module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Algebra.Order.AddGroupWithTop | {
"line": 149,
"column": 51
} | {
"line": 149,
"column": 73
} | {
"line": 151,
"column": 0
} | [
{
"pp": "α : Type u_2\ninst✝ : LinearOrderedAddCommGroupWithTop α\na b : α\n⊢ a + b ≠ ⊤ ↔ a ≠ ⊤ ∧ b ≠ ⊤",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"instIsDedekindFiniteAddMonoid",
"Ne",
"IsAddU... | [] | simp [← isAddUnit_iff] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.AddGroupWithTop | {
"line": 157,
"column": 13
} | {
"line": 157,
"column": 28
} | {
"line": 157,
"column": 29
} | [
{
"pp": "α : Type u_2\ninst✝ : LinearOrderedAddCommGroupWithTop α\na : α\nh : -a = ⊤\n⊢ a = ⊤",
"ppTerm": "?m.12",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝ : LinearOrderedAddCommGroupWithTop α\na : α\nh : -a = ⊤\n⊢ a = ⊤"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.AddGroupWithTop | {
"line": 185,
"column": 2
} | {
"line": 185,
"column": 30
} | {
"line": 185,
"column": 31
} | [
{
"pp": "α : Type u_2\ninst✝ : LinearOrderedAddCommGroupWithTop α\nb : α\nh : b ≠ ⊤\n⊢ Function.Injective fun x ↦ x - b",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"AddMonoid.toAddZeroClass",
"sub_eq_add_neg",
"HSub.hSub",
"AddZ... | [
"α : Type u_2\ninst✝ : LinearOrderedAddCommGroupWithTop α\nb : α\nh : b ≠ ⊤\n⊢ Function.Injective fun x ↦ x + -b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.AddGroupWithTop | {
"line": 205,
"column": 2
} | {
"line": 205,
"column": 30
} | {
"line": 205,
"column": 31
} | [
{
"pp": "α : Type u_2\ninst✝ : LinearOrderedAddCommGroupWithTop α\nb : α\nh : b ≠ ⊤\n⊢ StrictMono fun x ↦ x - b",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"StrictMono",
"congrArg",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"su... | [
"α : Type u_2\ninst✝ : LinearOrderedAddCommGroupWithTop α\nb : α\nh : b ≠ ⊤\n⊢ StrictMono fun x ↦ x + -b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.AddGroupWithTop | {
"line": 233,
"column": 2
} | {
"line": 233,
"column": 13
} | {
"line": 233,
"column": 14
} | [
{
"pp": "α : Type u_2\ninst✝ : LinearOrderedAddCommGroupWithTop α\na : α\n⊢ 0 < -a ↔ a < 0 ∨ a = ⊤",
"ppTerm": "?m.14",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝ : LinearOrderedAddCommGroupWithTop α\na : α\n⊢ 0 < -a ↔ a < 0 ∨ a = ⊤"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 140,
"column": 4
} | {
"line": 140,
"column": 53
} | {
"line": 140,
"column": 54
} | [
{
"pp": "case some.some\nα : Type u\ninst✝¹ : Add α\na : α\ninst✝ : LE α\nha : AddLECancellable a\nb c : α\n⊢ ↑a + Option.some b ≤ ↑a + Option.some c → Option.some b ≤ Option.some c",
"ppTerm": "?some.some",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"WithTop.coe_le_coe._simp_1",
... | [
"case some.some\nα : Type u\ninst✝¹ : Add α\na : α\ninst✝ : LE α\nha : AddLECancellable a\nb c : α\n⊢ a + b ≤ a + c → b ≤ c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 156,
"column": 58
} | {
"line": 156,
"column": 69
} | {
"line": 156,
"column": 70
} | [
{
"pp": "case coe.coe.coe\nα : Type u\nβ : Type v\ninst✝² : Add α\nw x y z : WithTop α\na b : α\ninst✝¹ : LE α\ninst✝ : AddLeftMono α\na✝² a✝¹ a✝ : α\n⊢ a✝¹ ≤ a✝ → a✝² + a✝¹ ≤ a✝² + a✝",
"ppTerm": "?coe.coe.coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case coe.coe.coe\nα : Type u\nβ : Type v\ninst✝² : Add α\nw x y z : WithTop α\na b : α\ninst✝¹ : LE α\ninst✝ : AddLeftMono α\na✝² a✝¹ a✝ : α\n⊢ a✝¹ ≤ a✝ → a✝² + a✝¹ ≤ a✝² + a✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 160,
"column": 64
} | {
"line": 160,
"column": 75
} | {
"line": 160,
"column": 76
} | [
{
"pp": "case coe.coe.coe\nα : Type u\nβ : Type v\ninst✝² : Add α\nw x y z : WithTop α\na b : α\ninst✝¹ : LE α\ninst✝ : AddRightMono α\na✝² a✝¹ a✝ : α\n⊢ a✝¹ ≤ a✝ → a✝¹ + a✝² ≤ a✝ + a✝²",
"ppTerm": "?coe.coe.coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case coe.coe.coe\nα : Type u\nβ : Type v\ninst✝² : Add α\nw x y z : WithTop α\na b : α\ninst✝¹ : LE α\ninst✝ : AddRightMono α\na✝² a✝¹ a✝ : α\n⊢ a✝¹ ≤ a✝ → a✝¹ + a✝² ≤ a✝ + a✝²"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 164,
"column": 58
} | {
"line": 164,
"column": 69
} | {
"line": 164,
"column": 70
} | [
{
"pp": "case coe.coe.coe\nα : Type u\nβ : Type v\ninst✝² : Add α\nw x y z : WithTop α\na b : α\ninst✝¹ : LT α\ninst✝ : AddLeftReflectLT α\na✝² a✝¹ a✝ : α\n⊢ a✝² + a✝¹ < a✝² + a✝ → a✝¹ < a✝",
"ppTerm": "?coe.coe.coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"case coe.coe.coe\nα : Type u\nβ : Type v\ninst✝² : Add α\nw x y z : WithTop α\na b : α\ninst✝¹ : LT α\ninst✝ : AddLeftReflectLT α\na✝² a✝¹ a✝ : α\n⊢ a✝² + a✝¹ < a✝² + a✝ → a✝¹ < a✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 168,
"column": 64
} | {
"line": 168,
"column": 75
} | {
"line": 168,
"column": 76
} | [
{
"pp": "case coe.coe.coe\nα : Type u\nβ : Type v\ninst✝² : Add α\nw x y z : WithTop α\na b : α\ninst✝¹ : LT α\ninst✝ : AddRightReflectLT α\na✝² a✝¹ a✝ : α\n⊢ a✝¹ + a✝² < a✝ + a✝² → a✝¹ < a✝",
"ppTerm": "?coe.coe.coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"case coe.coe.coe\nα : Type u\nβ : Type v\ninst✝² : Add α\nw x y z : WithTop α\na b : α\ninst✝¹ : LT α\ninst✝ : AddRightReflectLT α\na✝² a✝¹ a✝ : α\n⊢ a✝¹ + a✝² < a✝ + a✝² → a✝¹ < a✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 172,
"column": 66
} | {
"line": 172,
"column": 77
} | {
"line": 172,
"column": 78
} | [
{
"pp": "case coe.coe\nα : Type u\ninst✝² : Add α\ninst✝¹ : LE α\ninst✝ : AddLeftReflectLE α\nx a✝¹ a✝ : α\n⊢ x + a✝¹ ≤ x + a✝ → a✝¹ ≤ a✝",
"ppTerm": "?coe.coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case coe.coe\nα : Type u\ninst✝² : Add α\ninst✝¹ : LE α\ninst✝ : AddLeftReflectLE α\nx a✝¹ a✝ : α\n⊢ x + a✝¹ ≤ x + a✝ → a✝¹ ≤ a✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 176,
"column": 66
} | {
"line": 176,
"column": 77
} | {
"line": 176,
"column": 78
} | [
{
"pp": "case coe.coe\nα : Type u\ninst✝² : Add α\ninst✝¹ : LE α\ninst✝ : AddRightReflectLE α\nz a✝¹ a✝ : α\n⊢ a✝¹ + z ≤ a✝ + z → a✝¹ ≤ a✝",
"ppTerm": "?coe.coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case coe.coe\nα : Type u\ninst✝² : Add α\ninst✝¹ : LE α\ninst✝ : AddRightReflectLE α\nz a✝¹ a✝ : α\n⊢ a✝¹ + z ≤ a✝ + z → a✝¹ ≤ a✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 180,
"column": 66
} | {
"line": 180,
"column": 77
} | {
"line": 180,
"column": 78
} | [
{
"pp": "case coe.coe\nα : Type u\ninst✝² : Add α\ninst✝¹ : LT α\ninst✝ : AddLeftStrictMono α\nx a✝¹ a✝ : α\n⊢ a✝¹ < a✝ → x + a✝¹ < x + a✝",
"ppTerm": "?coe.coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case coe.coe\nα : Type u\ninst✝² : Add α\ninst✝¹ : LT α\ninst✝ : AddLeftStrictMono α\nx a✝¹ a✝ : α\n⊢ a✝¹ < a✝ → x + a✝¹ < x + a✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 184,
