module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Data.Bool.Basic | {
"line": 152,
"column": 16
} | {
"line": 152,
"column": 22
} | {
"line": 154,
"column": 0
} | [
{
"pp": "⊢ ∀ (a b : Bool), min a b = if a ≤ b then a else b",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"Bool.instMin",
"of_decide_eq_true",
"inferInstance",
"id",
"instDecidableEqBool",
"LE.le",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Bool.Basic | {
"line": 152,
"column": 16
} | {
"line": 152,
"column": 22
} | {
"line": 154,
"column": 0
} | [
{
"pp": "⊢ ∀ (a b : Bool), min a b = if a ≤ b then a else b",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"Bool.instMin",
"of_decide_eq_true",
"inferInstance",
"id",
"instDecidableEqBool",
"LE.le",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Bool.Basic | {
"line": 151,
"column": 16
} | {
"line": 151,
"column": 22
} | {
"line": 152,
"column": 2
} | [
{
"pp": "⊢ ∀ (a b : Bool), max a b = if a ≤ b then b else a",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"inferInstance",
"id",
"instDecidableEqBool",
"LE.le",
"Bool.true",
"B... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Bool.Basic | {
"line": 151,
"column": 16
} | {
"line": 151,
"column": 22
} | {
"line": 152,
"column": 2
} | [
{
"pp": "⊢ ∀ (a b : Bool), max a b = if a ≤ b then b else a",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"inferInstance",
"id",
"instDecidableEqBool",
"LE.le",
"Bool.true",
"B... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Bool.Basic | {
"line": 151,
"column": 16
} | {
"line": 151,
"column": 22
} | {
"line": 152,
"column": 2
} | [
{
"pp": "⊢ ∀ (a b : Bool), max a b = if a ≤ b then b else a",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"inferInstance",
"id",
"instDecidableEqBool",
"LE.le",
"Bool.true",
"B... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Bool.Basic | {
"line": 154,
"column": 68
} | {
"line": 154,
"column": 74
} | {
"line": 156,
"column": 0
} | [
{
"pp": "⊢ ∀ {x y : Bool}, x < y ↔ x = false ∧ y = true",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"Bool.instLT",
"Bool.true",
"Bool.instDecidableLt",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Bool.Basic | {
"line": 154,
"column": 68
} | {
"line": 154,
"column": 74
} | {
"line": 156,
"column": 0
} | [
{
"pp": "⊢ ∀ {x y : Bool}, x < y ↔ x = false ∧ y = true",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"Bool.instLT",
"Bool.true",
"Bool.instDecidableLt",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Bool.Basic | {
"line": 154,
"column": 68
} | {
"line": 154,
"column": 74
} | {
"line": 156,
"column": 0
} | [
{
"pp": "⊢ ∀ {x y : Bool}, x < y ↔ x = false ∧ y = true",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"Bool.instLT",
"Bool.true",
"Bool.instDecidableLt",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Bool.Basic | {
"line": 160,
"column": 57
} | {
"line": 160,
"column": 63
} | {
"line": 162,
"column": 0
} | [
{
"pp": "⊢ ∀ {x y : Bool}, x ≤ y ↔ x = true → y = true",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"forall_prop_decidable",
"LE.le",
"Bool.true",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Bool.Basic | {
"line": 160,
"column": 57
} | {
"line": 160,
"column": 63
} | {
"line": 162,
"column": 0
} | [
{
"pp": "⊢ ∀ {x y : Bool}, x ≤ y ↔ x = true → y = true",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"forall_prop_decidable",
"LE.le",
"Bool.true",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Bool.Basic | {
"line": 160,
"column": 57
} | {
"line": 160,
"column": 63
} | {
"line": 162,
"column": 0
} | [
{
"pp": "⊢ ∀ {x y : Bool}, x ≤ y ↔ x = true → y = true",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"forall_prop_decidable",
"LE.le",
"Bool.true",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Bool.Basic | {
"line": 162,
"column": 55
} | {
"line": 162,
"column": 61
} | {
"line": 164,
"column": 0
} | [
{
"pp": "⊢ ∀ (x y : Bool), (x && y) ≤ x",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"Bool.and",
"LE.le",
"Bool.true",
"Bool.instLE",
"Bool",
"Eq.refl",
"Bool... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Bool.Basic | {
"line": 162,
"column": 55
} | {
"line": 162,
"column": 61
} | {
"line": 164,
"column": 0
} | [
{
"pp": "⊢ ∀ (x y : Bool), (x && y) ≤ x",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"Bool.and",
"LE.le",
"Bool.true",
"Bool.instLE",
"Bool",
"Eq.refl",
"Bool... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Bool.Basic | {
"line": 162,
"column": 55
} | {
"line": 162,
"column": 61
} | {
"line": 164,
"column": 0
} | [
{
"pp": "⊢ ∀ (x y : Bool), (x && y) ≤ x",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"Bool.and",
"LE.le",
"Bool.true",
"Bool.instLE",
"Bool",
"Eq.refl",
"Bool... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Bool.Basic | {
"line": 164,
"column": 56
} | {
"line": 164,
"column": 62
} | {
"line": 166,
"column": 0
} | [
{
"pp": "⊢ ∀ (x y : Bool), (x && y) ≤ y",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"Bool.and",
"LE.le",
"Bool.true",
"Bool.instLE",
"Bool",
"Eq.refl",
"Bool... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Bool.Basic | {
"line": 164,
"column": 56
} | {
"line": 164,
"column": 62
} | {
"line": 166,
"column": 0
} | [
{
"pp": "⊢ ∀ (x y : Bool), (x && y) ≤ y",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"Bool.and",
"LE.le",
"Bool.true",
"Bool.instLE",
"Bool",
"Eq.refl",
"Bool... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Bool.Basic | {
"line": 164,
"column": 56
} | {
"line": 164,
"column": 62
} | {
"line": 166,
"column": 0
} | [
{
"pp": "⊢ ∀ (x y : Bool), (x && y) ≤ y",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"Bool.and",
"LE.le",
"Bool.true",
"Bool.instLE",
"Bool",
