module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Algebra.Order.Floor.Ring | {
"line": 714,
"column": 2
} | {
"line": 714,
"column": 7
} | {
"line": 716,
"column": 0
} | [
{
"pp": "R : Type u_2\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : FloorRing R\ninst✝ : IsOrderedRing R\na : R\n⊢ ↑⌈a⌉ = a ↔ a ∈ range Int.cast",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Int.cast",
"Eq.mpr",
"congrArg",
"Membership.mem",
"Exists",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Order.Floor.Ring | {
"line": 714,
"column": 2
} | {
"line": 714,
"column": 7
} | {
"line": 716,
"column": 0
} | [
{
"pp": "R : Type u_2\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : FloorRing R\ninst✝ : IsOrderedRing R\na : R\n⊢ ↑⌈a⌉ = a ↔ a ∈ range Int.cast",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Int.cast",
"Eq.mpr",
"congrArg",
"Membership.mem",
"Exists",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Floor.Ring | {
"line": 714,
"column": 2
} | {
"line": 714,
"column": 7
} | {
"line": 716,
"column": 0
} | [
{
"pp": "R : Type u_2\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : FloorRing R\ninst✝ : IsOrderedRing R\na : R\n⊢ ↑⌈a⌉ = a ↔ a ∈ range Int.cast",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Int.cast",
"Eq.mpr",
"congrArg",
"Membership.mem",
"Exists",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Floor.Ring | {
"line": 823,
"column": 2
} | {
"line": 824,
"column": 26
} | {
"line": 826,
"column": 0
} | [
{
"pp": "R : Type u_2\ninst✝² : Ring R\ninst✝¹ : LinearOrder R\ninst✝ : FloorRing R\na b : R\n⊢ Int.cast ⁻¹' Icc a b = Icc ⌈a⌉ ⌊b⌋",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Set.ext",
"Int.cast",
"_private.Mathlib.Algebra.Order.Floor.Ring.0.Int.preimage_Icc._simp_1_... | [] | ext
simp [ceil_le, le_floor] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Floor.Ring | {
"line": 823,
"column": 2
} | {
"line": 824,
"column": 26
} | {
"line": 826,
"column": 0
} | [
{
"pp": "R : Type u_2\ninst✝² : Ring R\ninst✝¹ : LinearOrder R\ninst✝ : FloorRing R\na b : R\n⊢ Int.cast ⁻¹' Icc a b = Icc ⌈a⌉ ⌊b⌋",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Set.ext",
"Int.cast",
"_private.Mathlib.Algebra.Order.Floor.Ring.0.Int.preimage_Icc._simp_1_... | [] | ext
simp [ceil_le, le_floor] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Floor.Ring | {
"line": 879,
"column": 2
} | {
"line": 880,
"column": 34
} | {
"line": 882,
"column": 0
} | [
{
"pp": "case neg\nR : Type u_2\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : FloorRing R\ninst✝ : IsStrictOrderedRing R\na : R\nha : -1 < a\nh : a < 0\n⊢ ↑⌈a⌉₊ < a + 1",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"... | [] | · rw [ceil_eq_zero.mpr h.le, cast_zero]
exact neg_lt_iff_pos_add.mp ha | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Data.Multiset.Count | {
"line": 170,
"column": 6
} | {
"line": 170,
"column": 18
} | {
"line": 170,
"column": 19
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\na : α\ns : Multiset α\n⊢ 1 ≤ count a s ↔ a ∈ s",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Membership.mem",
"Multiset.count",
"Multiset",
"id",
"instOfNatNat",
"LE.le",
... | [
"α : Type u_1\ninst✝ : DecidableEq α\na : α\ns : Multiset α\n⊢ 0 < count a s ↔ a ∈ s"
] | succ_le_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.List.Nodup | {
"line": 75,
"column": 6
} | {
"line": 79,
"column": 44
} | {
"line": 79,
"column": 44
} | [
{
"pp": "α : Type u\nl : List α\nh : ∀ (i j : ℕ) (_hi : i < l.length) (_hj : j < l.length), i < j → l[i] ≠ l[j]\ni j : Fin l.length\nhg : (fun i ↦ l[↑i]) i = (fun i ↦ l[↑i]) j\n⊢ i = j",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Nat.lt_trichotomy",
"Fin.casesOn",
"Fa... | [] | obtain ⟨i, hi⟩ := i; obtain ⟨j, hj⟩ := j
rcases Nat.lt_trichotomy i j with (hij | rfl | hji)
· exact (h i j hi hj hij hg).elim
· rfl
· exact (h j i hj hi hji hg.symm).elim | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.List.Nodup | {
"line": 75,
"column": 6
} | {
"line": 79,
"column": 44
} | {
"line": 79,
"column": 44
} | [
{
"pp": "α : Type u\nl : List α\nh : ∀ (i j : ℕ) (_hi : i < l.length) (_hj : j < l.length), i < j → l[i] ≠ l[j]\ni j : Fin l.length\nhg : (fun i ↦ l[↑i]) i = (fun i ↦ l[↑i]) j\n⊢ i = j",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Nat.lt_trichotomy",
"Fin.casesOn",
"Fa... | [] | obtain ⟨i, hi⟩ := i; obtain ⟨j, hj⟩ := j
rcases Nat.lt_trichotomy i j with (hij | rfl | hji)
· exact (h i j hi hj hij hg).elim
· rfl
· exact (h j i hj hi hji hg.symm).elim | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.Nodup | {
"line": 248,
"column": 29
} | {
"line": 248,
"column": 34
} | {
"line": 248,
"column": 34
} | [
{
"pp": "α : Type u\na : α\nl : List α\nih : l[0]? = l.getLast? → (l.dropLast.Nodup ↔ l.tail.Nodup)\nh : (a :: l)[0]? = (a :: l).getLast?\nhl : ¬l = []\n⊢ l.length ≠ 0",
"ppTerm": "?m.57",
"assigned": true,
"usedConstants": [
"False",
"eq_false",
"congrArg",
"List.length_eq_z... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.List.Nodup | {
"line": 248,
"column": 29
} | {
"line": 248,
"column": 34
} | {
"line": 248,
"column": 34
} | [
{
"pp": "α : Type u\na : α\nl : List α\nih : l[0]? = l.getLast? → (l.dropLast.Nodup ↔ l.tail.Nodup)\nh : (a :: l)[0]? = (a :: l).getLast?\nhl : ¬l = []\n⊢ l.length ≠ 0",
"ppTerm": "?m.57",
"assigned": true,
"usedConstants": [
"False",
"eq_false",
"congrArg",
"List.length_eq_z... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.List.Nodup | {
"line": 248,
"column": 29
} | {
"line": 248,
"column": 34
} | {
"line": 248,
"column": 34
} | [
{
"pp": "α : Type u\na : α\nl : List α\nih : l[0]? = l.getLast? → (l.dropLast.Nodup ↔ l.tail.Nodup)\nh : (a :: l)[0]? = (a :: l).getLast?\nhl : ¬l = []\n⊢ l.length ≠ 0",
"ppTerm": "?m.57",
"assigned": true,
"usedConstants": [
"False",
"eq_false",
"congrArg",
"List.length_eq_z... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Multiset.ZeroCons | {
"line": 472,
"column": 17
