module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 334,
"column": 2
} | {
"line": 334,
"column": 13
} | {
"line": 334,
"column": 14
} | [
{
"pp": "M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na : M\nha : a ∈ Set.Iic 1\nb : M\nhb : b ∈ Set.Iic 1\nhab : ∀ (n : ℕ), |a|ₘ ^ n < |b|ₘ\nh : a⁻¹ ^ 1 < b⁻¹\n⊢ b < a",
"ppTerm": "?m.67",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"us... | [
"M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na : M\nha : a ∈ Set.Iic 1\nb : M\nhb : b ∈ Set.Iic 1\nhab : ∀ (n : ℕ), |a|ₘ ^ n < |b|ₘ\nh : a⁻¹ ^ 1 < b⁻¹\n⊢ b < a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 364,
"column": 2
} | {
"line": 364,
"column": 30
} | {
"line": 364,
"column": 31
} | [
{
"pp": "M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na b : M\n⊢ min (mk a) (mk b) ≤ mk (a / b)",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"Lattice.toSemilatticeSup",
"instHDiv",
"H... | [
"M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na b : M\n⊢ mk a ≤ mk (a * b⁻¹) ∨ mk b ≤ mk (a * b⁻¹)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 368,
"column": 2
} | {
"line": 368,
"column": 19
} | {
"line": 368,
"column": 20
} | [
{
"pp": "M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na b : M\nhab : mk a ≤ mk b\n⊢ mk a ≤ mk (a * b)",
"ppTerm": "?m.27",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na b : M\nhab : mk a ≤ mk b\n⊢ mk a ≤ mk (a * b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 372,
"column": 2
} | {
"line": 372,
"column": 19
} | {
"line": 372,
"column": 20
} | [
{
"pp": "M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na b : M\nhba : mk b ≤ mk a\n⊢ mk b ≤ mk (a * b)",
"ppTerm": "?m.27",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na b : M\nhba : mk b ≤ mk a\n⊢ mk b ≤ mk (a * b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 376,
"column": 2
} | {
"line": 376,
"column": 35
} | {
"line": 376,
"column": 36
} | [
{
"pp": "M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na b : M\nhab : mk a ≤ mk b\n⊢ mk a ≤ mk (a / b)",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"instHDiv",
"HMul.hMul",
"Monoid.toM... | [
"M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na b : M\nhab : mk a ≤ mk b\n⊢ mk a ≤ mk (a * b⁻¹)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 380,
"column": 2
} | {
"line": 380,
"column": 35
} | {
"line": 380,
"column": 36
} | [
{
"pp": "M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na b : M\nhba : mk b ≤ mk a\n⊢ mk b ≤ mk (a / b)",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"instHDiv",
"HMul.hMul",
"Monoid.toM... | [
"M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na b : M\nhba : mk b ≤ mk a\n⊢ mk b ≤ mk (a * b⁻¹)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 384,
"column": 13
} | {
"line": 384,
"column": 24
} | {
"line": 384,
"column": 25
} | [
{
"pp": "M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na b : M\nh : mk a ≤ mk (a * b)\n⊢ mk a ≤ mk b",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na b : M\nh : mk a ≤ mk (a * b)\n⊢ mk a ≤ mk b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 393,
"column": 13
} | {
"line": 393,
"column": 24
} | {
"line": 393,
"column": 25
} | [
{
"pp": "M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na b : M\nh : mk a ≤ mk (a / b)\n⊢ mk a ≤ mk b",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na b : M\nh : mk a ≤ mk (a / b)\n⊢ mk a ≤ mk b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Rearrangement | {
"line": 176,
"column": 4
} | {
"line": 176,
"column": 15
} | {
"line": 176,
"column": 16
} | [
{
"pp": "ι : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝⁸ : Semiring α\ninst✝⁷ : LinearOrder α\ninst✝⁶ : IsStrictOrderedRing α\ninst✝⁵ : ExistsAddOfLE α\ninst✝⁴ : AddCommMonoid β\ninst✝³ : LinearOrder β\ninst✝² : IsOrderedCancelAddMonoid β\ninst✝¹ : Module α β\ninst✝ : PosSMulStrictMono α β\ns : Finset ι\nσ : P... | [
"ι : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝⁸ : Semiring α\ninst✝⁷ : LinearOrder α\ninst✝⁶ : IsStrictOrderedRing α\ninst✝⁵ : ExistsAddOfLE α\ninst✝⁴ : AddCommMonoid β\ninst✝³ : LinearOrder β\ninst✝² : IsOrderedCancelAddMonoid β\ninst✝¹ : Module α β\ninst✝ : PosSMulStrictMono α β\ns : Finset ι\nσ : Perm ι\nf : ι... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 432,
"column": 2
} | {
"line": 432,
"column": 33
} | {
"line": 432,
"column": 34
} | [
{
"pp": "M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na b : M\nh : mk a < mk b\n⊢ mk (a / b) = mk a",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"instHDiv",
"HMul.hMul",
"Monoid.toMul... | [
"M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na b : M\nh : mk a < mk b\n⊢ mk (a * b⁻¹) = mk a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 436,
"column": 2
} | {
"line": 436,
"column": 33
} | {
"line": 436,
"column": 34
} | [
{
"pp": "M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na b : M\nh : mk b < mk a\n⊢ mk (a / b) = mk b",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"instHDiv",
"HMul.hMul",
"Monoid.toMul... | [
"M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na b : M\nh : mk b < mk a\n⊢ mk (a * b⁻¹) = mk b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Floor.Div | {
"line": 185,
"column": 25
} | {
"line": 185,
"column": 47
} | {
"line": 185,
"column": 48
} | [
{
"pp": "ι : Type u_1\nα : Type u_2\nβ : Type u_3\na : ℕ\nha : 0 < a\n⊢ GaloisConnection (fun x ↦ a • x) fun x ↦ x / a",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"instHSMul",
"instHDiv",
"instDistribSMul",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreor... | [
"ι : Type u_1\nα : Type u_2\nβ : Type u_3\na : ℕ\nha : 0 < a\n⊢ GaloisConnection (fun x ↦ a * x) fun x ↦ x / a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Floor.Div | {
"line": 246,
"column": 4
} | {
"line": 246,
"column": 62
} | {
"line": 246,
"column": 63
} | [
{