"Eq.refl",
"Bool... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Bool.Basic | {
"line": 166,
"column": 70
} | {
"line": 166,
"column": 76
} | {
"line": 168,
"column": 0
} | [
{
"pp": "⊢ ∀ {x y z : Bool}, x ≤ y → x ≤ z → x ≤ (y && z)",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"Bool.and",
"forall_prop_decidable",
"LE.le",
"Bool.true",
"Bool.in... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Bool.Basic | {
"line": 166,
"column": 70
} | {
"line": 166,
"column": 76
} | {
"line": 168,
"column": 0
} | [
{
"pp": "⊢ ∀ {x y z : Bool}, x ≤ y → x ≤ z → x ≤ (y && z)",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"Bool.and",
"forall_prop_decidable",
"LE.le",
"Bool.true",
"Bool.in... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Bool.Basic | {
"line": 166,
"column": 70
} | {
"line": 166,
"column": 76
} | {
"line": 168,
"column": 0
} | [
{
"pp": "⊢ ∀ {x y z : Bool}, x ≤ y → x ≤ z → x ≤ (y && z)",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"Bool.and",
"forall_prop_decidable",
"LE.le",
"Bool.true",
"Bool.in... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Bool.Basic | {
"line": 168,
"column": 54
} | {
"line": 168,
"column": 60
} | {
"line": 170,
"column": 0
} | [
{
"pp": "⊢ ∀ (x y : Bool), x ≤ (x || y)",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"LE.le",
"Bool.true",
"Bool.instLE",
"Bool",
"Bool.or",
"Eq.refl",
"Bool.... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Bool.Basic | {
"line": 168,
"column": 54
} | {
"line": 168,
"column": 60
} | {
"line": 170,
"column": 0
} | [
{
"pp": "⊢ ∀ (x y : Bool), x ≤ (x || y)",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"LE.le",
"Bool.true",
"Bool.instLE",
"Bool",
"Bool.or",
"Eq.refl",
"Bool.... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Bool.Basic | {
"line": 168,
"column": 54
} | {
"line": 168,
"column": 60
} | {
"line": 170,
"column": 0
} | [
{
"pp": "⊢ ∀ (x y : Bool), x ≤ (x || y)",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"LE.le",
"Bool.true",
"Bool.instLE",
"Bool",
"Bool.or",
"Eq.refl",
"Bool.... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Bool.Basic | {
"line": 170,
"column": 55
} | {
"line": 170,
"column": 61
} | {
"line": 172,
"column": 0
} | [
{
"pp": "⊢ ∀ (x y : Bool), y ≤ (x || y)",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"LE.le",
"Bool.true",
"Bool.instLE",
"Bool",
"Bool.or",
"Eq.refl",
"Bool.... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Bool.Basic | {
"line": 170,
"column": 55
} | {
"line": 170,
"column": 61
} | {
"line": 172,
"column": 0
} | [
{
"pp": "⊢ ∀ (x y : Bool), y ≤ (x || y)",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"LE.le",
"Bool.true",
"Bool.instLE",
"Bool",
"Bool.or",
"Eq.refl",
"Bool.... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Bool.Basic | {
"line": 170,
"column": 55
} | {
"line": 170,
"column": 61
} | {
"line": 172,
"column": 0
} | [
{
"pp": "⊢ ∀ (x y : Bool), y ≤ (x || y)",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"LE.le",
"Bool.true",
"Bool.instLE",
"Bool",
"Bool.or",
"Eq.refl",
"Bool.... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Bool.Basic | {
"line": 172,
"column": 62
} | {
"line": 172,
"column": 68
} | {
"line": 174,
"column": 0
} | [
{
"pp": "⊢ ∀ {x y z : Bool}, x ≤ z → y ≤ z → (x || y) ≤ z",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"forall_prop_decidable",
"LE.le",
"Bool.true",
"Bool.instLE",
"Boo... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Bool.Basic | {
"line": 172,
"column": 62
} | {
"line": 172,
"column": 68
} | {
"line": 174,
"column": 0
} | [
{
"pp": "⊢ ∀ {x y z : Bool}, x ≤ z → y ≤ z → (x || y) ≤ z",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"forall_prop_decidable",
"LE.le",
"Bool.true",
"Bool.instLE",
"Boo... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Bool.Basic | {
"line": 172,
"column": 62
} | {
"line": 172,
"column": 68
} | {
"line": 174,
"column": 0
} | [
{
"pp": "⊢ ∀ {x y z : Bool}, x ≤ z → y ≤ z → (x || y) ≤ z",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"forall_prop_decidable",
"LE.le",
"Bool.true",
"Bool.instLE",
"Boo... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Nat.Basic | {
"line": 93,
"column": 4
} | {
"line": 93,
"column": 24
} | {
"line": 95,
"column": 0
} | [
{
"pp": "case step\nC : ℕ → Sort u_1\nn m : ℕ\nnext : {k : ℕ} → C k → C (k + 1)\nHnext : ∀ (n : ℕ), Injective next\nm✝ : ℕ\nhnm : n.le m✝\nih : Injective (leRecOn hnm fun {k} ↦ next)\nx y : C n\nH : next (leRecOn hnm (fun {k} ↦ next) x) = next (leRecOn hnm (fun {k} ↦ next) y)\n⊢ x = y",
"ppTerm": "?step",
... | [] | exact ih (Hnext _ H) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Data.Nat.Basic | {
"line": 158,
"column": 4
} | {
"line": 158,
"column": 10
} | {
"line": 159,
"column": 2
} | [
{
"pp": "case inl\n⊢ 2 * 0 ^ 2 + 1 ≤ 2 ^ (2 * 0)",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"instPowNat",
"HMul.hMul",
"of_decide_eq_true",
"id",
"instMulNat",
"instOfNatNat",
"LE.le",
"instLENat",
"instNatPowNat",
"Bool.true"... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Nat.Basic | {
"line": 158,
"column": 4
} | {
"line": 158,
"column": 10
} | {
"line": 159,
"column": 2
} | [
{
"pp": "case inl\n⊢ 2 * 0 ^ 2 + 1 ≤ 2 ^ (2 * 0)",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"instPowNat",
"HMul.hMul",
"of_decide_eq_true",
"id",
"instMulNat",
"instOfNatNat",
"LE.le",
"instLENat",
"instNatPowNat",
"Bool.true"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Nat.Basic | {
"line": 158,
"column": 4
} | {
"line": 158,
"column": 10
} | {
"line": 159,
"column": 2
} | [
{
"pp": "case inl\n⊢ 2 * 0 ^ 2 + 1 ≤ 2 ^ (2 * 0)",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"instPowNat",
"HMul.hMul",
"of_decide_eq_true",
"id",