} | {
"line": 472,
"column": 22
} | {
"line": 472,
"column": 22
} | [
{
"pp": "α : Type u_1\ns : Multiset α\nn : ℕ\n⊢ (∃ a t, a ::ₘ t = s ∧ t.card = n) → s.card = n + 1",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"congrArg",
"Exists",
"Multiset",
"Multiset.cons",
"instOfNatNat",
"Multiset.card_cons",
"And.casesOn... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Multiset.ZeroCons | {
"line": 472,
"column": 17
} | {
"line": 472,
"column": 22
} | {
"line": 472,
"column": 22
} | [
{
"pp": "α : Type u_1\ns : Multiset α\nn : ℕ\n⊢ (∃ a t, a ::ₘ t = s ∧ t.card = n) → s.card = n + 1",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"congrArg",
"Exists",
"Multiset",
"Multiset.cons",
"instOfNatNat",
"Multiset.card_cons",
"And.casesOn... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Multiset.ZeroCons | {
"line": 472,
"column": 17
} | {
"line": 472,
"column": 22
} | {
"line": 472,
"column": 22
} | [
{
"pp": "α : Type u_1\ns : Multiset α\nn : ℕ\n⊢ (∃ a t, a ::ₘ t = s ∧ t.card = n) → s.card = n + 1",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"congrArg",
"Exists",
"Multiset",
"Multiset.cons",
"instOfNatNat",
"Multiset.card_cons",
"And.casesOn... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Multiset.ZeroCons | {
"line": 473,
"column": 59
} | {
"line": 473,
"column": 64
} | {
"line": 475,
"column": 0
} | [
{
"pp": "case empty\nα : Type u_1\nn : ℕ\n⊢ card 0 = n + 1 → ∃ a t, a ::ₘ t = 0 ∧ t.card = n",
"ppTerm": "?empty",
"assigned": true,
"usedConstants": [
"False",
"congrArg",
"False.elim",
"Nat.add_eq_zero_iff._simp_1",
"Exists",
"Multiset",
"Eq.mp",
"Mu... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Multiset.ZeroCons | {
"line": 473,
"column": 59
} | {
"line": 473,
"column": 64
} | {
"line": 475,
"column": 0
} | [
{
"pp": "case cons\nα : Type u_1\na✝¹ : α\ns✝ : Multiset α\na✝ : ∀ {n : ℕ}, s✝.card = n + 1 → ∃ a t, a ::ₘ t = s✝ ∧ t.card = n\nn : ℕ\n⊢ (a✝¹ ::ₘ s✝).card = n + 1 → ∃ a t, a ::ₘ t = a✝¹ ::ₘ s✝ ∧ t.card = n",
"ppTerm": "?cons",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Multiset.MapFold | {
"line": 477,
"column": 6
} | {
"line": 477,
"column": 11
} | {
"line": 478,
"column": 4
} | [
{
"pp": "α : Type u_1\nβ : Type v\nγ : Type u_2\nf : α → γ\ng : β → γ\ns : Multiset α\nt : Multiset β\nhs : s.Nodup\nht : t.Nodup\ni : (a : α) → a ∈ s → β\nhi : ∀ (a : α) (ha : a ∈ s), i a ha ∈ t\ni_inj : ∀ (a₁ : α) (ha₁ : a₁ ∈ s) (a₂ : α) (ha₂ : a₂ ∈ s), i a₁ ha₁ = i a₂ ha₂ → a₁ = a₂\ni_surj : ∀ (b : β), b ∈ t... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Multiset.MapFold | {
"line": 477,
"column": 6
} | {
"line": 477,
"column": 11
} | {
"line": 478,
"column": 4
} | [
{
"pp": "α : Type u_1\nβ : Type v\nγ : Type u_2\nf : α → γ\ng : β → γ\ns : Multiset α\nt : Multiset β\nhs : s.Nodup\nht : t.Nodup\ni : (a : α) → a ∈ s → β\nhi : ∀ (a : α) (ha : a ∈ s), i a ha ∈ t\ni_inj : ∀ (a₁ : α) (ha₁ : a₁ ∈ s) (a₂ : α) (ha₂ : a₂ ∈ s), i a₁ ha₁ = i a₂ ha₂ → a₁ = a₂\ni_surj : ∀ (b : β), b ∈ t... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Multiset.MapFold | {
"line": 477,
"column": 6
} | {
"line": 477,
"column": 11
} | {
"line": 478,
"column": 4
} | [
{
"pp": "α : Type u_1\nβ : Type v\nγ : Type u_2\nf : α → γ\ng : β → γ\ns : Multiset α\nt : Multiset β\nhs : s.Nodup\nht : t.Nodup\ni : (a : α) → a ∈ s → β\nhi : ∀ (a : α) (ha : a ∈ s), i a ha ∈ t\ni_inj : ∀ (a₁ : α) (ha₁ : a₁ ∈ s) (a₂ : α) (ha₂ : a₂ ∈ s), i a₁ ha₁ = i a₂ ha₂ → a₁ = a₂\ni_surj : ∀ (b : β), b ∈ t... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Multiset.UnionInter | {
"line": 323,
"column": 25
} | {
"line": 323,
"column": 43
} | {
"line": 323,
"column": 43
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Multiset α\n⊢ (∀ (a : α), count a s + count a t = max (count a s) (count a t)) ↔ ∀ (a : α), count a s = 0 ∨ count a t = 0",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"congrArg",
"Multiset.count",
"instOfNatNat",
... | [] | Nat.add_eq_max_iff | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Data.Finset.SDiff | {
"line": 188,
"column": 7
} | {
"line": 188,
"column": 12
} | {
"line": 190,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\ns : Finset α\na b : α\nhab : a ≠ b\nha : a ∉ s\na✝ : α\n⊢ a✝ ∈ insert a s \\ insert b s ↔ a✝ ∈ {a}",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"eq_false",
"congrArg",
"and_self",
"Finse... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Finset.Basic | {
"line": 145,
"column": 2
} | {
"line": 145,
"column": 7
} | {
"line": 147,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\na : α\nhs : a ∈ s\nht : a ∉ t\n⊢ s.erase a = t ↔ s = insert a t",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"False",
"eq_false",
"congrArg",
"Finset",
"Membership.mem",
"Insert.insert",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Finset.Basic | {
"line": 145,
"column": 2
} | {
"line": 145,
"column": 7
} | {
"line": 147,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\na : α\nhs : a ∈ s\nht : a ∉ t\n⊢ s.erase a = t ↔ s = insert a t",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"False",
"eq_false",
"congrArg",
"Finset",
"Membership.mem",
"Insert.insert",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Finset.Basic | {
"line": 145,
"column": 2
} | {
"line": 145,
"column": 7
} | {
"line": 147,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\na : α\nhs : a ∈ s\nht : a ∉ t\n⊢ s.erase a = t ↔ s = insert a t",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"False",
"eq_false",
"congrArg",
"Finset",
"Membership.mem",
"Insert.insert",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Finset.Basic | {
"line": 197,
"column": 7
} | {
"line": 197,
"column": 12
} | {
"line": 201,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\ns : Finset α\na b : α\nhab : a ≠ b\nhb : b ∈ s\na✝ : α\n⊢ a✝ ∈ s.erase a \\ s.erase b ↔ a✝ ∈ {b}",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"and_true",
"congrArg",
"Finset",