"pp": "ι : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝⁵ : AddCommMonoid α\ninst✝⁴ : PartialOrder α\ninst✝³ : AddCommMonoid β\ninst✝² : PartialOrder β\ninst✝¹ : SMulZeroClass α β\ninst✝ : FloorDiv α β\nf✝ : ι →₀ β\na _a : α\nha : 0 < _a\nf _g : ι →₀ β\ni : ι\n⊢ ((fun x ↦ _a • x) f) i ≤ _g i ↔ f i ≤ ((fun x ↦ m... | [
"ι : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝⁵ : AddCommMonoid α\ninst✝⁴ : PartialOrder α\ninst✝³ : AddCommMonoid β\ninst✝² : PartialOrder β\ninst✝¹ : SMulZeroClass α β\ninst✝ : FloorDiv α β\nf✝ : ι →₀ β\na _a : α\nha : 0 < _a\nf _g : ι →₀ β\ni : ι\n⊢ _a • f i ≤ _g i ↔ f i ≤ _g i ⌊/⌋ _a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Floor.Extended | {
"line": 108,
"column": 2
} | {
"line": 108,
"column": 13
} | {
"line": 108,
"column": 14
} | [
{
"pp": "r : ℝ≥0∞\nn : ℕ∞\nhn₀ : n ≠ 0\nhn : n ≠ ⊤\n⊢ ⌈r⌉ₑ < n ↔ r ≤ ↑n - 1",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"r : ℝ≥0∞\nn : ℕ∞\nhn₀ : n ≠ 0\nhn : n ≠ ⊤\n⊢ ⌈r⌉ₑ < n ↔ r ≤ ↑n - 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Floor.Extended | {
"line": 111,
"column": 19
} | {
"line": 111,
"column": 30
} | {
"line": 111,
"column": 31
} | [
{
"pp": "r s : ℝ≥0∞\nhrs : r ≤ s\n⊢ ⌊r⌋ₑ ≤ ⌊s⌋ₑ",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLE",
"instPreorderENat",
"id",
"ENat.toENNReal",
"LE.le",
"ENat.floor",
"ENat",
"ENNReal.instLE",
"ENNReal",
... | [
"r s : ℝ≥0∞\nhrs : r ≤ s\n⊢ ↑⌊r⌋ₑ ≤ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Floor.Extended | {
"line": 113,
"column": 66
} | {
"line": 113,
"column": 77
} | {
"line": 113,
"column": 78
} | [
{
"pp": "r s : ℝ≥0∞\nhrs : r ≤ s\n⊢ ⌈r⌉ₑ ≤ ⌈s⌉ₑ",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLE",
"instPreorderENat",
"id",
"ENat.ceil",
"ENat.toENNReal",
"ENat.ceil_le._simp_1",
"LE.le",
"ENat",
"ENNReal.i... | [
"r s : ℝ≥0∞\nhrs : r ≤ s\n⊢ r ≤ ↑⌈s⌉ₑ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Floor.Extended | {
"line": 120,
"column": 42
} | {
"line": 120,
"column": 53
} | {
"line": 120,
"column": 54
} | [
{
"pp": "⊢ ⌊0⌋ₑ = 0",
"ppTerm": "?m.6",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"⊢ ⌊0⌋ₑ = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Floor.Extended | {
"line": 121,
"column": 41
} | {
"line": 121,
"column": 52
} | {
"line": 121,
"column": 53
} | [
{
"pp": "⊢ ⌈0⌉ₑ = 0",
"ppTerm": "?m.6",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"⊢ ⌈0⌉ₑ = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Floor.Extended | {
"line": 122,
"column": 41
} | {
"line": 122,
"column": 52
} | {
"line": 122,
"column": 53
} | [
{
"pp": "⊢ ⌊1⌋ₑ = 1",
"ppTerm": "?m.6",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"⊢ ⌊1⌋ₑ = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Floor.Extended | {
"line": 123,
"column": 40
} | {
"line": 123,
"column": 51
} | {
"line": 123,
"column": 52
} | [
{
"pp": "⊢ ⌈1⌉ₑ = 1",
"ppTerm": "?m.6",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"⊢ ⌈1⌉ₑ = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Floor.Div | {
"line": 266,
"column": 4
} | {
"line": 266,
"column": 62
} | {
"line": 266,
"column": 63
} | [
{
"pp": "ι : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝⁵ : AddCommMonoid α\ninst✝⁴ : PartialOrder α\ninst✝³ : AddCommMonoid β\ninst✝² : PartialOrder β\ninst✝¹ : SMulZeroClass α β\ninst✝ : CeilDiv α β\nf✝ : ι →₀ β\na _a : α\nha : 0 < _a\nf _g : ι →₀ β\ni : ι\n⊢ ((fun x ↦ mapRange (fun x ↦ x ⌈/⌉ _a) ⋯ x) f) i ≤ ... | [
"ι : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝⁵ : AddCommMonoid α\ninst✝⁴ : PartialOrder α\ninst✝³ : AddCommMonoid β\ninst✝² : PartialOrder β\ninst✝¹ : SMulZeroClass α β\ninst✝ : CeilDiv α β\nf✝ : ι →₀ β\na _a : α\nha : 0 < _a\nf _g : ι →₀ β\ni : ι\n⊢ f i ⌈/⌉ _a ≤ _g i ↔ f i ≤ _a • _g i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Floor.Extended | {
"line": 131,
"column": 52
} | {
"line": 131,
"column": 63
} | {
"line": 131,
"column": 64
} | [
{
"pp": "r : ℝ≥0∞\n⊢ ⌈r⌉ₑ = 0 ↔ r = 0",
"ppTerm": "?m.7",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"r : ℝ≥0∞\n⊢ ⌈r⌉ₑ = 0 ↔ r = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Floor.Extended | {
"line": 137,
"column": 20
} | {
"line": 137,
"column": 31
} | {
"line": 137,
"column": 32
} | [
{
"pp": "r : ℝ≥0\n⊢ ⌈↑r⌉ₑ ≤ ⌊↑r⌋ₑ + 1",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"ENNReal.ofNNReal",
"instAddMonoidWithOneENat",
"instAddENat",
"id",
"ENat.ceil",
"LE.le",
"instLEENat",
"AddMonoidWithOne.toOne",
"instHAdd",
"... | [
"r : ℝ≥0\n⊢ ↑⌈r⌉₊ ≤ ↑⌊r⌋₊ + 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Floor.Extended | {
"line": 212,
"column": 26
} | {
"line": 212,
"column": 37
} | {
"line": 212,
"column": 38
} | [
{
"pp": "r : ℝ≥0\n⊢ ↑⌈↑r⌉ₑ < ↑r + 1",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"ENNReal.instAdd",
"ENNReal.ofNNReal",
"Preorder.toLT",
"PartialOrder.toPreorder",
"id",
"ENat.ceil",
"ENat.toENNReal",
"instHAdd",
"HAdd.hAdd",
"... | [
"r : ℝ≥0\n⊢ ↑⌈r⌉₊ < ↑r + 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 494,
"column": 4
} | {
"line": 494,
"column": 15
} | {
"line": 494,
"column": 16
} | [
{
"pp": "M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na b : M\nha : 1 < a\nhab : mk a < mk (b / a)\nthis : a⁻¹ < b / a\n⊢ 1 < b",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"InvOneClass.toOne",
... | [
"M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na b : M\nha : 1 < a\nhab : mk a < mk (b / a)\nthis : a⁻¹ < b / a\n⊢ 1 < b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 496,
"column": 4
} | {
"line": 496,
"column": 15
} | {
"line": 496,
"column": 16
} | [
{
"pp": "case h\nM : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na b : M\nha : 1 < a\nhab : mk a < mk (b / a)\n⊢ mk a⁻¹ < mk (b / a)",
"ppTerm": "?h",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"instHDiv",
"DivisionC... | [
"case h\nM : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na b : M\nha : 1 < a\nhab : mk a < mk (b / a)\n⊢ mk a < mk (b / a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 497,
