module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Algebra.EuclideanDomain.Int | {
"line": 28,
"column": 6
} | {
"line": 29,
"column": 32
} | {
"line": 30,
"column": 4
} | [
{
"pp": "a b : ℤ\nb0 : b ≠ 0\n⊢ ↑(a % b).natAbs < ↑b.natAbs",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"Int.emod_lt_abs",
"Eq.mpr",
"abs",
"congrArg",
"id",
"instHMod",
"Int",
"Nat.cast",
"Int.natAbs_of_nonneg",
"Int.instLTIn... | [] | rw [Int.natAbs_of_nonneg (Int.emod_nonneg _ b0), ← Int.abs_eq_natAbs]
exact Int.emod_lt_abs _ b0 | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Set.Card | {
"line": 477,
"column": 18
} | {
"line": 477,
"column": 77
} | {
"line": 477,
"column": 77
} | [
{
"pp": "α : Type u_1\nn : ℕ\nt₀ : Set α\nht₀ : t₀.encard = ↑n\nIH : ↑n ≤ t₀.encard → ∃ t ⊆ t₀, t.encard = ↑n\nht₀s : t₀ ⊆ t₀\nhk : ↑n + 1 ≤ t₀.encard\n⊢ False",
"ppTerm": "?m.78",
"assigned": true,
"usedConstants": [
"Set.encard",
"instCharZeroENat",
"instAddMonoidWithOneENat",
... | [
"α : Type u_1\nn : ℕ\nt₀ : Set α\nht₀ : t₀.encard = ↑n\nIH : ↑n ≤ t₀.encard → ∃ t ⊆ t₀, t.encard = ↑n\nht₀s : t₀ ⊆ t₀\nhk : n + 1 ≤ n\n⊢ False"
] | rw [ht₀, ← Nat.cast_one, ← Nat.cast_add, Nat.cast_le] at hk | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Set.Card | {
"line": 547,
"column": 4
} | {
"line": 547,
"column": 33
} | {
"line": 547,
"column": 34
} | [
{
"pp": "α : Type u_1\nP Q : Set α\nx✝¹ x✝ : ↑(P ↓∩ Q)\nh :\n (fun x ↦\n match x with\n | ⟨⟨x, property⟩, hx⟩ => ⟨x, hx⟩)\n x✝¹ =\n (fun x ↦\n match x with\n | ⟨⟨x, property⟩, hx⟩ => ⟨x, hx⟩)\n x✝\n⊢ x✝¹ = x✝",
"ppTerm": "?m.48",
"assigned": false,
"usedCons... | [
"α : Type u_1\nP Q : Set α\nx✝¹ x✝ : ↑(P ↓∩ Q)\nh :\n (fun x ↦\n match x with\n | ⟨⟨x, property⟩, hx⟩ => ⟨x, hx⟩)\n x✝¹ =\n (fun x ↦\n match x with\n | ⟨⟨x, property⟩, hx⟩ => ⟨x, hx⟩)\n x✝\n⊢ x✝¹ = x✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Cardinal.NatCard | {
"line": 141,
"column": 2
} | {
"line": 141,
"column": 45
} | {
"line": 141,
"column": 46
} | [
{
"pp": "α : Type u_1\ninst✝ : Finite α\np : α → Prop\nthis : Fintype α\n⊢ Nat.card { x // p x } ≤ Nat.card α",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Classical.propDecidable",
"Subtype.fintype",
"Fintype.card",
"id",
"... | [
"α : Type u_1\ninst✝ : Finite α\np : α → Prop\nthis : Fintype α\n⊢ Fintype.card { x // p x } ≤ Fintype.card α"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Submonoid.Finite | {
"line": 47,
"column": 8
} | {
"line": 47,
"column": 25
} | {
"line": 47,
"column": 26
} | [
{
"pp": "case neg\nη : Type u_1\nf : η → Type u_2\ninst✝³ : (i : η) → MulOneClass (f i)\nS : Type u_3\ninst✝² : SetLike S ((i : η) → f i)\ninst✝¹ : SubmonoidClass S ((i : η) → f i)\ninst✝ : DecidableEq η\nH : S\ni : η\nI : Finset η\nhnotMem : i ∉ I\nx : (i : η) → f i\nh1 : ∀ i_1 ∉ insert i I, x i_1 = 1\nh2 : ∀ ... | [
