"column": 41
} | {
"line": 181,
"column": 2
} | [
{
"pp": "case zero\nn : ℕ\n⊢ ∑ i ∈ range (n + 1), multichoose 0 i = (n + 0).choose 0",
"ppTerm": "?zero",
"assigned": true,
"usedConstants": [
"Nat.choose",
"congrArg",
"Finset",
"AddMonoid.toAddZeroClass",
"Nat.instAddMonoid",
"Membership.mem",
"AddZeroClas... | [] | simp [Finset.sum_range_succ'] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Nat.Choose.Sum | {
"line": 180,
"column": 12
} | {
"line": 180,
"column": 41
} | {
"line": 181,
"column": 2
} | [
{
"pp": "case zero\nn : ℕ\n⊢ ∑ i ∈ range (n + 1), multichoose 0 i = (n + 0).choose 0",
"ppTerm": "?zero",
"assigned": true,
"usedConstants": [
"Nat.choose",
"congrArg",
"Finset",
"AddMonoid.toAddZeroClass",
"Nat.instAddMonoid",
"Membership.mem",
"AddZeroClas... | [] | simp [Finset.sum_range_succ'] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.Ideal.Basic | {
"line": 74,
"column": 31
} | {
"line": 74,
"column": 42
} | {
"line": 74,
"column": 43
} | [
{
"pp": "ι : Type u_1\nR : ι → Type u_5\ninst✝ : (i : ι) → Semiring (R i)\nI J : (i : ι) → Ideal (R i)\nle : pi I ≤ pi J\ni : ι\nr : R i\nhr : r ∈ I i\n⊢ r ∈ J i",
"ppTerm": "?m.22",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"ι : Type u_1\nR : ι → Type u_5\ninst✝ : (i : ι) → Semiring (R i)\nI J : (i : ι) → Ideal (R i)\nle : pi I ≤ pi J\ni : ι\nr : R i\nhr : r ∈ I i\n⊢ r ∈ J i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Ideal.Basic | {
"line": 91,
"column": 2
} | {
"line": 91,
"column": 20
} | {
"line": 92,
"column": 2
} | [
{
"pp": "α : Type u_6\ninst✝ : Semiring α\nI : Ideal α\na b : α\nm n k : ℕ\nha : a ^ m ∈ I\nhb : b ^ n ∈ I\nhk : m + n ≤ k + 1\nhab : Commute a b\nc : ℕ\na✝ : c ∈ Finset.range (k + 1)\n⊢ a ^ c * b ^ (k - c) ∈ I",
"ppTerm": "?m.67",
"assigned": true,
"usedConstants": [
"Semiring.toModule",
... | [
"case pos\nα : Type u_6\ninst✝ : Semiring α\nI : Ideal α\na b : α\nm n k : ℕ\nha : a ^ m ∈ I\nhb : b ^ n ∈ I\nhk : m + n ≤ k + 1\nhab : Commute a b\nc : ℕ\na✝ : c ∈ Finset.range (k + 1)\nh : m ≤ c\n⊢ a ^ c * b ^ (k - c) ∈ I",
"case neg\nα : Type u_6\ninst✝ : Semiring α\nI : Ideal α\na b : α\nm n k : ℕ\nha : a ^ m... | by_cases h : m ≤ c | «_aux_Init_ByCases___macroRules_tacticBy_cases_:__2» | «tacticBy_cases_:_» |
Mathlib.Data.Nat.Choose.Sum | {
"line": 220,
"column": 6
} | {
"line": 220,
"column": 29
} | {
"line": 220,
"column": 29
} | [
{
"pp": "α : Type u_2\ninst✝ : DecidableEq α\nx : Finset α\n⊢ ∑ m ∈ x.powerset, (-1) ^ #m = if x = ∅ then 1 else 0",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Int.instAddCommMonoid",
"instHSMul",
"Nat.choose",
"congrArg",
"Finset",
"... | [
"α : Type u_2\ninst✝ : DecidableEq α\nx : Finset α\n⊢ ∑ m ∈ range (#x + 1), (#x).choose m • (-1) ^ m = if x = ∅ then 1 else 0"
] | sum_powerset_apply_card | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Nat.Choose.Sum | {