"instMulNat",
"instOfNatNat",
"LE.le",
"instLENat",
"instNatPowNat",
"Bool.true"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Nat.Basic | {
"line": 163,
"column": 65
} | {
"line": 163,
"column": 71
} | {
"line": 163,
"column": 72
} | [
{
"pp": "k : ℕ\nhk : k > 0\nhk0 : 0 < 2 * k ^ 2\n⊢ 2 ≠ 1",
"ppTerm": "?m.198",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Ne",
"instOfNatNat",
"Bool.true",
"Nat",
"Bool",
"Eq.refl",
"instDecidableEq... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Nat.Basic | {
"line": 163,
"column": 65
} | {
"line": 163,
"column": 71
} | {
"line": 163,
"column": 72
} | [
{
"pp": "k : ℕ\nhk : k > 0\nhk0 : 0 < 2 * k ^ 2\n⊢ 2 ≠ 1",
"ppTerm": "?m.198",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Ne",
"instOfNatNat",
"Bool.true",
"Nat",
"Bool",
"Eq.refl",
"instDecidableEq... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Nat.Basic | {
"line": 163,
"column": 65
} | {
"line": 163,
"column": 71
} | {
"line": 163,
"column": 72
} | [
{
"pp": "k : ℕ\nhk : k > 0\nhk0 : 0 < 2 * k ^ 2\n⊢ 2 ≠ 1",
"ppTerm": "?m.198",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Ne",
"instOfNatNat",
"Bool.true",
"Nat",
"Bool",
"Eq.refl",
"instDecidableEq... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Monotone.Basic | {
"line": 144,
"column": 87
} | {
"line": 145,
"column": 57
} | {
"line": 147,
"column": 0
} | [
{
"pp": "α : Type u\nβ : Type v\ninst✝¹ : Preorder α\ninst✝ : Preorder β\nf : α → β\n⊢ Antitone (⇑toDual ∘ f ∘ ⇑ofDual) ↔ Antitone f",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"OrderDual.toDual",
"Eq.mpr",
"Equiv.instEquivLike",
"OrderDual.ofDual",
"congr... | [] | by
rw [antitone_toDual_comp_iff, monotone_comp_ofDual_iff] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.Monotone.Basic | {
"line": 148,
"column": 2
} | {
"line": 148,
"column": 61
} | {
"line": 150,
"column": 0
} | [
{
"pp": "α : Type u\nβ : Type v\ninst✝¹ : Preorder α\ninst✝ : Preorder β\nf : α → β\ns : Set α\n⊢ MonotoneOn (⇑toDual ∘ f ∘ ⇑ofDual) s ↔ MonotoneOn f s",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"OrderDual.toDual",
"Eq.mpr",
"Equiv.instEquivLike",
"OrderDual.of... | [] | rw [monotoneOn_toDual_comp_iff, antitoneOn_comp_ofDual_iff] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Order.Monotone.Basic | {
"line": 148,
"column": 2
} | {
"line": 148,
"column": 61
} | {
"line": 150,
"column": 0
} | [
{
"pp": "α : Type u\nβ : Type v\ninst✝¹ : Preorder α\ninst✝ : Preorder β\nf : α → β\ns : Set α\n⊢ MonotoneOn (⇑toDual ∘ f ∘ ⇑ofDual) s ↔ MonotoneOn f s",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"OrderDual.toDual",
"Eq.mpr",
"Equiv.instEquivLike",
"OrderDual.of... | [] | rw [monotoneOn_toDual_comp_iff, antitoneOn_comp_ofDual_iff] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Monotone.Basic | {
"line": 148,
"column": 2
} | {
"line": 148,
"column": 61
} | {
"line": 150,
"column": 0
} | [
{
"pp": "α : Type u\nβ : Type v\ninst✝¹ : Preorder α\ninst✝ : Preorder β\nf : α → β\ns : Set α\n⊢ MonotoneOn (⇑toDual ∘ f ∘ ⇑ofDual) s ↔ MonotoneOn f s",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"OrderDual.toDual",
"Eq.mpr",
"Equiv.instEquivLike",
"OrderDual.of... | [] | rw [monotoneOn_toDual_comp_iff, antitoneOn_comp_ofDual_iff] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Monotone.Basic | {
"line": 576,
"column": 2
} | {
"line": 576,
"column": 43
} | {
"line": 577,
"column": 2
} | [
{
"pp": "α : Type u\ninst✝¹ : Preorder α\ninst✝ : NoMaxOrder α\na : α\n⊢ ∃ f, StrictMono f ∧ f 0 = a",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"NoMaxOrder.exists_gt",
"Classical.choose_spec",
"LT.lt",
"Classical.choose"
],
"usedF... | [
"α : Type u\ninst✝¹ : Preorder α\ninst✝ : NoMaxOrder α\na : α\ng : α → α\nhg : ∀ (x : α), x < g x\n⊢ ∃ f, StrictMono f ∧ f 0 = a"
] | choose g hg using fun x : α ↦ exists_gt x | Mathlib.Tactic.Choose._aux_Mathlib_Tactic_Choose___elabRules_Mathlib_Tactic_Choose_choose_1 | Mathlib.Tactic.Choose.choose |
Mathlib.Order.Monotone.Basic | {
"line": 607,
"column": 6
} | {
"line": 607,
"column": 18
} | {
"line": 607,
"column": 18
} | [
{
"pp": "n : ℕ\n⊢ n ^ n ≤ (n + 1) ^ (n + 1)",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"instPowNat",
"Eq.mpr",
"HMul.hMul",
"congrArg",
"Preorder.toLE",
"Nat.pow_succ",
"id",
"instMulNat",
"instOfNatNat",
"LE.le",
"inst... | [
"n : ℕ\n⊢ n ^ n ≤ (n + 1) ^ n * (n + 1)"
] | Nat.pow_succ | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.Monotone.Basic | {
"line": 623,
"column": 2
} | {
"line": 625,
"column": 86
} | {
"line": 627,
"column": 0
} | [
{
"pp": "β : Type v\nr : β → β → Prop\ninst✝ : IsTrans β r\nf : ℤ → β\nh : ∀ (n : ℤ), r (f n) (f (n + 1))\na : ℤ\nn : ℕ\n⊢ r (f a) (f (a + ↑n.succ))",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.recAux",
"trans",
"congrArg",
"Int.add_assoc",
... | [] | induction n with
| zero => rw [Int.ofNat_one]; apply h
| succ n ihn => rw [Int.natCast_succ, ← Int.add_assoc]; exact _root_.trans ihn (h _) | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | Lean.Parser.Tactic.induction |
Mathlib.Tactic.Lift | {
"line": 55,
"column": 2
} | {
"line": 57,
"column": 31
} | {
"line": 59,
"column": 0
} | [
{
"pp": "ι : Sort u_1\nα : ι → Sort u_2\nne : ∀ (i : ι), Nonempty (α i)\np : ι → Prop\nf : (i : Subtype p) → α i.val\n⊢ ∃ g, (fun i ↦ g i.val) = f",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Classical.choice",
"Classical.propDecidable",
"dif_pos",
"Subtype",
... | [] | haveI : DecidablePred p := fun i ↦ Classical.propDecidable (p i)
exact ⟨fun i => if hi : p i then f ⟨i, hi⟩ else Classical.choice (ne i),
funext fun i ↦ dif_pos i.2⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Tactic.Lift | {
"line": 55,
"column": 2
} | {
"line": 57,