"column": 4
} | {
"line": 497,
"column": 15
} | {
"line": 497,
"column": 16
} | [
{
"pp": "case hneg\nM : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na b : M\nha : 1 < a\nhab : mk a < mk (b / a)\n⊢ a⁻¹ ≤ 1",
"ppTerm": "?hneg",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Left.inv_le_one_iff._simp_2",
"InvOneClass.toOne",... | [
"case hneg\nM : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na b : M\nha : 1 < a\nhab : mk a < mk (b / a)\n⊢ 1 ≤ a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 505,
"column": 6
} | {
"line": 505,
"column": 17
} | {
"line": 505,
"column": 18
} | [
{
"pp": "case h\nM : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\nh : ∀ (a : M), a ≠ 1 → ∀ (b : M), b ≠ 1 → mk a = mk b\nx y : M\nhy : 1 < y\nhx : x ≤ 1\n⊢ x ≤ y ^ 0",
"ppTerm": "?h",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
... | [
"case h\nM : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\nh : ∀ (a : M), a ≠ 1 → ∀ (b : M), b ≠ 1 → mk a = mk b\nx y : M\nhy : 1 < y\nhx : x ≤ 1\n⊢ x ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 514,
"column": 58
} | {
"line": 514,
"column": 69
} | {
"line": 514,
"column": 70
} | [
{
"pp": "M : Type u_1\ninst✝³ : CommGroup M\ninst✝² : LinearOrder M\ninst✝¹ : IsOrderedMonoid M\na b : M\ninst✝ : MulArchimedean M\nha : a ≠ 1\nhb : b ≠ 1\n⊢ 1 < |a|ₘ",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"InvOneClass.toOne",
"Di... | [
"M : Type u_1\ninst✝³ : CommGroup M\ninst✝² : LinearOrder M\ninst✝¹ : IsOrderedMonoid M\na b : M\ninst✝ : MulArchimedean M\nha : a ≠ 1\nhb : b ≠ 1\n⊢ ¬a = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 515,
"column": 58
} | {
"line": 515,
"column": 69
} | {
"line": 515,
"column": 70
} | [
{
"pp": "M : Type u_1\ninst✝³ : CommGroup M\ninst✝² : LinearOrder M\ninst✝¹ : IsOrderedMonoid M\na b : M\ninst✝ : MulArchimedean M\nha : a ≠ 1\nhb : b ≠ 1\nhm : ∃ n, |b|ₘ ≤ |a|ₘ ^ n\n⊢ 1 < |b|ₘ",
"ppTerm": "?m.64",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"In... | [
"M : Type u_1\ninst✝³ : CommGroup M\ninst✝² : LinearOrder M\ninst✝¹ : IsOrderedMonoid M\na b : M\ninst✝ : MulArchimedean M\nha : a ≠ 1\nhb : b ≠ 1\nhm : ∃ n, |b|ₘ ≤ |a|ₘ ^ n\n⊢ ¬b = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 546,
"column": 2
} | {
"line": 546,
"column": 70
} | {
"line": 547,
"column": 2
} | [
{
"pp": "case mk.mk\nM : Type u_1\ninst✝⁵ : CommGroup M\ninst✝⁴ : LinearOrder M\ninst✝³ : IsOrderedMonoid M\nN : Type u_2\ninst✝² : CommGroup N\ninst✝¹ : LinearOrder N\ninst✝ : IsOrderedMonoid N\nf : M →*o N\nh : Function.Injective ⇑f\na b : M\n⊢ ((∃ m, f |b|ₘ ≤ f (|a|ₘ ^ m)) ∧ ∃ n, f |a|ₘ ≤ f (|b|ₘ ^ n)) → (∃ ... | [
"case mk.mk\nM : Type u_1\ninst✝⁵ : CommGroup M\ninst✝⁴ : LinearOrder M\ninst✝³ : IsOrderedMonoid M\nN : Type u_2\ninst✝² : CommGroup N\ninst✝¹ : LinearOrder N\ninst✝ : IsOrderedMonoid N\nf : M →*o N\nh : Function.Injective ⇑f\na b : M\nhmono : StrictMono ⇑f\n⊢ ((∃ m, f |b|ₘ ≤ f (|a|ₘ ^ m)) ∧ ∃ n, f |a|ₘ ≤ f (|b|ₘ ... | obtain hmono := (OrderHomClass.monotone f).strictMono_of_injective h | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 570,
"column": 4
} | {
"line": 570,
"column": 15
} | {
"line": 570,
"column": 16
} | [
{
"pp": "case mk.mk\nM : Type u_1\ninst✝³ : CommGroup M\ninst✝² : LinearOrder M\ninst✝¹ : IsOrderedMonoid M\na✝ b✝ : M\nα : Type u_2\ninst✝ : PartialOrder α\nf : M → α\nh : ∀ (a b : M), mk a ≤ mk b → f a ≤ f b\na b : M\nhle : mk a ≤ mk b\n⊢ lift f ⋯ (mk a) ≤ lift f ⋯ (mk b)",
"ppTerm": "?mk.mk",
"assign... | [
"case mk.mk\nM : Type u_1\ninst✝³ : CommGroup M\ninst✝² : LinearOrder M\ninst✝¹ : IsOrderedMonoid M\na✝ b✝ : M\nα : Type u_2\ninst✝ : PartialOrder α\nf : M → α\nh : ∀ (a b : M), mk a ≤ mk b → f a ≤ f b\na b : M\nhle : mk a ≤ mk b\n⊢ f a ≤ f b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 600,
"column": 2
} | {
"line": 600,
"column": 83
} | {
"line": 600,
"column": 84
} | [
{
"pp": "M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\ns t : UpperSet (MulArchimedeanClass M)\nheq : ↑(subsemigroup t) = ↑(subsemigroup s)\n⊢ t = s",
"ppTerm": "?m.49",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\ns t : UpperSet (MulArchimedeanClass M)\nheq : ↑(subsemigroup t) = ↑(subsemigroup s)\n⊢ t = s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 615,
"column": 6
} | {
"line": 615,
"column": 17
} | {
"line": 615,
"column": 18
} | [
{
"pp": "M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na b : M\ns : UpperSet (MulArchimedeanClass M)\nhs : ¬s = ⊤\nu : MulArchimedeanClass M\nhu : u ∈ ↑s\n⊢ mk 1 ∈ ↑s",
"ppTerm": "?m.57",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SetLike.mem... | [
"M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na b : M\ns : UpperSet (MulArchimedeanClass M)\nhs : ¬s = ⊤\nu : MulArchimedeanClass M\nhu : u ∈ ↑s\n⊢ ⊤ ∈ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 641,
"column": 43
} | {
"line": 641,
"column": 69
} | {
"line": 641,
"column": 70
} | [
{
"pp": "M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\ns : UpperSet (MulArchimedeanClass M)\nhs : s ∈ Set.Iio ⊤\nt : UpperSet (MulArchimedeanClass M)\nht : t ∈ Set.Iio ⊤\nhst : s < t\n⊢ ↑(subsemigroup t) ⊆ ↑(subsemigroup s)",
"ppTerm": "?m.78",
"assigned": true,
... | [
"M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\ns : UpperSet (MulArchimedeanClass M)\nhs : s ∈ Set.Iio ⊤\nt : UpperSet (MulArchimedeanClass M)\nht : t ∈ Set.Iio ⊤\nhst : s < t\n⊢ s ≤ t"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 644,
"column": 2
} | {
"line": 644,
"column": 43
} | {
"line": 644,
"column": 44
} | [
{
"pp": "M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\ns : UpperSet (MulArchimedeanClass M)\nhs : s ∈ Set.Iio ⊤\nt : UpperSet (MulArchimedeanClass M)\nht : t ∈ Set.Iio ⊤\nheq : ↑(subsemigroup t) = ↑(subsemigroup s)\n⊢ t = s",
"ppTerm": "?m.99",
"assigned": false,... | [