"line": 240,
"column": 2
} | {
"line": 240,
"column": 73
} | {
"line": 240,
"column": 74
} | [
{
"pp": "M : Type u_2\ninst✝ : CommMonoid M\nf : ℕ → ℕ → M\nn : ℕ\nA :\n (∏ i ∈ range (n + 1), f (i + 1) (n - i) ^ n.choose (i + 1)) * f 0 (n + 1) =\n ∏ i ∈ range (n + 1), f i (n + 1 - i) ^ n.choose i\n⊢ (∏ k ∈ range (n + 1), f (k + 1) (n + 1 - (k + 1)) ^ (n + 1).choose (k + 1)) * f 0 (n + 1 - 0) ^ (n + 1).... | [
"M : Type u_2\ninst✝ : CommMonoid M\nf : ℕ → ℕ → M\nn : ℕ\nA :\n (∏ i ∈ range (n + 1), f (i + 1) (n - i) ^ n.choose (i + 1)) * f 0 (n + 1) =\n ∏ i ∈ range (n + 1), f i (n + 1 - i) ^ n.choose i\n⊢ (∏ x ∈ range (n + 1), f (x + 1) (n - x) ^ n.choose x) * ∏ i ∈ range (n + 1), f i (n + 1 - i) ^ n.choose i =\n (∏ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Choose.Sum | {
"line": 248,
"column": 53
} | {
"line": 248,
"column": 82
} | {
"line": 248,
"column": 83
} | [
{
"pp": "M : Type u_2\ninst✝ : CommMonoid M\nf : ℕ → ℕ → M\nn i : ℕ\nhi : i ∈ range (n + 1)\n⊢ i ≤ n",
"ppTerm": "?m.101",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"M : Type u_2\ninst✝ : CommMonoid M\nf : ℕ → ℕ → M\nn i : ℕ\nhi : i ∈ range (n + 1)\n⊢ i ≤ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Choose.Sum | {
"line": 261,
"column": 2
} | {
"line": 261,
"column": 33
} | {
"line": 261,
"column": 34
} | [
{
"pp": "R : Type u_1\ninst✝ : NonAssocSemiring R\nf : ℕ → ℕ → R\nn : ℕ\n⊢ ∑ i ∈ range (n + 2), ↑((n + 1).choose i) * f i (n + 1 - i) =\n ∑ i ∈ range (n + 1), ↑(n.choose i) * f i (n + 1 - i) + ∑ i ∈ range (n + 1), ↑(n.choose i) * f (i + 1) (n - i)",
"ppTerm": "?m.87",
"assigned": false,
"usedCons... | [
"R : Type u_1\ninst✝ : NonAssocSemiring R\nf : ℕ → ℕ → R\nn : ℕ\n⊢ ∑ i ∈ range (n + 2), ↑((n + 1).choose i) * f i (n + 1 - i) =\n ∑ i ∈ range (n + 1), ↑(n.choose i) * f i (n + 1 - i) + ∑ i ∈ range (n + 1), ↑(n.choose i) * f (i + 1) (n - i)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Choose.Sum | {
"line": 269,
"column": 2
} | {
"line": 269,
"column": 33
} | {
"line": 269,
"column": 34
} | [
{
"pp": "R : Type u_1\ninst✝ : NonAssocSemiring R\nf : ℕ → ℕ → R\nn : ℕ\n⊢ ∑ ij ∈ antidiagonal (n + 1), ↑((n + 1).choose ij.1) * f ij.1 ij.2 =\n ∑ ij ∈ antidiagonal n, ↑(n.choose ij.1) * f ij.1 (ij.2 + 1) +\n ∑ ij ∈ antidiagonal n, ↑(n.choose ij.2) * f (ij.1 + 1) ij.2",
"ppTerm": "?m.84",
"assig... | [
"R : Type u_1\ninst✝ : NonAssocSemiring R\nf : ℕ → ℕ → R\nn : ℕ\n⊢ ∑ ij ∈ antidiagonal (n + 1), ↑((n + 1).choose ij.1) * f ij.1 ij.2 =\n ∑ ij ∈ antidiagonal n, ↑(n.choose ij.1) * f ij.1 (ij.2 + 1) +\n ∑ ij ∈ antidiagonal n, ↑(n.choose ij.2) * f (ij.1 + 1) ij.2"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.SuccPred.PartialSups | {
"line": 43,
"column": 2
} | {
"line": 43,
"column": 39
} | {
"line": 43,
"column": 40
} | [
{
