module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Algebra.Order.Module.Defs | {
"line": 1081,
"column": 29
} | {
"line": 1081,
"column": 43
} | {
"line": 1081,
"column": 44
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\na : α\nb₁ b₂ : β\ninst✝⁷ : Ring α\ninst✝⁶ : PartialOrder α\ninst✝⁵ : IsOrderedRing α\ninst✝⁴ : AddCommGroup β\ninst✝³ : PartialOrder β\ninst✝² : IsOrderedAddMonoid β\ninst✝¹ : Module α β\ninst✝ : PosSMulReflectLT α β\nh : -(-a • b₁) < - -a • b₂\nha : a ≤ 0\n⊢ b₂ < b₁",
"... | [
"α : Type u_1\nβ : Type u_2\na : α\nb₁ b₂ : β\ninst✝⁷ : Ring α\ninst✝⁶ : PartialOrder α\ninst✝⁵ : IsOrderedRing α\ninst✝⁴ : AddCommGroup β\ninst✝³ : PartialOrder β\ninst✝² : IsOrderedAddMonoid β\ninst✝¹ : Module α β\ninst✝ : PosSMulReflectLT α β\nh : -(-a • b₁) < -(-a • b₂)\nha : a ≤ 0\n⊢ b₂ < b₁"
] | neg_smul (-a), | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Module.Defs | {
"line": 1090,
"column": 29
} | {
"line": 1090,
"column": 43
} | {
"line": 1090,
"column": 44
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\na : α\nb₁ b₂ : β\ninst✝⁸ : Ring α\ninst✝⁷ : PartialOrder α\ninst✝⁶ : IsOrderedRing α\ninst✝⁵ : AddCommGroup β\ninst✝⁴ : PartialOrder β\ninst✝³ : IsOrderedAddMonoid β\ninst✝² : Module α β\ninst✝¹ : PosSMulMono α β\ninst✝ : PosSMulReflectLE α β\nha : a < 0\n⊢ -(-a • b₁) ≤ - -a... | [
"α : Type u_1\nβ : Type u_2\na : α\nb₁ b₂ : β\ninst✝⁸ : Ring α\ninst✝⁷ : PartialOrder α\ninst✝⁶ : IsOrderedRing α\ninst✝⁵ : AddCommGroup β\ninst✝⁴ : PartialOrder β\ninst✝³ : IsOrderedAddMonoid β\ninst✝² : Module α β\ninst✝¹ : PosSMulMono α β\ninst✝ : PosSMulReflectLE α β\nha : a < 0\n⊢ -(-a • b₁) ≤ -(-a • b₂) ↔ b₂ ... | neg_smul (-a), | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Module.Defs | {
"line": 1097,
"column": 29
} | {
"line": 1097,
"column": 43
} | {
"line": 1097,
"column": 44
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\na : α\nb₁ b₂ : β\ninst✝⁸ : Ring α\ninst✝⁷ : PartialOrder α\ninst✝⁶ : IsOrderedRing α\ninst✝⁵ : AddCommGroup β\ninst✝⁴ : PartialOrder β\ninst✝³ : IsOrderedAddMonoid β\ninst✝² : Module α β\ninst✝¹ : PosSMulStrictMono α β\ninst✝ : PosSMulReflectLT α β\nha : a < 0\n⊢ -(-a • b₁) ... | [
"α : Type u_1\nβ : Type u_2\na : α\nb₁ b₂ : β\ninst✝⁸ : Ring α\ninst✝⁷ : PartialOrder α\ninst✝⁶ : IsOrderedRing α\ninst✝⁵ : AddCommGroup β\ninst✝⁴ : PartialOrder β\ninst✝³ : IsOrderedAddMonoid β\ninst✝² : Module α β\ninst✝¹ : PosSMulStrictMono α β\ninst✝ : PosSMulReflectLT α β\nha : a < 0\n⊢ -(-a • b₁) < -(-a • b₂)... | neg_smul (-a), | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Module.Defs | {
"line": 1148,
"column": 6
} | {
"line": 1148,
"column": 21
} | {
"line": 1148,
"column": 22
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝⁷ : Ring α\ninst✝⁶ : LinearOrder α\ninst✝⁵ : IsStrictOrderedRing α\ninst✝⁴ : AddCommGroup β\ninst✝³ : LinearOrder β\ninst✝² : IsOrderedAddMonoid β\ninst✝¹ : Module α β\ninst✝ : PosSMulStrictMono α β\na : α\nb : β\n⊢ 0 ≤ a • b ↔ (a < 0 → b ≤ 0) ∧ (b < 0 → a ≤ 0)",
"p... | [
"α : Type u_1\nβ : Type u_2\ninst✝⁷ : Ring α\ninst✝⁶ : LinearOrder α\ninst✝⁵ : IsStrictOrderedRing α\ninst✝⁴ : AddCommGroup β\ninst✝³ : LinearOrder β\ninst✝² : IsOrderedAddMonoid β\ninst✝¹ : Module α β\ninst✝ : PosSMulStrictMono α β\na : α\nb : β\n⊢ 0 ≤ -a • -b ↔ (a < 0 → b ≤ 0) ∧ (b < 0 → a ≤ 0)"
] | ← neg_smul_neg, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Module.Defs | {
"line": 1210,
"column": 30
} | {
"line": 1214,
"column": 44
} | {
"line": 1216,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\na a₁ a₂ : α\nb b₁ b₂ : β\nγ : Type u_3\ninst✝⁹ : Zero α\ninst✝⁸ : PartialOrder α\ninst✝⁷ : PartialOrder β\ninst✝⁶ : PartialOrder γ\ninst✝⁵ : Zero β\ninst✝⁴ : Zero γ\ninst✝³ : SMulWithZero α β\ninst✝² : SMulWithZero α γ\ninst✝¹ : SMulPosReflectLT α β\ninst✝ : SMulPosReflectLT... | [] | by
simp_rw [lt_iff]
rintro b hb _a₁ _a₂ (⟨h₁, h₂⟩ | ⟨h₁, h₂⟩)
· exact lt_of_smul_lt_smul_right h₁ hb.1
· exact lt_of_smul_lt_smul_right h₂ hb.2 | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.SetTheory.Ordinal.Basic | {
"line": 393,
"column": 2
} | {
"line": 393,
"column": 7
} | {
"line": 395,
"column": 0
} | [
{
"pp": "α : Type u\ninst✝¹ : LinearOrder α\ninst✝ : WellFoundedLT α\ns t : Set α\nh : s ⊆ t\n⊢ ∀ {a b : ↑s}, (s.embeddingOfSubset t h) a < (s.embeddingOfSubset t h) b ↔ a < b",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"congrArg",
"If... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.SetTheory.Ordinal.Basic | {
"line": 417,
"column": 2
} | {
"line": 418,
"column": 21
} | {
"line": 419,
"column": 2
} | [
{
"pp": "case refine_1\nα : Type u\nβ : Type v\nγ : Type w\nr✝ : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nr : α → α → Prop\ninst✝ : IsWellOrder α r\na b : α\nha : r a b\n⊢ ∀ (a_1 : { x // r x a }), (PrincipalSeg.ofElement r a).toRelEmbedding a_1 ∈ fun x ↦ r x b",
"ppTerm": "?refine_1",
"assigne... | [
"case refine_2\nα : Type u\nβ : Type v\nγ : Type w\nr✝ : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nr : α → α → Prop\ninst✝ : IsWellOrder α r\na b : α\nha : r a b\n⊢ (PrincipalSeg.ofElement r a).top ∈ fun x ↦ r x b",
"case refine_3\nα : Type u\nβ : Type v\nγ : Type w\nr✝ : α → α → Prop\ns : β → β → Prop\nt... | · rintro ⟨c, hc⟩
exact trans hc ha | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.SetTheory.Ordinal.Arithmetic | {
"line": 110,
"column": 2
} | {
"line": 110,
"column": 51
} | {
"line": 112,
"column": 0
} | [
{
"pp": "a b : Ordinal.{u_4}\nn : ℕ\n⊢ a + ↑n = b + ↑n ↔ a = b",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Ordinal.partialOrder",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"AddMonoidWithOne.toNatCast",
"LE.le",
"Nat.cast",
... | [] | simp only [le_antisymm_iff, add_le_add_iff_right] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.SetTheory.Ordinal.Arithmetic | {
"line": 110,
"column": 2
} | {
"line": 110,
"column": 51
} | {
"line": 112,
"column": 0
} | [
{
"pp": "a b : Ordinal.{u_4}\nn : ℕ\n⊢ a + ↑n = b + ↑n ↔ a = b",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Ordinal.partialOrder",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"AddMonoidWithOne.toNatCast",
"LE.le",
"Nat.cast",
... | [] | simp only [le_antisymm_iff, add_le_add_iff_right] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.SetTheory.Ordinal.Arithmetic | {
"line": 110,
"column": 2
} | {
"line": 110,
"column": 51
} | {
"line": 112,
"column": 0
} | [
{
"pp": "a b : Ordinal.{u_4}\nn : ℕ\n⊢ a + ↑n = b + ↑n ↔ a = b",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Ordinal.partialOrder",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"AddMonoidWithOne.toNatCast",
"LE.le",
"Nat.cast",
... | [] | simp only [le_antisymm_iff, add_le_add_iff_right] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.SetTheory.Ordinal.Arithmetic | {
"line": 300,
"column": 2
} | {
"line": 300,
"column": 60
} | {
"line": 301,
"column": 2
} | [
{
"pp": "o : Ordinal.{u_4}\n⊢ o.pred = o ↔ IsSuccPrelimit o",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"Order.succ",
"Order.mem_range_succ_or_isSuccPrelimit",
"Order.IsSuccPrelimit",
"Ordinal.partialOrder",
"PartialOrder.toPreorder",... | [
"case inl\na : Ordinal.{u_4}\n⊢ (succ a).pred = succ a ↔ IsSuccPrelimit (succ a)",
"case inr\no : Ordinal.{u_4}\nho : IsSuccPrelimit o\n⊢ o.pred = o ↔ IsSuccPrelimit o"
] | obtain ⟨a, rfl⟩ | ho := mem_range_succ_or_isSuccPrelimit o | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.SetTheory.Ordinal.Arithmetic | {
"line": 309,
"column": 42
} | {
"line": 309,
"column": 54
} | {
"line": 309,