"column": 66
} | {
"line": 184,
"column": 77
} | {
"line": 184,
"column": 78
} | [
{
"pp": "case coe.coe\nα : Type u\ninst✝² : Add α\ninst✝¹ : LT α\ninst✝ : AddRightStrictMono α\nz a✝¹ a✝ : α\n⊢ a✝¹ < a✝ → a✝¹ + z < a✝ + z",
"ppTerm": "?coe.coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case coe.coe\nα : Type u\ninst✝² : Add α\ninst✝¹ : LT α\ninst✝ : AddRightStrictMono α\nz a✝¹ a✝ : α\n⊢ a✝¹ < a✝ → a✝¹ + z < a✝ + z"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Sub.Basic | {
"line": 102,
"column": 6
} | {
"line": 102,
"column": 45
} | {
"line": 102,
"column": 46
} | [
{
"pp": "α : Type u_1\ninst✝⁵ : AddCommMonoid α\ninst✝⁴ : PartialOrder α\ninst✝³ : CanonicallyOrderedAdd α\ninst✝² : Sub α\ninst✝¹ : OrderedSub α\na✝ b✝ c✝ : α\ninst✝ : AddLeftReflectLE α\na b c : α\nh : (fun x ↦ a + x) b = (fun x ↦ a + x) c\n⊢ b = c",
"ppTerm": "?m.20",
"assigned": false,
"usedCons... | [
"α : Type u_1\ninst✝⁵ : AddCommMonoid α\ninst✝⁴ : PartialOrder α\ninst✝³ : CanonicallyOrderedAdd α\ninst✝² : Sub α\ninst✝¹ : OrderedSub α\na✝ b✝ c✝ : α\ninst✝ : AddLeftReflectLE α\na b c : α\nh : (fun x ↦ a + x) b = (fun x ↦ a + x) c\n⊢ b = c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 488,
"column": 73
} | {
"line": 488,
"column": 84
} | {
"line": 488,
"column": 85
} | [
{
"pp": "case some.some\nα : Type u\ninst✝ : Add α\na : α\nha : IsAddLeftRegular a\nb c : α\n⊢ a + b = a + c → b = c",
"ppTerm": "?some.some",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case some.some\nα : Type u\ninst✝ : Add α\na : α\nha : IsAddLeftRegular a\nb c : α\n⊢ a + b = a + c → b = c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Sub.Basic | {
"line": 230,
"column": 8
} | {
"line": 230,
"column": 19
} | {
"line": 230,
"column": 20
} | [
{
"pp": "case neg.mp\nα : Type u_1\ninst✝³ : AddCommMonoid α\ninst✝² : LinearOrder α\ninst✝¹ : CanonicallyOrderedAdd α\ninst✝ : AddRightReflectLE α\na b c : α\nh : a < b\nh' : 0 ≤ c\n⊢ a ≤ c + b",
"ppTerm": "?neg.mp✝",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"case neg.mp\nα : Type u_1\ninst✝³ : AddCommMonoid α\ninst✝² : LinearOrder α\ninst✝¹ : CanonicallyOrderedAdd α\ninst✝ : AddRightReflectLE α\na b c : α\nh : a < b\nh' : 0 ≤ c\n⊢ a ≤ c + b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 492,
"column": 73
} | {
"line": 492,
"column": 84
} | {
"line": 492,
"column": 85
} | [
{
"pp": "case some.some\nα : Type u\ninst✝ : Add α\na : α\nha : IsAddRightRegular a\nb c : α\n⊢ b + a = c + a → b = c",
"ppTerm": "?some.some",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case some.some\nα : Type u\ninst✝ : Add α\na : α\nha : IsAddRightRegular a\nb c : α\n⊢ b + a = c + a → b = c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 500,
"column": 4
} | {
"line": 500,
"column": 53
} | {
"line": 500,
"column": 54
} | [
{
"pp": "case some.some\nα : Type u\ninst✝¹ : Add α\na : α\ninst✝ : LE α\nha : AddLECancellable a\nb c : α\n⊢ ↑a + Option.some b ≤ ↑a + Option.some c → Option.some b ≤ Option.some c",
"ppTerm": "?some.some",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"WithBot.some",
"WithBot",
... | [
"case some.some\nα : Type u\ninst✝¹ : Add α\na : α\ninst✝ : LE α\nha : AddLECancellable a\nb c : α\n⊢ a + b ≤ a + c → b ≤ c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 500,
"column": 4
} | {
"line": 500,
"column": 66
} | {
"line": 502,
"column": 0
} | [
{
"pp": "case some.some\nα : Type u\ninst✝¹ : Add α\na : α\ninst✝ : LE α\nha : AddLECancellable a\nb c : α\n⊢ ↑a + Option.some b ≤ ↑a + Option.some c → Option.some b ≤ Option.some c",
"ppTerm": "?some.some",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"WithBot.some",
"WithBot",
... | [] | simpa [none_eq_bot, some_eq_coe, ← coe_add] using fun a ↦ ha a | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 500,
"column": 4
} | {
"line": 500,
"column": 66
} | {
"line": 502,
"column": 0
} | [
{
"pp": "case some.some\nα : Type u\ninst✝¹ : Add α\na : α\ninst✝ : LE α\nha : AddLECancellable a\nb c : α\n⊢ ↑a + Option.some b ≤ ↑a + Option.some c → Option.some b ≤ Option.some c",
"ppTerm": "?some.some",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"WithBot.some",
"WithBot",
... | [] | simpa [none_eq_bot, some_eq_coe, ← coe_add] using fun a ↦ ha a | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 500,
"column": 4
} | {
"line": 500,
"column": 66
} | {
"line": 502,
"column": 0
} | [
{
"pp": "case some.some\nα : Type u\ninst✝¹ : Add α\na : α\ninst✝ : LE α\nha : AddLECancellable a\nb c : α\n⊢ ↑a + Option.some b ≤ ↑a + Option.some c → Option.some b ≤ Option.some c",
"ppTerm": "?some.some",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"WithBot.some",
"WithBot",
... | [] | simpa [none_eq_bot, some_eq_coe, ← coe_add] using fun a ↦ ha a | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 516,
"column": 58
} | {
"line": 516,
"column": 69
} | {
"line": 516,
"column": 70
} | [
{
"pp": "case coe.coe.coe\nα : Type u\nβ : Type v\ninst✝² : Add α\nw x y z : WithBot α\na b : α\ninst✝¹ : LE α\ninst✝ : AddLeftMono α\na✝² a✝¹ a✝ : α\n⊢ a✝¹ ≤ a✝ → a✝² + a✝¹ ≤ a✝² + a✝",
"ppTerm": "?coe.coe.coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case coe.coe.coe\nα : Type u\nβ : Type v\ninst✝² : Add α\nw x y z : WithBot α\na b : α\ninst✝¹ : LE α\ninst✝ : AddLeftMono α\na✝² a✝¹ a✝ : α\n⊢ a✝¹ ≤ a✝ → a✝² + a✝¹ ≤ a✝² + a✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 520,
"column": 64
} | {
"line": 520,
"column": 75
} | {
"line": 520,
"column": 76
} | [
{
"pp": "case coe.coe.coe\nα : Type u\nβ : Type v\ninst✝² : Add α\nw x y z : WithBot α\na b : α\ninst✝¹ : LE α\ninst✝ : AddRightMono α\na✝² a✝¹ a✝ : α\n⊢ a✝¹ ≤ a✝ → a✝¹ + a✝² ≤ a✝ + a✝²",
"ppTerm": "?coe.coe.coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case coe.coe.coe\nα : Type u\nβ : Type v\ninst✝² : Add α\nw x y z : WithBot α\na b : α\ninst✝¹ : LE α\ninst✝ : AddRightMono α\na✝² a✝¹ a✝ : α\n⊢ a✝¹ ≤ a✝ → a✝¹ + a✝² ≤ a✝ + a✝²"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 524,
"column": 58
} | {
"line": 524,
"column": 69
} | {
"line": 524,
"column": 70
} | [
{
"pp": "case coe.coe.coe\nα : Type u\nβ : Type v\ninst✝² : Add α\nw x y z : WithBot α\na b : α\ninst✝¹ : LT α\ninst✝ : AddLeftReflectLT α\na✝² a✝¹ a✝ : α\n⊢ a✝² + a✝¹ < a✝² + a✝ → a✝¹ < a✝",
"ppTerm": "?coe.coe.coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"case coe.coe.coe\nα : Type u\nβ : Type v\ninst✝² : Add α\nw x y z : WithBot α\na b : α\ninst✝¹ : LT α\ninst✝ : AddLeftReflectLT α\na✝² a✝¹ a✝ : α\n⊢ a✝² + a✝¹ < a✝² + a✝ → a✝¹ < a✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 528,