"False.eli... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Finset.Basic | {
"line": 214,
"column": 6
} | {
"line": 214,
"column": 28
} | {
"line": 214,
"column": 29
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\na : α\nha : a ∉ s\n⊢ Disjoint (insert a s) (t.erase a) ↔ Disjoint s t",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Finset",
"Disjoint",
"id",
"Insert.insert",
"... | [
"α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\na : α\nha : a ∉ s\n⊢ Disjoint ((insert a s).erase a) t ↔ Disjoint s t"
] | ← disjoint_erase_comm, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Finset.Basic | {
"line": 217,
"column": 25
} | {
"line": 217,
"column": 47
} | {
"line": 217,
"column": 48
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\na : α\nha : a ∉ t\nhst : Disjoint (s.erase a) t\n⊢ Disjoint s ((insert a t).erase a)",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Finset",
"Disjoint",
"id",
"Insert.i... | [
"α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\na : α\nha : a ∉ t\nhst : Disjoint (s.erase a) t\n⊢ Disjoint (s.erase a) (insert a t)"
] | ← disjoint_erase_comm, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Finset.Basic | {
"line": 217,
"column": 2
} | {
"line": 218,
"column": 31
} | {
"line": 220,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\na : α\nha : a ∉ t\nhst : Disjoint (s.erase a) t\n⊢ Disjoint s t",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Finset",
"Disjoint",
"Membership.mem",
"id",
"Inser... | [] | rw [← erase_insert ha, ← disjoint_erase_comm, disjoint_insert_right]
exact ⟨notMem_erase _ _, hst⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Finset.Basic | {
"line": 217,
"column": 2
} | {
"line": 218,
"column": 31
} | {
"line": 220,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\na : α\nha : a ∉ t\nhst : Disjoint (s.erase a) t\n⊢ Disjoint s t",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Finset",
"Disjoint",
"Membership.mem",
"id",
"Inser... | [] | rw [← erase_insert ha, ← disjoint_erase_comm, disjoint_insert_right]
exact ⟨notMem_erase _ _, hst⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Finset.Basic | {
"line": 695,
"column": 47
} | {
"line": 695,
"column": 52
} | {
"line": 697,
"column": 0
} | [
{
"pp": "α : Type u_4\na : α\nH : {a} = ∅\n⊢ False",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"False",
"Finset",
"False.elim",
"Eq.mp",
"Finset.instEmptyCollection",
"Finset.singleton_ne_empty._simp_1",
"EmptyCollection.emptyCollection",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Finset.Image | {
"line": 117,
"column": 44
} | {
"line": 119,
"column": 6
} | {
"line": 121,
"column": 0
} | [
{
"pp": "α β : Type u_4\nh : α = β\ns : Finset α\n⊢ map (Equiv.cast h).toEmbedding s ≍ s",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"congrArg",
"Finset",
"Equiv.cast",
"heq_eq_eq",
"Finset.map",
"Eq.rec",
"Equiv.toEmbedding",
"congrFun",... | [] | by
subst h
simp | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Fin.Basic | {
"line": 313,
"column": 31
} | {
"line": 313,
"column": 48
} | {
"line": 313,
"column": 48
} | [
{
"pp": "n✝ m n : ℕ\n⊢ NeZero (1 + n)",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Zero.ofOfNat0",
"id",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"NeZero",
"OfNat.ofNat",
... | [
"n✝ m n : ℕ\n⊢ NeZero (n + 1)"
] | rw [Nat.add_comm] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Order.Fin.Basic | {
"line": 388,
"column": 2
} | {
"line": 388,
"column": 7
} | {
"line": 390,
"column": 0
} | [
{
"pp": "n : ℕ\ni : Fin (n + 1)\n⊢ range ⇑i.succAboveOrderEmb = {i}ᶜ",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Set.ext",
"Fin.succAbove",
"congrArg",
"Compl.compl",
"Membership.mem",
"Exists",
"Set.instSingletonSet",
"Ne",
"instO... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.Fin.Basic | {
"line": 388,
"column": 2
} | {
"line": 388,
"column": 7
} | {
"line": 390,
"column": 0
} | [
{
"pp": "n : ℕ\ni : Fin (n + 1)\n⊢ range ⇑i.succAboveOrderEmb = {i}ᶜ",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Set.ext",
"Fin.succAbove",
"congrArg",
"Compl.compl",
"Membership.mem",
"Exists",
"Set.instSingletonSet",
"Ne",
"instO... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Fin.Basic | {
"line": 388,
"column": 2
} | {
"line": 388,
"column": 7
} | {
"line": 390,
"column": 0
} | [
{
"pp": "n : ℕ\ni : Fin (n + 1)\n⊢ range ⇑i.succAboveOrderEmb = {i}ᶜ",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Set.ext",
"Fin.succAbove",
"congrArg",
"Compl.compl",
"Membership.mem",
"Exists",
"Set.instSingletonSet",
"Ne",
"instO... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.OfFn | {
"line": 70,
"column": 49
} | {
"line": 70,
"column": 81
} | {
"line": 70,
"column": 81
} | [
{
"pp": "α : Type u\nm n : ℕ\nf : Fin (m * n) → α\ni : Fin m\nj : Fin n\n⊢ ↑i * n + n = (↑i + 1) * n",
"ppTerm": "?m.70",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"congrArg",
"id",
"instMulNat",
"instOfNatNat",
"Fin.val",
"instHAdd",... | [] | by rw [Nat.add_mul, Nat.one_mul] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Fin.Tuple.Basic | {
"line": 254,
"column": 4
} | {
"line": 255,
"column": 7
} | {
"line": 256,
"column": 2
} | [
{
"pp": "case pos\nn : ℕ\nα : Sort u_1\nβ : Sort u_2\ng : α → β\ny : α\nq : Fin n → α\nj : Fin (n + 1)\nh : j = 0\n⊢ (g ∘ cons y q) j = cons (g y) (g ∘ q) j",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instNeZeroNatHAdd_1",
"congrArg",
"Fin.cons",
... | [] | rw [h]
rfl | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Fin.Tuple.Basic | {
"line": 254,
"column": 4
} | {
"line": 255,
"column": 7
} | {
"line": 256,
"column": 2
} | [
{
"pp": "case pos\nn : ℕ\nα : Sort u_1\nβ : Sort u_2\ng : α → β\ny : α\nq : Fin n → α\nj : Fin (n + 1)\nh : j = 0\n⊢ (g ∘ cons y q) j = cons (g y) (g ∘ q) j",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instNeZeroNatHAdd_1",
"congrArg",
"Fin.cons",
... | [] | rw [h]
rfl | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Fin.SuccPred | {