"column": 31
} | {
"line": 59,
"column": 0
} | [
{
"pp": "ι : Sort u_1\nα : ι → Sort u_2\nne : ∀ (i : ι), Nonempty (α i)\np : ι → Prop\nf : (i : Subtype p) → α i.val\n⊢ ∃ g, (fun i ↦ g i.val) = f",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Classical.choice",
"Classical.propDecidable",
"dif_pos",
"Subtype",
... | [] | haveI : DecidablePred p := fun i ↦ Classical.propDecidable (p i)
exact ⟨fun i => if hi : p i then f ⟨i, hi⟩ else Classical.choice (ne i),
funext fun i ↦ dif_pos i.2⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Set.Insert | {
"line": 267,
"column": 61
} | {
"line": 269,
"column": 88
} | {
"line": 271,
"column": 0
} | [
{
"pp": "α : Type u_1\nl : List α\na : α\n⊢ {x | x ∈ l} = {a} ↔ ∃ n, n > 0 ∧ l = List.replicate n a",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"List.replicate",
"and_true",
"congrArg",
"_private.Mathlib.Data.Set.Insert.0.Set.setOf_mem_list_eq_re... | [] | by
simpa +contextual [Set.ext_iff, iff_iff_implies_and_implies, forall_and, List.eq_replicate_iff,
List.length_pos_iff_exists_mem] using ⟨fun _ _ ↦ ⟨_, ‹_›⟩, fun x hx h ↦ h _ hx ▸ hx⟩ | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.Lattice | {
"line": 847,
"column": 4
} | {
"line": 849,
"column": 85
} | {
"line": 851,
"column": 0
} | [
{
"pp": "case inl.refine_3\nα : Type u\nβ : Type v\nf : α → β\ns : Set α\nx y : α\ninst✝¹ : LinearOrder α\ninst✝ : SemilatticeInf β\nhf : AntitoneOn f s\nhx : x ∈ s\nhy : y ∈ s\nh✝ : x ≤ y\nthis : f y ≤ f x\n⊢ f (max x y) = f x ⊓ f y",
"ppTerm": "?inl.refine_3",
"assigned": true,
"usedConstants": [
... | [] | first
| assumption
| simp only [*, sup_of_le_left, sup_of_le_right, inf_of_le_left, inf_of_le_right] | Lean.Elab.Tactic.evalFirst | Lean.Parser.Tactic.first |
Mathlib.Order.Lattice | {
"line": 847,
"column": 4
} | {
"line": 849,
"column": 85
} | {
"line": 851,
"column": 0
} | [
{
"pp": "case inl.refine_1\nα : Type u\nβ : Type v\nf : α → β\ns : Set α\nx y : α\ninst✝¹ : LinearOrder α\ninst✝ : SemilatticeInf β\nhf : AntitoneOn f s\nhx : x ∈ s\nhy : y ∈ s\nh✝ : x ≤ y\n⊢ x ∈ s",
"ppTerm": "?inl.refine_1",
"assigned": true,
"usedConstants": [],
"usedFVars": [
"hx"
... | [] | first
| assumption
| simp only [*, sup_of_le_left, sup_of_le_right, inf_of_le_left, inf_of_le_right] | Lean.Elab.Tactic.evalFirst | Lean.Parser.Tactic.first |
Mathlib.Order.Lattice | {
"line": 847,
"column": 4
} | {
"line": 849,
"column": 85
} | {
"line": 851,
"column": 0
} | [
{
"pp": "case inl.refine_2\nα : Type u\nβ : Type v\nf : α → β\ns : Set α\nx y : α\ninst✝¹ : LinearOrder α\ninst✝ : SemilatticeInf β\nhf : AntitoneOn f s\nhx : x ∈ s\nhy : y ∈ s\nh✝ : x ≤ y\n⊢ y ∈ s",
"ppTerm": "?inl.refine_2",
"assigned": true,
"usedConstants": [],
"usedFVars": [
"hy"
... | [] | first
| assumption
| simp only [*, sup_of_le_left, sup_of_le_right, inf_of_le_left, inf_of_le_right] | Lean.Elab.Tactic.evalFirst | Lean.Parser.Tactic.first |
Mathlib.Order.Lattice | {
"line": 847,
"column": 4
} | {
"line": 849,
"column": 85
} | {
"line": 851,
"column": 0
} | [
{
"pp": "case inr.refine_3\nα : Type u\nβ : Type v\nf : α → β\ns : Set α\nx y : α\ninst✝¹ : LinearOrder α\ninst✝ : SemilatticeInf β\nhf : AntitoneOn f s\nhx : x ∈ s\nhy : y ∈ s\nh✝ : y ≤ x\nthis : f x ≤ f y\n⊢ f (max x y) = f x ⊓ f y",
"ppTerm": "?inr.refine_3",
"assigned": true,
"usedConstants": [
... | [] | first
| assumption
| simp only [*, sup_of_le_left, sup_of_le_right, inf_of_le_left, inf_of_le_right] | Lean.Elab.Tactic.evalFirst | Lean.Parser.Tactic.first |
Mathlib.Order.Lattice | {
"line": 847,
"column": 4
} | {
"line": 849,
"column": 85
} | {
"line": 851,
"column": 0
} | [
{
"pp": "case inr.refine_1\nα : Type u\nβ : Type v\nf : α → β\ns : Set α\nx y : α\ninst✝¹ : LinearOrder α\ninst✝ : SemilatticeInf β\nhf : AntitoneOn f s\nhx : x ∈ s\nhy : y ∈ s\nh✝ : y ≤ x\n⊢ y ∈ s",
"ppTerm": "?inr.refine_1",
"assigned": true,
"usedConstants": [],
"usedFVars": [
"hy"
... | [] | first
| assumption
| simp only [*, sup_of_le_left, sup_of_le_right, inf_of_le_left, inf_of_le_right] | Lean.Elab.Tactic.evalFirst | Lean.Parser.Tactic.first |
Mathlib.Order.Lattice | {
"line": 847,
"column": 4
} | {
"line": 849,
"column": 85
} | {
"line": 851,
"column": 0
} | [
{
"pp": "case inr.refine_2\nα : Type u\nβ : Type v\nf : α → β\ns : Set α\nx y : α\ninst✝¹ : LinearOrder α\ninst✝ : SemilatticeInf β\nhf : AntitoneOn f s\nhx : x ∈ s\nhy : y ∈ s\nh✝ : y ≤ x\n⊢ x ∈ s",
"ppTerm": "?inr.refine_2",
"assigned": true,
"usedConstants": [],
"usedFVars": [
"hx"
... | [] | first
| assumption
| simp only [*, sup_of_le_left, sup_of_le_right, inf_of_le_left, inf_of_le_right] | Lean.Elab.Tactic.evalFirst | Lean.Parser.Tactic.first |
Mathlib.Order.Heyting.Basic | {
"line": 310,
"column": 56
} | {
"line": 310,
"column": 67
} | {
"line": 310,
"column": 68
} | [
{
"pp": "α : Type u_2\ninst✝ : GeneralizedHeytingAlgebra α\na b c d : α\n⊢ d ⊓ a ≤ b ⊓ c ↔ d ≤ (a ⇨ b) ⊓ (a ⇨ c)",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
... | [
"α : Type u_2\ninst✝ : GeneralizedHeytingAlgebra α\na b c d : α\n⊢ d ⊓ a ≤ b ∧ d ⊓ a ≤ c ↔ d ≤ a ⇨ b ∧ d ≤ a ⇨ c"
] | le_inf_iff, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Order.Heyting.Basic | {
"line": 314,
"column": 8
} | {
"line": 314,
"column": 19
} | {
"line": 314,
"column": 20
} | [
{
"pp": "α : Type u_2\ninst✝ : GeneralizedHeytingAlgebra α\na b c d : α\n⊢ d ≤ a ⊔ b ⇨ c ↔ d ≤ (a ⇨ c) ⊓ (b ⇨ c)",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
... | [
"α : Type u_2\ninst✝ : GeneralizedHeytingAlgebra α\na b c d : α\n⊢ d ≤ a ⊔ b ⇨ c ↔ d ≤ a ⇨ c ∧ d ≤ b ⇨ c"
] | le_inf_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.Heyting.Basic | {
"line": 375,
"column": 27
} | {
"line": 375,
"column": 59
} | {
"line": 377,
"column": 0
} | [
{