"column": 64
} | {
"line": 528,
"column": 75
} | {
"line": 528,
"column": 76
} | [
{
"pp": "case coe.coe.coe\nα : Type u\nβ : Type v\ninst✝² : Add α\nw x y z : WithBot α\na b : α\ninst✝¹ : LT α\ninst✝ : AddRightReflectLT α\na✝² a✝¹ a✝ : α\n⊢ a✝¹ + a✝² < a✝ + a✝² → a✝¹ < a✝",
"ppTerm": "?coe.coe.coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"case coe.coe.coe\nα : Type u\nβ : Type v\ninst✝² : Add α\nw x y z : WithBot α\na b : α\ninst✝¹ : LT α\ninst✝ : AddRightReflectLT α\na✝² a✝¹ a✝ : α\n⊢ a✝¹ + a✝² < a✝ + a✝² → a✝¹ < a✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 532,
"column": 66
} | {
"line": 532,
"column": 77
} | {
"line": 532,
"column": 78
} | [
{
"pp": "case coe.coe\nα : Type u\ninst✝² : Add α\ninst✝¹ : LE α\ninst✝ : AddLeftReflectLE α\nx a✝¹ a✝ : α\n⊢ x + a✝¹ ≤ x + a✝ → a✝¹ ≤ a✝",
"ppTerm": "?coe.coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case coe.coe\nα : Type u\ninst✝² : Add α\ninst✝¹ : LE α\ninst✝ : AddLeftReflectLE α\nx a✝¹ a✝ : α\n⊢ x + a✝¹ ≤ x + a✝ → a✝¹ ≤ a✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 536,
"column": 66
} | {
"line": 536,
"column": 77
} | {
"line": 536,
"column": 78
} | [
{
"pp": "case coe.coe\nα : Type u\ninst✝² : Add α\ninst✝¹ : LE α\ninst✝ : AddRightReflectLE α\nz a✝¹ a✝ : α\n⊢ a✝¹ + z ≤ a✝ + z → a✝¹ ≤ a✝",
"ppTerm": "?coe.coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case coe.coe\nα : Type u\ninst✝² : Add α\ninst✝¹ : LE α\ninst✝ : AddRightReflectLE α\nz a✝¹ a✝ : α\n⊢ a✝¹ + z ≤ a✝ + z → a✝¹ ≤ a✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 540,
"column": 66
} | {
"line": 540,
"column": 77
} | {
"line": 540,
"column": 78
} | [
{
"pp": "case coe.coe\nα : Type u\ninst✝² : Add α\ninst✝¹ : LT α\ninst✝ : AddLeftStrictMono α\nx a✝¹ a✝ : α\n⊢ a✝¹ < a✝ → x + a✝¹ < x + a✝",
"ppTerm": "?coe.coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case coe.coe\nα : Type u\ninst✝² : Add α\ninst✝¹ : LT α\ninst✝ : AddLeftStrictMono α\nx a✝¹ a✝ : α\n⊢ a✝¹ < a✝ → x + a✝¹ < x + a✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | {
"line": 544,
"column": 66
} | {
"line": 544,
"column": 77
} | {
"line": 544,
"column": 78
} | [
{
"pp": "case coe.coe\nα : Type u\ninst✝² : Add α\ninst✝¹ : LT α\ninst✝ : AddRightStrictMono α\nz a✝¹ a✝ : α\n⊢ a✝¹ < a✝ → a✝¹ + z < a✝ + z",
"ppTerm": "?coe.coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case coe.coe\nα : Type u\ninst✝² : Add α\ninst✝¹ : LT α\ninst✝ : AddRightStrictMono α\nz a✝¹ a✝ : α\n⊢ a✝¹ < a✝ → a✝¹ + z < a✝ + z"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Cast | {
"line": 54,
"column": 4
} | {
"line": 54,
"column": 70
} | {
"line": 54,
"column": 71
} | [
{
"pp": "R : Type u_1\ninst✝⁴ : AddCommGroupWithOne R\ninst✝³ : PartialOrder R\ninst✝² : AddLeftMono R\ninst✝¹ : ZeroLEOneClass R\ninst✝ : NeZero 1\nn : ℕ\nthis : -↑n < 1\n⊢ 0 ≤ ↑-[n+1] ↔ 0 ≤ -[n+1]",
"ppTerm": "?m.56",
"assigned": true,
"usedConstants": [
"neg_add_rev",
"AddGroup.toSubt... | [
"R : Type u_1\ninst✝⁴ : AddCommGroupWithOne R\ninst✝³ : PartialOrder R\ninst✝² : AddLeftMono R\ninst✝¹ : ZeroLEOneClass R\ninst✝ : NeZero 1\nn : ℕ\nthis : -↑n < 1\n⊢ ¬1 ≤ -↑n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.WithBot | {
"line": 235,
"column": 4
} | {
"line": 235,
"column": 15
} | {
"line": 235,
"column": 16
} | [
{
"pp": "case bot\nα : Type u_1\nb : α\nh : ⊥ ≠ ⊥\n⊢ ⊥.unbot h = b ↔ ⊥ = ↑b",
"ppTerm": "?bot",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"WithBot.some",
"WithBot",
"iff_false",
"congrArg",
"id",
"Bot.bot",
"WithBot.unbot",
"I... | [
"case bot\nα : Type u_1\nb : α\nh : ⊥ ≠ ⊥\n⊢ ¬⊥.unbot h = b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.WithBot | {
"line": 242,
"column": 4
} | {
"line": 242,
"column": 15
} | {
"line": 242,
"column": 16
} | [
{
"pp": "case bot\nα : Type u_1\na : α\nh : ⊥ ≠ ⊥\n⊢ a = ⊥.unbot h ↔ ↑a = ⊥",
"ppTerm": "?bot",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"WithBot.some",
"WithBot",
"iff_false",
"congrArg",
"WithBot.coe_ne_bot._simp_3",
"id",
"Bot.b... | [
"case bot\nα : Type u_1\na : α\nh : ⊥ ≠ ⊥\n⊢ ¬a = ⊥.unbot h"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.WithBot | {
"line": 430,
"column": 31
} | {
"line": 430,
"column": 42
} | {
"line": 430,
"column": 43
} | [
{
"pp": "case coe\nα : Type u_1\na : α\ninst✝ : LE α\nh : IsMax a\na✝ : α\n⊢ a ≤ a✝ → a✝ ≤ a",
"ppTerm": "?coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case coe\nα : Type u_1\na : α\ninst✝ : LE α\nh : IsMax a\na✝ : α\n⊢ a ≤ a✝ → a✝ ≤ a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.WithBot | {
"line": 523,
"column": 74
} | {
"line": 523,
"column": 85
} | {
"line": 523,
"column": 86
} | [
{
"pp": "case coe.coe.coe\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\na b : α\ninst✝ : Preorder α\na✝² a✝¹ a✝ : α\n⊢ a✝² ≤ a✝¹ → a✝¹ ≤ a✝ → a✝² ≤ a✝",
"ppTerm": "?coe.coe.coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case coe.coe.coe\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\na b : α\ninst✝ : Preorder α\na✝² a✝¹ a✝ : α\n⊢ a✝² ≤ a✝¹ → a✝¹ ≤ a✝ → a✝² ≤ a✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.WithBot | {
"line": 584,
"column": 20
} | {
"line": 584,
"column": 31
} | {
"line": 584,
"column": 32
} | [
{
"pp": "case coe\nα : Type u_1\ninst✝ : Preorder α\na✝ : α\n⊢ ∃ x, ¬a✝ < x",
"ppTerm": "?coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case coe\nα : Type u_1\ninst✝ : Preorder α\na✝ : α\n⊢ ∃ x, ¬a✝ < x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.WithBot | {
"line": 628,
"column": 63
} | {
"line": 628,
"column": 74
} | {
"line": 628,
"column": 75
} | [
{
"pp": "case coe.coe\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\na b : α\ninst✝ : PartialOrder α\na✝¹ a✝ : α\n⊢ a✝¹ ≤ a✝ → a✝ ≤ a✝¹ → a✝¹ = a✝",
"ppTerm": "?coe.coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case coe.coe\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\na b : α\ninst✝ : PartialOrder α\na✝¹ a✝ : α\n⊢ a✝¹ ≤ a✝ → a✝ ≤ a✝¹ → a✝¹ = a✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.WithBot | {
"line": 647,
"column": 4
} | {
"line": 647,
"column": 46
} | {
"line": 647,
"column": 47
} | [
{
"pp": "case coe\nα : Type u_1\ninst✝² : PartialOrder α\ninst✝¹ : Nonempty α\ninst✝ : NoTopOrder α\na✝ : WithTop α\nH : ∀ (a : α), ↑↑a ≤ ↑a✝\n⊢ ↑a✝ = ⊤",
"ppTerm": "?coe",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"WithBot.some",
"WithBot",
"WithTop.instPreorder",
... | [
"case coe\nα : Type u_1\ninst✝² : PartialOrder α\ninst✝¹ : Nonempty α\ninst✝ : NoTopOrder α\na✝ : WithTop α\nH : ∀ (a : α), ↑↑a ≤ ↑a✝\n⊢ ∀ (b : α), ↑b ≤ a✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Canonical | {
"line": 94,
"column": 32