"pp": "α : Type u_1\nι : Type u_2\ninst✝⁶ : SemilatticeSup α\ninst✝⁵ : LinearOrder ι\ninst✝⁴ : Add ι\ninst✝³ : One ι\ninst✝² : OrderBot ι\ninst✝¹ : LocallyFiniteOrder ι\ninst✝ : SuccAddOrder ι\nf : ι → α\ni : ι\n⊢ (partialSups f) (i + 1) = f ⊥ ⊔ (partialSups (f ∘ fun k ↦ k + 1)) i",
"ppTerm": "?m.40",
... | [
"α : Type u_1\nι : Type u_2\ninst✝⁶ : SemilatticeSup α\ninst✝⁵ : LinearOrder ι\ninst✝⁴ : Add ι\ninst✝³ : One ι\ninst✝² : OrderBot ι\ninst✝¹ : LocallyFiniteOrder ι\ninst✝ : SuccAddOrder ι\nf : ι → α\ni : ι\n⊢ (partialSups f) i ⊔ f (Order.succ i) = f ⊥ ⊔ (partialSups (f ∘ fun k ↦ Order.succ k)) i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.Bases.Basic | {
"line": 175,
"column": 12
} | {
"line": 175,
"column": 16
} | {
"line": 176,
"column": 4
} | [
{
"pp": "case a\nα : Type u_1\nB : FilterBasis α\nU : Set α\n⊢ U ∈ B.filter → U ∈ generate B.sets",
"ppTerm": "?a✝",
"assigned": true,
"usedConstants": [
"Filter.instMembership",
"Membership.mem",
"FilterBasis.filter",
"Filter",
"Set"
],
"usedFVars": [
"α"... | [
"case a\nα : Type u_1\nB : FilterBasis α\nU : Set α\nU_in : U ∈ B.filter\n⊢ U ∈ generate B.sets"
] | U_in | Lean.Elab.Tactic.evalIntro | ident |
Mathlib.Order.Filter.Bases.Basic | {
"line": 261,
"column": 4
} | {
"line": 261,
"column": 32
} | {
"line": 261,
"column": 33
} | [
{
"pp": "α : Type u_1\nι : Sort u_4\nl : Filter α\np : ι → Prop\ns : ι → Set α\nh : l.HasBasis p s\ni✝ j✝ : ι\nhi : p i✝\nhj : p j✝\n⊢ ∃ k, p k ∧ s k ⊆ s i✝ ∩ s j✝",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nι : Sort u_4\nl : Filter α\np : ι → Prop\ns : ι → Set α\nh : l.HasBasis p s\ni✝ j✝ : ι\nhi : p i✝\nhj : p j✝\n⊢ ∃ k, p k ∧ s k ⊆ s i✝ ∩ s j✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.Bases.Basic | {
"line": 382,
"column": 84
} | {
"line": 383,
"column": 31
} | {
"line": 385,
"column": 0
} | [
{
"pp": "α : Type u_1\nι : Sort u_4\nl : Filter α\np : ι → Prop\ns : ι → Set α\nh : l.HasBasis p s\n⊢ l = ⊤ ↔ ∀ (i : ι), p i → s i = univ",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Filter.instMembership",
"congrArg",
"Set.univ",
"_private.Mathlib.Order.Filter.B... | [] | by
simp [← top_le_iff, h.ge_iff] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.Filter.Bases.Basic | {
"line": 390,
"column": 4
} | {
"line": 390,
"column": 15
} | {
"line": 390,
"column": 16
} | [
{
"pp": "case a\nα : Type u_1\nι : Sort u_4\nι' : Sort u_5\nl l' : Filter α\np : ι → Prop\ns : ι → Set α\np' : ι' → Prop\ns' : ι' → Set α\nhl : l.HasBasis p s\nhl' : l'.HasBasis p' s'\nh : ∀ (i : ι), p i → ∃ i', p' i' ∧ s' i' ⊆ s i\nh' : ∀ (i' : ι'), p' i' → ∃ i, p i ∧ s i ⊆ s' i'\n⊢ ∀ (i' : ι'), p' i' → ∃ i, p... | [
"case a\nα : Type u_1\nι : Sort u_4\nι' : Sort u_5\nl l' : Filter α\np : ι → Prop\ns : ι → Set α\np' : ι' → Prop\ns' : ι' → Set α\nhl : l.HasBasis p s\nhl' : l'.HasBasis p' s'\nh : ∀ (i : ι), p i → ∃ i', p' i' ∧ s' i' ⊆ s i\nh' : ∀ (i' : ι'), p' i' → ∃ i, p i ∧ s i ⊆ s' i'\n⊢ ∀ (i' : ι'), p' i' → ∃ i, p i ∧ s i ⊆ s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.Bases.Basic | {