"pp": "ι : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝ : GeneralizedHeytingAlgebra α\na✝ b✝ c✝ d : α\na b c : αᵒᵈ\n⊢ toDual (ofDual b ⇨ ofDual a) ≤ c ↔ a ≤ b ⊔ c",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"OrderDual.toDual",
"Eq.mpr",
"Lattice.toSemilatticeSup",
... | [] | rw [sup_comm]; exact le_himp_iff | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Heyting.Basic | {
"line": 375,
"column": 27
} | {
"line": 375,
"column": 59
} | {
"line": 377,
"column": 0
} | [
{
"pp": "ι : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝ : GeneralizedHeytingAlgebra α\na✝ b✝ c✝ d : α\na b c : αᵒᵈ\n⊢ toDual (ofDual b ⇨ ofDual a) ≤ c ↔ a ≤ b ⊔ c",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"OrderDual.toDual",
"Eq.mpr",
"Lattice.toSemilatticeSup",
... | [] | rw [sup_comm]; exact le_himp_iff | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Heyting.Basic | {
"line": 600,
"column": 47
} | {
"line": 600,
"column": 58
} | {
"line": 600,
"column": 59
} | [
{
"pp": "ι : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝ : GeneralizedCoheytingAlgebra α\na✝ b✝ c✝ d a b c : α\n⊢ ((a ⊔ b) ⊓ (a ⊔ c)) \\ a ≤ b ⊓ c",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"PartialOrder.toPreorder",
"Preor... | [
"ι : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝ : GeneralizedCoheytingAlgebra α\na✝ b✝ c✝ d a b c : α\n⊢ ((a ⊔ b) ⊓ (a ⊔ c)) \\ a ≤ b ∧ ((a ⊔ b) ⊓ (a ⊔ c)) \\ a ≤ c"
] | le_inf_iff, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Order.BooleanAlgebra.Basic | {
"line": 82,
"column": 2
} | {
"line": 82,
"column": 38
} | {
"line": 85,
"column": 0
} | [
{
"pp": "α : Type u\nx y z : α\ninst✝ : GeneralizedBooleanAlgebra α\ns : z ⊔ x ⊓ y = x \\ y ⊔ x ⊓ y\ni : z ⊓ (x ⊓ y) = x \\ y ⊓ (x ⊓ y)\n⊢ x \\ y = z",
"ppTerm": "?m.70",
"assigned": true,
"usedConstants": [
"eq_of_inf_eq_sup_eq",
"DistribLattice.toLattice",
"SemilatticeInf.toMin",... | [] | exact (eq_of_inf_eq_sup_eq i s).symm | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Order.Heyting.Basic | {
"line": 711,
"column": 2
} | {
"line": 711,
"column": 48
} | {
"line": 713,
"column": 0
} | [
{
"pp": "α : Type u_2\ninst✝ : HeytingAlgebra α\na : α\n⊢ a ≤ aᶜ ↔ a = ⊥",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"congrArg",
"Compl.compl",
"OrderBot.toBot",
"Iff.rfl",
"PartialOrder.toPreorder",
"... | [] | rw [le_compl_iff_disjoint_left, disjoint_self] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Order.Heyting.Basic | {
"line": 711,
"column": 2
} | {
"line": 711,
"column": 48
} | {
"line": 713,
"column": 0
} | [
{
"pp": "α : Type u_2\ninst✝ : HeytingAlgebra α\na : α\n⊢ a ≤ aᶜ ↔ a = ⊥",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"congrArg",
"Compl.compl",
"OrderBot.toBot",
"Iff.rfl",
"PartialOrder.toPreorder",
"... | [] | rw [le_compl_iff_disjoint_left, disjoint_self] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Heyting.Basic | {
"line": 711,
"column": 2
} | {
"line": 711,
"column": 48
} | {
"line": 713,
"column": 0
} | [
{
"pp": "α : Type u_2\ninst✝ : HeytingAlgebra α\na : α\n⊢ a ≤ aᶜ ↔ a = ⊥",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"congrArg",
"Compl.compl",
"OrderBot.toBot",
"Iff.rfl",
"PartialOrder.toPreorder",
"... | [] | rw [le_compl_iff_disjoint_left, disjoint_self] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Heyting.Basic | {
"line": 757,
"column": 21
} | {
"line": 757,
"column": 46
} | {
"line": 757,
"column": 46
} | [
{
"pp": "case a\nα : Type u_2\ninst✝ : HeytingAlgebra α\na b : α\n⊢ (a ⇨ b)ᶜᶜ ⊓ aᶜᶜ ≤ bᶜᶜ",
"ppTerm": "?a✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Compl.compl",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
... | [
"case a\nα : Type u_2\ninst✝ : HeytingAlgebra α\na b : α\n⊢ ((a ⇨ b) ⊓ a)ᶜᶜ ≤ bᶜᶜ"
] | ← compl_compl_inf_distrib | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.Heyting.Basic | {
"line": 767,
"column": 27
} | {
"line": 767,
"column": 59
} | {
"line": 768,
"column": 2
} | [
{
"pp": "ι : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝ : HeytingAlgebra α\na✝ b✝ : α\na b c : αᵒᵈ\n⊢ toDual (ofDual b ⇨ ofDual a) ≤ c ↔ a ≤ b ⊔ c",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"OrderDual.toDual",
"Eq.mpr",
"Lattice.toSemilatticeSup",
"Equiv.instE... | [] | rw [sup_comm]; exact le_himp_iff | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Heyting.Basic | {
"line": 767,
"column": 27
} | {
"line": 767,
"column": 59
} | {
"line": 768,
"column": 2
} | [
{
"pp": "ι : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝ : HeytingAlgebra α\na✝ b✝ : α\na b c : αᵒᵈ\n⊢ toDual (ofDual b ⇨ ofDual a) ≤ c ↔ a ≤ b ⊔ c",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"OrderDual.toDual",
"Eq.mpr",
"Lattice.toSemilatticeSup",
"Equiv.instE... | [] | rw [sup_comm]; exact le_himp_iff | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Heyting.Basic | {
"line": 812,
"column": 47
} | {
"line": 812,
"column": 58
} | {
"line": 812,
"column": 59
} | [
{
"pp": "ι : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝ : CoheytingAlgebra α\na✝ b✝ a b c : α\n⊢ ((a ⊔ b) ⊓ (a ⊔ c)) \\ a ≤ b ⊓ c",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"PartialOrder.toPreorder",
"Preorder.toLE",
... | [
"ι : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝ : CoheytingAlgebra α\na✝ b✝ a b c : α\n⊢ ((a ⊔ b) ⊓ (a ⊔ c)) \\ a ≤ b ∧ ((a ⊔ b) ⊓ (a ⊔ c)) \\ a ≤ c"
] | le_inf_iff, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Order.Heyting.Basic | {
"line": 891,
"column": 2
} | {
"line": 892,
"column": 86
} | {
"line": 893,
"column": 2
} | [
{
"pp": "α : Type u_2\ninst✝ : CoheytingAlgebra α\na b : α\n⊢ ￢￢(a ⊔ b) ≤ ￢￢a ⊔ ￢￢b",
"ppTerm": "?m.44",
"assigned": true,
"usedConstants": [
"CoheytingAlgebra.toHNot",
"Eq.mpr",
"Codisjoint",