} | {
"line": 94,
"column": 43
} | {
"line": 94,
"column": 44
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝ : LinearOrderedCommMonoidWithZero α\na b : α\nn✝ n : ℕ\nhn : n ≠ 0\n⊢ Function.Injective fun a ↦ a ^ n",
"ppTerm": "?m.6",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nβ : Type u_2\ninst✝ : LinearOrderedCommMonoidWithZero α\na b : α\nn✝ n : ℕ\nhn : n ≠ 0\n⊢ Function.Injective fun a ↦ a ^ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Canonical | {
"line": 122,
"column": 2
} | {
"line": 122,
"column": 28
} | {
"line": 122,
"column": 29
} | [
{
"pp": "α : Type u_1\ninst✝ : LinearOrderedCommGroupWithZero α\na b c : α\nh : b ≤ a * c⁻¹\n⊢ b * c ≤ a",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝ : LinearOrderedCommGroupWithZero α\na b c : α\nh : b ≤ a * c⁻¹\n⊢ b * c ≤ a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Canonical | {
"line": 131,
"column": 2
} | {
"line": 132,
"column": 9
} | {
"line": 132,
"column": 10
} | [
{
"pp": "α : Type u_1\ninst✝ : LinearOrderedCommGroupWithZero α\na b c d : α\nh : a * b < c * d\nhc : 0 < c\nhh : a⁻¹ ≤ c⁻¹\nha : a ≠ 0\n⊢ b < d",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"... | [
"α : Type u_1\ninst✝ : LinearOrderedCommGroupWithZero α\na b c d : α\nh : a * b < c * d\nhc : 0 < c\nhh : a⁻¹ ≤ c⁻¹\nha : a ≠ 0\n⊢ b < d"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.WithBot | {
"line": 670,
"column": 63
} | {
"line": 670,
"column": 74
} | {
"line": 670,
"column": 75
} | [
{
"pp": "case coe.coe.coe\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\na b : α\ninst✝ : SemilatticeSup α\na✝² a✝¹ a✝ : α\n⊢ a✝² ≤ a✝ → a✝¹ ≤ a✝ → a✝² ≤ a✝ ∧ a✝¹ ≤ a✝",
"ppTerm": "?coe.coe.coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case coe.coe.coe\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\na b : α\ninst✝ : SemilatticeSup α\na✝² a✝¹ a✝ : α\n⊢ a✝² ≤ a✝ → a✝¹ ≤ a✝ → a✝² ≤ a✝ ∧ a✝¹ ≤ a✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Canonical | {
"line": 155,
"column": 37
} | {
"line": 155,
"column": 64
} | {
"line": 155,
"column": 65
} | [
{
"pp": "α : Type u_1\ninst✝ : LinearOrderedCommGroupWithZero α\nH : DenselyOrdered α\nx : α\nhx : 0 < x\nhx' : x < 1\n⊢ Units.mk0 x ⋯ ≠ 1",
"ppTerm": "?m.72",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearO... | [
"α : Type u_1\ninst✝ : LinearOrderedCommGroupWithZero α\nH : DenselyOrdered α\nx : α\nhx : 0 < x\nhx' : x < 1\n⊢ ¬x = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Canonical | {
"line": 166,
"column": 16
} | {
"line": 166,
"column": 33
} | {
"line": 166,
"column": 33
} | [
{
"pp": "α : Type u_1\ninst✝ : LinearOrderedCommGroupWithZero α\nx✝ : Nontrivial αˣ ∧ DenselyOrdered αˣ\nH₁ : Nontrivial αˣ\nH₂ : DenselyOrdered αˣ\ny x : αˣ\nh : ↑x < ↑y\nhx : 0 < ↑x\nz : αˣ\nhz : x < z\nhz' : z < y\n⊢ ↑x < ↑z ∧ ↑z < ↑y",
"ppTerm": "?m.282",
"assigned": true,
"usedConstants": [
... | [] | by simp [hz, hz'] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Order.Floor.Defs | {
"line": 95,
"column": 2
} | {
"line": 95,
"column": 13
} | {
"line": 95,
"column": 14
} | [
{
"pp": "α : Type u_2\ninst✝² : Semiring α\ninst✝¹ : PartialOrder α\ninst✝ : FloorSemiring α\nn : ℕ\n⊢ 0 ≤ ↑n",
"ppTerm": "?m.7",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝² : Semiring α\ninst✝¹ : PartialOrder α\ninst✝ : FloorSemiring α\nn : ℕ\n⊢ 0 ≤ ↑n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Floor.Defs | {
"line": 106,
"column": 35
} | {
"line": 106,
"column": 66
} | {
"line": 106,
"column": 67
} | [
{
"pp": "F : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝² : Semiring α\ninst✝¹ : PartialOrder α\ninst✝ : FloorSemiring α\n⊢ 0 ≤ 1",
"ppTerm": "?m.10",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"F : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝² : Semiring α\ninst✝¹ : PartialOrder α\ninst✝ : FloorSemiring α\n⊢ 0 ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.WithBot | {
"line": 682,
"column": 63
} | {
"line": 682,
"column": 74
} | {
"line": 682,
"column": 75
} | [
{
"pp": "case coe.coe.coe\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\na b : α\ninst✝ : SemilatticeInf α\na✝² a✝¹ a✝ : α\n⊢ a✝² ≤ a✝¹ → a✝² ≤ a✝ → a✝² ≤ a✝¹ ∧ a✝² ≤ a✝",
"ppTerm": "?coe.coe.coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case coe.coe.coe\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\na b : α\ninst✝ : SemilatticeInf α\na✝² a✝¹ a✝ : α\n⊢ a✝² ≤ a✝¹ → a✝² ≤ a✝ → a✝² ≤ a✝¹ ∧ a✝² ≤ a✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.WithBot | {
"line": 688,
"column": 63
} | {
"line": 688,
"column": 74
} | {
"line": 688,
"column": 75
} | [
{
"pp": "case coe.coe.coe\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\na b : α\ninst✝ : SemilatticeInf α\na✝² a✝¹ a✝ : α\n⊢ a✝² ≤ a✝¹ → a✝² ≤ a✝ → a✝² ≤ a✝¹ ∧ a✝² ≤ a✝",
"ppTerm": "?coe.coe.coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case coe.coe.coe\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\na b : α\ninst✝ : SemilatticeInf α\na✝² a✝¹ a✝ : α\n⊢ a✝² ≤ a✝¹ → a✝² ≤ a✝ → a✝² ≤ a✝¹ ∧ a✝² ≤ a✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Floor.Semiring | {
"line": 63,
"column": 54
} | {
"line": 63,
"column": 65
} | {
"line": 63,
"column": 66
} | [
{
"pp": "R : Type u_1\ninst✝² : Semiring R\ninst✝¹ : LinearOrder R\ninst✝ : FloorSemiring R\na : R\n⊢ a < ↑⌊a⌋₊ + 1",
"ppTerm": "?m.15",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_1\ninst✝² : Semiring R\ninst✝¹ : LinearOrder R\ninst✝ : FloorSemiring R\na : R\n⊢ a < ↑⌊a⌋₊ + 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.WithBot | {
"line": 695,
"column": 63
} | {
"line": 695,
"column": 74
} | {
"line": 695,
"column": 75
} | [
{
"pp": "case coe.coe.coe\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\na b : α\ninst✝ : SemilatticeSup α\na✝² a✝¹ a✝ : α\n⊢ a✝² ≤ a✝ → a✝¹ ≤ a✝ → a✝² ≤ a✝ ∧ a✝¹ ≤ a✝",
"ppTerm": "?coe.coe.coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case coe.coe.coe\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\na b : α\ninst✝ : SemilatticeSup α\na✝² a✝¹ a✝ : α\n⊢ a✝² ≤ a✝ → a✝¹ ≤ a✝ → a✝² ≤ a✝ ∧ a✝¹ ≤ a✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.WithBot | {
"line": 713,
"column": 4
} | {
"line": 713,
"column": 38
} | {
"line": 713,
"column": 39
} | [
{
"pp": "case coe.coe.coe\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\na b : α\ninst✝ : DistribLattice α\na✝² a✝¹ a✝ : α\n⊢ (a✝² ⊔ a✝¹) ⊓ (a✝² ⊔ a✝) ≤ a✝² ⊔ a✝¹ ⊓ a✝",
"ppTerm": "?coe.coe.coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case coe.coe.coe\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\na b : α\ninst✝ : DistribLattice α\na✝² a✝¹ a✝ : α\n⊢ (a✝² ⊔ a✝¹) ⊓ (a✝² ⊔ a✝) ≤ a✝² ⊔ a✝¹ ⊓ a✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Canonical | {