"column": 55
} | [
{
"pp": "o : Ordinal.{u_4}\n⊢ succ o.pred ≤ o ↔ ¬IsSuccPrelimit o",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Order.succ",
"Order.IsSuccPrelimit",
"Ordinal.partialOrder",
"congrArg",
"PartialOrder.toPreorder",
... | [
"o : Ordinal.{u_4}\n⊢ o.pred < o ↔ ¬IsSuccPrelimit o"
] | succ_le_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.SetTheory.Ordinal.Arithmetic | {
"line": 313,
"column": 2
} | {
"line": 313,
"column": 60
} | {
"line": 314,
"column": 2
} | [
{
"pp": "o : Ordinal.{v}\n⊢ lift.{u, v} o.pred = (lift.{u, v} o).pred",
"ppTerm": "?m.2",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"Order.succ",
"Order.mem_range_succ_or_isSuccPrelimit",
"Order.IsSuccPrelimit",
"Ordinal.partialOrder",
"PartialOrder.to... | [
"case inl\na : Ordinal.{v}\n⊢ lift.{u, v} (succ a).pred = (lift.{u, v} (succ a)).pred",
"case inr\no : Ordinal.{v}\nho : IsSuccPrelimit o\n⊢ lift.{u, v} o.pred = (lift.{u, v} o).pred"
] | obtain ⟨a, rfl⟩ | ho := mem_range_succ_or_isSuccPrelimit o | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.SetTheory.Ordinal.Family | {
"line": 377,
"column": 92
} | {
"line": 379,
"column": 28
} | {
"line": 381,
"column": 0
} | [
{
"pp": "o : Ordinal.{u_3}\nf : (a : Ordinal.{u_3}) → a < o → Ordinal.{max u_3 u_4}\n⊢ sSup (o.brange f) = o.bsup f",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Ordinal.familyOfBFamily",
"Ordinal.brange",
"Eq.rec",
"id",
"S... | [] | by
congr
rw [range_familyOfBFamily] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.SetTheory.Ordinal.Basic | {
"line": 1042,
"column": 80
} | {
"line": 1045,
"column": 22
} | {
"line": 1047,
"column": 0
} | [
{
"pp": "o : Ordinal.{u_1}\na : (succ o).ToType\n⊢ a ≤ (enum fun x1 x2 ↦ x1 < x2) ⟨o, ⋯⟩",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Ordinal.instLinearOrder",
"Preorder.toLT",
"Order.succ",
"isWellOrder_lt",
"Ordinal.partialOrder",
"... | [] | by
rw [← enum_typein (α := (succ o).ToType) (· < ·) a, enum_le_enum', Subtype.mk_le_mk,
← lt_succ_iff]
apply typein_lt_self | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.SetTheory.Ordinal.Family | {
"line": 544,
"column": 6
} | {
"line": 544,
"column": 18
} | {
"line": 544,
"column": 19
} | [
{
"pp": "case refine_2\nι : Type u_3\nf : ι → Ordinal.{max u_4 u_3}\nw✝ : ι\nhf : f w✝ = iSup f\n⊢ succ (iSup f) ≤ lsub f",
"ppTerm": "?refine_2",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Order.succ",
"Ordinal.partialOrder",
"congrArg",
"iS... | [
"case refine_2\nι : Type u_3\nf : ι → Ordinal.{max u_4 u_3}\nw✝ : ι\nhf : f w✝ = iSup f\n⊢ iSup f < lsub f"
] | succ_le_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.SetTheory.Cardinal.Cofinality.Enum | {
"line": 168,
"column": 4
} | {
"line": 173,
"column": 11
} | {
"line": 174,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : WellFoundedLT α\ninst✝ : IsRegularCardinalOrder α\ns : Set α\nhs : IsCofinal s\nH : StrictMono (Subtype.val ∘ ⇑(enum s hs)) := ⋯\nhs' : ∀ ⦃d : Set α⦄, d ⊆ s → d.Nonempty → ∀ ⦃a : α⦄, IsLUB d a → a ∈ s\na : α\nha : IsSuccLimit a\nb : α\nhb : ∀ b_1 < a, (Sub... | [] | refine enum_le_of_forall_lt (hs' ?_ ?_ (isLUB_csSup' bdd)) fun b hb ↦ ?_
· grind
· simpa using ha.ne_bot
· obtain ⟨c, hca, hbc⟩ := ha.lt_iff_exists_lt.1 hb
refine (H hbc).trans_le <| le_csSup bdd ⟨c, ?_⟩
simpa | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.SetTheory.Cardinal.Cofinality.Enum | {
"line": 168,
"column": 4
} | {
"line": 173,
"column": 11
} | {
"line": 174,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : WellFoundedLT α\ninst✝ : IsRegularCardinalOrder α\ns : Set α\nhs : IsCofinal s\nH : StrictMono (Subtype.val ∘ ⇑(enum s hs)) := ⋯\nhs' : ∀ ⦃d : Set α⦄, d ⊆ s → d.Nonempty → ∀ ⦃a : α⦄, IsLUB d a → a ∈ s\na : α\nha : IsSuccLimit a\nb : α\nhb : ∀ b_1 < a, (Sub... | [] | refine enum_le_of_forall_lt (hs' ?_ ?_ (isLUB_csSup' bdd)) fun b hb ↦ ?_
· grind
· simpa using ha.ne_bot
· obtain ⟨c, hca, hbc⟩ := ha.lt_iff_exists_lt.1 hb
refine (H hbc).trans_le <| le_csSup bdd ⟨c, ?_⟩
simpa | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.SetTheory.Ordinal.Enum | {
"line": 123,
"column": 2
} | {
"line": 124,
"column": 51
} | {
"line": 125,
"column": 2
} | [
{
"pp": "case mp\ns : Set Ordinal.{u}\nf : Ordinal.{u} → Ordinal.{u}\nhs : ¬BddAbove s\n⊢ enumOrd s = f → StrictMono f ∧ range f = s",
"ppTerm": "?mp",
"assigned": true,
"usedConstants": [
"StrictMono",
"Ordinal.partialOrder",
"PartialOrder.toPreorder",
"Ordinal.enumOrd",
... | [
"case mpr\ns : Set Ordinal.{u}\nf : Ordinal.{u} → Ordinal.{u}\nhs : ¬BddAbove s\n⊢ StrictMono f ∧ range f = s → enumOrd s = f"
] | · rintro rfl
exact ⟨enumOrd_strictMono hs, range_enumOrd hs⟩ | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.SetTheory.Ordinal.Basic | {
"line": 1207,
"column": 2
} | {
"line": 1208,
"column": 22
} | {
"line": 1210,
"column": 0
} | [
{
"pp": "α : Type u\nr : α → α → Prop\ninst✝ : IsWellOrder α r\nx : α\nh : (#α).ord = type r\n⊢ ((typein r).toRelEmbedding x).card < #α",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Ordinal.partialOrder",
"Cardinal",
"congrArg",
... | [] | rw [← lt_ord, h]
apply typein_lt_type | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.SetTheory.Ordinal.Basic | {
"line": 1207,
"column": 2
} | {
"line": 1208,
"column": 22
} | {
"line": 1210,
"column": 0
} | [
{
"pp": "α : Type u\nr : α → α → Prop\ninst✝ : IsWellOrder α r\nx : α\nh : (#α).ord = type r\n⊢ ((typein r).toRelEmbedding x).card < #α",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Ordinal.partialOrder",
"Cardinal",
"congrArg",
... | [] | rw [← lt_ord, h]
apply typein_lt_type | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.SetTheory.Ordinal.Enum | {
"line": 138,
"column": 6
} | {
"line": 141,
"column": 28
} | {
"line": 142,
"column": 4
} | [
{
"pp": "case refine_1\ns : Set Ordinal.{u}\nH : ∀ t ⊆ s, t.Nonempty → BddAbove t → sSup t ∈ s\nhs : ¬BddAbove s\no : Ordinal.{u}\nho : IsSuccLimit o\na : Ordinal.{u}\nha : ∀ b < o, enumOrd s b ≤ a\n⊢ ⨆ b, enumOrd s ↑b ∈ s",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"Ordinal.... | [] | have : Nonempty (Iio o) := ⟨0, ho.bot_lt⟩
apply H _ _ (range_nonempty _) bddAbove_of_small
rintro _ ⟨c, rfl⟩
exact enumOrd_mem hs c | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.SetTheory.Ordinal.Enum | {
"line": 138,
"column": 6
} | {
"line": 141,
"column": 28
} | {
"line": 142,
"column": 4
} | [
{
"pp": "case refine_1\ns : Set Ordinal.{u}\nH : ∀ t ⊆ s, t.Nonempty → BddAbove t → sSup t ∈ s\nhs : ¬BddAbove s\no : Ordinal.{u}\nho : IsSuccLimit o\na : Ordinal.{u}\nha : ∀ b < o, enumOrd s b ≤ a\n⊢ ⨆ b, enumOrd s ↑b ∈ s",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"Ordinal.... | [] | have : Nonempty (Iio o) := ⟨0, ho.bot_lt⟩
apply H _ _ (range_nonempty _) bddAbove_of_small
rintro _ ⟨c, rfl⟩
exact enumOrd_mem hs c | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.SetTheory.Ordinal.Family | {
"line": 745,
"column": 6
} | {
"line": 745,
"column": 18
} | {
"line": 745,
"column": 19
} | [
{
"pp": "case refine_2\no : Ordinal.{u}\nf : (a : Ordinal.{u}) → a < o → Ordinal.{max u v}\nw✝¹ : Ordinal.{u}\nw✝ : w✝¹ < o\nhf : f w✝¹ w✝ = o.bsup f\n⊢ succ (o.bsup f) ≤ o.blsub f",
"ppTerm": "?refine_2",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Order.succ"... | [
"case refine_2\no : Ordinal.{u}\nf : (a : Ordinal.{u}) → a < o → Ordinal.{max u v}\nw✝¹ : Ordinal.{u}\nw✝ : w✝¹ < o\nhf : f w✝¹ w✝ = o.bsup f\n⊢ o.bsup f < o.blsub f"
] | succ_le_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.SetTheory.Ordinal.Arithmetic | {
"line": 905,