"line": 453,
"column": 39
} | {
"line": 453,
"column": 60
} | {
"line": 453,
"column": 61
} | [
{
"pp": "n : ℕ\na : Fin (n + 1)\nha : a ≠ last n\n⊢ a < (a.castPred ha).succ",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Fin.succ",
"congrArg",
"id",
"Fin.castPred",
"instOfNatNat",
"LE.le",
"instLEFin",
"instHAdd",
... | [
"n : ℕ\na : Fin (n + 1)\nha : a ≠ last n\n⊢ a ≤ a"
] | lt_succ_castPred_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Fin.Tuple.Basic | {
"line": 558,
"column": 2
} | {
"line": 561,
"column": 26
} | {
"line": 563,
"column": 0
} | [
{
"pp": "n : ℕ\nα : Fin (n + 1) → Sort u_1\nx : α (last n)\np : (i : Fin n) → α i.castSucc\ni : Fin n\ny : α i.castSucc\n⊢ snoc (update p i y) x = update (snoc p x) i.castSucc y",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"False",
"Fin.castSucc_ne_last._simp_1",
"Func... | [] | ext j
cases j using lastCases with
| cast j => rcases eq_or_ne j i with rfl | hne <;> simp [*]
| last => simp [Ne.symm] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Fin.Tuple.Basic | {
"line": 558,
"column": 2
} | {
"line": 561,
"column": 26
} | {
"line": 563,
"column": 0
} | [
{
"pp": "n : ℕ\nα : Fin (n + 1) → Sort u_1\nx : α (last n)\np : (i : Fin n) → α i.castSucc\ni : Fin n\ny : α i.castSucc\n⊢ snoc (update p i y) x = update (snoc p x) i.castSucc y",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"False",
"Fin.castSucc_ne_last._simp_1",
"Func... | [] | ext j
cases j using lastCases with
| cast j => rcases eq_or_ne j i with rfl | hne <;> simp [*]
| last => simp [Ne.symm] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Fin.Tuple.Basic | {
"line": 675,
"column": 4
} | {
"line": 679,
"column": 27
} | {
"line": 681,
"column": 0
} | [
{
"pp": "case succ\nm n : ℕ\nα : Sort u_2\na : α\nas : Fin n → α\nbs : Fin m → α\ni : ℕ\nisLt✝ : i + 1 < n + 1 + m\n⊢ (if h : i + 1 < n + 1 then cases a as ⟨i + 1, ⋯⟩ else ⋯ ▸ bs (subNat (n + 1) (Fin.cast ⋯ ⟨i + 1, isLt✝⟩) ⋯)) =\n cases a (addCases as bs) (Fin.cast ⋯ ⟨i + 1, isLt✝⟩)",
"ppTerm": "?succ",
... | [] | split_ifs with h
· have : i < n := Nat.lt_of_succ_lt_succ h
simp [addCases, this]
· have : ¬i < n := Nat.not_le_of_gt <| Nat.le_of_lt_succ <| Nat.gt_of_not_le h
simp [addCases, this] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Fin.Tuple.Basic | {
"line": 675,
"column": 4
} | {
"line": 679,
"column": 27
} | {
"line": 681,
"column": 0
} | [
{
"pp": "case succ\nm n : ℕ\nα : Sort u_2\na : α\nas : Fin n → α\nbs : Fin m → α\ni : ℕ\nisLt✝ : i + 1 < n + 1 + m\n⊢ (if h : i + 1 < n + 1 then cases a as ⟨i + 1, ⋯⟩ else ⋯ ▸ bs (subNat (n + 1) (Fin.cast ⋯ ⟨i + 1, isLt✝⟩) ⋯)) =\n cases a (addCases as bs) (Fin.cast ⋯ ⟨i + 1, isLt✝⟩)",
"ppTerm": "?succ",
... | [] | split_ifs with h
· have : i < n := Nat.lt_of_succ_lt_succ h
simp [addCases, this]
· have : ¬i < n := Nat.not_le_of_gt <| Nat.le_of_lt_succ <| Nat.gt_of_not_le h
simp [addCases, this] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Fin.Tuple.Basic | {
"line": 1067,
"column": 2
} | {
"line": 1067,
"column": 46
} | {
"line": 1069,
"column": 0
} | [
{
"pp": "n : ℕ\nα : Fin (n + 2) → Sort u_3\nm : (i : Fin (n + 2)) → α i\ni : Fin (n + 1)\nj : Fin (n + 2)\nk : Fin n\n⊢ j.succAbove (i.succAbove k) = (j.succAbove i).succAbove ((i.predAbove j).succAbove k)",
"ppTerm": "?m.67",
"assigned": true,
"usedConstants": [
"Fin.succAbove",
"Eq.mpr... | [] | rw [succAbove_succAbove_succAbove_predAbove] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Fin.Tuple.Basic | {
"line": 1259,
"column": 2
} | {
"line": 1259,
"column": 51
} | {
"line": 1260,
"column": 2
} | [
{
"pp": "n : ℕ\nα : Sort u_1\nj : Fin (n + 1)\nop : α → α → α\ng : Fin (n + 1) → α\nk : Fin n\nh : ↑k = ↑j\n⊢ j.contractNth op g k = op (g k.castSucc) (g k.succ)",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Preorder.toLT",
"PartialOrder.toPreorder",
"... | [
"n : ℕ\nα : Sort u_1\nj : Fin (n + 1)\nop : α → α → α\ng : Fin (n + 1) → α\nk : Fin n\nh : ↑k = ↑j\nthis : ¬↑k < ↑j\n⊢ j.contractNth op g k = op (g k.castSucc) (g k.succ)"
] | have : ¬(k : ℕ) < j := not_lt.2 (le_of_eq h.symm) | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Data.Set.Finite.Basic | {
"line": 661,
"column": 2
} | {
"line": 661,
"column": 7
} | {
"line": 663,
"column": 0
} | [
{
"pp": "α : Type u\nβ : Type v\nf : α → β\ns : Set α\np : Set β → Prop\n⊢ (∃ s_1, (∃ s', ↑s' ⊆ s ∧ Finset.image f s' = s_1) ∧ p ↑s_1) ↔ ∃ s_1, ↑s_1 ⊆ s ∧ p (f '' ↑s_1)",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"and_true",
"congrArg",
"Finset",
"Classical.prop... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.BigOperators.Group.Multiset.Defs | {
"line": 85,
"column": 73
} | {
"line": 86,
"column": 39
} | {
"line": 88,
"column": 0
} | [
{
"pp": "M : Type u_3\ninst✝ : CommMonoid M\nn : ℕ\na : M\n⊢ (replicate n a).prod = a ^ n",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"congrArg",
"Multiset.prod",
"NPow.toPow",
"HPow.hPow",
"CommMonoid.toMonoid",
"Nat",
"True",
"eq_self",
... | [] | by
simp [replicate, List.prod_replicate] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.BigOperators.Group.Multiset.Defs | {
"line": 113,
"column": 13
} | {
"line": 113,
"column": 23
} | {
"line": 114,
"column": 2
} | [
{
"pp": "case empty\nM : Type u_3\ninst✝ : CommMonoid M\ns : Multiset M\np : M → Prop\np_mul : ∀ (a b : M), p a → p b → p (a * b)\nhs : 0 ≠ ∅\np_s : ∀ (a : M), a ∈ 0 → p a\n⊢ p (prod 0)",
"ppTerm": "?empty",
"assigned": true,
"usedConstants": [
"False",
"congrArg",
"False.elim",
... | [] | simp at hs | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.BigOperators.Group.Multiset.Defs | {
"line": 113,
"column": 13
} | {
"line": 113,
"column": 23
} | {
"line": 114,
"column": 2
} | [
{
"pp": "case empty\nM : Type u_3\ninst✝ : CommMonoid M\ns : Multiset M\np : M → Prop\np_mul : ∀ (a b : M), p a → p b → p (a * b)\nhs : 0 ≠ ∅\np_s : ∀ (a : M), a ∈ 0 → p a\n⊢ p (prod 0)",
"ppTerm": "?empty",
"assigned": true,
"usedConstants": [
"False",