"line": 392,
"column": 4
} | {
"line": 392,
"column": 15
} | {
"line": 392,
"column": 16
} | [
{
"pp": "case a\nα : Type u_1\nι : Sort u_4\nι' : Sort u_5\nl l' : Filter α\np : ι → Prop\ns : ι → Set α\np' : ι' → Prop\ns' : ι' → Set α\nhl : l.HasBasis p s\nhl' : l'.HasBasis p' s'\nh : ∀ (i : ι), p i → ∃ i', p' i' ∧ s' i' ⊆ s i\nh' : ∀ (i' : ι'), p' i' → ∃ i, p i ∧ s i ⊆ s' i'\n⊢ ∀ (i' : ι), p i' → ∃ i, p' ... | [
"case a\nα : Type u_1\nι : Sort u_4\nι' : Sort u_5\nl l' : Filter α\np : ι → Prop\ns : ι → Set α\np' : ι' → Prop\ns' : ι' → Set α\nhl : l.HasBasis p s\nhl' : l'.HasBasis p' s'\nh : ∀ (i : ι), p i → ∃ i', p' i' ∧ s' i' ⊆ s i\nh' : ∀ (i' : ι'), p' i' → ∃ i, p i ∧ s i ⊆ s' i'\n⊢ ∀ (i' : ι), p i' → ∃ i, p' i ∧ s' i ⊆ s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.Basic | {
"line": 327,
"column": 55
} | {
"line": 327,
"column": 66
} | {
"line": 327,
"column": 67
} | [
{
"pp": "α : Type u\nι : Sort x\nf : ι → Filter α\ns✝ : Set α\nhs✝ : s✝ ∈ iInf f\np : Set α → Prop\nuni : p univ\nins : ∀ {i : ι} {s₁ s₂ : Set α}, s₁ ∈ f i → p s₂ → p (s₁ ∩ s₂)\ni : ι\ns : Set α\nhs : s ∈ f i\n⊢ p s",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"α : Type u\nι : Sort x\nf : ι → Filter α\ns✝ : Set α\nhs✝ : s✝ ∈ iInf f\np : Set α → Prop\nuni : p univ\nins : ∀ {i : ι} {s₁ s₂ : Set α}, s₁ ∈ f i → p s₂ → p (s₁ ∩ s₂)\ni : ι\ns : Set α\nhs : s ∈ f i\n⊢ p s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.Basic | {
"line": 343,
"column": 34
} | {
"line": 343,
"column": 59
} | {
"line": 343,
"column": 60
} | [
{
"pp": "α : Type u\nι : Sort x\nf : ι → Filter α\ns✝ : Set α\nhs : s✝ ∈ iInf f\np : Set α → Prop\nuni : p univ\nins : ∀ {i : ι} {s₁ s₂ : Set α}, s₁ ∈ f i → p s₂ → p (s₁ ∩ s₂)\np_of_f : ∀ (i : ι), ∀ s ∈ f i, p s\nq : Set α → Prop := fun t ↦ t ∈ iInf f ∧ ∀ (t' : Set α), t ⊆ t' → p t'\nq_mono : Monotone q\nA : ∀ ... | [
"α : Type u\nι : Sort x\nf : ι → Filter α\ns✝ : Set α\nhs : s✝ ∈ iInf f\np : Set α → Prop\nuni : p univ\nins : ∀ {i : ι} {s₁ s₂ : Set α}, s₁ ∈ f i → p s₂ → p (s₁ ∩ s₂)\np_of_f : ∀ (i : ι), ∀ s ∈ f i, p s\nq : Set α → Prop := fun t ↦ t ∈ iInf f ∧ ∀ (t' : Set α), t ⊆ t' → p t'\nq_mono : Monotone q\nA : ∀ (i : ι), ∀ s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.Basic | {
"line": 349,
"column": 20
} | {
"line": 349,
"column": 35
} | {
"line": 349,
"column": 36
} | [
{
"pp": "α : Type u\nι : Sort x\nf : ι → Filter α\ns : Set α\nhs : s ∈ iInf f\np : Set α → Prop\nuni : p univ\nins : ∀ {i : ι} {s₁ s₂ : Set α}, s₁ ∈ f i → p s₂ → p (s₁ ∩ s₂)\np_of_f : ∀ (i : ι), ∀ s ∈ f i, p s\nq : Set α → Prop := fun t ↦ t ∈ iInf f ∧ ∀ (t' : Set α), t ⊆ t' → p t'\nq_mono : Monotone q\nA : ∀ (i... | [