"column": 4
} | {
"line": 905,
"column": 75
} | {
"line": 907,
"column": 0
} | [
{
"pp": "case inr\nx y z : Ordinal.{u_4}\nhx : x ≠ 0\n⊢ (x * y + z) % x = z % x",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHDiv",
"HMul.hMul",
"MulZeroClass.toMul",
"congrArg",
"Ordinal.mul_add_div",
"HSub.hSub",
"Ordinal.m... | [] | rwa [mod_def, mul_add_div, mul_add, ← sub_sub, add_sub_cancel, mod_def] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticRwa___1 | Lean.Parser.Tactic.tacticRwa__ |
Mathlib.SetTheory.Ordinal.Arithmetic | {
"line": 905,
"column": 4
} | {
"line": 905,
"column": 75
} | {
"line": 907,
"column": 0
} | [
{
"pp": "case inr\nx y z : Ordinal.{u_4}\nhx : x ≠ 0\n⊢ (x * y + z) % x = z % x",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHDiv",
"HMul.hMul",
"MulZeroClass.toMul",
"congrArg",
"Ordinal.mul_add_div",
"HSub.hSub",
"Ordinal.m... | [] | rwa [mod_def, mul_add_div, mul_add, ← sub_sub, add_sub_cancel, mod_def] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.SetTheory.Ordinal.Arithmetic | {
"line": 905,
"column": 4
} | {
"line": 905,
"column": 75
} | {
"line": 907,
"column": 0
} | [
{
"pp": "case inr\nx y z : Ordinal.{u_4}\nhx : x ≠ 0\n⊢ (x * y + z) % x = z % x",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHDiv",
"HMul.hMul",
"MulZeroClass.toMul",
"congrArg",
"Ordinal.mul_add_div",
"HSub.hSub",
"Ordinal.m... | [] | rwa [mod_def, mul_add_div, mul_add, ← sub_sub, add_sub_cancel, mod_def] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.SetTheory.Ordinal.Exponential | {
"line": 305,
"column": 4
} | {
"line": 305,
"column": 9
} | {
"line": 307,
"column": 0
} | [
{
"pp": "case e'_2\nb : Ordinal.{u_1}\nhb : b ≠ 0\n⊢ (fun x ↦ b ^ x) ⁻¹' Iic 0 = ∅",
"ppTerm": "?e'_2",
"assigned": true,
"usedConstants": [
"Set.ext",
"False",
"eq_false",
"Ordinal.partialOrder",
"Set.mem_empty_iff_false._simp_1",
"congrArg",
"instIsBotZero... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.SetTheory.Ordinal.Arithmetic | {
"line": 1135,
"column": 9
} | {
"line": 1135,
"column": 29
} | {
"line": 1135,
"column": 29
} | [
{
"pp": "case isSuccPrelimit\nc : Cardinal.{u_1}\nhc : ℵ₀ ≤ c\na : Ordinal.{u_1}\nha : c ≤ a.card + 1\n⊢ c ≤ a.card",
"ppTerm": "?isSuccPrelimit",
"assigned": true,
"usedConstants": [
"Cardinal.instOne",
"Cardinal",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE"... | [
"case isSuccPrelimit\nc : Cardinal.{u_1}\nhc : ℵ₀ ≤ c\na : Ordinal.{u_1}\nha : c ≤ a.card\n⊢ c ≤ a.card",
"case isSuccPrelimit\nc : Cardinal.{u_1}\nhc : ℵ₀ ≤ c\na : Ordinal.{u_1}\nha : c ≤ a.card + 1\n⊢ ℵ₀ ≤ a.card"
] | add_one_of_aleph0_le | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Nat.Log | {
"line": 419,
"column": 2
} | {
"line": 419,
"column": 47
} | {
"line": 419,
"column": 48
} | [
{
"pp": "case hn\nb n : ℕ\nhn : 2 ≤ n\nh : n ≤ b\n⊢ (n + b - 1) / b ≤ 1",
"ppTerm": "?hn",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHDiv",
"HMul.hMul",
"congrArg",
"HSub.hSub",
"id",
"HDiv.hDiv",
"instSubNat",
"instMulNat",
"inst... | [
"case hn\nb n : ℕ\nhn : 2 ≤ n\nh : n ≤ b\n⊢ n + b - 1 < succ 1 * b",
"case hn\nb n : ℕ\nhn : 2 ≤ n\nh : n ≤ b\n⊢ 0 < b"
] | rw [← Nat.lt_succ_iff, Nat.div_lt_iff_lt_mul] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.SetTheory.Ordinal.FixedPoint | {
"line": 181,
"column": 4
} | {
"line": 181,
"column": 49
} | {
"line": 182,
"column": 4
} | [
{
"pp": "case limit\nι : Type u_1\nf : ι → Ordinal.{u} → Ordinal.{u}\ninst✝ : Small.{u, u_1} ι\ni : ι\nH : IsNormal (f i)\no : Ordinal.{u}\nl : IsSuccLimit o\nIH : ∀ o' < o, f i (derivFamily f o') = derivFamily f o'\nthis : Nonempty ↑(Set.Iio o)\nc : Ordinal.{u}\n⊢ ⨆ i_1, f i (derivFamily f ↑i_1) ≤ c ↔ ⨆ b, der... | [
"case limit\nι : Type u_1\nf : ι → Ordinal.{u} → Ordinal.{u}\ninst✝ : Small.{u, u_1} ι\ni : ι\nH : IsNormal (f i)\no : Ordinal.{u}\nl : IsSuccLimit o\nIH : ∀ o' < o, f i (derivFamily f o') = derivFamily f o'\nthis : Nonempty ↑(Set.Iio o)\nc : Ordinal.{u}\n⊢ (∀ (i_1 : ↑(Set.Iio o)), f i (derivFamily f ↑i_1) ≤ c) ↔ ∀... | rw [Ordinal.iSup_le_iff, Ordinal.iSup_le_iff] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.SetTheory.Ordinal.FixedPoint | {
"line": 429,
"column": 4
} | {
"line": 429,
"column": 21
} | {
"line": 430,
"column": 4
} | [
{
"pp": "case refine_2\na b : Ordinal.{u_1}\nh : a * ω ≤ b\nthis : a * ω + (b - a * ω) = b\n⊢ a + b = b",
"ppTerm": "?refine_2",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"Ordinal.omega0",
"MulZeroClass.toMul",
"congrArg",
"HSub.hSub",
"id"... | [
"case refine_2\na b : Ordinal.{u_1}\nh : a * ω ≤ b\nthis : a * ω + (b - a * ω) = b\n⊢ a + (a * ω + (b - a * ω)) = b"
] | nth_rw 1 [← this] | Mathlib.Tactic._aux_Mathlib_Tactic_NthRewrite___macroRules_Mathlib_Tactic_tacticNth_rw______1 | Mathlib.Tactic.tacticNth_rw_____ |
Mathlib.SetTheory.Ordinal.Principal | {
"line": 229,
"column": 4
} | {
"line": 230,
"column": 47
} | {
"line": 232,
"column": 0
} | [
{
"pp": "case refine_2\no : Ordinal.{u}\nh : ∀ a < o, a + o = o\na b : Ordinal.{u}\nhao : a < o\nhbo : b < o\n⊢ (fun x1 x2 ↦ x1 + x2) a b < o",
"ppTerm": "?refine_2",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Ordinal.instLinearOrder",
"Preorder.toLT",
"Ordinal.partialOr... | [] | rw [← h a hao]
exact (isNormal_add_right a).strictMono hbo | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.SetTheory.Ordinal.Principal | {
"line": 229,
"column": 4
} | {
"line": 230,
"column": 47
} | {
"line": 232,
"column": 0
} | [
{
"pp": "case refine_2\no : Ordinal.{u}\nh : ∀ a < o, a + o = o\na b : Ordinal.{u}\nhao : a < o\nhbo : b < o\n⊢ (fun x1 x2 ↦ x1 + x2) a b < o",
"ppTerm": "?refine_2",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Ordinal.instLinearOrder",
"Preorder.toLT",
"Ordinal.partialOr... | [] | rw [← h a hao]
exact (isNormal_add_right a).strictMono hbo | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.SetTheory.Cardinal.Aleph | {
"line": 520,
"column": 2
} | {
"line": 520,
"column": 55
} | {
"line": 522,
"column": 0
} | [
{
"pp": "c : Cardinal.{u_1}\nhc : c ∈ Ici ℵ₀\n⊢ ω ≤ preAleph.symm c",
"ppTerm": "?m.49",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Ordinal.omega0",
"OrderIso.apply_symm_apply",
"Ordinal.partialOrder",
"Cardinal",
"congrArg",
"PartialOrder.toPreorder",
... | [] | rwa [← aleph0_le_preAleph, preAleph.apply_symm_apply] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticRwa___1 | Lean.Parser.Tactic.tacticRwa__ |
Mathlib.SetTheory.Cardinal.Cofinality.Ordinal | {
"line": 204,
"column": 50
} | {
"line": 204,
"column": 79
} | {
"line": 205,
"column": 8
} | [
{
"pp": "case refine_2.refine_2\nβ : Type v\ninst✝¹ : LinearOrder β\ninst✝ : Small.{u, v} β\nf : β → Ordinal.{u}\nhf : StrictMono f\nthis✝ : StrictMono fun i ↦ ⟨f i, ⋯⟩\nthis : Cardinal.lift.{u + 1, v} (Order.cof β) = Cardinal.lift.{v, u + 1} (Order.cof ↑(Iio (⨆ i, f i + 1)))\n⊢ Cardinal.lift.{max (u + 1) v, ma... | [
"case refine_2.refine_2\nβ : Type v\ninst✝¹ : LinearOrder β\ninst✝ : Small.{u, v} β\nf : β → Ordinal.{u}\nhf : StrictMono f\nthis✝ : StrictMono fun i ↦ ⟨f i, ⋯⟩\nthis : Cardinal.lift.{u + 1, v} (Order.cof β) = Cardinal.lift.{v, u + 1} (Order.cof ↑(Iio (⨆ i, f i + 1)))\n⊢ Cardinal.lift.{max (u + 1) v, max u v} (Card... | Cardinal.lift_lift.{_, _, v}, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.SetTheory.Cardinal.Aleph | {
"line": 948,
"column": 2
} | {
"line": 948,
"column": 33
} | {
"line": 950,
"column": 0
} | [
{
"pp": "o : Ordinal.{u}\nn : ℕ\n⊢ ω_ ↑n ≤ lift.{v, u} o ↔ ω_ ↑n ≤ o",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Ordinal.partialOrder",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Ordinal.lift",