"line": 428,
"column": 63
} | {
"line": 428,
"column": 74
} | {
"line": 428,
"column": 75
} | [
{
"pp": "case coe.coe.coe\nα : Type u_1\nβ : Type u_2\ninst✝ : SemilatticeSup α\na✝² a✝¹ a✝ : α\n⊢ a✝² ≤ a✝ → a✝¹ ≤ a✝ → a✝² ≤ a✝ ∧ a✝¹ ≤ a✝",
"ppTerm": "?coe.coe.coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case coe.coe.coe\nα : Type u_1\nβ : Type u_2\ninst✝ : SemilatticeSup α\na✝² a✝¹ a✝ : α\n⊢ a✝² ≤ a✝ → a✝¹ ≤ a✝ → a✝² ≤ a✝ ∧ a✝¹ ≤ a✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.WithBot | {
"line": 719,
"column": 4
} | {
"line": 719,
"column": 38
} | {
"line": 719,
"column": 39
} | [
{
"pp": "case coe.coe.coe\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\na b : α\ninst✝ : DistribLattice α\na✝² a✝¹ a✝ : α\n⊢ (a✝² ⊔ a✝¹) ⊓ (a✝² ⊔ a✝) ≤ a✝² ⊔ a✝¹ ⊓ a✝",
"ppTerm": "?coe.coe.coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case coe.coe.coe\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\na b : α\ninst✝ : DistribLattice α\na✝² a✝¹ a✝ : α\n⊢ (a✝² ⊔ a✝¹) ⊓ (a✝² ⊔ a✝) ≤ a✝² ⊔ a✝¹ ⊓ a✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Canonical | {
"line": 437,
"column": 63
} | {
"line": 437,
"column": 74
} | {
"line": 437,
"column": 75
} | [
{
"pp": "case coe.coe.coe\nα : Type u_1\nβ : Type u_2\ninst✝ : SemilatticeInf α\na✝² a✝¹ a✝ : α\n⊢ a✝² ≤ a✝¹ → a✝² ≤ a✝ → a✝² ≤ a✝¹ ∧ a✝² ≤ a✝",
"ppTerm": "?coe.coe.coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case coe.coe.coe\nα : Type u_1\nβ : Type u_2\ninst✝ : SemilatticeInf α\na✝² a✝¹ a✝ : α\n⊢ a✝² ≤ a✝¹ → a✝² ≤ a✝ → a✝² ≤ a✝¹ ∧ a✝² ≤ a✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.WithBot | {
"line": 738,
"column": 48
} | {
"line": 738,
"column": 59
} | {
"line": 738,
"column": 60
} | [
{
"pp": "case coe.coe\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\na b : α\ninst✝¹ : LE α\ninst✝ : Std.Total fun x1 x2 ↦ x1 ≤ x2\na✝¹ a✝ : α\n⊢ a✝¹ ≤ a✝ ∨ a✝ ≤ a✝¹",
"ppTerm": "?coe.coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case coe.coe\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\na b : α\ninst✝¹ : LE α\ninst✝ : Std.Total fun x1 x2 ↦ x1 ≤ x2\na✝¹ a✝ : α\n⊢ a✝¹ ≤ a✝ ∨ a✝ ≤ a✝¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.WithBot | {
"line": 742,
"column": 48
} | {
"line": 742,
"column": 59
} | {
"line": 742,
"column": 60
} | [
{
"pp": "case coe.coe\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\na b : α\ninst✝¹ : LE α\ninst✝ : Std.Total fun x1 x2 ↦ x1 ≤ x2\na✝¹ a✝ : α\n⊢ a✝¹ ≤ a✝ ∨ a✝ ≤ a✝¹",
"ppTerm": "?coe.coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case coe.coe\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\na b : α\ninst✝¹ : LE α\ninst✝ : Std.Total fun x1 x2 ↦ x1 ≤ x2\na✝¹ a✝ : α\n⊢ a✝¹ ≤ a✝ ∨ a✝ ≤ a✝¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Canonical | {
"line": 460,
"column": 48
} | {
"line": 460,
"column": 59
} | {
"line": 460,
"column": 60
} | [
{
"pp": "case coe.coe\nα : Type u_1\nβ : Type u_2\ninst✝¹ : Preorder α\ninst✝ : Std.Total fun x1 x2 ↦ x1 ≤ x2\na✝¹ a✝ : α\n⊢ a✝¹ ≤ a✝ ∨ a✝ ≤ a✝¹",
"ppTerm": "?coe.coe",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case coe.coe\nα : Type u_1\nβ : Type u_2\ninst✝¹ : Preorder α\ninst✝ : Std.Total fun x1 x2 ↦ x1 ≤ x2\na✝¹ a✝ : α\n⊢ a✝¹ ≤ a✝ ∨ a✝ ≤ a✝¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Canonical | {
"line": 503,
"column": 39
} | {
"line": 503,
"column": 61
} | {
"line": 503,
"column": 62
} | [
{
"pp": "α : Type u_1\ninst✝² : AddCommMonoid α\ninst✝¹ : PartialOrder α\ninst✝ : IsOrderedAddMonoid α\nzero_le : ∀ (a : α), 0 ≤ a\nthis : AddLeftMono (WithZero α)\n⊢ ∀ (a b : WithZero α), a ≤ b → ∀ (c : WithZero α), c + a ≤ c + b",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Eq.m... | [
"α : Type u_1\ninst✝² : AddCommMonoid α\ninst✝¹ : PartialOrder α\ninst✝ : IsOrderedAddMonoid α\nzero_le : ∀ (a : α), 0 ≤ a\nthis : AddLeftMono (WithZero α)\n⊢ ∀ (a b : WithZero α), a ≤ b → ∀ (c : WithZero α), a + c ≤ b + c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.WithBot | {
"line": 773,
"column": 28
} | {
"line": 773,
"column": 39
} | {
"line": 773,
"column": 40
} | [
{
"pp": "α : Type u_1\ninst✝¹ : LT α\ninst✝ : NoMinOrder α\nh : DenselyOrdered (WithBot α)\na b : α\nhab : a < b\nc : α\nhc : ↑a < ↑c ∧ ↑c < ↑b\n⊢ a < c ∧ c < b",
"ppTerm": "?m.65",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝¹ : LT α\ninst✝ : NoMinOrder α\nh : DenselyOrdered (WithBot α)\na b : α\nhab : a < b\nc : α\nhc : ↑a < ↑c ∧ ↑c < ↑b\n⊢ a < c ∧ c < b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Canonical | {
"line": 548,
"column": 39
} | {
"line": 548,
"column": 61
} | {
"line": 548,
"column": 62
} | [
{
"pp": "G : Type u_3\ninst✝¹ : Preorder G\na : G\ninst✝ : AddGroup G\nx : Multiplicative G\n⊢ (↑x).log ≤ a ↔ ↑x ≤ exp a",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Equiv.instEquivLike",
"congrArg",
"Preorder.toLE",
"WithZero.log",
"id",
... | [
"G : Type u_3\ninst✝¹ : Preorder G\na : G\ninst✝ : AddGroup G\nx : Multiplicative G\n⊢ Multiplicative.toAdd x ≤ a ↔ x ≤ Multiplicative.ofAdd a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Canonical | {
"line": 551,
"column": 39
} | {
"line": 551,
"column": 61
} | {
"line": 551,
"column": 62
} | [
{
"pp": "G : Type u_3\ninst✝¹ : Preorder G\na : G\ninst✝ : AddGroup G\nx : Multiplicative G\n⊢ (↑x).log < a ↔ ↑x < exp a",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Equiv.instEquivLike",
"congrArg",
"WithZero.coe_lt_coe._simp_1"... | [
"G : Type u_3\ninst✝¹ : Preorder G\na : G\ninst✝ : AddGroup G\nx : Multiplicative G\n⊢ Multiplicative.toAdd x < a ↔ x < Multiplicative.ofAdd a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.WithBot | {
"line": 774,
"column": 4
} | {
"line": 774,
"column": 59
} | {
"line": 774,
"column": 60
} | [
{
"pp": "case mpr\nα : Type u_1\ninst✝¹ : LT α\ninst✝ : NoMinOrder α\nh : DenselyOrdered α\n⊢ ∀ (a₁ a₂ : WithBot α), a₁ < a₂ → ∃ a, a₁ < a ∧ a < a₂",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"WithBot.some",
"WithBot",
"WithBot.instLT",
... | [
"case mpr\nα : Type u_1\ninst✝¹ : LT α\ninst✝ : NoMinOrder α\nh : DenselyOrdered α\n⊢ ∀ (x x_1 : α), x < x_1 → ∃ x_2, x < x_2 ∧ x_2 < x_1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Canonical | {
"line": 554,
"column": 39
} | {
"line": 554,
"column": 61
} | {
"line": 554,
"column": 62
} | [
{
"pp": "G : Type u_3\ninst✝¹ : Preorder G\na : G\ninst✝ : AddGroup G\nx : Multiplicative G\n⊢ a ≤ (↑x).log ↔ exp a ≤ ↑x",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Equiv.instEquivLike",
"congrArg",
"Preorder.toLE",
"WithZero.log",
"id",
... | [