"congrArg",
"False.elim",
... | [] | simp at hs | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.BigOperators.Group.Multiset.Defs | {
"line": 113,
"column": 13
} | {
"line": 113,
"column": 23
} | {
"line": 114,
"column": 2
} | [
{
"pp": "case empty\nM : Type u_3\ninst✝ : CommMonoid M\ns : Multiset M\np : M → Prop\np_mul : ∀ (a b : M), p a → p b → p (a * b)\nhs : 0 ≠ ∅\np_s : ∀ (a : M), a ∈ 0 → p a\n⊢ p (prod 0)",
"ppTerm": "?empty",
"assigned": true,
"usedConstants": [
"False",
"congrArg",
"False.elim",
... | [] | simp at hs | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.Rotate | {
"line": 190,
"column": 39
} | {
"line": 190,
"column": 54
} | {
"line": 190,
"column": 55
} | [
{
"pp": "α : Type u\nβ : Type u_1\nγ : Type u_2\nf : α → β → γ\nl : List α\nl' : List β\nn : ℕ\nh : l.length = l'.length\n⊢ drop (n % (zipWith f l l').length) (zipWith f l l') ++ take (n % (zipWith f l l').length) (zipWith f l l') =\n zipWith f (drop (n % l'.length) l ++ take (n % l'.length) l) (drop (n % l'... | [
"α : Type u\nβ : Type u_1\nγ : Type u_2\nf : α → β → γ\nl : List α\nl' : List β\nn : ℕ\nh : l.length = l'.length\n⊢ drop (n % (zipWith f l l').length) (zipWith f l l') ++ take (n % (zipWith f l l').length) (zipWith f l l') =\n zipWith f (drop (n % l'.length) l) (drop (n % l'.length) l') ++\n zipWith f (take... | zipWith_append, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Group.Multiset | {
"line": 165,
"column": 31
} | {
"line": 165,
"column": 76
} | {
"line": 167,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\ns : Multiset α\nn : ℕ\nhn : n ≠ 0\n⊢ (n • s).dedup = s.dedup",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"False",
"instHSMul",
"eq_false",
"Multiset.Nodup",
"congrArg",
"and_self",
"Multiset.dedup",... | [] | by ext a; by_cases h : a ∈ s <;> simp [h, hn] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.BigOperators.Group.Multiset.Basic | {
"line": 90,
"column": 34
} | {
"line": 90,
"column": 96
} | {
"line": 92,
"column": 0
} | [
{
"pp": "M : Type u_5\nN : Type u_6\ninst✝³ : CommMonoid M\ninst✝² : CommMonoid N\ns : Multiset M\nF : Type u_8\ninst✝¹ : FunLike F M N\ninst✝ : MonoidHomClass F M N\nf : F\nl : List M\n⊢ (map ⇑f ⟦l⟧).prod = f (prod ⟦l⟧)",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"MulOne.toOne",... | [] | by simp only [l.prod_hom f, quot_mk_to_coe, map_coe, prod_coe] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.BigOperators.Group.List.Lemmas | {
"line": 176,
"column": 28
} | {
"line": 176,
"column": 37
} | {
"line": 176,
"column": 38
} | [
{
"pp": "G : Type u_7\ninst✝ : CommGroup G\na : G\nl₁ l₂ : List G\n⊢ a / (l₁.alternatingProd * l₂.alternatingProd ^ (-1) ^ l₁.length) =\n a / l₁.alternatingProd * l₂.alternatingProd ^ (-(-1) ^ l₁.length)",
"ppTerm": "?m.64",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHDiv",
... | [
"G : Type u_7\ninst✝ : CommGroup G\na : G\nl₁ l₂ : List G\n⊢ a / (l₁.alternatingProd * l₂.alternatingProd ^ (-1) ^ l₁.length) =\n a / l₁.alternatingProd * (l₂.alternatingProd ^ (-1) ^ l₁.length)⁻¹"
] | zpow_neg, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Algebra.BigOperators.Group.List.Lemmas | {
"line": 185,
"column": 28
} | {
"line": 185,
"column": 37
} | {
"line": 185,
"column": 38
} | [
{
"pp": "G : Type u_7\ninst✝ : CommGroup G\na : G\nl : List G\n⊢ l.alternatingProd ^ (-(-1) ^ l.length) * a ^ (-1) ^ l.length = (a / l.alternatingProd) ^ (- -(-1) ^ l.length)",
"ppTerm": "?m.58",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHDiv",
"InvOneClass.toOne",
... | [
"G : Type u_7\ninst✝ : CommGroup G\na : G\nl : List G\n⊢ (l.alternatingProd ^ (-1) ^ l.length)⁻¹ * a ^ (-1) ^ l.length = ((a / l.alternatingProd) ^ (-1) ^ l.length)⁻¹⁻¹"
] | zpow_neg, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Data.Finset.Union | {
"line": 209,
"column": 2
} | {
"line": 209,
"column": 7
} | {
"line": 211,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ns : Finset α\nt : α → Finset β\ninst✝¹ : DecidableEq β\ninst✝ : DecidableEq α\na : α\n⊢ (insert a s).biUnion t = t a ∪ s.biUnion t",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Finset.instUnion",
"congrArg",
"Finset",
"Finset.... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Finset.Union | {
"line": 209,
"column": 2
} | {
"line": 209,
"column": 7
} | {
"line": 211,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ns : Finset α\nt : α → Finset β\ninst✝¹ : DecidableEq β\ninst✝ : DecidableEq α\na : α\n⊢ (insert a s).biUnion t = t a ∪ s.biUnion t",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Finset.instUnion",
"congrArg",
"Finset",
"Finset.... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Finset.Union | {
"line": 209,
"column": 2
} | {
"line": 209,
"column": 7
} | {
"line": 211,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ns : Finset α\nt : α → Finset β\ninst✝¹ : DecidableEq β\ninst✝ : DecidableEq α\na : α\n⊢ (insert a s).biUnion t = t a ∪ s.biUnion t",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Finset.instUnion",
"congrArg",
"Finset",
"Finset.... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Finset.Union | {
"line": 307,
"column": 85
} | {
"line": 307,
"column": 90
} | {
"line": 309,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ns : Finset α\ninst✝ : DecidableEq β\nf : α → Finset β\n⊢ (s.attach.biUnion fun x ↦ f ↑x) = s.biUnion f",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Iff.of_eq",
"congrArg",
"Finset",
"Finset.mem_biUnion._simp_1",
"Finset... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Finset.Union | {
"line": 307,
"column": 85
} | {
"line": 307,
"column": 90
} | {
"line": 309,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ns : Finset α\ninst✝ : DecidableEq β\nf : α → Finset β\n⊢ (s.attach.biUnion fun x ↦ f ↑x) = s.biUnion f",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Iff.of_eq",
"congrArg",
"Finset",
"Finset.mem_biUnion._simp_1",
"Finset... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Finset.Union | {