"Lattice.toSemilatticeSup",
"hnot_le_iff_codisjoint_left",
"congrArg",
... | [
"α : Type u_2\ninst✝ : CoheytingAlgebra α\na b : α\n⊢ Codisjoint (a ⊔ b) (￢(a ⊔ b))"
] | rw [hnot_le_iff_codisjoint_left, codisjoint_assoc, codisjoint_hnot_hnot_left_iff,
codisjoint_left_comm, codisjoint_hnot_hnot_left_iff, ← codisjoint_assoc, sup_comm] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Order.Heyting.Basic | {
"line": 897,
"column": 4
} | {
"line": 897,
"column": 67
} | {
"line": 898,
"column": 4
} | [
{
"pp": "case a\nα : Type u_2\ninst✝ : CoheytingAlgebra α\na b : α\n⊢ ￢￢(a \\ b) ≤ ￢￢a \\ ￢￢b",
"ppTerm": "?a✝",
"assigned": true,
"usedConstants": [
"CoheytingAlgebra.toHNot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"SemilatticeInf.... | [
"case a\nα : Type u_2\ninst✝ : CoheytingAlgebra α\na b : α\n⊢ ￢(￢￢a \\ ￢￢b) ≤ ￢(a ⊓ ￢b)"
] | refine hnot_le_comm.1 ((hnot_anti sdiff_le_inf_hnot).trans' ?_) | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Logic.Equiv.Option | {
"line": 56,
"column": 2
} | {
"line": 56,
"column": 6
} | {
"line": 57,
"column": 2
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\ne₁ : α ≃ β\ne₂ : β ≃ γ\nx : Option α\n⊢ (e₁.trans e₂).optionCongr x = (e₁.optionCongr.trans e₂.optionCongr) x",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"Equiv.trans",
"Equiv",
"Eq.symm",... | [
"α : Type u_1\nβ : Type u_2\nγ : Type u_3\ne₁ : α ≃ β\ne₂ : β ≃ γ\nx : Option α\n⊢ (e₁.optionCongr.trans e₂.optionCongr) x = (e₁.trans e₂).optionCongr x"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Order.SymmDiff | {
"line": 95,
"column": 67
} | {
"line": 95,
"column": 73
} | {
"line": 97,
"column": 0
} | [
{
"pp": "⊢ ∀ (p q : Bool), p ∆ q = (p ^^ q)",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"Bool.instBooleanAlgebra",
"id",
"instDecidableEqBool",
"BooleanAlgebra.toSDiff",
"Bool.true"... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Order.SymmDiff | {
"line": 95,
"column": 67
} | {
"line": 95,
"column": 73
} | {
"line": 97,
"column": 0
} | [
{
"pp": "⊢ ∀ (p q : Bool), p ∆ q = (p ^^ q)",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"Bool.instBooleanAlgebra",
"id",
"instDecidableEqBool",
"BooleanAlgebra.toSDiff",
"Bool.true"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.SymmDiff | {
"line": 95,
"column": 67
} | {
"line": 95,
"column": 73
} | {
"line": 97,
"column": 0
} | [
{
"pp": "⊢ ∀ (p q : Bool), p ∆ q = (p ^^ q)",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"Bool.instBooleanAlgebra",
"id",
"instDecidableEqBool",
"BooleanAlgebra.toSDiff",
"Bool.true"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.SymmDiff | {
"line": 240,
"column": 19
} | {
"line": 240,
"column": 30
} | {
"line": 240,
"column": 31
} | [
{
"pp": "α : Type u_2\ninst✝ : GeneralizedHeytingAlgebra α\na b c : α\n⊢ a ≤ (c ⇨ b) ⊓ (b ⇨ c) ↔ a ⊓ b ≤ c ∧ a ⊓ c ≤ b",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOr... | [
"α : Type u_2\ninst✝ : GeneralizedHeytingAlgebra α\na b c : α\n⊢ a ≤ c ⇨ b ∧ a ≤ b ⇨ c ↔ a ⊓ b ≤ c ∧ a ⊓ c ≤ b"
] | le_inf_iff, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Order.SymmDiff | {
"line": 300,
"column": 6
} | {
"line": 300,
"column": 17
} | {
"line": 300,
"column": 18
} | [
{
"pp": "α : Type u_2\ninst✝ : CoheytingAlgebra α\na : α\n⊢ (￢a) ∆ a = ⊤",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"CoheytingAlgebra.toHNot",
"Eq.mpr",
"Lattice.toSemilatticeSup",
"eq_top_iff",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.... | [
"α : Type u_2\ninst✝ : CoheytingAlgebra α\na : α\n⊢ ⊤ ≤ (￢a) ∆ a"
] | eq_top_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Logic.Equiv.Basic | {
"line": 438,
"column": 30
} | {
"line": 438,
"column": 43
} | {
"line": 439,
"column": 2
} | [
{
"pp": "α✝ : Sort u_1\nα₁ : Sort u_2\nα₂ : Sort u_3\nβ✝ : Sort u_4\nβ₁ : Sort u_5\nβ₂ : Sort u_6\nγ : Sort u_7\nδ : Sort u_8\nα : Type u_9\nβ : α → Type u_10\na✝ : α\nx✝ : { s // s.fst = a✝ }\na : Sigma β\nh : a.fst = a✝\n⊢ (fun b ↦ ⟨⟨a✝, b⟩, ⋯⟩)\n ((fun x ↦\n match x with\n | ⟨⟨fst, b⟩,... | [] | cases h; simp | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Logic.Equiv.Basic | {
"line": 438,
"column": 30
} | {
"line": 438,
"column": 43
} | {
"line": 439,
"column": 2
} | [
{
"pp": "α✝ : Sort u_1\nα₁ : Sort u_2\nα₂ : Sort u_3\nβ✝ : Sort u_4\nβ₁ : Sort u_5\nβ₂ : Sort u_6\nγ : Sort u_7\nδ : Sort u_8\nα : Type u_9\nβ : α → Type u_10\na✝ : α\nx✝ : { s // s.fst = a✝ }\na : Sigma β\nh : a.fst = a✝\n⊢ (fun b ↦ ⟨⟨a✝, b⟩, ⋯⟩)\n ((fun x ↦\n match x with\n | ⟨⟨fst, b⟩,... | [] | cases h; simp | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.SymmDiff | {
"line": 354,
"column": 2
} | {
"line": 354,
"column": 45
} | {
"line": 356,
"column": 0
} | [
{
"pp": "α : Type u_2\ninst✝ : GeneralizedBooleanAlgebra α\na b c : α\n⊢ c \\ a ∆ b = c ⊓ a ⊓ b ⊔ c \\ a ⊓ c \\ b",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Lattice.toSemilatticeSup",
"sdiff_sdiff_sup_sdiff'",
"congrArg",
"SemilatticeSup.toMax",
"Semilat... | [] | simp only [(· ∆ ·), sdiff_sdiff_sup_sdiff'] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Order.SymmDiff | {
"line": 354,
"column": 2
} | {
"line": 354,
"column": 45
} | {
"line": 356,
"column": 0
} | [
{
"pp": "α : Type u_2\ninst✝ : GeneralizedBooleanAlgebra α\na b c : α\n⊢ c \\ a ∆ b = c ⊓ a ⊓ b ⊔ c \\ a ⊓ c \\ b",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Lattice.toSemilatticeSup",
"sdiff_sdiff_sup_sdiff'",
"congrArg",
"SemilatticeSup.toMax",
"Semilat... | [] | simp only [(· ∆ ·), sdiff_sdiff_sup_sdiff'] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.SymmDiff | {
"line": 354,
"column": 2
} | {
"line": 354,
"column": 45
} | {
"line": 356,
"column": 0
} | [
{