"case neg\nη : Type u_1\nf : η → Type u_2\ninst✝³ : (i : η) → MulOneClass (f i)\nS : Type u_3\ninst✝² : SetLike S ((i : η) → f i)\ninst✝¹ : SubmonoidClass S ((i : η) → f i)\ninst✝ : DecidableEq η\nH : S\ni : η\nI : Finset η\nhnotMem : i ∉ I\nx : (i : η) → f i\nh1 : ∀ i_1 ∉ insert i I, x i_1 = 1\nh2 : ∀ i_1 ∈ insert... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Cardinal.NatCard | {
"line": 147,
"column": 2
} | {
"line": 147,
"column": 56
} | {
"line": 147,
"column": 57
} | [
{
"pp": "α : Type u_1\ninst✝ : Finite α\np : α → Prop\nx : α\nhx : ¬p x\nthis : Fintype α\n⊢ Nat.card { x // p x } < Nat.card α",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"_private.Mathlib.SetTheory.Cardinal.NatCard.0.Finite.card_subtype_lt._simp... | [
"α : Type u_1\ninst✝ : Finite α\np : α → Prop\nx : α\nhx : ¬p x\nthis : Fintype α\n⊢ Fintype.card { x // p x } < Fintype.card α"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Submonoid.Finite | {
"line": 47,
"column": 35
} | {
"line": 47,
"column": 52
} | {
"line": 47,
"column": 53
} | [
{
"pp": "η : Type u_1\nf : η → Type u_2\ninst✝³ : (i : η) → MulOneClass (f i)\nS : Type u_3\ninst✝² : SetLike S ((i : η) → f i)\ninst✝¹ : SubmonoidClass S ((i : η) → f i)\ninst✝ : DecidableEq η\nH : S\ni : η\nI : Finset η\nhnotMem : i ∉ I\nx : (i : η) → f i\nh1 : ∀ i_1 ∉ insert i I, x i_1 = 1\nh2 : ∀ i_1 ∈ inse... | [
"η : Type u_1\nf : η → Type u_2\ninst✝³ : (i : η) → MulOneClass (f i)\nS : Type u_3\ninst✝² : SetLike S ((i : η) → f i)\ninst✝¹ : SubmonoidClass S ((i : η) → f i)\ninst✝ : DecidableEq η\nH : S\ni : η\nI : Finset η\nhnotMem : i ∉ I\nx : (i : η) → f i\nh1 : ∀ i_1 ∉ insert i I, x i_1 = 1\nh2 : ∀ i_1 ∈ insert i I, Pi.m... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Submonoid.Finite | {
"line": 47,
"column": 35
} | {
"line": 47,
"column": 55
} | {
"line": 47,
"column": 55
} | [
{
"pp": "η : Type u_1\nf : η → Type u_2\ninst✝³ : (i : η) → MulOneClass (f i)\nS : Type u_3\ninst✝² : SetLike S ((i : η) → f i)\ninst✝¹ : SubmonoidClass S ((i : η) → f i)\ninst✝ : DecidableEq η\nH : S\ni : η\nI : Finset η\nhnotMem : i ∉ I\nx : (i : η) → f i\nh1 : ∀ i_1 ∉ insert i I, x i_1 = 1\nh2 : ∀ i_1 ∈ inse... | [] | simpa [heq] using hj | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Algebra.Group.Submonoid.Finite | {
"line": 47,
"column": 35
} | {
"line": 47,
"column": 55
} | {
"line": 47,
"column": 55
} | [
{