"M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\ns : UpperSet (MulArchimedeanClass M)\nhs : s ∈ Set.Iio ⊤\nt : UpperSet (MulArchimedeanClass M)\nht : t ∈ Set.Iio ⊤\nheq : ↑(subsemigroup t) = ↑(subsemigroup s)\n⊢ t = s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 751,
"column": 31
} | {
"line": 751,
"column": 40
} | {
"line": 751,
"column": 40
} | [
{
"pp": "case mk.mk\nM : Type u_1\ninst✝³ : CommGroup M\ninst✝² : LinearOrder M\ninst✝¹ : IsOrderedMonoid M\na✝ b✝ : M\ninst✝ : MulArchimedean M\na : M\nha : a ≠ 1\nb : M\nhb : b ≠ 1\n⊢ mk a ha = mk b hb",
"ppTerm": "?mk.mk",
"assigned": true,
"usedConstants": [],
"usedFVars": [],
"usedGoals... | [
"case mk.mk\nM : Type u_1\ninst✝³ : CommGroup M\ninst✝² : LinearOrder M\ninst✝¹ : IsOrderedMonoid M\na✝ b✝ : M\ninst✝ : MulArchimedean M\na : M\nha : a ≠ 1\nb : M\nhb : b ≠ 1\n⊢ mk a ha = mk b hb"
] | | mk b hb
=> | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 752,
"column": 4
} | {
"line": 752,
"column": 20
} | {
"line": 752,
"column": 21
} | [
{
"pp": "case mk.mk\nM : Type u_1\ninst✝³ : CommGroup M\ninst✝² : LinearOrder M\ninst✝¹ : IsOrderedMonoid M\na✝ b✝ : M\ninst✝ : MulArchimedean M\na : M\nha : a ≠ 1\nb : M\nhb : b ≠ 1\n⊢ mk a ha = mk b hb",
"ppTerm": "?mk.mk",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"PartialOrder.t... | [
"case mk.mk\nM : Type u_1\ninst✝³ : CommGroup M\ninst✝² : LinearOrder M\ninst✝¹ : IsOrderedMonoid M\na✝ b✝ : M\ninst✝ : MulArchimedean M\na : M\nha : a ≠ 1\nb : M\nhb : b ≠ 1\n⊢ MulArchimedeanClass.mk a = MulArchimedeanClass.mk b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 757,
"column": 21
} | {
"line": 757,
"column": 32
} | {
"line": 757,
"column": 33
} | [
{
"pp": "M : Type u_1\ninst✝³ : CommGroup M\ninst✝² : LinearOrder M\ninst✝¹ : IsOrderedMonoid M\na b : M\ninst✝ : Nontrivial M\nx : M\nhx : x ≠ 1\n⊢ ↑(mk x hx) ≠ ⊤",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulArchimedeanClass.mk_eq_top_iff._simp_2",
"InvO... | [
"M : Type u_1\ninst✝³ : CommGroup M\ninst✝² : LinearOrder M\ninst✝¹ : IsOrderedMonoid M\na b : M\ninst✝ : Nontrivial M\nx : M\nhx : x ≠ 1\n⊢ ¬x = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Group.Cone | {
"line": 79,
"column": 38
} | {
"line": 79,
"column": 49
} | {
"line": 79,
"column": 50
} | [
{
"pp": "H : Type u_1\ninst✝² : CommGroup H\ninst✝¹ : PartialOrder H\ninst✝ : IsOrderedMonoid H\na✝ a : H\n⊢ a ∈ (Submonoid.oneLE H).carrier → a⁻¹ ∈ (Submonoid.oneLE H).carrier → a = 1",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"InvOneClass.... | [
"H : Type u_1\ninst✝² : CommGroup H\ninst✝¹ : PartialOrder H\ninst✝ : IsOrderedMonoid H\na✝ a : H\n⊢ 1 ≤ a → a ≤ 1 → a = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 770,
"column": 32
} | {
"line": 770,
"column": 48
} | {
"line": 770,
"column": 49
} | [
{
"pp": "M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na✝ b✝ : M\nα : Type u_2\nf : { a // a ≠ 1 } → α\nh : ∀ (a b : { a // a ≠ 1 }), mk ↑a ⋯ = mk ↑b ⋯ → f a = f b\nx✝ : FiniteMulArchimedeanClass M\nA : MulArchimedeanClass M\nhA : A ≠ ⊤\na b : M\nh' : MulArchimedeanClass... | [
"M : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na✝ b✝ : M\nα : Type u_2\nf : { a // a ≠ 1 } → α\nh : ∀ (a b : { a // a ≠ 1 }), mk ↑a ⋯ = mk ↑b ⋯ → f a = f b\nx✝ : FiniteMulArchimedeanClass M\nA : MulArchimedeanClass M\nhA : A ≠ ⊤\na b : M\nh' : MulArchimedeanClass.mk a = MulA... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Group.Cone | {
"line": 91,
"column": 23
} | {
"line": 91,
"column": 34
} | {
"line": 91,
"column": 35
} | [
{
"pp": "H✝ : Type u_1\ninst✝⁵ : CommGroup H✝\ninst✝⁴ : PartialOrder H✝\ninst✝³ : IsOrderedMonoid H✝\na : H✝\nH : Type u_2\ninst✝² : CommGroup H\ninst✝¹ : LinearOrder H\ninst✝ : IsOrderedMonoid H\n⊢ ∀ (a : H), a ∈ oneLE H ∨ a⁻¹ ∈ oneLE H",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
... | [
"H✝ : Type u_1\ninst✝⁵ : CommGroup H✝\ninst✝⁴ : PartialOrder H✝\ninst✝³ : IsOrderedMonoid H✝\na : H✝\nH : Type u_2\ninst✝² : CommGroup H\ninst✝¹ : LinearOrder H\ninst✝ : IsOrderedMonoid H\n⊢ ∀ (a : H), 1 ≤ a ∨ a ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Group.Cone | {
"line": 102,
"column": 31
} | {
"line": 102,
"column": 42
} | {
"line": 102,
"column": 43
} | [
{
"pp": "S : Type u_1\nG : Type u_2\ninst✝² : CommGroup G\ninst✝¹ : SetLike S G\nC : S\ninst✝ : GroupConeClass S G\na b c : G\nnab : b / a ∈ C\nnbc : c / b ∈ C\n⊢ c / a ∈ C",
"ppTerm": "?m.32",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"S : Type u_1\nG : Type u_2\ninst✝² : CommGroup G\ninst✝¹ : SetLike S G\nC : S\ninst✝ : GroupConeClass S G\na b c : G\nnab : b / a ∈ C\nnbc : c / b ∈ C\n⊢ c / a ∈ C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Group.Cone | {
"line": 104,
"column": 4
} | {
"line": 104,
"column": 37
} | {
"line": 104,
"column": 38
} | [
{
"pp": "S : Type u_1\nG : Type u_2\ninst✝² : CommGroup G\ninst✝¹ : SetLike S G\nC : S\ninst✝ : GroupConeClass S G\na b : G\nnab : b / a ∈ C\nnba : a / b ∈ C\n⊢ a = b",
"ppTerm": "?m.54",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"S : Type u_1\nG : Type u_2\ninst✝² : CommGroup G\ninst✝¹ : SetLike S G\nC : S\ninst✝ : GroupConeClass S G\na b : G\nnab : b / a ∈ C\nnba : a / b ∈ C\n⊢ a = b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Group.Cone | {
"line": 104,
"column": 71
} | {
"line": 104,
"column": 82
} | {
"line": 104,
"column": 83
} | [
{
"pp": "S : Type u_1\nG : Type u_2\ninst✝² : CommGroup G\ninst✝¹ : SetLike S G\nC : S\ninst✝ : GroupConeClass S G\na b : G\nnab : b / a ∈ C\nnba : a / b ∈ C\n⊢ (b / a)⁻¹ ∈ C",
"ppTerm": "?m.62",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHDiv",
"DivisionCommMonoid.toDivis... | [
"S : Type u_1\nG : Type u_2\ninst✝² : CommGroup G\ninst✝¹ : SetLike S G\nC : S\ninst✝ : GroupConeClass S G\na b : G\nnab : b / a ∈ C\nnba : a / b ∈ C\n⊢ a / b ∈ C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Group.Cone | {