"G : Type u_3\ninst✝¹ : Preorder G\na : G\ninst✝ : AddGroup G\nx : Multiplicative G\n⊢ a ≤ Multiplicative.toAdd x ↔ Multiplicative.ofAdd a ≤ x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.GroupWithZero.Canonical | {
"line": 557,
"column": 39
} | {
"line": 557,
"column": 61
} | {
"line": 557,
"column": 62
} | [
{
"pp": "G : Type u_3\ninst✝¹ : Preorder G\na : G\ninst✝ : AddGroup G\nx : Multiplicative G\n⊢ a < (↑x).log ↔ exp a < ↑x",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Equiv.instEquivLike",
"congrArg",
"WithZero.coe_lt_coe._simp_1"... | [
"G : Type u_3\ninst✝¹ : Preorder G\na : G\ninst✝ : AddGroup G\nx : Multiplicative G\n⊢ a < Multiplicative.toAdd x ↔ Multiplicative.ofAdd a < x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Floor.Semiring | {
"line": 321,
"column": 27
} | {
"line": 328,
"column": 58
} | {
"line": 330,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝⁶ : Semiring R\ninst✝⁵ : LinearOrder R\ninst✝⁴ : FloorSemiring R\ninst✝³ : IsStrictOrderedRing R\ninst✝² : Sub R\ninst✝¹ : OrderedSub R\ninst✝ : ExistsAddOfLE R\na : R\nn : ℕ\n⊢ ⌊a - ↑n⌋₊ = ⌊a⌋₊ - n",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Eq.mpr",... | [] | by
obtain ha | ha := le_total a 0
· rw [floor_of_nonpos ha, floor_of_nonpos (tsub_nonpos_of_le (ha.trans n.cast_nonneg)), zero_tsub]
rcases le_total a n with h | h
· rw [floor_of_nonpos (tsub_nonpos_of_le h), eq_comm, tsub_eq_zero_iff_le]
exact Nat.cast_le.1 ((Nat.floor_le ha).trans h)
· rw [eq_tsub_iff_a... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.WithBot | {
"line": 784,
"column": 28
} | {
"line": 784,
"column": 39
} | {
"line": 784,
"column": 40
} | [
{
"pp": "α : Type u_1\ninst✝¹ : LT α\ninst✝ : NoMaxOrder α\nh : DenselyOrdered (WithTop α)\na b : α\nhab : a < b\nc : α\nhc : ↑a < ↑c ∧ ↑c < ↑b\n⊢ a < c ∧ c < b",
"ppTerm": "?m.65",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝¹ : LT α\ninst✝ : NoMaxOrder α\nh : DenselyOrdered (WithTop α)\na b : α\nhab : a < b\nc : α\nhc : ↑a < ↑c ∧ ↑c < ↑b\n⊢ a < c ∧ c < b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.WithBot | {
"line": 785,
"column": 4
} | {
"line": 785,
"column": 59
} | {
"line": 785,
"column": 60
} | [
{
"pp": "case mpr\nα : Type u_1\ninst✝¹ : LT α\ninst✝ : NoMaxOrder α\nh : DenselyOrdered α\n⊢ ∀ (a₁ a₂ : WithTop α), a₁ < a₂ → ∃ a, a₁ < a ∧ a < a₂",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"WithTop.not_top_lt._simp_1",
"_private.Mathlib.Order.WithBot.0.WithTop.denselyOrde... | [
"case mpr\nα : Type u_1\ninst✝¹ : LT α\ninst✝ : NoMaxOrder α\nh : DenselyOrdered α\n⊢ ∀ (x x_1 : α), x < x_1 → ∃ x_2, x < x_2 ∧ x_2 < x_1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Floor.Semiring | {
"line": 374,
"column": 63
} | {
"line": 374,
"column": 74
} | {
"line": 374,
"column": 75
} | [
{
"pp": "R : Type u_1\ninst✝⁶ : Semiring R\ninst✝⁵ : LinearOrder R\ninst✝⁴ : FloorSemiring R\ninst✝³ : IsStrictOrderedRing R\ninst✝² : Sub R\ninst✝¹ : OrderedSub R\ninst✝ : ExistsAddOfLE R\na : R\n⊢ ⌈a - 1⌉₊ = ⌈a⌉₊ - 1",
"ppTerm": "?m.31",
"assigned": false,
"usedConstants": [],
"usedFVars": [],... | [
"R : Type u_1\ninst✝⁶ : Semiring R\ninst✝⁵ : LinearOrder R\ninst✝⁴ : FloorSemiring R\ninst✝³ : IsStrictOrderedRing R\ninst✝² : Sub R\ninst✝¹ : OrderedSub R\ninst✝ : ExistsAddOfLE R\na : R\n⊢ ⌈a - 1⌉₊ = ⌈a⌉₊ - 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Floor.Semiring | {
"line": 397,
"column": 4
} | {
"line": 397,
"column": 15
} | {
"line": 397,
"column": 16
} | [
{
"pp": "case refine_1\nR : Type u_1\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : IsStrictOrderedRing R\ninst✝ : FloorSemiring R\na : R\nha : 0 ≤ a\n⊢ -1 ≤ a - ↑⌊a⌋₊",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"AddGroupWithOne... | [
"case refine_1\nR : Type u_1\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : IsStrictOrderedRing R\ninst✝ : FloorSemiring R\na : R\nha : 0 ≤ a\n⊢ ↑⌊a⌋₊ ≤ a + 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Floor.Semiring | {
"line": 398,
"column": 4
} | {
"line": 398,
"column": 26
} | {
"line": 398,
"column": 27
} | [
{
"pp": "case refine_2\nR : Type u_1\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : IsStrictOrderedRing R\ninst✝ : FloorSemiring R\na : R\nha : 0 ≤ a\n⊢ a - ↑⌊a⌋₊ ≤ 1",
"ppTerm": "?refine_2",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"AddGroupWithOne.toAddGroup",
"congrArg... | [
"case refine_2\nR : Type u_1\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : IsStrictOrderedRing R\ninst✝ : FloorSemiring R\na : R\nha : 0 ≤ a\n⊢ a ≤ ↑⌊a⌋₊ + 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Floor.Semiring | {
"line": 405,
"column": 4
} | {
"line": 405,
"column": 15
} | {
"line": 405,
"column": 16
} | [
{
"pp": "case refine_1\nR : Type u_1\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : IsStrictOrderedRing R\ninst✝ : FloorSemiring R\na : R\nha : 0 ≤ a\n⊢ -1 ≤ a - ↑⌈a⌉₊",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"AddGroupWithOne... | [
"case refine_1\nR : Type u_1\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : IsStrictOrderedRing R\ninst✝ : FloorSemiring R\na : R\nha : 0 ≤ a\n⊢ ↑⌈a⌉₊ ≤ a + 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Floor.Semiring | {
"line": 406,
"column": 4
} | {
"line": 406,
"column": 15
} | {
"line": 406,
"column": 16
} | [
{
"pp": "case refine_2\nR : Type u_1\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : IsStrictOrderedRing R\ninst✝ : FloorSemiring R\na : R\nha : 0 ≤ a\n⊢ a - ↑⌈a⌉₊ ≤ 1",
"ppTerm": "?refine_2",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"AddGroupWithOne.toAddGroup",
"covarian... | [
"case refine_2\nR : Type u_1\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : IsStrictOrderedRing R\ninst✝ : FloorSemiring R\na : R\nha : 0 ≤ a\n⊢ a ≤ 1 + ↑⌈a⌉₊"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Floor.Semiring | {
"line": 418,
"column": 32
} | {
"line": 418,
"column": 60
} | {
"line": 418,
"column": 61
} | [
{
"pp": "R : Type u_1\ninst✝⁷ : Semiring R\ninst✝⁶ : LinearOrder R\ninst✝⁵ : FloorSemiring R\na : R\nS : Type u_3\ninst✝⁴ : Semiring S\ninst✝³ : LinearOrder S\ninst✝² : FloorSemiring S\nb : S\ninst✝¹ : IsStrictOrderedRing R\ninst✝ : IsStrictOrderedRing S\nh : ∀ (n : ℕ), ↑n ≤ a ↔ ↑n ≤ b\n⊢ 0 ≤ a ↔ 0 ≤ b",
"p... | [
"R : Type u_1\ninst✝⁷ : Semiring R\ninst✝⁶ : LinearOrder R\ninst✝⁵ : FloorSemiring R\na : R\nS : Type u_3\ninst✝⁴ : Semiring S\ninst✝³ : LinearOrder S\ninst✝² : FloorSemiring S\nb : S\ninst✝¹ : IsStrictOrderedRing R\ninst✝ : IsStrictOrderedRing S\nh : ∀ (n : ℕ), ↑n ≤ a ↔ ↑n ≤ b\n⊢ 0 ≤ a ↔ 0 ≤ b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Invertible.Defs | {
"line": 246,
"column": 15
} | {
"line": 246,
"column": 26