"pp": "α : Type u_2\ninst✝ : GeneralizedBooleanAlgebra α\na b c : α\n⊢ c \\ a ∆ b = c ⊓ a ⊓ b ⊔ c \\ a ⊓ c \\ b",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Lattice.toSemilatticeSup",
"sdiff_sdiff_sup_sdiff'",
"congrArg",
"SemilatticeSup.toMax",
"Semilat... | [] | simp only [(· ∆ ·), sdiff_sdiff_sup_sdiff'] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Set.Image | {
"line": 146,
"column": 2
} | {
"line": 148,
"column": 71
} | {
"line": 150,
"column": 0
} | [
{
"pp": "α : Type u_1\nf : α → α\nn : ℕ\n⊢ preimage f^[n] = (preimage f)^[n]",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.recAux",
"Function.iterate_succ",
"congrArg",
"Function.iterate_succ'",
"Function.comp",
"id",
"instOfN... | [] | induction n with
| zero => simp
| succ n ih => rw [iterate_succ, iterate_succ', preimage_comp_eq, ih] | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | Lean.Parser.Tactic.induction |
Mathlib.Data.Set.Image | {
"line": 146,
"column": 2
} | {
"line": 148,
"column": 71
} | {
"line": 150,
"column": 0
} | [
{
"pp": "α : Type u_1\nf : α → α\nn : ℕ\n⊢ preimage f^[n] = (preimage f)^[n]",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.recAux",
"Function.iterate_succ",
"congrArg",
"Function.iterate_succ'",
"Function.comp",
"id",
"instOfN... | [] | induction n with
| zero => simp
| succ n ih => rw [iterate_succ, iterate_succ', preimage_comp_eq, ih] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Set.Image | {
"line": 146,
"column": 2
} | {
"line": 148,
"column": 71
} | {
"line": 150,
"column": 0
} | [
{
"pp": "α : Type u_1\nf : α → α\nn : ℕ\n⊢ preimage f^[n] = (preimage f)^[n]",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.recAux",
"Function.iterate_succ",
"congrArg",
"Function.iterate_succ'",
"Function.comp",
"id",
"instOfN... | [] | induction n with
| zero => simp
| succ n ih => rw [iterate_succ, iterate_succ', preimage_comp_eq, ih] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Set.Image | {
"line": 547,
"column": 4
} | {
"line": 547,
"column": 82
} | {
"line": 548,
"column": 4
} | [
{
"pp": "case inr\nα : Type u_1\ns : Set α\nσ : Equiv.Perm α\nhs : {a | σ a ≠ a} ⊆ s\ni : α\nhi : σ i ≠ i\n⊢ i ∈ ⇑σ '' s ↔ i ∈ s",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"Equiv.apply_symm_apply",
"Equiv.instEquivLike",
"Membership.mem",
"Equiv",
"And",
... | [
"case inr\nα : Type u_1\ns : Set α\nσ : Equiv.Perm α\nhs : {a | σ a ≠ a} ⊆ s\ni : α\nhi : σ i ≠ i\nh : σ ((Equiv.symm σ) i) = (Equiv.symm σ) i\n⊢ σ i = i"
] | refine iff_of_true ⟨σ.symm i, hs fun h => hi ?_, σ.apply_symm_apply _⟩ (hs hi) | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Data.Set.Image | {
"line": 671,
"column": 37
} | {
"line": 671,
"column": 58
} | {
"line": 671,
"column": 58
} | [
{
"pp": "α : Type u_1\nι : Sort u_4\nf : ι → α\ninst✝ : Nonempty ι\ny : α\nh : ∀ (x : α), (∃ y, f y = x) ↔ x = y\nx✝ : ι\n⊢ ∃ y, f y = f x✝",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"Exists",
"of_eq_true",
"Eq",
"_private.Mathlib.Data.Set.Image.0.Set.range_eq_... | [] | exists_apply_eq_apply | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Data.Set.Prod | {
"line": 342,
"column": 2
} | {
"line": 342,
"column": 6
} | {
"line": 343,
"column": 2
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ns s₁ : Set α\nt t₁ : Set β\n⊢ s ×ˢ t = s₁ ×ˢ t₁ ↔ s = s₁ ∧ t = t₁ ∨ (s = ∅ ∨ t = ∅) ∧ (s₁ = ∅ ∨ t₁ = ∅)",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Set.instSProd",
"SProd.sprod",
"And",
"Set.instEmptyCollection",
"Or",... | [
"α : Type u_1\nβ : Type u_2\ns s₁ : Set α\nt t₁ : Set β\n⊢ s = s₁ ∧ t = t₁ ∨ (s = ∅ ∨ t = ∅) ∧ (s₁ = ∅ ∨ t₁ = ∅) ↔ s ×ˢ t = s₁ ×ˢ t₁"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Data.Set.Prod | {
"line": 656,
"column": 2
} | {
"line": 656,
"column": 39
} | {
"line": 658,
"column": 0
} | [
{
"pp": "ι : Type u_1\nα : ι → Type u_2\ns : Set ι\nt : (i : ι) → Set (α i)\n⊢ (s.pi t).Nonempty ↔ ∀ (i : ι), ∃ x, i ∈ s → x ∈ t i",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"congrArg",
"_private.Mathlib.Data.Set.Prod.0.Set.pi_nonempty_iff._simp_1_1",
"Membership.mem... | [] | simp [Classical.skolem, Set.Nonempty] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Set.Prod | {
"line": 656,
"column": 2
} | {
"line": 656,
"column": 39
} | {
"line": 658,
"column": 0
} | [
{
"pp": "ι : Type u_1\nα : ι → Type u_2\ns : Set ι\nt : (i : ι) → Set (α i)\n⊢ (s.pi t).Nonempty ↔ ∀ (i : ι), ∃ x, i ∈ s → x ∈ t i",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"congrArg",
"_private.Mathlib.Data.Set.Prod.0.Set.pi_nonempty_iff._simp_1_1",
"Membership.mem... | [] | simp [Classical.skolem, Set.Nonempty] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Set.Prod | {
"line": 656,
"column": 2
} | {
"line": 656,
"column": 39
} | {
"line": 658,
"column": 0
} | [
{
"pp": "ι : Type u_1\nα : ι → Type u_2\ns : Set ι\nt : (i : ι) → Set (α i)\n⊢ (s.pi t).Nonempty ↔ ∀ (i : ι), ∃ x, i ∈ s → x ∈ t i",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"congrArg",
"_private.Mathlib.Data.Set.Prod.0.Set.pi_nonempty_iff._simp_1_1",
"Membership.mem... | [] | simp [Classical.skolem, Set.Nonempty] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Set.Prod | {
"line": 659,
"column": 2
} | {
"line": 659,
"column": 39
} | {
"line": 661,
"column": 0
} | [
{
"pp": "ι : Type u_1\nα : ι → Type u_2\nt : (i : ι) → Set (α i)\n⊢ (univ.pi t).Nonempty ↔ ∀ (i : ι), (t i).Nonempty",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"congrArg",
"Set.mem_univ._simp_1",
"Set.univ",
"instInhabitedTrue",
"Membership.mem",
"E... | [] | simp [Classical.skolem, Set.Nonempty] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Set.Prod | {
"line": 659,
"column": 2
} | {
"line": 659,
"column": 39
} | {
"line": 661,
"column": 0
} | [
{