"line": 116,
"column": 21
} | {
"line": 116,
"column": 32
} | {
"line": 116,
"column": 33
} | [
{
"pp": "S : Type u_1\nG : Type u_2\ninst✝⁴ : CommGroup G\ninst✝³ : SetLike S G\nC : S\ninst✝² : GroupConeClass S G\ninst✝¹ : HasMemOrInvMem C\ninst✝ : DecidablePred fun x ↦ x ∈ C\na b : G\n⊢ a ≤ b ∨ b ≤ a",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHDiv",
... | [
"S : Type u_1\nG : Type u_2\ninst✝⁴ : CommGroup G\ninst✝³ : SetLike S G\nC : S\ninst✝² : GroupConeClass S G\ninst✝¹ : HasMemOrInvMem C\ninst✝ : DecidablePred fun x ↦ x ∈ C\na b : G\n⊢ b / a ∈ C ∨ a / b ∈ C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Group.Cone | {
"line": 126,
"column": 42
} | {
"line": 126,
"column": 61
} | {
"line": 126,
"column": 62
} | [
{
"pp": "S : Type u_1\nG : Type u_2\ninst✝² : CommGroup G\ninst✝¹ : SetLike S G\nC : S\ninst✝ : GroupConeClass S G\nx✝ : PartialOrder G := PartialOrder.mkOfGroupCone C\na b : G\nnab : a ≤ b\nc : G\n⊢ a * c ≤ b * c",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instH... | [
"S : Type u_1\nG : Type u_2\ninst✝² : CommGroup G\ninst✝¹ : SetLike S G\nC : S\ninst✝ : GroupConeClass S G\nx✝ : PartialOrder G := PartialOrder.mkOfGroupCone C\na b : G\nnab : a ≤ b\nc : G\n⊢ b / a ∈ C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 772,
"column": 4
} | {
"line": 772,
"column": 15
} | {
"line": 772,
"column": 16
} | [
{
"pp": "case refine_2.mk\nM : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na✝ b : M\nα : Type u_2\nf : { a // a ≠ 1 } → α\nh : ∀ (a b : { a // a ≠ 1 }), mk ↑a ⋯ = mk ↑b ⋯ → f a = f b\nx✝ : FiniteMulArchimedeanClass M\na : M\nhA : MulArchimedeanClass.mk a ≠ ⊤\n⊢ MulArchimed... | [
"case refine_2.mk\nM : Type u_1\ninst✝² : CommGroup M\ninst✝¹ : LinearOrder M\ninst✝ : IsOrderedMonoid M\na✝ b : M\nα : Type u_2\nf : { a // a ≠ 1 } → α\nh : ∀ (a b : { a // a ≠ 1 }), mk ↑a ⋯ = mk ↑b ⋯ → f a = f b\nx✝ : FiniteMulArchimedeanClass M\na : M\nhA : MulArchimedeanClass.mk a ≠ ⊤\n⊢ ¬a = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 791,
"column": 31
} | {
"line": 791,
"column": 40
} | {
"line": 791,
"column": 40
} | [
{
"pp": "case mk.mk\nM : Type u_1\ninst✝³ : CommGroup M\ninst✝² : LinearOrder M\ninst✝¹ : IsOrderedMonoid M\na✝ b✝ : M\nα : Type u_2\ninst✝ : PartialOrder α\nf : { a // a ≠ 1 } → α\nh : ∀ (a b : { a // a ≠ 1 }), mk ↑a ⋯ ≤ mk ↑b ⋯ → f a ≤ f b\na : M\nha : a ≠ 1\nb : M\nhb : b ≠ 1\nhAB : mk a ha ≤ mk b hb\n⊢ lift... | [
"case mk.mk\nM : Type u_1\ninst✝³ : CommGroup M\ninst✝² : LinearOrder M\ninst✝¹ : IsOrderedMonoid M\na✝ b✝ : M\nα : Type u_2\ninst✝ : PartialOrder α\nf : { a // a ≠ 1 } → α\nh : ∀ (a b : { a // a ≠ 1 }), mk ↑a ⋯ ≤ mk ↑b ⋯ → f a ≤ f b\na : M\nha : a ≠ 1\nb : M\nhb : b ≠ 1\nhAB : mk a ha ≤ mk b hb\n⊢ lift f ⋯ (mk a h... | | mk b hb
=> | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.Algebra.Order.Archimedean.Class | {
"line": 792,
"column": 4
} | {
"line": 792,
"column": 15
} | {
"line": 792,
"column": 16
} | [
{
"pp": "case mk.mk\nM : Type u_1\ninst✝³ : CommGroup M\ninst✝² : LinearOrder M\ninst✝¹ : IsOrderedMonoid M\na✝ b✝ : M\nα : Type u_2\ninst✝ : PartialOrder α\nf : { a // a ≠ 1 } → α\nh : ∀ (a b : { a // a ≠ 1 }), mk ↑a ⋯ ≤ mk ↑b ⋯ → f a ≤ f b\na : M\nha : a ≠ 1\nb : M\nhb : b ≠ 1\nhAB : mk a ha ≤ mk b hb\n⊢ lift... | [
"case mk.mk\nM : Type u_1\ninst✝³ : CommGroup M\ninst✝² : LinearOrder M\ninst✝¹ : IsOrderedMonoid M\na✝ b✝ : M\nα : Type u_2\ninst✝ : PartialOrder α\nf : { a // a ≠ 1 } → α\nh : ∀ (a b : { a // a ≠ 1 }), mk ↑a ⋯ ≤ mk ↑b ⋯ → f a ≤ f b\na : M\nha : a ≠ 1\nb : M\nhb : b ≠ 1\nhAB : mk a ha ≤ mk b hb\n⊢ f ⟨a, ha⟩ ≤ f ⟨b... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Group.DenselyOrdered | {
"line": 36,
"column": 4
} | {
"line": 36,
"column": 46
} | {
"line": 36,
"column": 47
} | [
{
"pp": "α : Type u_1\ninst✝³ : Group α\ninst✝² : LinearOrder α\ninst✝¹ : MulLeftMono α\ninst✝ : DenselyOrdered α\na b : α\nh : ∀ (ε : α), 1 < ε → a / ε ≤ b\nε : α\nε1 : ε < 1\n⊢ a * ε ≤ b",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝³ : Group α\ninst✝² : LinearOrder α\ninst✝¹ : MulLeftMono α\ninst✝ : DenselyOrdered α\na b : α\nh : ∀ (ε : α), 1 < ε → a / ε ≤ b\nε : α\nε1 : ε < 1\n⊢ a * ε ≤ b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Group.DenselyOrdered | {
"line": 105,
"column": 19
} | {
"line": 105,
"column": 41
} | {
"line": 105,
"column": 42
} | [
{
"pp": "M : Type u_2\ninst✝⁴ : LinearOrder M\ninst✝³ : DenselyOrdered M\ninst✝² : CommMonoid M\ninst✝¹ : ExistsMulOfLE M\ninst✝ : IsOrderedCancelMonoid M\ny : M\nhy : 1 < y\nz : M\nhz : 1 < z\nhx : 1 < y * z\nhyx : y < y * z\nhxy : y * z ≤ y ^ 2\n⊢ z ^ 2 ≤ y * z",
"ppTerm": "?m.127",
"assigned": true,
... | [
"M : Type u_2\ninst✝⁴ : LinearOrder M\ninst✝³ : DenselyOrdered M\ninst✝² : CommMonoid M\ninst✝¹ : ExistsMulOfLE M\ninst✝ : IsOrderedCancelMonoid M\ny : M\nhy : 1 < y\nz : M\nhz : 1 < z\nhx : 1 < y * z\nhyx : y < y * z\nhxy : y * z ≤ y ^ 2\n⊢ z ≤ y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Group.DenselyOrdered | {
"line": 110,
"column": 12
} | {
"line": 110,
"column": 23
} | {
"line": 110,
"column": 24
} | [
{
"pp": "M : Type u_2\ninst✝⁴ : LinearOrder M\ninst✝³ : DenselyOrdered M\nx : M\ninst✝² : CommMonoid M\ninst✝¹ : ExistsMulOfLE M\ninst✝ : IsOrderedCancelMonoid M\nhx : 1 < x\n⊢ ∃ y, 1 < y ∧ y ^ 1 < x",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
... | [
"M : Type u_2\ninst✝⁴ : LinearOrder M\ninst✝³ : DenselyOrdered M\nx : M\ninst✝² : CommMonoid M\ninst✝¹ : ExistsMulOfLE M\ninst✝ : IsOrderedCancelMonoid M\nhx : 1 < x\n⊢ ∃ y, 1 < y ∧ y < x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Group.DenselyOrdered | {
"line": 129,
"column": 2
} | {
"line": 129,
"column": 23
} | {
"line": 129,
"column": 24
} | [
{
"pp": "case right\nM : Type u_2\ninst✝³ : LinearOrder M\ninst✝² : DenselyOrdered M\nx : M\ninst✝¹ : CommGroup M\ninst✝ : IsOrderedCancelMonoid M\nhx : x < 1\nn : ℕ\ny : M\nhy : 1 < y\nhy' : y ^ n < x⁻¹\n⊢ x < y⁻¹ ^ n",