"α : Type u\nι : Sort x\nf : ι → Filter α\ns : Set α\nhs : s ∈ iInf f\np : Set α → Prop\nuni : p univ\nins : ∀ {i : ι} {s₁ s₂ : Set α}, s₁ ∈ f i → p s₂ → p (s₁ ∩ s₂)\np_of_f : ∀ (i : ι), ∀ s ∈ f i, p s\nq : Set α → Prop := fun t ↦ t ∈ iInf f ∧ ∀ (t' : Set α), t ⊆ t' → p t'\nq_mono : Monotone q\nA : ∀ (i : ι), ∀ s ∈... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.Basic | {
"line": 522,
"column": 22
} | {
"line": 523,
"column": 34
} | {
"line": 523,
"column": 35
} | [
{
"pp": "α : Type u\nι : Sort x\nf : ι → Filter α\ninst✝ : Nonempty ι\nhd : Directed (fun x1 x2 ↦ x1 ≥ x2) f\n⊢ ¬(iInf f).NeBot → ¬∀ (i : ι), (f i).NeBot",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Filter.instMembership",
"Eq.mpr",
"_private.Mathlib.Order.Filter.Basi... | [
"α : Type u\nι : Sort x\nf : ι → Filter α\ninst✝ : Nonempty ι\nhd : Directed (fun x1 x2 ↦ x1 ≥ x2) f\n⊢ (∃ i, ∅ ∈ f i) → ∃ i, ∅ ∈ f i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.Bases.Basic | {
"line": 478,
"column": 4
} | {
"line": 479,
"column": 24
} | {
"line": 479,
"column": 24
} | [
{
"pp": "α : Type u_1\nι : Sort u_4\nl : Filter α\np : ι → Prop\ns : ι → Set α\nhl : l.HasBasis p s\nt u : Set α\n⊢ u ∈ l ⊔ 𝓟 t ↔ ∃ i, p i ∧ s i ∪ t ⊆ u",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Filter.instMembership",
"Filter.HasBasis.mem_iff",
"PProd.mk",
... | [] | simp only [(hl.sup' (hasBasis_principal t)).mem_iff, PProd.exists, and_true,
Unique.exists_iff] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Order.Filter.Bases.Basic | {
"line": 478,
"column": 4
} | {
"line": 479,
"column": 24
} | {
"line": 479,
"column": 24
} | [
{
"pp": "α : Type u_1\nι : Sort u_4\nl : Filter α\np : ι → Prop\ns : ι → Set α\nhl : l.HasBasis p s\nt u : Set α\n⊢ u ∈ l ⊔ 𝓟 t ↔ ∃ i, p i ∧ s i ∪ t ⊆ u",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Filter.instMembership",
"Filter.HasBasis.mem_iff",
"PProd.mk",
... | [] | simp only [(hl.sup' (hasBasis_principal t)).mem_iff, PProd.exists, and_true,
Unique.exists_iff] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Filter.Bases.Basic | {
"line": 478,
"column": 4
} | {
"line": 479,
"column": 24
} | {
"line": 479,
"column": 24
} | [
{
"pp": "α : Type u_1\nι : Sort u_4\nl : Filter α\np : ι → Prop\ns : ι → Set α\nhl : l.HasBasis p s\nt u : Set α\n⊢ u ∈ l ⊔ 𝓟 t ↔ ∃ i, p i ∧ s i ∪ t ⊆ u",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Filter.instMembership",
"Filter.HasBasis.mem_iff",
"PProd.mk",
... | [] | simp only [(hl.sup' (hasBasis_principal t)).mem_iff, PProd.exists, and_true,
Unique.exists_iff] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Filter.Bases.Basic | {
"line": 492,
"column": 2
} | {
"line": 492,
"column": 41
} | {
"line": 492,
"column": 42
} | [
{
"pp": "α : Type u_1\nι : Sort u_4\nl : Filter α\np : ι → Prop\ns : ι → Set α\nhl : l.HasBasis p s\ns' : Set α\n⊢ (𝓟 s' ⊓ l).HasBasis p fun i ↦ s' ∩ s i",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CompleteLattice.toLattice",