"line": 307,
"column": 85
} | {
"line": 307,
"column": 90
} | {
"line": 309,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ns : Finset α\ninst✝ : DecidableEq β\nf : α → Finset β\n⊢ (s.attach.biUnion fun x ↦ f ↑x) = s.biUnion f",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Iff.of_eq",
"congrArg",
"Finset",
"Finset.mem_biUnion._simp_1",
"Finset... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Finset.Union | {
"line": 313,
"column": 83
} | {
"line": 313,
"column": 88
} | {
"line": 315,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ns : Finset α\ninst✝¹ : DecidableEq β\ninst✝ : DecidableEq α\nf : ↥s → Finset β\n⊢ s.attach.biUnion f = s.biUnion fun a ↦ if h : a ∈ s then f ⟨a, h⟩ else ∅",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"dite_cond_eq_true",
"Eq.mpr",
"... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Finset.Union | {
"line": 313,
"column": 83
} | {
"line": 313,
"column": 88
} | {
"line": 315,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ns : Finset α\ninst✝¹ : DecidableEq β\ninst✝ : DecidableEq α\nf : ↥s → Finset β\n⊢ s.attach.biUnion f = s.biUnion fun a ↦ if h : a ∈ s then f ⟨a, h⟩ else ∅",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"dite_cond_eq_true",
"Eq.mpr",
"... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Finset.Union | {
"line": 313,
"column": 83
} | {
"line": 313,
"column": 88
} | {
"line": 315,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ns : Finset α\ninst✝¹ : DecidableEq β\ninst✝ : DecidableEq α\nf : ↥s → Finset β\n⊢ s.attach.biUnion f = s.biUnion fun a ↦ if h : a ∈ s then f ⟨a, h⟩ else ∅",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"dite_cond_eq_true",
"Eq.mpr",
"... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Fintype.Pi | {
"line": 101,
"column": 56
} | {
"line": 101,
"column": 61
} | {
"line": 101,
"column": 61
} | [
{
"pp": "α : Type u_1\ninst✝² : DecidableEq α\ninst✝¹ : Fintype α\nδ : α → Type u_4\nt : (a : α) → Finset (δ a)\na : α\ninst✝ : DecidableEq (δ a)\nx : δ a\nh : x ∈ t a\nf : (b : α) → a ≠ b → δ b\nhf : ∀ (b : α) (a : a ≠ b), f b a ∈ t b\n⊢ (fun b ↦ if h : a = b then h ▸ x else f b h) ∈ piFinset t",
"ppTerm":... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Fintype.Pi | {
"line": 101,
"column": 56
} | {
"line": 101,
"column": 61
} | {
"line": 101,
"column": 61
} | [
{
"pp": "α : Type u_1\ninst✝² : DecidableEq α\ninst✝¹ : Fintype α\nδ : α → Type u_4\nt : (a : α) → Finset (δ a)\na : α\ninst✝ : DecidableEq (δ a)\nx : δ a\nh : x ∈ t a\nf : (b : α) → a ≠ b → δ b\nhf : ∀ (b : α) (a : a ≠ b), f b a ∈ t b\n⊢ (fun b ↦ if h : a = b then h ▸ x else f b h) ∈ piFinset t",
"ppTerm":... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Fintype.Pi | {
"line": 101,
"column": 56
} | {
"line": 101,
"column": 61
} | {
"line": 101,
"column": 61
} | [
{
"pp": "α : Type u_1\ninst✝² : DecidableEq α\ninst✝¹ : Fintype α\nδ : α → Type u_4\nt : (a : α) → Finset (δ a)\na : α\ninst✝ : DecidableEq (δ a)\nx : δ a\nh : x ∈ t a\nf : (b : α) → a ≠ b → δ b\nhf : ∀ (b : α) (a : a ≠ b), f b a ∈ t b\n⊢ (fun b ↦ if h : a = b then h ▸ x else f b h) ∈ piFinset t",
"ppTerm":... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Multiset.Pi | {
"line": 175,
"column": 4
} | {
"line": 175,
"column": 86
} | {
"line": 176,
"column": 4
} | [
{
"pp": "case cons.mpr\nα : Type u_1\ninst✝ : DecidableEq α\nβ : α → Type u_2\nt : (a : α) → Multiset (β a)\na : α\nm : Multiset α\nih : ∀ (f : (a : α) → a ∈ m → β a), f ∈ m.pi t ↔ ∀ (a : α) (h : a ∈ m), f a h ∈ t a\nf : (a_1 : α) → a_1 ∈ a ::ₘ m → β a_1\nhf : ∀ (a_1 : α) (h : a_1 ∈ a ::ₘ m), f a_1 h ∈ t a_1\n⊢... | [
"case cons.mpr\nα : Type u_1\ninst✝ : DecidableEq α\nβ : α → Type u_2\nt : (a : α) → Multiset (β a)\na : α\nm : Multiset α\nih : ∀ (f : (a : α) → a ∈ m → β a), f ∈ m.pi t ↔ ∀ (a : α) (h : a ∈ m), f a h ∈ t a\nf : (a_1 : α) → a_1 ∈ a ::ₘ m → β a_1\nhf : ∀ (a_1 : α) (h : a_1 ∈ a ::ₘ m), f a_1 h ∈ t a_1\n⊢ (Pi.cons m ... | refine ⟨_, hf a (mem_cons_self _ _), _, fun a ha => hf a (mem_cons_of_mem ha), ?_⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Data.Fintype.Pi | {
"line": 175,
"column": 85
} | {
"line": 175,
"column": 90
} | {
"line": 177,
"column": 0
} | [
{
"pp": "α : Type u_1\nι : Type u_3\ninst✝² : DecidableEq (ι → α)\ns : Finset α\ninst✝¹ : DecidableEq ι\ninst✝ : Fintype ι\n⊢ {f ∈ Fintype.piFinset fun x ↦ s | ∃ a ∈ s, const ι a = f} = s.piDiag ι",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.mem_filter._sim... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Fintype.Pi | {
"line": 175,
"column": 85
} | {
"line": 175,
"column": 90
} | {
"line": 177,
"column": 0
} | [
{
"pp": "α : Type u_1\nι : Type u_3\ninst✝² : DecidableEq (ι → α)\ns : Finset α\ninst✝¹ : DecidableEq ι\ninst✝ : Fintype ι\n⊢ {f ∈ Fintype.piFinset fun x ↦ s | ∃ a ∈ s, const ι a = f} = s.piDiag ι",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.mem_filter._sim... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Fintype.Pi | {
"line": 175,
"column": 85
} | {
"line": 175,
"column": 90
} | {
"line": 177,
"column": 0
} | [
{
"pp": "α : Type u_1\nι : Type u_3\ninst✝² : DecidableEq (ι → α)\ns : Finset α\ninst✝¹ : DecidableEq ι\ninst✝ : Fintype ι\n⊢ {f ∈ Fintype.piFinset fun x ↦ s | ∃ a ∈ s, const ι a = f} = s.piDiag ι",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.mem_filter._sim... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Group.Action.End | {
"line": 195,
"column": 2
} | {
"line": 195,
"column": 7
} | {
"line": 197,
"column": 0
} | [
{
"pp": "G : Type u_1\nα : Type u_5\ninst✝¹ : Group G\ninst✝ : MulAction G α\n⊢ toPerm 1 = 1",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"instHSMul",
"InvOneClass.toOne",
"Equiv.instEquivLike",
"Equiv.Perm.instOne",
"DivInvOneMonoid.toInvOneClass",
"... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Group.Action.End | {
"line": 195,
"column": 2
} | {
"line": 195,
"column": 7
} | {
"line": 197,
"column": 0
} | [