"Eq.mp",
"AddMonoidWithOne.toNatCast... | [] | simpa using lift_le (a := ω_ n) | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.SetTheory.Cardinal.Aleph | {
"line": 948,
"column": 2
} | {
"line": 948,
"column": 33
} | {
"line": 950,
"column": 0
} | [
{
"pp": "o : Ordinal.{u}\nn : ℕ\n⊢ ω_ ↑n ≤ lift.{v, u} o ↔ ω_ ↑n ≤ o",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Ordinal.partialOrder",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Ordinal.lift",
"Eq.mp",
"AddMonoidWithOne.toNatCast... | [] | simpa using lift_le (a := ω_ n) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.SetTheory.Cardinal.Aleph | {
"line": 948,
"column": 2
} | {
"line": 948,
"column": 33
} | {
"line": 950,
"column": 0
} | [
{
"pp": "o : Ordinal.{u}\nn : ℕ\n⊢ ω_ ↑n ≤ lift.{v, u} o ↔ ω_ ↑n ≤ o",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Ordinal.partialOrder",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Ordinal.lift",
"Eq.mp",
"AddMonoidWithOne.toNatCast... | [] | simpa using lift_le (a := ω_ n) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.SetTheory.Cardinal.Cofinality.Ordinal | {
"line": 429,
"column": 2
} | {
"line": 429,
"column": 47
} | {
"line": 430,
"column": 2
} | [
{
"pp": "ι : Type u\nf : ι → Ordinal.{max u v} → Ordinal.{max u v}\nc : Ordinal.{max u v}\nhc : ℵ₀ < c.cof\nhc' : Cardinal.lift.{v, u} #ι < c.cof\nhf : ∀ (i : ι), ∀ b < c, f i b < c\na : Ordinal.{max u v}\nha : a < c\n⊢ nfpFamily f a < c",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
... | [
"case refine_1\nι : Type u\nf : ι → Ordinal.{max u v} → Ordinal.{max u v}\nc : Ordinal.{max u v}\nhc : ℵ₀ < c.cof\nhc' : Cardinal.lift.{v, u} #ι < c.cof\nhf : ∀ (i : ι), ∀ b < c, f i b < c\na : Ordinal.{max u v}\nha : a < c\n⊢ Cardinal.lift.{max u v, u} #(List ι) < (lift.{u, max u v} c).cof",
"case refine_2\nι : ... | refine lift_iSup_lt_of_lt_cof ?_ (fun l ↦ ?_) | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.SetTheory.Cardinal.Regular | {
"line": 343,
"column": 2
} | {
"line": 345,
"column": 7
} | {
"line": 347,
"column": 0
} | [
{
"pp": "c : Cardinal.{u_1}\n⊢ c < ℵ₀ ∨ c.IsRegular ∨ c.IsSingular",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"not_le",
"Iff.mpr",
"Eq.mpr",
"Preorder.toLT",
"Cardinal.IsSingular",
"Cardinal.IsRegular",
"Cardinal",
"congrArg",
"Fals... | [] | have := isRegular_or_isSingular (c := c)
rw [← not_le]
tauto | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.SetTheory.Cardinal.Regular | {
"line": 343,
"column": 2
} | {
"line": 345,
"column": 7
} | {
"line": 347,
"column": 0
} | [
{
"pp": "c : Cardinal.{u_1}\n⊢ c < ℵ₀ ∨ c.IsRegular ∨ c.IsSingular",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"not_le",
"Iff.mpr",
"Eq.mpr",
"Preorder.toLT",
"Cardinal.IsSingular",
"Cardinal.IsRegular",
"Cardinal",
"congrArg",
"Fals... | [] | have := isRegular_or_isSingular (c := c)
rw [← not_le]
tauto | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.SetTheory.Cardinal.Regular | {
"line": 429,
"column": 2
} | {
"line": 429,
"column": 46
} | {
"line": 431,
"column": 0
} | [
{
"pp": "c : Cardinal.{u_1}\nhc : c.IsInaccessible\n⊢ preAleph.symm c = c.ord",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Ordinal.partialOrder",
"Cardinal",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"id",
"OrderIso... | [] | rw [OrderIso.symm_apply_eq, hc.preAleph_ord] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.SetTheory.Cardinal.Regular | {
"line": 429,
"column": 2
} | {
"line": 429,
"column": 46
} | {
"line": 431,
"column": 0
} | [
{
"pp": "c : Cardinal.{u_1}\nhc : c.IsInaccessible\n⊢ preAleph.symm c = c.ord",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Ordinal.partialOrder",
"Cardinal",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"id",
"OrderIso... | [] | rw [OrderIso.symm_apply_eq, hc.preAleph_ord] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.SetTheory.Cardinal.Regular | {
"line": 429,
"column": 2
} | {
"line": 429,
"column": 46
} | {
"line": 431,
"column": 0
} | [
{
"pp": "c : Cardinal.{u_1}\nhc : c.IsInaccessible\n⊢ preAleph.symm c = c.ord",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Ordinal.partialOrder",
"Cardinal",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"id",
"OrderIso... | [] | rw [OrderIso.symm_apply_eq, hc.preAleph_ord] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.SetTheory.Cardinal.Arithmetic | {
"line": 765,
"column": 2
} | {
"line": 765,
"column": 36
} | {
"line": 766,
"column": 2
} | [
{
"pp": "α : Type u\ninst✝ : Infinite α\nc : Cardinal.{u}\n⊢ #{ t // #↑t ≤ c } ≤ #α ^ c",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Cardinal.instOne",
"Cardinal.add_one_eq",
"Cardinal.instPowCardinal",
"Cardinal",
"congrArg",
"Cardin... | [
"α : Type u\ninst✝ : Infinite α\nc : Cardinal.{u}\n⊢ #{ t // #↑t ≤ c } ≤ (#α + 1) ^ c"
] | rw [← add_one_eq (aleph0_le_mk α)] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.DFinsupp.Submonoid | {
"line": 58,
"column": 4
} | {
"line": 60,
"column": 70
} | {
"line": 61,
"column": 2
} | [
{
"pp": "case a\nι : Type u\nγ : Type w\ninst✝¹ : DecidableEq ι\ninst✝ : AddCommMonoid γ\nS : ι → AddSubmonoid γ\n⊢ iSup S ≤ AddMonoidHom.mrange (sumAddHom fun i ↦ (S i).subtype)",
"ppTerm": "?a✝",
"assigned": true,
"usedConstants": [
"AddSubmonoid.subtype",
"AddMonoidHom.instAddMonoidHo... | [] | apply iSup_le _
intro i y hy
exact ⟨DFinsupp.single i ⟨y, hy⟩, DFinsupp.sumAddHom_single _ _ _⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.DFinsupp.Submonoid | {
"line": 58,
"column": 4
} | {
"line": 60,
"column": 70
} | {
"line": 61,
"column": 2
} | [
{
"pp": "case a\nι : Type u\nγ : Type w\ninst✝¹ : DecidableEq ι\ninst✝ : AddCommMonoid γ\nS : ι → AddSubmonoid γ\n⊢ iSup S ≤ AddMonoidHom.mrange (sumAddHom fun i ↦ (S i).subtype)",
"ppTerm": "?a✝",
"assigned": true,
"usedConstants": [
"AddSubmonoid.subtype",
"AddMonoidHom.instAddMonoidHo... | [] | apply iSup_le _
intro i y hy
exact ⟨DFinsupp.single i ⟨y, hy⟩, DFinsupp.sumAddHom_single _ _ _⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.Pi | {
"line": 102,
"column": 57
} | {
"line": 103,
"column": 60
} | {
"line": 105,
"column": 0
} | [
{
"pp": "ι : Type u_1\ninst✝ : DecidableEq ι\nα : ι → Type u_2\nl : List ι\nfs : (i : ι) → List (α i)\nf : (i : ι) → i ∈ l → α i\n⊢ f ∈ l.pi fs ↔ ∀ (i : ι) (hi : i ∈ l), f i hi ∈ fs i",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Multiset.mem_pi",
"congrArg",
"Multiset... | [] | by
simpa [Multiset.pi_coe] using! Multiset.mem_pi ↑l (fs ·) f | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.DFinsupp.Defs | {
"line": 508,
"column": 61
} | {
"line": 512,
"column": 7
} | {
"line": 514,
"column": 0
} | [
{
"pp": "ι : Type u\nβ : ι → Type v\ninst✝² : (i : ι) → Zero (β i)\ninst✝¹ : DecidableEq ι\np : ι → Prop\ninst✝ : DecidablePred p\ni : ι\nx : β i\n⊢ filter p (single i x) = if p i then single i x else 0",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"DFinsupp.ext",
"DFinsupp.s... | [] | by
ext j
have := apply_ite (fun x : Π₀ i, β i => x j) (p i) (single i x) 0
dsimp at this
grind | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.DFinsupp.BigOperators | {
"line": 134,
"column": 2
} | {
"line": 137,
"column": 13
} | {
"line": 139,
"column": 0
} | [
{
"pp": "case refine_2\nι : Type u\nγ : Type w\ninst✝⁵ : DecidableEq ι\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ninst✝⁴ : (i : ι) → Zero (β₁ i)\ninst✝³ : (i : ι) → Zero (β₂ i)\ninst✝² : (i : ι) → (x : β₁ i) → Decidable (x ≠ 0)\ninst✝¹ : (i : ι) → (x : β₂ i) → Decidable (x ≠ 0)\ninst✝ : CommMonoid γ\nf : (i : ι) → β₁... | [] | · refine Finset.prod_congr rfl ?_