"congrArg",
"Filter.inst... | [
"α : Type u_1\nι : Sort u_4\nl : Filter α\np : ι → Prop\ns : ι → Set α\nhl : l.HasBasis p s\ns' : Set α\n⊢ (l ⊓ 𝓟 s').HasBasis p fun i ↦ s' ∩ s i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Finsupp.Pi | {
"line": 215,
"column": 22
} | {
"line": 215,
"column": 33
} | {
"line": 215,
"column": 34
} | [
{
"pp": "R : Type u_1\nM : Type u_2\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nα : Type u_5\np : α → Submodule R M\ni : α\nx : M\nhx : x ∈ comap (lsingle i) (submodule p)\n⊢ x ∈ p i",
"ppTerm": "?m.48",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGo... | [
"R : Type u_1\nM : Type u_2\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nα : Type u_5\np : α → Submodule R M\ni : α\nx : M\nhx : x ∈ comap (lsingle i) (submodule p)\n⊢ x ∈ p i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.Bases.Basic | {
"line": 525,
"column": 20
} | {
"line": 525,
"column": 56
} | {
"line": 525,
"column": 57
} | [
{
"pp": "α : Type u_1\nf : Filter α\ns : Set α\nh : ∀ U ∈ f, (U ∩ sᶜ).Nonempty\nhs : s ∈ f\n⊢ False",
"ppTerm": "?m.35",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nf : Filter α\ns : Set α\nh : ∀ U ∈ f, (U ∩ sᶜ).Nonempty\nhs : s ∈ f\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.Basic | {
"line": 575,
"column": 2
} | {
"line": 575,
"column": 37
} | {
"line": 575,
"column": 38
} | [
{
"pp": "α : Type u\ns : Set α\n⊢ ￢𝓟 s = 𝓟 sᶜ",
"ppTerm": "?m.8",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\ns : Set α\n⊢ ￢𝓟 s = 𝓟 sᶜ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.Map | {
"line": 529,
"column": 36
} | {
"line": 529,
"column": 74
} | {
"line": 531,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf g : Filter α\nm : α → β\nhm : Injective m\n⊢ map m f ≤ map m g ↔ f ≤ g",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Filter.map",
"Iff.rfl",
"PartialOrder.toPreorder",
"Preorder.toLE",
... | [] | rw [map_le_iff_le_comap, comap_map hm] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Order.Filter.Map | {
"line": 529,
"column": 36
} | {
"line": 529,
"column": 74
} | {
"line": 531,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf g : Filter α\nm : α → β\nhm : Injective m\n⊢ map m f ≤ map m g ↔ f ≤ g",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Filter.map",
"Iff.rfl",
"PartialOrder.toPreorder",
"Preorder.toLE",
... | [] | rw [map_le_iff_le_comap, comap_map hm] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Filter.Map | {
"line": 529,
"column": 36
} | {
"line": 529,
"column": 74
} | {
"line": 531,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf g : Filter α\nm : α → β\nhm : Injective m\n⊢ map m f ≤ map m g ↔ f ≤ g",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Filter.map",
"Iff.rfl",
"PartialOrder.toPreorder",
"Preorder.toLE",