"ppTerm": "?right",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"case right\nM : Type u_2\ninst✝³ : LinearOrder M\ninst✝² : DenselyOrdered M\nx : M\ninst✝¹ : CommGroup M\ninst✝ : IsOrderedCancelMonoid M\nhx : x < 1\nn : ℕ\ny : M\nhy : 1 < y\nhy' : y ^ n < x⁻¹\n⊢ x < (y ^ n)⁻¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Group.Ideal | {
"line": 61,
"column": 4
} | {
"line": 61,
"column": 22
} | {
"line": 61,
"column": 23
} | [
{
"pp": "M : Type u_1\ninst✝³ : CommMonoid M\ninst✝² : PartialOrder M\ninst✝¹ : WellQuasiOrderedLE M\ninst✝ : CanonicallyOrderedMul M\nf : ℕ →o SemigroupIdeal M\ns : Finset M\nhI : ⨆ i, f i = closure ↑s\nx : M\nhx : x ∈ ↑(closure ↑s)\n⊢ ∃ i, x ∈ f i",
"ppTerm": "?m.61",
"assigned": false,
"usedConst... | [
"M : Type u_1\ninst✝³ : CommMonoid M\ninst✝² : PartialOrder M\ninst✝¹ : WellQuasiOrderedLE M\ninst✝ : CanonicallyOrderedMul M\nf : ℕ →o SemigroupIdeal M\ns : Finset M\nhI : ⨆ i, f i = closure ↑s\nx : M\nhx : x ∈ ↑(closure ↑s)\n⊢ ∃ i, x ∈ f i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Group.Int.Sum | {
"line": 60,
"column": 2
} | {
"line": 69,
"column": 11
} | {
"line": 71,
"column": 0
} | [
{
"pp": "s : Finset ℤ\nc : ℤ\nhs : ∀ x ∈ s, c ≤ x\nr : Finset ℤ := Ico c (c + ↑(#s))\n⊢ ∑ x ∈ r, x ≤ ∑ x ∈ s, x",
"ppTerm": "?m.44",
"assigned": true,
"usedConstants": [
"Int.instAddCommGroup",
"_private.Mathlib.Algebra.Order.Group.Int.Sum.0.Finset.sum_Ico_le_sum._proof_1_1",
"Eq.m... | [] | calc
_ ≤ ∑ x ∈ r ∩ s, x + #(r \ s) • (c + #s) := by
grw [← sum_inter_add_sum_sdiff r s, ← sum_le_card_nsmul _ _ _ fun x mx ↦ ?_]
rw [mem_sdiff, mem_Ico] at mx; exact mx.1.2.le
_ = ∑ x ∈ s ∩ r, x + #(s \ r) • (c + #s) := by
rw [inter_comm, card_sdiff_comm]
rw [Int.card_Ico, add_sub_cancel... | Lean.Elab.Tactic._aux_Mathlib_Tactic_Widget_Calc___elabRules_Lean_calcTactic_1 | Lean.calcTactic |
Mathlib.Algebra.Order.GroupWithZero.Lex | {
"line": 86,
"column": 18
} | {
"line": 86,
"column": 29
} | {
"line": 86,
"column": 30
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrderedCommGroupWithZero α\ninst✝ : LinearOrderedCommGroupWithZero β\n⊢ Monotone (↑((WithZero.map' (toLexMulEquiv (αˣ × βˣ)).toMonoidHom).comp (MonoidWithZeroHom.inl α β))).toFun",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Grou... | [
"α : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrderedCommGroupWithZero α\ninst✝ : LinearOrderedCommGroupWithZero β\n⊢ Monotone (⇑(WithZero.map' ↑(toLexMulEquiv (αˣ × βˣ))) ∘ ⇑(MonoidWithZeroHom.inl α β))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Lex | {
"line": 94,
"column": 18
} | {
"line": 94,
"column": 29
} | {
"line": 94,
"column": 30
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrderedCommGroupWithZero α\ninst✝ : LinearOrderedCommGroupWithZero β\n⊢ Monotone (↑((WithZero.map' (toLexMulEquiv (αˣ × βˣ)).toMonoidHom).comp (MonoidWithZeroHom.inr α β))).toFun",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Grou... | [
"α : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrderedCommGroupWithZero α\ninst✝ : LinearOrderedCommGroupWithZero β\n⊢ Monotone (⇑(WithZero.map' ↑(toLexMulEquiv (αˣ × βˣ))) ∘ ⇑(MonoidWithZeroHom.inr α β))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Lex | {
"line": 110,
"column": 6
} | {
"line": 110,
"column": 17
} | {
"line": 110,
"column": 18
} | [
{
"pp": "case coe.coe\nα : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrderedCommGroupWithZero α\ninst✝ : LinearOrderedCommGroupWithZero β\na✝¹ a✝ : Lex (αˣ × βˣ)\n⊢ ↑a✝¹ ≤ ↑a✝ →\n (↑((MonoidWithZeroHom.fst α β).comp (WithZero.map' (toLexMulEquiv (αˣ × βˣ)).symm.toMonoidHom))).toFun ↑a✝¹ ≤\n (↑((MonoidWithZ... | [
"case coe.coe\nα : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrderedCommGroupWithZero α\ninst✝ : LinearOrderedCommGroupWithZero β\na✝¹ a✝ : Lex (αˣ × βˣ)\n⊢ a✝¹ ≤ a✝ → (ofLex a✝¹).1 ≤ (ofLex a✝).1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Module.Archimedean | {
"line": 32,
"column": 56
} | {
"line": 32,
"column": 67
} | {
"line": 32,
"column": 68
} | [
{
"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|",
... | [
"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⊢ ¬k = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Module.Archimedean | {
"line": 58,
"column": 4
} | {
"line": 58,
"column": 40
} | {
"line": 58,
"column": 41
} | [
{
"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\... | [
"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\nhs : s ≠ ⊤\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 50,
"column": 2
} | {
"line": 50,
"column": 31
} | {
"line": 50,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\na b : α\n⊢ Ico (a + 1) b = Ioo a b",
"ppTerm": "?m.15",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\na b : α\n⊢ Ico (a + 1) b = Ioo a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 53,
"column": 2
} | {
"line": 53,
"column": 31
} | {
"line": 53,
"column": 32
} | [
{
"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\nb : α\n⊢ Icc (a + 1) b = Ioc a b",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\na : α\nha : ¬IsMax a\nb : α\n⊢ Icc (a + 1) b = Ioc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 56,
"column": 2
} | {
"line": 56,
"column": 31
} | {
"line": 56,
"column": 32
} | [
{
"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\na : α\n⊢ Ico a (b + 1) = Icc a b",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\nb : α\nhb : ¬IsMax b\na : α\n⊢ Ico a (b + 1) = Icc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Module.Archimedean | {
"line": 107,
"column": 2
} | {
"line": 107,
"column": 13
} | {
"line": 107,
"column": 14
} | [
{
"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 : ... | [
"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 : a ∈ ball K c... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 59,
"column": 2
} | {
"line": 59,
"column": 31
} | {
"line": 59,