intro i h1
simp only [mem_support_toFun, ne_eq] at h1
simp [h1] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Data.DFinsupp.Defs | {
"line": 834,
"column": 76
} | {
"line": 834,
"column": 81
} | {
"line": 836,
"column": 0
} | [
{
"pp": "ι : Type u\nβ : ι → Type v\ninst✝² : DecidableEq ι\ninst✝¹ : (i : ι) → Zero (β i)\ninst✝ : (i : ι) → (x : β i) → Decidable (x ≠ 0)\nf : Π₀ (i : ι), β i\n⊢ f = mk f.support fun i ↦ f ↑i",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"DFinsupp.ext",
"Classical.ite_not",... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.DFinsupp.Defs | {
"line": 834,
"column": 76
} | {
"line": 834,
"column": 81
} | {
"line": 836,
"column": 0
} | [
{
"pp": "ι : Type u\nβ : ι → Type v\ninst✝² : DecidableEq ι\ninst✝¹ : (i : ι) → Zero (β i)\ninst✝ : (i : ι) → (x : β i) → Decidable (x ≠ 0)\nf : Π₀ (i : ι), β i\n⊢ f = mk f.support fun i ↦ f ↑i",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"DFinsupp.ext",
"Classical.ite_not",... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.DFinsupp.Defs | {
"line": 834,
"column": 76
} | {
"line": 834,
"column": 81
} | {
"line": 836,
"column": 0
} | [
{
"pp": "ι : Type u\nβ : ι → Type v\ninst✝² : DecidableEq ι\ninst✝¹ : (i : ι) → Zero (β i)\ninst✝ : (i : ι) → (x : β i) → Decidable (x ≠ 0)\nf : Π₀ (i : ι), β i\n⊢ f = mk f.support fun i ↦ f ↑i",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"DFinsupp.ext",
"Classical.ite_not",... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.DFinsupp.BigOperators | {
"line": 286,
"column": 57
} | {
"line": 286,
"column": 74
} | {
"line": 286,
"column": 74
} | [
{
"pp": "ι : Type u\nγ : Type w\nβ : ι → Type v\ninst✝² : DecidableEq ι\ninst✝¹ : (i : ι) → Zero (β i)\ninst✝ : AddCommMonoid γ\nφ : (i : ι) → ZeroHom (β i) γ\ni : ι\nx : β i\n⊢ (φ i) (Pi.single i x i) = (φ i) x",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"ZeroHom... | [
"ι : Type u\nγ : Type w\nβ : ι → Type v\ninst✝² : DecidableEq ι\ninst✝¹ : (i : ι) → Zero (β i)\ninst✝ : AddCommMonoid γ\nφ : (i : ι) → ZeroHom (β i) γ\ni : ι\nx : β i\n⊢ (φ i) x = (φ i) x"
] | Pi.single_eq_same | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.DFinsupp.BigOperators | {
"line": 294,
"column": 65
} | {
"line": 294,
"column": 82
} | {
"line": 294,
"column": 82
} | [
{
"pp": "case mk\nι : Type u\nγ : Type w\nβ : ι → Type v\ninst✝² : DecidableEq ι\ninst✝¹ : (i : ι) → Zero (β i)\ninst✝ : AddCommMonoid γ\ni : ι\nφ : ZeroHom (β i) γ\nf : (i : ι) → β i\nsupport'✝ : Trunc { s // ∀ (i : ι), i ∈ s ∨ f i = 0 }\nsf : Multiset ι\nhf : ∀ (i : ι), i ∈ sf ∨ f i = 0\n⊢ (Pi.single i φ i) (... | [
"case mk\nι : Type u\nγ : Type w\nβ : ι → Type v\ninst✝² : DecidableEq ι\ninst✝¹ : (i : ι) → Zero (β i)\ninst✝ : AddCommMonoid γ\ni : ι\nφ : ZeroHom (β i) γ\nf : (i : ι) → β i\nsupport'✝ : Trunc { s // ∀ (i : ι), i ∈ s ∨ f i = 0 }\nsf : Multiset ι\nhf : ∀ (i : ι), i ∈ sf ∨ f i = 0\n⊢ φ (f i) = φ (f i)",
"ι : Type... | Pi.single_eq_same | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.DFinsupp.BigOperators | {
"line": 466,
"column": 55
} | {
"line": 466,
"column": 60
} | {
"line": 468,
"column": 0
} | [
{
"pp": "case refine_1\nι : Type u\nγ : Type w\nβ : ι → Type v\ninst✝⁴ : DecidableEq ι\ninst✝³ : (i : ι) → Zero (β i)\ninst✝² : (i : ι) → (x : β i) → Decidable (x ≠ 0)\ninst✝¹ : CommMonoid γ\nv : Π₀ (i : ι), β i\np : ι → Prop\ninst✝ : DecidablePred p\nh : (i : ι) → β i → γ\nhp : ∀ x ∈ v.support, p x\n⊢ ∀ a ∈ (s... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.DFinsupp.BigOperators | {
"line": 466,
"column": 55
} | {
"line": 466,
"column": 60
} | {
"line": 468,
"column": 0
} | [
{
"pp": "case refine_2\nι : Type u\nγ : Type w\nβ : ι → Type v\ninst✝⁴ : DecidableEq ι\ninst✝³ : (i : ι) → Zero (β i)\ninst✝² : (i : ι) → (x : β i) → Decidable (x ≠ 0)\ninst✝¹ : CommMonoid γ\nv : Π₀ (i : ι), β i\np : ι → Prop\ninst✝ : DecidablePred p\nh : (i : ι) → β i → γ\nhp : ∀ x ∈ v.support, p x\n⊢ ∀ a₁ ∈ (... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.DFinsupp.BigOperators | {
"line": 466,
"column": 55
} | {
"line": 466,
"column": 60
} | {
"line": 468,
"column": 0
} | [
{
"pp": "case refine_3\nι : Type u\nγ : Type w\nβ : ι → Type v\ninst✝⁴ : DecidableEq ι\ninst✝³ : (i : ι) → Zero (β i)\ninst✝² : (i : ι) → (x : β i) → Decidable (x ≠ 0)\ninst✝¹ : CommMonoid γ\nv : Π₀ (i : ι), β i\np : ι → Prop\ninst✝ : DecidablePred p\nh : (i : ι) → β i → γ\nhp : ∀ x ∈ v.support, p x\n⊢ ∀ b ∈ v.... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.DFinsupp.BigOperators | {
"line": 466,
"column": 55
} | {
"line": 466,
"column": 60
} | {
"line": 468,
"column": 0
} | [
{
"pp": "case refine_4\nι : Type u\nγ : Type w\nβ : ι → Type v\ninst✝⁴ : DecidableEq ι\ninst✝³ : (i : ι) → Zero (β i)\ninst✝² : (i : ι) → (x : β i) → Decidable (x ≠ 0)\ninst✝¹ : CommMonoid γ\nv : Π₀ (i : ι), β i\np : ι → Prop\ninst✝ : DecidablePred p\nh : (i : ι) → β i → γ\nhp : ∀ x ∈ v.support, p x\n⊢ ∀ a ∈ (s... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.LinearAlgebra.Dual.Defs | {
"line": 366,
"column": 9
} | {
"line": 366,
"column": 14
} | {
"line": 368,
"column": 0
} | [
{
"pp": "R : Type u_1\nM : Type u_2\ninst✝⁴ : CommSemiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\nN : Type u_3\ninst✝¹ : AddCommMonoid N\ninst✝ : Module R N\nW : Submodule R M\nf : N →ₗ[R] M\nx✝ : Dual R N\n⊢ x✝ ∈ map f.dualMap W.dualAnnihilator → x✝ ∈ (comap f W).dualAnnihilator",
"ppTerm": "?m.... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.LinearAlgebra.DFinsupp | {
"line": 263,
"column": 12
} | {
"line": 263,
"column": 87
} | {
"line": 265,
"column": 0
} | [
{
"pp": "ι : Type u_1\nR : Type u_3\nN : Type u_6\ninst✝⁷ : Semiring R\ninst✝⁶ : AddCommMonoid N\ninst✝⁵ : Module R N\nβ₁ : ι → Type u_8\nβ₂ : ι → Type u_9\ninst✝⁴ : (i : ι) → AddCommMonoid (β₁ i)\ninst✝³ : (i : ι) → AddCommMonoid (β₂ i)\ninst✝² : (i : ι) → Module R (β₁ i)\ninst✝¹ : (i : ι) → Module R (β₂ i)\ni... | [] | simpa [DFinsupp.sumAddHom_apply] using! sum_mapRange_index fun i => by simp | Lean.Elab.Tactic.Simpa.evalSimpaUsingBang | Lean.Parser.Tactic.simpaUsingBang |
Mathlib.LinearAlgebra.DFinsupp | {
"line": 263,
"column": 12
} | {
"line": 263,
"column": 87
} | {
"line": 265,
"column": 0
} | [
{
"pp": "ι : Type u_1\nR : Type u_3\nN : Type u_6\ninst✝⁷ : Semiring R\ninst✝⁶ : AddCommMonoid N\ninst✝⁵ : Module R N\nβ₁ : ι → Type u_8\nβ₂ : ι → Type u_9\ninst✝⁴ : (i : ι) → AddCommMonoid (β₁ i)\ninst✝³ : (i : ι) → AddCommMonoid (β₂ i)\ninst✝² : (i : ι) → Module R (β₁ i)\ninst✝¹ : (i : ι) → Module R (β₂ i)\ni... | [] | simpa [DFinsupp.sumAddHom_apply] using! sum_mapRange_index fun i => by simp | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.DFinsupp | {
"line": 263,
"column": 12
} | {
"line": 263,
"column": 87
} | {
"line": 265,
"column": 0
} | [
{
"pp": "ι : Type u_1\nR : Type u_3\nN : Type u_6\ninst✝⁷ : Semiring R\ninst✝⁶ : AddCommMonoid N\ninst✝⁵ : Module R N\nβ₁ : ι → Type u_8\nβ₂ : ι → Type u_9\ninst✝⁴ : (i : ι) → AddCommMonoid (β₁ i)\ninst✝³ : (i : ι) → AddCommMonoid (β₂ i)\ninst✝² : (i : ι) → Module R (β₁ i)\ninst✝¹ : (i : ι) → Module R (β₂ i)\ni... | [] | simpa [DFinsupp.sumAddHom_apply] using! sum_mapRange_index fun i => by simp | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.LinearAlgebra.DFinsupp | {
"line": 498,
"column": 2
} | {
"line": 500,
"column": 38
} | {
"line": 501,
"column": 2
} | [
{