} | {
"line": 246,
"column": 27
} | [
{
"pp": "α : Type u\ninst✝¹ : Monoid α\na b c : α\ninst✝ : Invertible c\nh : a * c = b * c\n⊢ a = b",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\ninst✝¹ : Monoid α\na b c : α\ninst✝ : Invertible c\nh : a * c = b * c\n⊢ a = b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Invertible.Defs | {
"line": 250,
"column": 15
} | {
"line": 250,
"column": 26
} | {
"line": 250,
"column": 27
} | [
{
"pp": "α : Type u\ninst✝¹ : Monoid α\na b c : α\ninst✝ : Invertible c\nh : c * a = c * b\n⊢ a = b",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\ninst✝¹ : Monoid α\na b c : α\ninst✝ : Invertible c\nh : c * a = c * b\n⊢ a = b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Invertible | {
"line": 101,
"column": 44
} | {
"line": 101,
"column": 55
} | {
"line": 101,
"column": 56
} | [
{
"pp": "R : Type u_1\ninst✝² : Ring R\na b : R\ninst✝¹ : Invertible a\ninst✝ : Invertible b\nh : -a = a * (⅟a * b + ⅟b * a)\n⊢ -1 = ⅟a * b + ⅟b * a",
"ppTerm": "?m.191",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_1\ninst✝² : Ring R\na b : R\ninst✝¹ : Invertible a\ninst✝ : Invertible b\nh : -a = a * (⅟a * b + ⅟b * a)\n⊢ -1 = ⅟a * b + ⅟b * a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Divisibility.Basic | {
"line": 123,
"column": 2
} | {
"line": 123,
"column": 37
} | {
"line": 123,
"column": 38
} | [
{
"pp": "α : Type u_1\ninst✝ : NonUnitalRing α\na b c : α\nh₁ : a ∣ b\nh₂ : a ∣ c\n⊢ a ∣ b - c",
"ppTerm": "?m.11",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝ : NonUnitalRing α\na b c : α\nh₁ : a ∣ b\nh₂ : a ∣ c\n⊢ a ∣ b - c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Divisibility.Basic | {
"line": 130,
"column": 15
} | {
"line": 130,
"column": 54
} | {
"line": 130,
"column": 55
} | [
{
"pp": "α : Type u_1\ninst✝ : NonUnitalRing α\na b c : α\nh : a ∣ c\nH : a ∣ b + c\n⊢ a ∣ b",
"ppTerm": "?m.14",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝ : NonUnitalRing α\na b c : α\nh : a ∣ c\nH : a ∣ b + c\n⊢ a ∣ b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Ring.Divisibility.Basic | {
"line": 139,
"column": 2
} | {
"line": 139,
"column": 37
} | {
"line": 139,
"column": 38
} | [
{
"pp": "α : Type u_1\ninst✝ : NonUnitalRing α\na b c : α\nh : a ∣ c\n⊢ a ∣ b - c ↔ a ∣ b",
"ppTerm": "?m.11",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝ : NonUnitalRing α\na b c : α\nh : a ∣ c\n⊢ a ∣ b - c ↔ a ∣ b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Field.Basic | {
"line": 55,
"column": 2
} | {
"line": 55,
"column": 28
} | {
"line": 55,
"column": 29
} | [
{
"pp": "K : Type u_1\ninst✝ : DivisionSemiring K\na b : K\nha : a ≠ 0\nhb : b ≠ 0\n⊢ 1 / a * (a + b) * (1 / b) = 1 / a + 1 / b",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"DivInvMonoid.toInv",
"instHDiv",
... | [
"K : Type u_1\ninst✝ : DivisionSemiring K\na b : K\nha : a ≠ 0\nhb : b ≠ 0\n⊢ a⁻¹ * (a + b) * b⁻¹ = a⁻¹ + b⁻¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Basic | {
"line": 51,
"column": 12
} | {
"line": 51,
"column": 26
} | {
"line": 51,
"column": 27
} | [
{
"pp": "R : Type u_3\ninst✝² : Semiring R\ninst✝¹ : PartialOrder R\ninst✝ : IsOrderedRing R\nx y : R\nhx : 0 ≤ x\nhy : 0 ≤ y\nk : ℕ\nih : k + 1 ≠ 0 → x ^ (k + 1) + y ^ (k + 1) ≤ (x + y) ^ (k + 1)\nhn : k + 1 + 1 ≠ 0\nn : ℕ := k.succ\nh1 : 0 ≤ x * y ^ n + y * x ^ n\nh2 : 0 ≤ x + y\n⊢ x ^ (n + 1) + y ^ (n + 1) ≤... | [
"R : Type u_3\ninst✝² : Semiring R\ninst✝¹ : PartialOrder R\ninst✝ : IsOrderedRing R\nx y : R\nhx : 0 ≤ x\nhy : 0 ≤ y\nk : ℕ\nih : k + 1 ≠ 0 → x ^ (k + 1) + y ^ (k + 1) ≤ (x + y) ^ (k + 1)\nhn : k + 1 + 1 ≠ 0\nn : ℕ := k.succ\nh1 : 0 ≤ x * y ^ n + y * x ^ n\nh2 : 0 ≤ x + y\n⊢ x * x ^ n + y ^ (n + 1) ≤ x * x ^ n + y... | pow_succ' _ n, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Field.Basic | {
"line": 101,
"column": 2
} | {
"line": 101,
"column": 40
} | {
"line": 101,
"column": 41
} | [
{
"pp": "K : Type u_1\ninst✝ : DivisionRing K\na b : K\nh : b ≠ 0\n⊢ (b - a) / b = 1 - a / b",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHDiv",
"GroupWithZero.toDivisionMonoid",
"InvOneClass.toOne",
"GroupWithZero.toDivInvMonoid",
"Div... | [
"K : Type u_1\ninst✝ : DivisionRing K\na b : K\nh : b ≠ 0\n⊢ (b - a) / b = b / b - a / b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Field.Basic | {
"line": 107,
"column": 2
} | {
"line": 107,
"column": 40
} | {
"line": 107,
"column": 41
} | [
{
"pp": "K : Type u_1\ninst✝ : DivisionRing K\na b : K\nh : b ≠ 0\n⊢ (a - b) / b = a / b - 1",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHDiv",
"GroupWithZero.toDivisionMonoid",
"InvOneClass.toOne",
"GroupWithZero.toDivInvMonoid",
"Div... | [
"K : Type u_1\ninst✝ : DivisionRing K\na b : K\nh : b ≠ 0\n⊢ (a - b) / b = a / b - b / b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Field.Basic | {
"line": 121,
"column": 2
} | {
"line": 121,
"column": 28
} | {
"line": 121,
"column": 29
} | [
{
"pp": "K : Type u_1\ninst✝ : DivisionRing K\na b : K\nha : a ≠ 0\nhb : b ≠ 0\n⊢ 1 / a * (b - a) * (1 / b) = 1 / a - 1 / b",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"instHDiv",
"HMul.hMul",
"AddGroupWithOne.toAddGroup",
... | [
"K : Type u_1\ninst✝ : DivisionRing K\na b : K\nha : a ≠ 0\nhb : b ≠ 0\n⊢ a⁻¹ * (b - a) * b⁻¹ = a⁻¹ - b⁻¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Field.Basic | {
"line": 137,
"column": 2
} | {
"line": 137,
"column": 55
} | {
"line": 137,
"column": 56
} | [
{
"pp": "K : Type u_1\ninst✝ : DivisionRing K\na b c d : K\nhbc : Commute b c\nhbd : Commute b d\nhb : b ≠ 0\nhd : d ≠ 0\n⊢ a / b - c / d = (a * d - b * c) / (b * d)",
"ppTerm": "?m.44",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"K : Type u_1\ninst✝ : DivisionRing K\na b c d : K\nhbc : Commute b c\nhbd : Commute b d\nhb : b ≠ 0\nhd : d ≠ 0\n⊢ a / b - c / d = (a * d - b * c) / (b * d)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Field.Basic | {
"line": 191,
"column": 2
} | {
"line": 191,
"column": 13
} | {
"line": 191,
"column": 14
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\na b c : K\nhc : c ≠ 0\n⊢ b - a / c = (b * c - a) / c",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"K : Type u_1\ninst✝ : Field K\na b c : K\nhc : c ≠ 0\n⊢ b - a / c = (b * c - a) / c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Field.Basic | {
"line": 194,
"column": 2
} | {
"line": 194,
"column": 13
} | {
"line": 194,
"column": 14
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\na b c : K\nhc : c ≠ 0\n⊢ a / c - b = (a - c * b) / c",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Eq.mpr",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocComm... | [