{
"pp": "G : Type u_1\nα : Type u_5\ninst✝¹ : Group G\ninst✝ : MulAction G α\n⊢ toPerm 1 = 1",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"instHSMul",
"InvOneClass.toOne",
"Equiv.instEquivLike",
"Equiv.Perm.instOne",
"DivInvOneMonoid.toInvOneClass",
"... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Group.Action.End | {
"line": 195,
"column": 2
} | {
"line": 195,
"column": 7
} | {
"line": 197,
"column": 0
} | [
{
"pp": "G : Type u_1\nα : Type u_5\ninst✝¹ : Group G\ninst✝ : MulAction G α\n⊢ toPerm 1 = 1",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"instHSMul",
"InvOneClass.toOne",
"Equiv.instEquivLike",
"Equiv.Perm.instOne",
"DivInvOneMonoid.toInvOneClass",
"... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Group.Action.End | {
"line": 213,
"column": 2
} | {
"line": 213,
"column": 7
} | {
"line": 215,
"column": 0
} | [
{
"pp": "G : Type u_1\nα : Type u_5\ninst✝¹ : AddGroup G\ninst✝ : AddAction G α\n⊢ toPerm 0 = 1",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Equiv.instEquivLike",
"Equiv.Perm.instOne",
"AddMonoid.toAddSemigroup",
"congrArg",... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Group.Action.End | {
"line": 213,
"column": 2
} | {
"line": 213,
"column": 7
} | {
"line": 215,
"column": 0
} | [
{
"pp": "G : Type u_1\nα : Type u_5\ninst✝¹ : AddGroup G\ninst✝ : AddAction G α\n⊢ toPerm 0 = 1",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Equiv.instEquivLike",
"Equiv.Perm.instOne",
"AddMonoid.toAddSemigroup",
"congrArg",... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Group.Action.End | {
"line": 213,
"column": 2
} | {
"line": 213,
"column": 7
} | {
"line": 215,
"column": 0
} | [
{
"pp": "G : Type u_1\nα : Type u_5\ninst✝¹ : AddGroup G\ninst✝ : AddAction G α\n⊢ toPerm 0 = 1",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Equiv.instEquivLike",
"Equiv.Perm.instOne",
"AddMonoid.toAddSemigroup",
"congrArg",... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Set.Lattice.Image | {
"line": 174,
"column": 2
} | {
"line": 174,
"column": 7
} | {
"line": 176,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nt : Set α\nS : Set (Set β)\nf : α → β → γ\n⊢ image2 f t (⋂₀ S) ⊆ ⋂ s ∈ S, image2 f t s",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.iInter",
"Membership.mem",
"Exists",
"id",
"LE.le",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Set.Lattice.Image | {
"line": 174,
"column": 2
} | {
"line": 174,
"column": 7
} | {
"line": 176,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nt : Set α\nS : Set (Set β)\nf : α → β → γ\n⊢ image2 f t (⋂₀ S) ⊆ ⋂ s ∈ S, image2 f t s",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.iInter",
"Membership.mem",
"Exists",
"id",
"LE.le",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Set.Lattice.Image | {
"line": 174,
"column": 2
} | {
"line": 174,
"column": 7
} | {
"line": 176,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nt : Set α\nS : Set (Set β)\nf : α → β → γ\n⊢ image2 f t (⋂₀ S) ⊆ ⋂ s ∈ S, image2 f t s",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.iInter",
"Membership.mem",
"Exists",
"id",
"LE.le",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Set.Lattice.Image | {
"line": 178,
"column": 2
} | {
"line": 178,
"column": 7
} | {
"line": 180,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nS : Set (Set α)\nt : Set β\nf : α → β → γ\n⊢ image2 f (⋂₀ S) t ⊆ ⋂ s ∈ S, image2 f s t",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.iInter",
"Membership.mem",
"Exists",
"id",
"LE.le",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Set.Lattice.Image | {
"line": 178,
"column": 2
} | {
"line": 178,
"column": 7
} | {
"line": 180,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nS : Set (Set α)\nt : Set β\nf : α → β → γ\n⊢ image2 f (⋂₀ S) t ⊆ ⋂ s ∈ S, image2 f s t",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.iInter",
"Membership.mem",
"Exists",
"id",
"LE.le",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Set.Lattice.Image | {
"line": 178,
"column": 2
} | {
"line": 178,
"column": 7
} | {
"line": 180,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nS : Set (Set α)\nt : Set β\nf : α → β → γ\n⊢ image2 f (⋂₀ S) t ⊆ ⋂ s ∈ S, image2 f s t",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.iInter",
"Membership.mem",
"Exists",
"id",
"LE.le",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Set.Lattice.Image | {
"line": 530,
"column": 2
} | {
"line": 530,
"column": 7
} | {
"line": 532,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : α → β → γ\nS : Set (Set α)\nt : Set β\n⊢ image2 f (⋃₀ S) t = ⋃ s ∈ S, image2 f s t",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"Iff.of_eq",
"congrArg",
"Set.mem_iUnion._simp_1",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Set.Lattice.Image | {
"line": 530,
"column": 2
} | {
"line": 530,
"column": 7
} | {
"line": 532,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : α → β → γ\nS : Set (Set α)\nt : Set β\n⊢ image2 f (⋃₀ S) t = ⋃ s ∈ S, image2 f s t",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"Iff.of_eq",
"congrArg",
"Set.mem_iUnion._simp_1",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Set.Lattice.Image | {
"line": 530,
"column": 2
} | {
"line": 530,
"column": 7
} | {
"line": 532,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : α → β → γ\nS : Set (Set α)\nt : Set β\n⊢ image2 f (⋃₀ S) t = ⋃ s ∈ S, image2 f s t",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"Iff.of_eq",
"congrArg",
"Set.mem_iUnion._simp_1",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Set.Lattice.Image | {
"line": 534,
"column": 2
} | {
"line": 534,
"column": 7
} | {
"line": 536,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : α → β → γ\ns : Set α\nT : Set (Set β)\n⊢ image2 f s (⋃₀ T) = ⋃ t ∈ T, image2 f s t",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"Iff.of_eq",
"congrArg",
"Set.mem_iUnion._simp_1",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Set.Lattice.Image | {
"line": 534,