"pp": "ι : Type u_1\nR : Type u_3\nN : Type u_6\ninst✝³ : DecidableEq ι\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid N\ninst✝ : Module R N\np : ι → Submodule R N\nh : Function.Injective ⇑((lsum ℕ) fun i ↦ (p i).subtype)\ni : ι\nx : ↥(p i)\nv : Π₀ (i : ι), ↥(p i)\nhv : ((lsum ℕ) fun i ↦ (p i).subtype) (erase i... | [
"ι : Type u_1\nR : Type u_3\nN : Type u_6\ninst✝³ : DecidableEq ι\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid N\ninst✝ : Module R N\np : ι → Submodule R N\nh : Function.Injective ⇑((lsum ℕ) fun i ↦ (p i).subtype)\ni : ι\nx : ↥(p i)\nv : Π₀ (i : ι), ↥(p i)\nhv : ((lsum ℕ) fun i ↦ (p i).subtype) (erase i v) = ((lsum... | replace hv : lsum ℕ (fun i => (p i).subtype) (erase i v) =
lsum ℕ (fun i => (p i).subtype) (single i x) := by
simpa only [lsum_single] using! hv | Lean.Elab.Tactic.evalReplace | Lean.Parser.Tactic.replace |
Mathlib.LinearAlgebra.LinearIndependent.Lemmas | {
"line": 183,
"column": 80
} | {
"line": 183,
"column": 85
} | {
"line": 183,
"column": 85
} | [
{
"pp": "case inl.inl\nR : Type u_2\nM : Type u_4\nM' : Type u_5\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid M'\ninst✝¹ : Module R M\ninst✝ : Module R M'\ns : Set M\nt : Set M'\nhs : LinearIndependent R fun (x : ↑s) ↦ ↑x\nht : LinearIndependent R fun (x : ↑t) ↦ ↑x\na✝ : Nontrivial R\n... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.LinearAlgebra.LinearIndependent.Lemmas | {
"line": 183,
"column": 80
} | {
"line": 183,
"column": 85
} | {
"line": 183,
"column": 85
} | [
{
"pp": "case inr.inr\nR : Type u_2\nM : Type u_4\nM' : Type u_5\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid M'\ninst✝¹ : Module R M\ninst✝ : Module R M'\ns : Set M\nt : Set M'\nhs : LinearIndependent R fun (x : ↑s) ↦ ↑x\nht : LinearIndependent R fun (x : ↑t) ↦ ↑x\na✝ : Nontrivial R\n... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.LinearAlgebra.LinearIndependent.Lemmas | {
"line": 184,
"column": 53
} | {
"line": 184,
"column": 58
} | {
"line": 184,
"column": 58
} | [
{
"pp": "case inl\nR : Type u_2\nM : Type u_4\nM' : Type u_5\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid M'\ninst✝¹ : Module R M\ninst✝ : Module R M'\ns : Set M\nt : Set M'\nhs : LinearIndependent R fun (x : ↑s) ↦ ↑x\nht : LinearIndependent R fun (x : ↑t) ↦ ↑x\na✝ : Nontrivial R\nw✝ :... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.LinearAlgebra.LinearIndependent.Lemmas | {
"line": 184,
"column": 53
} | {
"line": 184,
"column": 58
} | {
"line": 184,
"column": 58
} | [
{
"pp": "case inr\nR : Type u_2\nM : Type u_4\nM' : Type u_5\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid M'\ninst✝¹ : Module R M\ninst✝ : Module R M'\ns : Set M\nt : Set M'\nhs : LinearIndependent R fun (x : ↑s) ↦ ↑x\nht : LinearIndependent R fun (x : ↑t) ↦ ↑x\na✝ : Nontrivial R\nw✝ :... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.LinearAlgebra.LinearIndependent.Lemmas | {
"line": 322,
"column": 4
} | {
"line": 323,
"column": 65
} | {
"line": 324,
"column": 4
} | [
{
"pp": "case right\nR : Type u_2\nM : Type u_4\ninst✝⁹ : Ring R\ninst✝⁸ : AddCommGroup M\ninst✝⁷ : Module R M\nx y : M\nS : Type u_6\ninst✝⁶ : CommRing S\ninst✝⁵ : IsDomain S\ninst✝⁴ : Module S R\ninst✝³ : Module S M\ninst✝² : SMulCommClass S R M\ninst✝¹ : IsScalarTower S R M\ninst✝ : IsTorsionFree S R\na b c ... | [
"case right\nR : Type u_2\nM : Type u_4\ninst✝⁹ : Ring R\ninst✝⁸ : AddCommGroup M\ninst✝⁷ : Module R M\nx y : M\nS : Type u_6\ninst✝⁶ : CommRing S\ninst✝⁵ : IsDomain S\ninst✝⁴ : Module S R\ninst✝³ : Module S M\ninst✝² : SMulCommClass S R M\ninst✝¹ : IsScalarTower S R M\ninst✝ : IsTorsionFree S R\na b c d : S\nh : a... | suffices (a * d) • t = (b * c) • t by
by_contra ht; exact h (_root_.smul_left_injective S ht ‹_›) | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticSuffices__1 | Lean.Parser.Tactic.tacticSuffices_ |
Mathlib.LinearAlgebra.BilinearMap | {
"line": 578,
"column": 12
} | {
"line": 578,
"column": 25
} | {
"line": 578,
"column": 26
} | [
{
"pp": "R : Type u_1\nS : Type u_2\nM : Type u_3\nP : Type u_4\nM' : Type u_5\nP' : Type u_6\ninst✝¹⁴ : Semiring R\ninst✝¹³ : Semiring S\ninst✝¹² : SMul S R\ninst✝¹¹ : AddCommMonoid M\ninst✝¹⁰ : Module R M\ninst✝⁹ : AddCommMonoid P\ninst✝⁸ : Module R P\ninst✝⁷ : Module S M\ninst✝⁶ : Module S P\ninst✝⁵ : IsScal... | [
"R : Type u_1\nS : Type u_2\nM : Type u_3\nP : Type u_4\nM' : Type u_5\nP' : Type u_6\ninst✝¹⁴ : Semiring R\ninst✝¹³ : Semiring S\ninst✝¹² : SMul S R\ninst✝¹¹ : AddCommMonoid M\ninst✝¹⁰ : Module R M\ninst✝⁹ : AddCommMonoid P\ninst✝⁸ : Module R P\ninst✝⁷ : Module S M\ninst✝⁶ : Module S P\ninst✝⁵ : IsScalarTower S R ... | comp_codLift, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.LinearAlgebra.LinearIndependent.Lemmas | {
"line": 340,
"column": 36
} | {
"line": 340,
"column": 41
} | {
"line": 340,
"column": 41
} | [
{
"pp": "R : Type u_2\nM : Type u_4\ninst✝¹⁰ : Ring R\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : Module R M\nx y : M\nS : Type u_6\ninst✝⁷ : CommRing S\ninst✝⁶ : IsDomain S\ninst✝⁵ : Module S R\ninst✝⁴ : Module S M\ninst✝³ : SMulCommClass S R M\ninst✝² : IsScalarTower S R M\ninst✝¹ : IsTorsionFree S R\na b c d : S\nins... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.LinearAlgebra.LinearIndependent.Lemmas | {
"line": 340,
"column": 36
} | {
"line": 340,
"column": 41
} | {
"line": 340,
"column": 41
} | [
{
"pp": "R : Type u_2\nM : Type u_4\ninst✝¹⁰ : Ring R\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : Module R M\nx y : M\nS : Type u_6\ninst✝⁷ : CommRing S\ninst✝⁶ : IsDomain S\ninst✝⁵ : Module S R\ninst✝⁴ : Module S M\ninst✝³ : SMulCommClass S R M\ninst✝² : IsScalarTower S R M\ninst✝¹ : IsTorsionFree S R\na b c d : S\nins... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.LinearIndependent.Lemmas | {
"line": 340,
"column": 36
} | {
"line": 340,
"column": 41
} | {
"line": 340,
"column": 41
} | [
{
"pp": "R : Type u_2\nM : Type u_4\ninst✝¹⁰ : Ring R\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : Module R M\nx y : M\nS : Type u_6\ninst✝⁷ : CommRing S\ninst✝⁶ : IsDomain S\ninst✝⁵ : Module S R\ninst✝⁴ : Module S M\ninst✝³ : SMulCommClass S R M\ninst✝² : IsScalarTower S R M\ninst✝¹ : IsTorsionFree S R\na b c d : S\nins... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.FreeAbelianGroup.Finsupp | {
"line": 137,
"column": 2
} | {
"line": 137,
"column": 18
} | {
"line": 139,
"column": 0
} | [
{
"pp": "X : Type u_1\nk : ℕ\nh : k ≠ 0\na : FreeAbelianGroup X\n⊢ ↑k ≠ 0",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"congrArg",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"cast",
"AddZeroClass.toAddZero",
"AddMonoidWithOne.to... | [] | exact mod_cast h | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Algebra.Module.BigOperators | {
"line": 69,
"column": 31
} | {
"line": 69,
"column": 48
} | {
"line": 69,
"column": 48
} | [
{
"pp": "ι : Type u_1\nα : Type u_3\ninst✝⁴ : DecidableEq ι\ninst✝³ : Fintype ι\ninst✝² : AddCommMonoid α\nR : Type u_7\ninst✝¹ : Semiring R\ninst✝ : Module R α\nf : ι → α\nr : R\ni₀ : ι\n⊢ Pi.single i₀ r i₀ • f i₀ = r • f i₀",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"ι : Type u_1\nα : Type u_3\ninst✝⁴ : DecidableEq ι\ninst✝³ : Fintype ι\ninst✝² : AddCommMonoid α\nR : Type u_7\ninst✝¹ : Semiring R\ninst✝ : Module R α\nf : ι → α\nr : R\ni₀ : ι\n⊢ r • f i₀ = r • f i₀",
"case h₀\nι : Type u_1\nα : Type u_3\ninst✝⁴ : DecidableEq ι\ninst✝³ : Fintype ι\ninst✝² : AddCommMonoid α\nR ... | Pi.single_eq_same | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Module.BigOperators | {
"line": 69,
"column": 54
} | {
"line": 69,
"column": 59
} | {
"line": 71,
"column": 0