"pp": "η : Type u_1\nf : η → Type u_2\ninst✝³ : (i : η) → MulOneClass (f i)\nS : Type u_3\ninst✝² : SetLike S ((i : η) → f i)\ninst✝¹ : SubmonoidClass S ((i : η) → f i)\ninst✝ : DecidableEq η\nH : S\ni : η\nI : Finset η\nhnotMem : i ∉ I\nx : (i : η) → f i\nh1 : ∀ i_1 ∉ insert i I, x i_1 = 1\nh2 : ∀ i_1 ∈ inse... | [] | simpa [heq] using hj | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Group.Submonoid.Finite | {
"line": 47,
"column": 35
} | {
"line": 47,
"column": 55
} | {
"line": 47,
"column": 55
} | [
{
"pp": "η : Type u_1\nf : η → Type u_2\ninst✝³ : (i : η) → MulOneClass (f i)\nS : Type u_3\ninst✝² : SetLike S ((i : η) → f i)\ninst✝¹ : SubmonoidClass S ((i : η) → f i)\ninst✝ : DecidableEq η\nH : S\ni : η\nI : Finset η\nhnotMem : i ∉ I\nx : (i : η) → f i\nh1 : ∀ i_1 ∉ insert i I, x i_1 = 1\nh2 : ∀ i_1 ∈ inse... | [] | simpa [heq] using hj | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Group.Submonoid.Finite | {
"line": 78,
"column": 10
} | {
"line": 78,
"column": 25
} | {
"line": 78,
"column": 26
} | [
{
"pp": "case neg\nη : Type u_1\nf : η → Type u_2\ninst✝¹ : (i : η) → MulOneClass (f i)\ninst✝ : Finite η\ns : (i : η) → Set (f i)\nhs : ∀ (i : η), 1 ∈ s i\ni : η\n_x : f i\nhx : _x ∈ s i\nj : η\nH : ¬j = i\n⊢ (MonoidHom.mulSingle f i) _x j ∈ s j",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants... | [
"case neg\nη : Type u_1\nf : η → Type u_2\ninst✝¹ : (i : η) → MulOneClass (f i)\ninst✝ : Finite η\ns : (i : η) → Set (f i)\nhs : ∀ (i : η), 1 ∈ s i\ni : η\n_x : f i\nhx : _x ∈ s i\nj : η\nH : ¬j = i\n⊢ 1 ∈ s j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Cardinal.NatCard | {
"line": 175,
"column": 81
} | {
"line": 179,
"column": 29
} | {
"line": 181,
"column": 0
} | [
{
"pp": "α : Type u_1\ns t : Set α\nht : t.Finite\nhsub : s ⊂ t\n⊢ Nat.card ↑s < Nat.card ↑t",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"ChainCompletePartialOrder.instOfCompleteLattice",
"congrArg",
"PartialOrder.toPreorder",
"Set.Elem",
"F... | [] | by
have : Fintype t := Finite.fintype ht
have : Fintype s := Finite.fintype (subset ht (subset_of_ssubset hsub))
simp only [Nat.card_eq_fintype_card]
exact Set.card_lt_card hsub | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Set.Card | {
"line": 966,
"column": 57
} | {
"line": 966,
"column": 68
} | {
"line": 966,
"column": 69
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ns : Set α\nt : Set β\nf : (a : α) → a ∈ s → β\nhf : ∀ (a : α) (ha : a ∈ s), f a ha ∈ t\nhinj : ∀ (a₁ a₂ : α) (ha₁ : a₁ ∈ s) (ha₂ : a₂ ∈ s), f a₁ ha₁ = f a₂ ha₂ → a₁ = a₂\nhst : t.ncard ≤ s.ncard\nht : t.Finite\nb : β\nhb : b ∈ t\nf' : ↑s → ↑t := fun x ↦ ⟨f ↑x ⋯, ⋯⟩\nfinj : F... | [