"column": 32
} | [
{
"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\na : α\n⊢ Ioo a (b + 1) = Ioc a b",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\nb : α\nhb : ¬IsMax b\na : α\n⊢ Ioo a (b + 1) = Ioc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 63,
"column": 2
} | {
"line": 63,
"column": 31
} | {
"line": 63,
"column": 32
} | [
{
"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\na : α\n⊢ Ico (a + 1) (b + 1) = Ioc a b",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\nb : α\nhb : ¬IsMax b\na : α\n⊢ Ico (a + 1) (b + 1) = Ioc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 68,
"column": 2
} | {
"line": 68,
"column": 31
} | {
"line": 68,
"column": 32
} | [
{
"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",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 72,
"column": 2
} | {
"line": 72,
"column": 33
} | {
"line": 72,
"column": 34
} | [
{
"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)",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Order.succ",
"congrArg",
"PartialOrde... | [
"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 (succ b) (Icc a b) = Icc a (succ b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 76,
"column": 2
} | {
"line": 76,
"column": 31
} | {
"line": 76,
"column": 32
} | [
{
"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)",
"ppTerm": "?m.22",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"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)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 79,
"column": 2
} | {
"line": 79,
"column": 31
} | {
"line": 79,
"column": 32
} | [
{
"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",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 83,
"column": 2
} | {
"line": 83,
"column": 31
} | {
"line": 83,
"column": 32
} | [
{
"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)",
"ppTerm": "?m.28",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"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)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 86,
"column": 2
} | {
"line": 86,
"column": 31
} | {
"line": 86,
"column": 32
} | [
{
"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",
"ppTerm": "?m.26",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 97,
"column": 2
} | {
"line": 97,
"column": 31
} | {
"line": 97,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : Add α\ninst✝¹ : SuccAddOrder α\ninst✝ : NoMaxOrder α\na b : α\n⊢ Icc (a + 1) b = Ioc a b",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : Add α\ninst✝¹ : SuccAddOrder α\ninst✝ : NoMaxOrder α\na b : α\n⊢ Icc (a + 1) b = Ioc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 100,
"column": 2
} | {
"line": 100,
"column": 31
} | {
"line": 100,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : Add α\ninst✝¹ : SuccAddOrder α\ninst✝ : NoMaxOrder α\na b : α\n⊢ Ico a (b + 1) = Icc a b",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : Add α\ninst✝¹ : SuccAddOrder α\ninst✝ : NoMaxOrder α\na b : α\n⊢ Ico a (b + 1) = Icc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 103,
"column": 2
} | {
"line": 103,
"column": 31
} | {
"line": 103,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : Add α\ninst✝¹ : SuccAddOrder α\ninst✝ : NoMaxOrder α\na b : α\n⊢ Ioo a (b + 1) = Ioc a b",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : Add α\ninst✝¹ : SuccAddOrder α\ninst✝ : NoMaxOrder α\na b : α\n⊢ Ioo a (b + 1) = Ioc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 106,
"column": 2
} | {
"line": 106,
"column": 31
} | {
"line": 106,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : Add α\ninst✝¹ : SuccAddOrder α\ninst✝ : NoMaxOrder α\na b : α\n⊢ Ico (a + 1) (b + 1) = Ioc a b",
"ppTerm": "?m.22",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : Add α\ninst✝¹ : SuccAddOrder α\ninst✝ : NoMaxOrder α\na b : α\n⊢ Ico (a + 1) (b + 1) = Ioc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 111,
"column": 2
} | {
"line": 111,
"column": 31
} | {
"line": 111,
"column": 32
} | [
{
"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)",
"ppTerm": "?m.21",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : Add α\ninst✝¹ : SuccAddOrder α\na b : α\ninst✝ : NoMaxOrder α\nh : a ≤ b\n⊢ insert b (Ico a b) = Ico a (b + 1)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 128,
"column": 2
} | {
"line": 128,
"column": 31
} | {
"line": 128,
"column": 32
} | [
{
"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",
"ppTerm": "?m.15",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na b : α\n⊢ Ioc a (b - 1) = Ioo a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 131,
"column": 2
} | {
"line": 131,
"column": 31
} | {
"line": 131,
"column": 32
} | [
{
"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",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\nb : α\nhb : ¬IsMin b\na : α\n⊢ Icc a (b - 1) = Ico a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 134,
"column": 2
} | {
"line": 134,
"column": 31
} | {
"line": 134,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na : α\nha : ¬IsMin a\nb : α\n⊢ Ioc (a - 1) b = Icc a b",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na : α\nha : ¬IsMin a\nb : α\n⊢ Ioc (a - 1) b = Icc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 137,
"column": 2
} | {
"line": 137,
"column": 31
} | {
"line": 137,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na : α\nha : ¬IsMin a\nb : α\n⊢ Ioo (a - 1) b = Ico a b",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na : α\nha : ¬IsMin a\nb : α\n⊢ Ioo (a - 1) b = Ico a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 141,
"column": 2
} | {
"line": 141,
"column": 31
} | {
"line": 141,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na : α\nha : ¬IsMin a\nb : α\n⊢ Ioc (a - 1) (b - 1) = Ico a b",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na : α\nha : ¬IsMin a\nb : α\n⊢ Ioc (a - 1) (b - 1) = Ico a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 146,