} | [
{
"pp": "case h₀\nι : Type u_1\nα : Type u_3\ninst✝⁴ : DecidableEq ι\ninst✝³ : Fintype ι\ninst✝² : AddCommMonoid α\nR : Type u_7\ninst✝¹ : Semiring R\ninst✝ : Module R α\nf : ι → α\nr : R\ni₀ : ι\n⊢ ∀ b ∈ univ, b ≠ i₀ → Pi.single i₀ r b • f b = 0",
"ppTerm": "?h₀",
"assigned": true,
"usedConstants":... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.Module.BigOperators | {
"line": 69,
"column": 54
} | {
"line": 69,
"column": 59
} | {
"line": 71,
"column": 0
} | [
{
"pp": "case h₁\nι : Type u_1\nα : Type u_3\ninst✝⁴ : DecidableEq ι\ninst✝³ : Fintype ι\ninst✝² : AddCommMonoid α\nR : Type u_7\ninst✝¹ : Semiring R\ninst✝ : Module R α\nf : ι → α\nr : R\ni₀ : ι\n⊢ i₀ ∉ univ → Pi.single i₀ r i₀ • f i₀ = 0",
"ppTerm": "?h₁",
"assigned": true,
"usedConstants": [
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.LinearAlgebra.LinearIndependent.Lemmas | {
"line": 438,
"column": 4
} | {
"line": 438,
"column": 74
} | {
"line": 439,
"column": 4
} | [
{
"pp": "ι : Type u'\nR : Type u_2\nM : Type u_4\ninst✝² : Ring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nv : ι → M\n⊢ ∃ s, LinearIndepOn R v s ∧ ∀ i ∉ s, ∃ a, a ≠ 0 ∧ a • v i ∈ span R (v '' s)",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"Submodule",
"instHSMul",
... | [
"ι : Type u'\nR : Type u_2\nM : Type u_4\ninst✝² : Ring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nv : ι → M\nI : Set ι\nhIlinind : LinearIndepOn R v I\nhImaximal : ∀ (t : Set ι), I ⊆ t → LinearIndepOn R v t → I = t\n⊢ ∃ s, LinearIndepOn R v s ∧ ∀ i ∉ s, ∃ a, a ≠ 0 ∧ a • v i ∈ span R (v '' s)"
] | rcases exists_maximal_linearIndepOn' R v with ⟨I, hIlinind, hImaximal⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.LinearAlgebra.LinearIndependent.Lemmas | {
"line": 669,
"column": 6
} | {
"line": 669,
"column": 54
} | {
"line": 669,
"column": 55
} | [
{
"pp": "K : Type u_3\nV : Type u\ninst✝² : DivisionRing K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nx : V\nn : ℕ\nv : Fin n → V\n⊢ LinearIndependent K (Fin.cons x v) ↔ LinearIndependent K v ∧ x ∉ span K (range v)",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"S... | [
"K : Type u_3\nV : Type u\ninst✝² : DivisionRing K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nx : V\nn : ℕ\nv : Fin n → V\n⊢ LinearIndependent K (Fin.cons x v ∘ ⇑(finSuccEquiv n).symm) ↔ LinearIndependent K v ∧ x ∉ span K (range v)"
] | ← linearIndependent_equiv (finSuccEquiv n).symm, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.LinearAlgebra.LinearIndependent.Lemmas | {
"line": 721,
"column": 2
} | {
"line": 721,
"column": 91
} | {
"line": 723,
"column": 0
} | [
{
"pp": "R : Type u_6\nK : Type u_7\nM : Type u_8\ninst✝⁷ : CommRing R\ninst✝⁶ : DivisionRing K\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Algebra R K\ninst✝³ : Module K M\ninst✝² : Module R M\ninst✝¹ : IsScalarTower R K M\ninst✝ : FaithfulSMul R K\nn : ℕ\nv : Fin n → M\nhv : LinearIndependent R v\nx : M\nhx : x ∉ span... | [] | exact Submodule.neg_mem _ (Submodule.smul_mem _ _ (Submodule.span_subset_span R K _ hcy)) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.LinearAlgebra.LinearIndependent.Lemmas | {
"line": 762,
"column": 4
} | {
"line": 762,
"column": 81
} | {
"line": 763,
"column": 4
} | [
{
"pp": "ι : Type u'\nK : Type u_3\nV : Type u\ninst✝² : DivisionRing K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nv : ι → V\ns t : Set ι\nhs : LinearIndepOn K v s\nhst : s ⊆ t\n⊢ ?m.32",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"AddCommGroup.toAddCommMonoid",
"setOf",
... | [
"ι : Type u'\nK : Type u_3\nV : Type u\ninst✝² : DivisionRing K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nv : ι → V\ns t : Set ι\nhs : LinearIndepOn K v s\nhst : s ⊆ t\n⊢ ∀ c ⊆ {b | b ⊆ t ∧ LinearIndepOn K v b},\n IsChain (fun x1 x2 ↦ x1 ⊆ x2) c → c.Nonempty → ∃ ub ∈ {b | b ⊆ t ∧ LinearIndepOn K v b}, ∀ s ∈ ... | refine zorn_subset_nonempty { b | b ⊆ t ∧ LinearIndepOn K v b} ?_ _ ⟨hst, hs⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.LinearAlgebra.LinearIndependent.Lemmas | {
"line": 794,
"column": 70
} | {
"line": 794,
"column": 75
} | {
"line": 794,
"column": 75
} | [
{
"pp": "ι : Type u'\nK : Type u_3\nV : Type u\ninst✝² : DivisionRing K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nv : ι → V\nt : Set V\nhsp : span K t = span K (range v)\nhli : LinearIndependent K Subtype.val\nf : ⦃a : V⦄ → a ∈ t → ι\nhf : ∀ ⦃a : V⦄ (a_1 : a ∈ t), v (f a_1) = a\ns : Set ι := range fun a ↦ f... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Finset.NAry | {
"line": 460,
"column": 28
} | {
"line": 460,
"column": 89
} | {
"line": 462,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_3\nγ : Type u_5\ninst✝ : DecidableEq γ\nf : α → β → γ\ns : Finset α\nt : Finset β\nhf : ∀ b ∈ t, Injective fun a ↦ f a b\nht : ((fun b ↦ image (fun a ↦ f a b) s) '' ↑t).PairwiseDisjoint id\n⊢ #s ∣ #(image₂ f s t)",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants... | [] | by rw [← image₂_swap]; exact card_dvd_card_image₂_right hf ht | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.MonoidAlgebra.MapDomain | {
"line": 353,
"column": 57
} | {
"line": 353,
"column": 62
} | {
"line": 355,
"column": 0
} | [
{
"pp": "R : Type u_3\nS : Type u_4\nM : Type u_6\nN : Type u_7\ninst✝³ : Semiring R\ninst✝² : Semiring S\ninst✝¹ : Monoid M\ninst✝ : Monoid N\nf : R →+* S\ng : M →* N\n⊢ (mapRingHom N f).comp (mapDomainRingHom R g) = (mapDomainRingHom S g).comp (mapRingHom M f)",
"ppTerm": "?m.38",
"assigned": true,
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Algebra.MonoidAlgebra.MapDomain | {
"line": 353,
"column": 57
} | {
"line": 353,
"column": 62
} | {
"line": 355,
"column": 0
} | [
{
"pp": "R : Type u_3\nS : Type u_4\nM : Type u_6\nN : Type u_7\ninst✝³ : Semiring R\ninst✝² : Semiring S\ninst✝¹ : Monoid M\ninst✝ : Monoid N\nf : R →+* S\ng : M →* N\n⊢ (mapRingHom N f).comp (mapDomainRingHom R g) = (mapDomainRingHom S g).comp (mapRingHom M f)",
"ppTerm": "?m.38",
"assigned": true,
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.MonoidAlgebra.MapDomain | {
"line": 353,
"column": 57
} | {
"line": 353,
"column": 62
} | {
"line": 355,
"column": 0
} | [
{
"pp": "R : Type u_3\nS : Type u_4\nM : Type u_6\nN : Type u_7\ninst✝³ : Semiring R\ninst✝² : Semiring S\ninst✝¹ : Monoid M\ninst✝ : Monoid N\nf : R →+* S\ng : M →* N\n⊢ (mapRingHom N f).comp (mapDomainRingHom R g) = (mapDomainRingHom S g).comp (mapRingHom M f)",
"ppTerm": "?m.38",
"assigned": true,
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.MonoidAlgebra.MapDomain | {
"line": 486,
"column": 4
} | {
"line": 489,
"column": 52
} | {
"line": 491,
"column": 0
} | [
{
"pp": "ι : Type u_1\nF : Type u_2\nR : Type u_3\nS : Type u_4\nT : Type u_5\nM : Type u_6\nN : Type u_7\nO : Type u_8\nk : Type ?u.12\nG : Type ?u.14\ninst✝¹ : Semiring k\ninst✝ : Add G\nx y : k[G]\n⊢ MonoidAlgebra.ofCoeff (Finsupp.mapDomain (⇑Multiplicative.ofAdd) (x * y).coeff) =\n MonoidAlgebra.ofCoeff ... | [] | classical
ext
simp [MonoidAlgebra.coeff_mul, AddMonoidAlgebra.coeff_mul, Finsupp.sum_mapDomain_index, add_mul,
mul_add, ite_add_zero, Multiplicative.ext_iff] | Lean.Elab.Tactic.evalClassical | Lean.Parser.Tactic.classical |
Mathlib.Algebra.MonoidAlgebra.MapDomain | {
"line": 486,
"column": 4
} | {
"line": 489,
"column": 52
} | {
"line": 491,
"column": 0
} | [
{
"pp": "ι : Type u_1\nF : Type u_2\nR : Type u_3\nS : Type u_4\nT : Type u_5\nM : Type u_6\nN : Type u_7\nO : Type u_8\nk : Type ?u.12\nG : Type ?u.14\ninst✝¹ : Semiring k\ninst✝ : Add G\nx y : k[G]\n⊢ MonoidAlgebra.ofCoeff (Finsupp.mapDomain (⇑Multiplicative.ofAdd) (x * y).coeff) =\n MonoidAlgebra.ofCoeff ... | [] | classical