"α : Type u_1\nβ : Type u_2\ns : Set α\nt : Set β\nf : (a : α) → a ∈ s → β\nhf : ∀ (a : α) (ha : a ∈ s), f a ha ∈ t\nhinj : ∀ (a₁ a₂ : α) (ha₁ : a₁ ∈ s) (ha₂ : a₂ ∈ s), f a₁ ha₁ = f a₂ ha₂ → a₁ = a₂\nhst : t.ncard ≤ s.ncard\nht : t.Finite\nb : β\nhb : b ∈ t\nf' : ↑s → ↑t := fun x ↦ ⟨f ↑x ⋯, ⋯⟩\nfinj : Function.Inje... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Subgroup.Finite | {
"line": 131,
"column": 46
} | {
"line": 131,
"column": 66
} | {
"line": 131,
"column": 67
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\nH : Subgroup G\ninst✝ : Finite ↥H\nh : H = ⊤\n⊢ Nat.card ↥H = Nat.card G",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Membership.mem",
"id",
"Subtype",
"Nat.card",
"Subgroup",
... | [
"G : Type u_1\ninst✝¹ : Group G\nH : Subgroup G\ninst✝ : Finite ↥H\nh : H = ⊤\n⊢ Nat.card ↥⊤ = Nat.card G"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Subgroup.Finite | {
"line": 212,
"column": 10
} | {
"line": 212,
"column": 25
} | {
"line": 212,
"column": 26
} | [
{
"pp": "case neg\nη : Type u_3\nf : η → Type u_4\ninst✝¹ : (i : η) → Group (f i)\ninst✝ : Finite η\ns : (i : η) → Set (f i)\nhs : ∀ (i : η), 1 ∈ s i\ni : η\n_x : f i\nhx : _x ∈ s i\nj : η\nH : ¬j = i\n⊢ (MonoidHom.mulSingle f i) _x j ∈ s j",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
... | [
"case neg\nη : Type u_3\nf : η → Type u_4\ninst✝¹ : (i : η) → Group (f i)\ninst✝ : Finite η\ns : (i : η) → Set (f i)\nhs : ∀ (i : η), 1 ∈ s i\ni : η\n_x : f i\nhx : _x ∈ s i\nj : η\nH : ¬j = i\n⊢ 1 ∈ s j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Card | {
"line": 988,
"column": 57
} | {
"line": 988,
"column": 68
} | {
"line": 988,
"column": 69
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ns : Set α\nt : Set β\nf : (a : α) → a ∈ s → β\nhf : ∀ (a : α) (ha : a ∈ s), f a ha ∈ t\nhsurj✝ : ∀ b ∈ t, ∃ a, ∃ (ha : a ∈ s), f a ha = b\nhst : s.ncard ≤ t.ncard\na₁ : α\nha₁ : a₁ ∈ s\na₂ : α\nha₂ : a₂ ∈ s\nha₁a₂ : f a₁ ha₁ = f a₂ ha₂\nhs : s.Finite\nf' : ↑s → ↑t := fun x ↦... | [
"α : Type u_1\nβ : Type u_2\ns : Set α\nt : Set β\nf : (a : α) → a ∈ s → β\nhf : ∀ (a : α) (ha : a ∈ s), f a ha ∈ t\nhsurj✝ : ∀ b ∈ t, ∃ a, ∃ (ha : a ∈ s), f a ha = b\nhst : s.ncard ≤ t.ncard\na₁ : α\nha₁ : a₁ ∈ s\na₂ : α\nha₂ : a₂ ∈ s\nha₁a₂ : f a₁ ha₁ = f a₂ ha₂\nhs : s.Finite\nf' : ↑s → ↑t := fun x ↦ ⟨f ↑x ⋯, ⋯⟩... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Basis.Submodule | {
"line": 92,
"column": 4
} | {
"line": 92,
"column": 23
} | {
"line": 92,
"column": 24
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nR : Type u_3\nR₂ : Type u_4\nM : Type u_5\nM' : Type u_6\ninst✝³ : Ring R\ninst✝² : IsDomain R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nb✝ : ι → M\nb : Basis ι R M\nP : Submodule R M → Sort u_7\nih :\n (N : Submodule R M) →\n ((N' : Submodule R M) → N' ≤ N → (x : M... | [