"column": 2
} | {
"line": 146,
"column": 31
} | {
"line": 146,
"column": 32
} | [
{
"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",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na b : α\nh : a ≤ b\n⊢ insert b (Icc a (b - 1)) = Icc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 150,
"column": 2
} | {
"line": 150,
"column": 33
} | {
"line": 150,
"column": 34
} | [
{
"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",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"PredSubOrder.toPredOrder",
"congrArg",
... | [
"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 (pred a) (Icc a b) = Icc (pred a) b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 154,
"column": 2
} | {
"line": 154,
"column": 31
} | {
"line": 154,
"column": 32
} | [
{
"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",
"ppTerm": "?m.22",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na 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.Set.SuccPred | {
"line": 157,
"column": 2
} | {
"line": 157,
"column": 31
} | {
"line": 157,
"column": 32
} | [
{
"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",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na 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.Set.SuccPred | {
"line": 161,
"column": 2
} | {
"line": 161,
"column": 31
} | {
"line": 161,
"column": 32
} | [
{
"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",
"ppTerm": "?m.28",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na 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.Algebra.Order.Interval.Set.SuccPred | {
"line": 164,
"column": 2
} | {
"line": 164,
"column": 31
} | {
"line": 164,
"column": 32
} | [
{
"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",
"ppTerm": "?m.26",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na 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.Set.SuccPred | {
"line": 175,
"column": 2
} | {
"line": 175,
"column": 31
} | {
"line": 175,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : Sub α\ninst✝¹ : PredSubOrder α\ninst✝ : NoMinOrder α\na b : α\n⊢ Icc a (b - 1) = Ico a b",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : Sub α\ninst✝¹ : PredSubOrder α\ninst✝ : NoMinOrder α\na b : α\n⊢ Icc a (b - 1) = Ico a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 178,
"column": 2
} | {
"line": 178,
"column": 31
} | {
"line": 178,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : Sub α\ninst✝¹ : PredSubOrder α\ninst✝ : NoMinOrder α\na b : α\n⊢ Ioc (a - 1) b = Icc a b",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : Sub α\ninst✝¹ : PredSubOrder α\ninst✝ : NoMinOrder α\na b : α\n⊢ Ioc (a - 1) b = Icc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 181,
"column": 2
} | {
"line": 181,
"column": 31
} | {
"line": 181,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : Sub α\ninst✝¹ : PredSubOrder α\ninst✝ : NoMinOrder α\na b : α\n⊢ Ioo (a - 1) b = Ico a b",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : Sub α\ninst✝¹ : PredSubOrder α\ninst✝ : NoMinOrder α\na b : α\n⊢ Ioo (a - 1) b = Ico a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 184,
"column": 2
} | {
"line": 184,
"column": 31
} | {
"line": 184,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : Sub α\ninst✝¹ : PredSubOrder α\ninst✝ : NoMinOrder α\na b : α\n⊢ Ioc (a - 1) (b - 1) = Ico a b",
"ppTerm": "?m.22",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : Sub α\ninst✝¹ : PredSubOrder α\ninst✝ : NoMinOrder α\na b : α\n⊢ Ioc (a - 1) (b - 1) = Ico a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 189,
"column": 2
} | {
"line": 189,
"column": 31
} | {
"line": 189,
"column": 32
} | [
{
"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",
"ppTerm": "?m.21",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : Sub α\ninst✝¹ : PredSubOrder α\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.Set.SuccPred | {
"line": 200,
"column": 2
} | {
"line": 200,
"column": 48
} | {
"line": 200,
"column": 49
} | [
{
"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",
"ppTerm": "?m.24",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedG... | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 210,
"column": 2
} | {
"line": 210,
"column": 31
} | {
"line": 210,
"column": 32
} | [
{
"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",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 215,
"column": 2
} | {
"line": 215,
"column": 31
} | {
"line": 215,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : Add α\ninst✝¹ : SuccAddOrder α\ninst✝ : NoMaxOrder α\nb : α\n⊢ Iio (b + 1) = Iic b",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : Add α\ninst✝¹ : SuccAddOrder α\ninst✝ : NoMaxOrder α\nb : α\n⊢ Iio (b + 1) = Iic b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 223,
"column": 2
} | {
"line": 223,
"column": 31
} | {
"line": 223,
"column": 32
} | [
{
"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",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\nb : α\nhb : ¬IsMin b\n⊢ Iic (b - 1) = Iio b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 228,
"column": 2
} | {
"line": 228,
"column": 31
} | {
"line": 228,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : Sub α\ninst✝¹ : PredSubOrder α\ninst✝ : NoMinOrder α\nb : α\n⊢ Iic (b - 1) = Iio b",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : Sub α\ninst✝¹ : PredSubOrder α\ninst✝ : NoMinOrder α\nb : α\n⊢ Iic (b - 1) = Iio b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Set.SuccPred | {
"line": 238,
"column": 2
} | {
"line": 238,
"column": 31
} | {
"line": 238,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : One α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\na : α\nha : ¬IsMax a\n⊢ Ici (a + 1) = Ioi a",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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