ext
simp [MonoidAlgebra.coeff_mul, AddMonoidAlgebra.coeff_mul, Finsupp.sum_mapDomain_index, add_mul,
mul_add, ite_add_zero, Multiplicative.ext_iff] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.MonoidAlgebra.MapDomain | {
"line": 486,
"column": 4
} | {
"line": 489,
"column": 52
} | {
"line": 491,
"column": 0
} | [
{
"pp": "ι : Type u_1\nF : Type u_2\nR : Type u_3\nS : Type u_4\nT : Type u_5\nM : Type u_6\nN : Type u_7\nO : Type u_8\nk : Type ?u.12\nG : Type ?u.14\ninst✝¹ : Semiring k\ninst✝ : Add G\nx y : k[G]\n⊢ MonoidAlgebra.ofCoeff (Finsupp.mapDomain (⇑Multiplicative.ofAdd) (x * y).coeff) =\n MonoidAlgebra.ofCoeff ... | [] | classical
ext
simp [MonoidAlgebra.coeff_mul, AddMonoidAlgebra.coeff_mul, Finsupp.sum_mapDomain_index, add_mul,
mul_add, ite_add_zero, Multiplicative.ext_iff] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Group.Pointwise.Finset.Basic | {
"line": 1011,
"column": 73
} | {
"line": 1011,
"column": 92
} | {
"line": 1013,
"column": 0
} | [
{
"pp": "α : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : DivisionMonoid α\na : α\nn : ℤ\n⊢ {a} ^ n = {a ^ n}",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"zpow_natCast",
"Finset.singleton_pow",
"DivInvMonoid.toInv",
"InvOneClass.toOne",
"DivInvOneMonoid.toInv... | [] | by cases n <;> simp | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Group.Pointwise.Finset.Basic | {
"line": 1173,
"column": 2
} | {
"line": 1173,
"column": 30
} | {
"line": 1173,
"column": 31
} | [
{
"pp": "α : Type u_2\ninst✝² : Mul α\ninst✝¹ : IsLeftCancelMul α\ninst✝ : DecidableEq α\ns : Finset α\n⊢ #s ≤ #(s * s)",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"Finset",
"LE.le",
"instLENat",
"Finset.instEmptyCollection",
"Or.casesOn... | [
"case inl\nα : Type u_2\ninst✝² : Mul α\ninst✝¹ : IsLeftCancelMul α\ninst✝ : DecidableEq α\ns : Finset α\nh✝ : s = ∅\n⊢ #s ≤ #(s * s)",
"case inr\nα : Type u_2\ninst✝² : Mul α\ninst✝¹ : IsLeftCancelMul α\ninst✝ : DecidableEq α\ns : Finset α\nh✝ : s.Nonempty\n⊢ #s ≤ #(s * s)"
] | cases s.eq_empty_or_nonempty | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | Lean.Parser.Tactic.cases |
Mathlib.Algebra.Group.Pointwise.Finset.Basic | {
"line": 1206,
"column": 2
} | {
"line": 1206,
"column": 30
} | {
"line": 1206,
"column": 31
} | [
{
"pp": "α : Type u_2\ninst✝² : Mul α\ninst✝¹ : IsRightCancelMul α\ninst✝ : DecidableEq α\ns : Finset α\n⊢ #s ≤ #(s * s)",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"Finset",
"LE.le",
"instLENat",
"Finset.instEmptyCollection",
"Or.casesO... | [
"case inl\nα : Type u_2\ninst✝² : Mul α\ninst✝¹ : IsRightCancelMul α\ninst✝ : DecidableEq α\ns : Finset α\nh✝ : s = ∅\n⊢ #s ≤ #(s * s)",
"case inr\nα : Type u_2\ninst✝² : Mul α\ninst✝¹ : IsRightCancelMul α\ninst✝ : DecidableEq α\ns : Finset α\nh✝ : s.Nonempty\n⊢ #s ≤ #(s * s)"
] | cases s.eq_empty_or_nonempty | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | Lean.Parser.Tactic.cases |
Mathlib.Algebra.Group.Pointwise.Finset.Basic | {
"line": 1247,
"column": 2
} | {
"line": 1247,
"column": 30
} | {
"line": 1247,
"column": 31
} | [
{
"pp": "α : Type u_2\ninst✝¹ : Group α\ninst✝ : DecidableEq α\ns : Finset α\n⊢ #s ≤ #(s / s)",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"instHDiv",
"Finset",
"HDiv.hDiv",
"LE.le",
"instLENat",
"Finset.instEmptyCollection",
"Or.casesOn",
... | [
"case inl\nα : Type u_2\ninst✝¹ : Group α\ninst✝ : DecidableEq α\ns : Finset α\nh✝ : s = ∅\n⊢ #s ≤ #(s / s)",
"case inr\nα : Type u_2\ninst✝¹ : Group α\ninst✝ : DecidableEq α\ns : Finset α\nh✝ : s.Nonempty\n⊢ #s ≤ #(s / s)"
] | cases s.eq_empty_or_nonempty | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | Lean.Parser.Tactic.cases |
Mathlib.Data.Finset.Sort | {
"line": 270,
"column": 4
} | {
"line": 270,
"column": 15
} | {
"line": 271,
"column": 2
} | [
{
"pp": "case refine_1\nα : Type u_1\ninst✝ : LinearOrder α\ns : Finset α\nk : ℕ\nh : #s = k\nf : Fin k → α\nhfs : ∀ (x : Fin k), f x ∈ s\nhmono : StrictMono f\nx : Fin k\nleft✝ : x ∈ univ\nhx : f x ∈ image f univ\n⊢ f x ∈ s",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [],
"usedFV... | [] | exact hfs x | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.LinearAlgebra.Finsupp.Span | {
"line": 144,
"column": 47
} | {
"line": 144,
"column": 59
} | {
"line": 144,
"column": 60
} | [
{
"pp": "R : Type u_1\nM : Type u_2\nN : Type u_3\nσ : Type u_4\ninst✝⁴ : CommSemiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid N\ninst✝¹ : Module R M\ninst✝ : Module R N\nφ : M →ₗ[R] N\nf : σ → R\n⊢ map ((lsum R) fun x ↦ f x • φ) (span R {x | ∃ i x_1, single i x_1 = x}) = Set.range f • map φ ⊤",
... | [
"R : Type u_1\nM : Type u_2\nN : Type u_3\nσ : Type u_4\ninst✝⁴ : CommSemiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid N\ninst✝¹ : Module R M\ninst✝ : Module R N\nφ : M →ₗ[R] N\nf : σ → R\n⊢ map ((lsum R) fun x ↦ f x • φ) (span R {x | ∃ i x_1, single i x_1 = x}) = Set.range f • map φ (span R univ)"
] | ← span_univ, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Algebra.Polynomial.Basic | {
"line": 1132,
"column": 61
} | {
"line": 1132,
"column": 78
} | {
"line": 1134,
"column": 0
} | [
{
"pp": "R : Type u\ninst✝ : Ring R\np : R[X]\n⊢ (-p).support = p.support",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Polynomial.instNeg",
"Polynomial.toFinsupp",
"AddGroupWithOne.toAddGroup",
"congrArg",
"Finset",
... | [] | by simp [support] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Group.UniqueProds.Basic | {
"line": 532,
"column": 4
} | {
"line": 532,
"column": 60
} | {
"line": 533,
"column": 4
} | [
{
"pp": "case refine_2.refine_1\nG✝ : Type u\nH : Type v\ninst✝³ : Mul G✝\ninst✝² : Mul H\nι : Type u_2\nG : ι → Type u_1\ninst✝¹ : (i : ι) → Mul (G i)\ninst✝ : ∀ (i : ι), TwoUniqueProds (G i)\nA✝ : Finset ((i : ι) → G i)\nx✝ : IsWellFounded (Finset ((i : ι) → G i)) fun x1 x2 ↦ x1 ⊂ x2 := isWellFounded_ssubset\... | [
"case refine_2.refine_1.inr\nG✝ : Type u\nH : Type v\ninst✝³ : Mul G✝\ninst✝² : Mul H\nι : Type u_2\nG : ι → Type u_1\ninst✝¹ : (i : ι) → Mul (G i)\ninst✝ : ∀ (i : ι), TwoUniqueProds (G i)\nA✝ : Finset ((i : ι) → G i)\nx✝ : IsWellFounded (Finset ((i : ι) → G i)) fun x1 x2 ↦ x1 ⊂ x2 := isWellFounded_ssubset\nA : Fin... | all_goals rcases hc with hc | hc; · exact ihA _ (hc.2 _) | Lean.Elab.Tactic.evalAllGoals | Lean.Parser.Tactic.allGoals |
Mathlib.LinearAlgebra.Projection | {
"line": 81,
"column": 4
} | {
"line": 81,
"column": 13
} | {
"line": 82,
"column": 2
} | [
{
"pp": "case left.hd\nR : Type u_1\ninst✝⁹ : Ring R\nE : Type u_2\ninst✝⁸ : AddCommGroup E\ninst✝⁷ : Module R E\nF : Type u_3\ninst✝⁶ : AddCommGroup F\ninst✝⁵ : Module R F\nG : Type u_4\ninst✝⁴ : AddCommGroup G\ninst✝³ : Module R G\np q : Submodule R E\nS : Type u_5\ninst✝² : Semiring S\nM : Type u_6\ninst✝¹ :... | [] | exact h.1 | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.LinearAlgebra.Projection | {
"line": 628,
"column": 50
} | {
"line": 632,
"column": 29
} | {
"line": 634,
"column": 0
} | [
{
"pp": "S : Type u_5\ninst✝² : Semiring S\nM : Type u_6\ninst✝¹ : AddCommMonoid M\ninst✝ : Module S M\nm : Submodule S M\nf : M →ₗ[S] M\nhf : IsProj m f\n⊢ m = ⊤ ↔ f = id",
"ppTerm": "?m.46",
"assigned": true,
"usedConstants": [
"LinearMap.id",
"Eq.mpr",
"LinearMap.range_id",
... | [] | by
constructor <;> rintro rfl
· ext
simp [hf.map_id]
· rw [← hf.range, range_id] | [anonymous] | Lean.Parser.Term.byTactic |
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