"K : Type u_1\ninst✝ : Field K\na b c : K\nhc : c ≠ 0\n⊢ a / c - b = (a - b * c) / c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Int.Units | {
"line": 70,
"column": 4
} | {
"line": 70,
"column": 29
} | {
"line": 70,
"column": 30
} | [
{
"pp": "case inr\nv : ℤ\nh : -1 * v = -1\n⊢ -1 = 1 ∧ v = -1 ∨ -1 = -1 ∧ v = 1",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"Int.ctorIdx",
"congrArg",
"False.elim",
"false_and",
"noConfusion_of_Nat",
"id",
"Int.inst... | [
"case inr\nv : ℤ\nh : -1 * v = -1\n⊢ v = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Basic | {
"line": 157,
"column": 72
} | {
"line": 157,
"column": 83
} | {
"line": 157,
"column": 84
} | [
{
"pp": "R : Type u_3\ninst✝³ : Semiring R\ninst✝² : LinearOrder R\ninst✝¹ : IsStrictOrderedRing R\na : R\ninst✝ : ExistsAddOfLE R\nk : ℕ\nh₀ : k + k ≠ 0\n⊢ k ≠ 0",
"ppTerm": "?m.60",
"assigned": true,
"usedConstants": [
"id",
"Ne",
"instOfNatNat",
"Nat",
"OfNat.ofNat"
... | [
"R : Type u_3\ninst✝³ : Semiring R\ninst✝² : LinearOrder R\ninst✝¹ : IsStrictOrderedRing R\na : R\ninst✝ : ExistsAddOfLE R\nk : ℕ\nh₀ : k + k ≠ 0\n⊢ ¬k = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Abs | {
"line": 81,
"column": 53
} | {
"line": 81,
"column": 74
} | {
"line": 81,
"column": 75
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Ring α\ninst✝ : LinearOrder α\na : α\n⊢ |a| ^ 2 = a ^ 2",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"Monoid.toMulOneClass",
"AddGroupWithOne.toAddGroup",
"abs",
"congrArg",
"DistribLattice.... | [
"α : Type u_1\ninst✝¹ : Ring α\ninst✝ : LinearOrder α\na : α\n⊢ |a| * |a| = a * a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Abs | {
"line": 83,
"column": 45
} | {
"line": 83,
"column": 66
} | {
"line": 83,
"column": 67
} | [
{
"pp": "α : Type u_1\ninst✝² : Ring α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedRing α\nx : α\n⊢ |x ^ 2| = x ^ 2",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"Monoid.toMulOneClass",
"AddGroupWithOne.toAddGroup",
"abs",
"congrAr... | [
"α : Type u_1\ninst✝² : Ring α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedRing α\nx : α\n⊢ |x * x| = x * x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Abs | {
"line": 111,
"column": 2
} | {
"line": 111,
"column": 37
} | {
"line": 111,
"column": 38
} | [
{
"pp": "α : Type u_1\ninst✝² : Ring α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na : α\n⊢ |a| ≤ 1 ↔ a * a ≤ 1",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝² : Ring α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na : α\n⊢ |a| ≤ 1 ↔ a * a ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Abs | {
"line": 114,
"column": 2
} | {
"line": 114,
"column": 27
} | {
"line": 114,
"column": 28
} | [
{
"pp": "α : Type u_1\ninst✝² : Ring α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na b : α\n⊢ a ^ 2 < b ^ 2 ↔ |a| < |b|",
"ppTerm": "?m.35",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝² : Ring α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na b : α\n⊢ a ^ 2 < b ^ 2 ↔ |a| < |b|"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Abs | {
"line": 120,
"column": 2
} | {
"line": 120,
"column": 27
} | {
"line": 120,
"column": 28
} | [
{
"pp": "α : Type u_1\ninst✝² : Ring α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na b : α\n⊢ a ^ 2 ≤ b ^ 2 ↔ |a| ≤ |b|",
"ppTerm": "?m.35",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝² : Ring α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na b : α\n⊢ a ^ 2 ≤ b ^ 2 ↔ |a| ≤ |b|"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Abs | {
"line": 144,
"column": 2
} | {
"line": 144,
"column": 37
} | {
"line": 144,
"column": 38
} | [
{
"pp": "α : Type u_1\ninst✝² : Ring α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na : α\n⊢ a ^ 2 ≤ 1 ↔ |a| ≤ 1",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝² : Ring α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na : α\n⊢ a ^ 2 ≤ 1 ↔ |a| ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Abs | {
"line": 147,
"column": 2
} | {
"line": 147,
"column": 37
} | {
"line": 147,
"column": 38
} | [
{
"pp": "α : Type u_1\ninst✝² : Ring α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na : α\n⊢ a ^ 2 < 1 ↔ |a| < 1",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝² : Ring α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na : α\n⊢ a ^ 2 < 1 ↔ |a| < 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Abs | {
"line": 150,
"column": 2
} | {
"line": 150,
"column": 37
} | {
"line": 150,
"column": 38
} | [
{
"pp": "α : Type u_1\ninst✝² : Ring α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na : α\n⊢ 1 ≤ a ^ 2 ↔ 1 ≤ |a|",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝² : Ring α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na : α\n⊢ 1 ≤ a ^ 2 ↔ 1 ≤ |a|"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Abs | {
"line": 153,
"column": 2
} | {
"line": 153,
"column": 37
} | {
"line": 153,
"column": 38
} | [
{
"pp": "α : Type u_1\ninst✝² : Ring α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na : α\n⊢ 1 < a ^ 2 ↔ 1 < |a|",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝² : Ring α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na : α\n⊢ 1 < a ^ 2 ↔ 1 < |a|"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Ring.Abs | {
"line": 173,
"column": 98
} | {
"line": 180,
"column": 61
} | {
"line": 182,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : CommRing α\ninst✝¹ : LinearOrder α\na b : α\nn : ℕ\ninst✝ : IsOrderedRing α\n⊢ |geomSum a b n| ≤ (↑n + 1) * max |a| |b| ^ n",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"NonUnitalNonAssocCommRing.toNonUnitalNonA... | [] | by
induction n with | zero => simp [geomSum] | succ n ih => ?_
refine (abs_add_le ..).trans ?_
rw [abs_mul, abs_pow, Nat.cast_succ, add_one_mul]
refine add_le_add ?_ (pow_le_pow_left₀ (abs_nonneg _) le_sup_right _)
rw [pow_succ, ← mul_assoc, mul_comm |a|]
gcongr
exacts [abs_nonneg _, (abs_nonneg _).trans ... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Order.Ring.Abs | {
"line": 245,
"column": 31
} | {
"line": 245,
"column": 70
} | {
"line": 245,
"column": 71
} | [
{
"pp": "R : Type u_2\ninst✝² : Ring R\ninst✝¹ : LinearOrder R\ninst✝ : IsStrictOrderedRing R\na b : R\nn : ℕ\nhb : b ≠ 0\nhe : Even n\nthis : a ^ n > -b ^ n\n⊢ a ^ n = -b ^ n ↔ a = -b ∧ Odd n",
"ppTerm": "?m.50",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Eq.mpr",
"NegZeroCl... | [
"R : Type u_2\ninst✝² : Ring R\ninst✝¹ : LinearOrder R\ninst✝ : IsStrictOrderedRing R\na b : R\nn : ℕ\nhb : b ≠ 0\nhe : Even n\nthis : a ^ n > -b ^ n\n⊢ ¬a ^ n = -b ^ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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