"column": 2
} | {
"line": 534,
"column": 7
} | {
"line": 536,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : α → β → γ\ns : Set α\nT : Set (Set β)\n⊢ image2 f s (⋃₀ T) = ⋃ t ∈ T, image2 f s t",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"Iff.of_eq",
"congrArg",
"Set.mem_iUnion._simp_1",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Set.Lattice.Image | {
"line": 534,
"column": 2
} | {
"line": 534,
"column": 7
} | {
"line": 536,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : α → β → γ\ns : Set α\nT : Set (Set β)\n⊢ image2 f s (⋃₀ T) = ⋃ t ∈ T, image2 f s t",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"Iff.of_eq",
"congrArg",
"Set.mem_iUnion._simp_1",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Group.Pointwise.Set.Basic | {
"line": 422,
"column": 80
} | {
"line": 422,
"column": 85
} | {
"line": 424,
"column": 0
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\ninst✝¹ : Mul α\ninst✝ : Mul β\ns₁ s₂ : Set α\nt₁ t₂ : Set β\nx✝ : α × β\n⊢ (∃ a b, (a ∈ s₁ ∧ b ∈ t₁) ∧ ∃ a_1 b_1, (a_1 ∈ s₂ ∧ b_1 ∈ t₂) ∧ (a * a_1, b * b_1) = x✝) ↔\n (∃ x, x ∈ s₁ ∧ ∃ y, y ∈ s₂ ∧ x * y = x✝.1) ∧ ∃ x, x ∈ t₁ ∧ ∃ y, y ∈ t₂ ∧ x * y = x✝.2",
"ppTerm": "?m... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Group.Pointwise.Set.Basic | {
"line": 835,
"column": 70
} | {
"line": 835,
"column": 75
} | {
"line": 837,
"column": 0
} | [
{
"pp": "case ofNat\nα : Type u_2\ninst✝ : DivisionMonoid α\na✝ : ℕ\nhn : Int.ofNat a✝ ≠ 0\n⊢ ∅ ^ Int.ofNat a✝ = ∅",
"ppTerm": "?ofNat",
"assigned": true,
"usedConstants": [
"zpow_natCast",
"Set.empty_pow",
"False",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Group.Pointwise.Set.Basic | {
"line": 835,
"column": 70
} | {
"line": 835,
"column": 75
} | {
"line": 837,
"column": 0
} | [
{
"pp": "case negSucc\nα : Type u_2\ninst✝ : DivisionMonoid α\na✝ : ℕ\nhn : Int.negSucc a✝ ≠ 0\n⊢ ∅ ^ Int.negSucc a✝ = ∅",
"ppTerm": "?negSucc",
"assigned": true,
"usedConstants": [
"Set.empty_pow",
"False",
"DivInvMonoid.toInv",
"InvOneClass.toOne",
"DivInvOneMonoid.to... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Group.Pointwise.Set.Basic | {
"line": 852,
"column": 70
} | {
"line": 852,
"column": 89
} | {
"line": 854,
"column": 0
} | [
{
"pp": "α : Type u_2\ninst✝ : DivisionMonoid α\na : α\nn : ℤ\n⊢ {a} ^ n = {a ^ n}",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"zpow_natCast",
"DivInvMonoid.toInv",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"Set.ZPow",
"Set.singleton_pow"... | [] | by cases n <;> simp | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Group.Subsemigroup.MulOpposite | {
"line": 163,
"column": 11
} | {
"line": 163,
"column": 19
} | {
"line": 163,
"column": 20
} | [
{
"pp": "M : Type u_2\ninst✝ : Mul M\ns : Set M\n⊢ (closure s).op = closure (MulOpposite.unop ⁻¹' s)",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"MulOpposite",
"id",
"Subsemigroup.op",
"Set.preimage",
"Subsemigroup",
"MulOpposite.unop",
"Eq",
... | [
"M : Type u_2\ninst✝ : Mul M\ns : Set M\n⊢ (sInf {S | s ⊆ ↑S}).op = sInf {S | MulOpposite.unop ⁻¹' s ⊆ ↑S}"
] | closure, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Algebra.Group.Subgroup.Ker | {
"line": 435,
"column": 18
} | {
"line": 436,
"column": 98
} | {
"line": 438,
"column": 0
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\nN : Type u_5\ninst✝ : Group N\nf : G →* N\nH : Subgroup N\n⊢ ↑(map f (comap f H)) = ↑(f.range ⊓ H)",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MonoidHom.range",
"MonoidHom.instFunLike",
"MonoidHom",
"Subg... | [] | by
rw [coe_map, coe_comap, Set.image_preimage_eq_inter_range, coe_inf, coe_range, Set.inter_comm] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Countable.Defs | {
"line": 158,
"column": 27
} | {
"line": 158,
"column": 59
} | {
"line": 158,
"column": 60
} | [
{
"pp": "α : Sort u\ninst✝ : Nonempty α\n⊢ ¬Countable α ↔ ∀ (f : ℕ → α), ¬Surjective f",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Exists",
"id",
"Iff",
"Nat",
"countable_iff_exists_surjective",
"propext",
"Cou... | [
"α : Sort u\ninst✝ : Nonempty α\n⊢ (¬∃ f, Surjective f) ↔ ∀ (f : ℕ → α), ¬Surjective f"
] | countable_iff_exists_surjective, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Group.Submonoid.MulOpposite | {
"line": 173,
"column": 11
} | {
"line": 173,
"column": 19
} | {
"line": 173,
"column": 20
} | [
{
"pp": "M : Type u_2\ninst✝ : MulOneClass M\ns : Set M\n⊢ (closure s).op = closure (MulOpposite.unop ⁻¹' s)",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Submonoid.op",
"MulOpposite",
"id",
"Set.preimage",
"Submonoid.closure",
"MulOpposite.instMulOne... | [
"M : Type u_2\ninst✝ : MulOneClass M\ns : Set M\n⊢ (sInf {S | s ⊆ ↑S}).op = sInf {S | MulOpposite.unop ⁻¹' s ⊆ ↑S}"
] | closure, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Algebra.Group.Subgroup.Basic | {
"line": 362,
"column": 50
} | {
"line": 362,
"column": 64
} | {
"line": 362,
"column": 65
} | [
{
"pp": "G : Type u_1\ninst✝ : Group G\ns : Set G\ng : G\n⊢ (∀ (h : G), h ∈ s ↔ g⁻¹ * h * g ∈ s) ↔ ∀ (x : G), x ∈ ⇑(MulAut.conj g) '' s ↔ x ∈ s",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulEquiv.instEquivLike",
"MonoidHom.instFunLike",
"HMul.hMul",
... | [
"G : Type u_1\ninst✝ : Group G\ns : Set G\ng : G\n⊢ (∀ (h : G), h ∈ s ↔ g⁻¹ * h * g ∈ s) ↔ ∀ (x : G), (∃ x_1 ∈ s, (MulAut.conj g) x_1 = x) ↔ x ∈ s"
] | Set.mem_image, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas | {
"line": 110,
"column": 11
} | {
"line": 110,
"column": 19
} | {
"line": 110,
"column": 20
} | [
{
"pp": "G : Type u_2\ninst✝ : Group G\ns : Set G\n⊢ (closure s).op = closure (MulOpposite.unop ⁻¹' s)",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Subgroup.closure",
"MulOpposite",
"id",
"Subgroup",
"MulOpposite.instGroup",
"Subgroup.op",
"Set... | [
"G : Type u_2\ninst✝ : Group G\ns : Set G\n⊢ (sInf {K | s ⊆ ↑K}).op = sInf {K | MulOpposite.unop ⁻¹' s ⊆ ↑K}"
] | closure, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.