"ι : Type u_1\nι' : Type u_2\nR : Type u_3\nR₂ : Type u_4\nM : Type u_5\nM' : Type u_6\ninst✝³ : Ring R\ninst✝² : IsDomain R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nb✝ : ι → M\nb : Basis ι R M\nP : Submodule R M → Sort u_7\nih :\n (N : Submodule R M) →\n ((N' : Submodule R M) → N' ≤ N → (x : M) → x ∈ N → ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Card | {
"line": 1100,
"column": 6
} | {
"line": 1100,
"column": 55
} | {
"line": 1100,
"column": 56
} | [
{
"pp": "α : Type u_1\ns t : Set α\nhs : s.Finite\nht : t.Finite\n⊢ (s \\ t).ncard + t.ncard = (s ∪ t).ncard",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Set.instUnion",
"Set.ncard_union_eq",
"id",
"SDiff.sdiff",
"instHAdd... | [
"α : Type u_1\ns t : Set α\nhs : s.Finite\nht : t.Finite\n⊢ (s \\ t ∪ t).ncard = (s ∪ t).ncard"
] | ← ncard_union_eq disjoint_sdiff_left hs.sdiff ht, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Set.Card | {
"line": 1212,
"column": 83
} | {
"line": 1212,
"column": 94
} | {
"line": 1212,
"column": 95
} | [
{
"pp": "α : Type u_1\nn : ℕ\ns : Finset α\nhsn : (↑s).ncard ≤ n\nt : Finset α\nhnt : n ≤ (↑t).ncard\nhst : ↑s ⊆ ↑t\n⊢ s.card ≤ n",
"ppTerm": "?m.122",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nn : ℕ\ns : Finset α\nhsn : (↑s).ncard ≤ n\nt : Finset α\nhnt : n ≤ (↑t).ncard\nhst : ↑s ⊆ ↑t\n⊢ s.card ≤ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Card | {
"line": 1212,
"column": 2
} | {
"line": 1213,
"column": 18
} | {
"line": 1214,
"column": 2
} | [
{
"pp": "case inr\nα : Type u_1\nn : ℕ\ns : Finset α\nhsn : (↑s).ncard ≤ n\nt : Finset α\nhnt : n ≤ (↑t).ncard\nhst : ↑s ⊆ ↑t\n⊢ ∃ u, ↑s ⊆ u ∧ u ⊆ ↑t ∧ u.ncard = n",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"SetLike.coe_subset_coe._simp_1",
"congrArg",
"Finset",
... | [
"case inr\nα : Type u_1\nn : ℕ\ns : Finset α\nhsn : (↑s).ncard ≤ n\nt : Finset α\nhnt : n ≤ (↑t).ncard\nhst : ↑s ⊆ ↑t\nu : Finset α\nhsu : s ⊆ u\nhut : u ⊆ t\nhu : u.card = n\n⊢ ∃ u, ↑s ⊆ u ∧ u ⊆ ↑t ∧ u.ncard = n"
] | obtain ⟨u, hsu, hut, hu⟩ := Finset.exists_subsuperset_card_eq (mod_cast hst) (by simpa using hsn)
(mod_cast hnt) | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Data.Set.Card | {
"line": 1218,
"column": 2
} | {
"line": 1218,
"column": 13
} | {
"line": 1218,
"column": 14
} | [
{
"pp": "α : Type u_1\ns : Set α\nn : ℕ\nhns : n ≤ s.ncard\n⊢ ∃ t ⊆ s, t.ncard = n",
"ppTerm": "?m.10",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ns : Set α\nn : ℕ\nhns : n ≤ s.ncard\n⊢ ∃ t ⊆ s, t.ncard = n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Card | {
"line": 1243,
"column": 26
} | {
"line": 1243,
"column": 37
} | {
"line": 1243,
"column": 38
} | [
{