"pp": "ι : Type u_1\nα : ι → Type u_2\nt : (i : ι) → Set (α i)\n⊢ (univ.pi t).Nonempty ↔ ∀ (i : ι), (t i).Nonempty",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"congrArg",
"Set.mem_univ._simp_1",
"Set.univ",
"instInhabitedTrue",
"Membership.mem",
"E... | [] | simp [Classical.skolem, Set.Nonempty] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Set.Prod | {
"line": 659,
"column": 2
} | {
"line": 659,
"column": 39
} | {
"line": 661,
"column": 0
} | [
{
"pp": "ι : Type u_1\nα : ι → Type u_2\nt : (i : ι) → Set (α i)\n⊢ (univ.pi t).Nonempty ↔ ∀ (i : ι), (t i).Nonempty",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"congrArg",
"Set.mem_univ._simp_1",
"Set.univ",
"instInhabitedTrue",
"Membership.mem",
"E... | [] | simp [Classical.skolem, Set.Nonempty] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Set.Image | {
"line": 1243,
"column": 6
} | {
"line": 1243,
"column": 36
} | {
"line": 1243,
"column": 37
} | [
{
"pp": "α : Type u_1\nt : Set α\np : Set α → Prop\n⊢ (∃ s, p (val '' s)) ↔ ∃ s, s ⊆ t ∧ p s",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Set.exists_subset_range_and_iff",
"Eq.mpr",
"congrArg",
"Membership.mem",
"Exists",
"Set.Elem",
"id",
... | [
"α : Type u_1\nt : Set α\np : Set α → Prop\n⊢ (∃ s, s ⊆ range val ∧ p s) ↔ ∃ s, s ⊆ t ∧ p s"
] | ← exists_subset_range_and_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Group.Hom.Defs | {
"line": 488,
"column": 7
} | {
"line": 488,
"column": 28
} | {
"line": 490,
"column": 0
} | [
{
"pp": "ι : Type u_1\nG : Type u_7\nH : Type u_8\nF : Type u_9\ninst✝³ : FunLike F G H\ninst✝² : DivInvMonoid G\ninst✝¹ : DivInvMonoid H\ninst✝ : MonoidHomClass F G H\nf : F\nhf : ∀ (x : G), f x⁻¹ = (f x)⁻¹\ng : ι → G\nn : ℤ\nx✝ : ι\n⊢ (⇑f ∘ (g ^ n)) x✝ = (⇑f ∘ g ^ n) x✝",
"ppTerm": "?m.34",
"assigned"... | [] | simp [map_zpow' f hf] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Set.Function | {
"line": 1012,
"column": 2
} | {
"line": 1012,
"column": 62
} | {
"line": 1014,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝ : Nonempty α\nf : α → β\ns : Set α\n⊢ invFunOn f s '' f '' s ⊆ s",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Function.invFunOn",
"Membership.mem",
"And.casesOn",
"Function.invFunOn_apply_mem",
"And",
"Exist... | [] | rintro _ ⟨_, ⟨x, hx, rfl⟩, rfl⟩; exact invFunOn_apply_mem hx | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Set.Function | {
"line": 1012,
"column": 2
} | {
"line": 1012,
"column": 62
} | {
"line": 1014,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝ : Nonempty α\nf : α → β\ns : Set α\n⊢ invFunOn f s '' f '' s ⊆ s",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Function.invFunOn",
"Membership.mem",
"And.casesOn",
"Function.invFunOn_apply_mem",
"And",
"Exist... | [] | rintro _ ⟨_, ⟨x, hx, rfl⟩, rfl⟩; exact invFunOn_apply_mem hx | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Set.Function | {
"line": 1088,
"column": 2
} | {
"line": 1088,
"column": 63
} | {
"line": 1089,
"column": 2
} | [
{
"pp": "case refine_4\nα : Type u_1\nβ : Type u_2\ns s₁ : Set α\nt : Set β\nf : α → β\nt' : Set β\nh : BijOn f s t\nhss₁ : s ⊆ s₁\nhtt' : t ⊆ t'\nht' : SurjOn f s₁ t'\nr : Set α\nhrss : r ⊆ (s₁ ∩ f ⁻¹' t') \\ f ⁻¹' t\nhbij : BijOn f r ((f '' s₁ ∩ t') \\ t)\ny : β\nhyt' : y ∈ t'\n⊢ y ∈ f '' (s ∪ r)",
"ppTer... | [
"case refine_4\nα : Type u_1\nβ : Type u_2\ns s₁ : Set α\nt : Set β\nf : α → β\nt' : Set β\nh : BijOn f s t\nhss₁ : s ⊆ s₁\nhtt' : t ⊆ t'\nht' : SurjOn f s₁ t'\nr : Set α\nhrss : r ⊆ (s₁ ∩ f ⁻¹' t') \\ f ⁻¹' t\nhbij : BijOn f r ((f '' s₁ ∩ t') \\ t)\ny : β\nhyt' : y ∈ t'\n⊢ y ∈ t ∪ f '' s₁ ∩ t'"
] | rw [image_union, h.image_eq, hbij.image_eq, union_sdiff_self] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Int.Init | {
"line": 354,
"column": 84
} | {
"line": 354,
"column": 94
} | {
"line": 355,
"column": 0
} | [
{
"pp": "m n : ℕ\n⊢ (↑m).gcd -[n+1] = m.gcd (n + 1)",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Nat.gcd",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"eq_self",
"of_eq_true",
"instAddNat",
"OfNat.ofNat",
"Eq"
],
"u... | [] | simp [gcd] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Int.Init | {
"line": 354,
"column": 84
} | {
"line": 354,
"column": 94
} | {
"line": 355,
"column": 0
} | [
{
"pp": "m n : ℕ\n⊢ (↑m).gcd -[n+1] = m.gcd (n + 1)",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Nat.gcd",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"eq_self",
"of_eq_true",
"instAddNat",
"OfNat.ofNat",
"Eq"
],
"u... | [] | simp [gcd] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Int.Init | {
"line": 354,
"column": 84
} | {
"line": 354,
"column": 94
} | {
"line": 355,
"column": 0
} | [
{
"pp": "m n : ℕ\n⊢ (↑m).gcd -[n+1] = m.gcd (n + 1)",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Nat.gcd",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"eq_self",
"of_eq_true",
"instAddNat",
"OfNat.ofNat",
"Eq"
],
"u... | [] | simp [gcd] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Int.Init | {
"line": 355,
"column": 84
} | {
"line": 355,
"column": 94
} | {
"line": 356,
"column": 0
} | [
{
"pp": "m n : ℕ\n⊢ -[m+1].gcd ↑n = (m + 1).gcd n",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Nat.gcd",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"eq_self",
"of_eq_true",
"instAddNat",
"OfNat.ofNat",
"Eq"
],
"use... | [] | simp [gcd] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Int.Init | {
"line": 355,
"column": 84
} | {
"line": 355,
"column": 94
} | {
"line": 356,
"column": 0
} | [
{
"pp": "m n : ℕ\n⊢ -[m+1].gcd ↑n = (m + 1).gcd n",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Nat.gcd",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"eq_self",
"of_eq_true",
"instAddNat",
"OfNat.ofNat",
"Eq"
],
"use... | [] | simp [gcd] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.