... | [] | rw [map_le_iff_le_comap, comap_map hm] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Filter.Bases.Basic | {
"line": 574,
"column": 2
} | {
"line": 574,
"column": 30
} | {
"line": 574,
"column": 31
} | [
{
"pp": "α : Type u_1\nι : Sort u_4\nl : Filter α\ns : ι → Set α\nh : l.HasBasis (fun x ↦ True) s\n⊢ l = ⨅ i, 𝓟 (s i)",
"ppTerm": "?m.11",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nι : Sort u_4\nl : Filter α\ns : ι → Set α\nh : l.HasBasis (fun x ↦ True) s\n⊢ l = ⨅ i, 𝓟 (s i)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.Basic | {
"line": 694,
"column": 50
} | {
"line": 694,
"column": 77
} | {
"line": 694,
"column": 78
} | [
{
"pp": "α : Type u\nf : Filter α\np q : α → Prop\nh : ∀ᶠ (x : α) in f, p x ↔ q x\nhq : ∀ᶠ (x : α) in f, q x\n⊢ ∀ᶠ (x : α) in f, q x ↔ p x",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Filter.Eventually",
"id",
"funext",
"Iff",
... | [
"α : Type u\nf : Filter α\np q : α → Prop\nh : ∀ᶠ (x : α) in f, p x ↔ q x\nhq : ∀ᶠ (x : α) in f, q x\n⊢ ∀ᶠ (x : α) in f, p x ↔ q x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.Basic | {
"line": 788,
"column": 2
} | {
"line": 788,
"column": 29
} | {
"line": 788,
"column": 30
} | [
{
"pp": "α : Type u\np q : α → Prop\nf : Filter α\nhp : ∀ᶠ (x : α) in f, p x\nhq : ∃ᶠ (x : α) in f, q x\n⊢ ∃ᶠ (x : α) in f, p x ∧ q x",
"ppTerm": "?m.7",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\np q : α → Prop\nf : Filter α\nhp : ∀ᶠ (x : α) in f, p x\nhq : ∃ᶠ (x : α) in f, q x\n⊢ ∃ᶠ (x : α) in f, p x ∧ q x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.Bases.Basic | {
"line": 697,
"column": 2
} | {
"line": 697,
"column": 58
} | {
"line": 697,
"column": 59
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nι' : Sort u_5\nlb : Filter β\npb : ι' → Prop\nsb : ι' → Set β\nsa : Set α\nh : lb.HasBasis pb sb\n⊢ (𝓟 sa ×ˢ lb).HasBasis pb fun x ↦ sa ×ˢ sb x",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Set.instSProd",
"Eq.mpr",
"SProd.sprod",
... | [
"α : Type u_1\nβ : Type u_2\nι' : Sort u_5\nlb : Filter β\npb : ι' → Prop\nsb : ι' → Set β\nsa : Set α\nh : lb.HasBasis pb sb\n⊢ (𝓟 (Prod.fst ⁻¹' sa) ⊓ Filter.comap Prod.snd lb).HasBasis pb fun x ↦ Prod.fst ⁻¹' sa ∩ Prod.snd ⁻¹' sb x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.Basic | {
"line": 809,
"column": 4
} | {
"line": 809,
"column": 53
} | {
"line": 809,
"column": 54
} | [
{
"pp": "α : Type u\np : α → Prop\nf : Filter α\nH : ∀ {q : α → Prop}, (∀ᶠ (x : α) in f, q x) → ∃ x, p x ∧ q x\nhp : ∀ᶠ (x : α) in f, ¬(fun x ↦ p x) x\n⊢ False",
"ppTerm": "?m.21",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\np : α → Prop\nf : Filter α\nH : ∀ {q : α → Prop}, (∀ᶠ (x : α) in f, q x) → ∃ x, p x ∧ q x\nhp : ∀ᶠ (x : α) in f, ¬(fun x ↦ p x) x\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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