"pp": "α : Type u_1\ns t : Set α\nn : ℕ\nhu : (s ∪ t).Finite\nhst : 2 * n < (⋯.toFinset ∪ ⋯.toFinset).card\nr' : Finset α\nhnr' : n < r'.card\nhr' : r' ⊆ ⋯.toFinset ∨ r' ⊆ ⋯.toFinset\n⊢ ↑r' ⊆ s ∨ ↑r' ⊆ t",
"ppTerm": "?m.94",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoa... | [
"α : Type u_1\ns t : Set α\nn : ℕ\nhu : (s ∪ t).Finite\nhst : 2 * n < (⋯.toFinset ∪ ⋯.toFinset).card\nr' : Finset α\nhnr' : n < r'.card\nhr' : r' ⊆ ⋯.toFinset ∨ r' ⊆ ⋯.toFinset\n⊢ ↑r' ⊆ s ∨ ↑r' ⊆ t"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Card | {
"line": 1356,
"column": 2
} | {
"line": 1356,
"column": 40
} | {
"line": 1356,
"column": 41
} | [
{
"pp": "α : Type u_1\ns : Set α\na : α\nhsf : s.Finite\nhs : 1 < hsf.toFinset.card\n⊢ ∃ b ∈ s, b ≠ a",
"ppTerm": "?m.41",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ns : Set α\na : α\nhsf : s.Finite\nhs : 1 < hsf.toFinset.card\n⊢ ∃ b ∈ s, b ≠ a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Coset.Basic | {
"line": 304,
"column": 2
} | {
"line": 304,
"column": 77
} | {
"line": 304,
"column": 78
} | [
{
"pp": "α : Type u_1\ninst✝ : Group α\ns : Subgroup α\nx x✝ : α\n⊢ Quotient.mk'' x✝ = ↑x ↔ x✝ ∈ x • ↑s",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SetLike.mem_coe._simp_1",
"instHSMul",
"instSMulOfMul",
"HMul.hMul",
"DivInvOneMonoid.toInv... | [
"α : Type u_1\ninst✝ : Group α\ns : Subgroup α\nx x✝ : α\n⊢ (orbitRel (↥s.op) α) x✝ x ↔ (leftRel s) x x✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Card | {
"line": 1426,
"column": 4
} | {
"line": 1426,
"column": 33
} | {
"line": 1426,
"column": 34
} | [
{
"pp": "case inr.refine_2\nα : Type u_1\nβ : Type u_2\ninst✝ : Finite α\nf : α → β\nhf✝ : Surjective f\nh✝ : Nonempty α\ng : β → α := surjInv hf✝\nhf : ∀ (b : β), f (g b) = b\nh : ∀ (a b c d : α), f a = f b → f c = f d → a ≠ b → c ≠ d → {a, b} = {c, d}\na : α\nha : ∀ (x : β), g x ≠ a\nb : α\nhb : ∀ (x : β), g ... | [
"case inr.refine_2\nα : Type u_1\nβ : Type u_2\ninst✝ : Finite α\nf : α → β\nhf✝ : Surjective f\nh✝ : Nonempty α\ng : β → α := surjInv hf✝\nhf : ∀ (b : β), f (g b) = b\nh : ∀ (a b c d : α), f a = f b → f c = f d → a ≠ b → c ≠ d → {a, b} = {c, d}\na : α\nha : ∀ (x : β), g x ≠ a\nb : α\nhb : ∀ (x : β), g x ≠ b\n⊢ a =... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Card | {
"line": 1434,
"column": 2
} | {
"line": 1435,
"column": 52
} | {
"line": 1436,
"column": 6
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ns : Set α\ninst✝ : Finite ↑s\nf : α → β\n⊢ s.ncard ≤ (f '' s).ncard + 1 ↔\n ∀ a ∈ s, ∀ b ∈ s, ∀ c ∈ s, ∀ d ∈ s, f a = f b → f c = f d → a ≠ b → c ≠ d → {a, b} = {c, d}",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"Membership.mem",
"Set... | [
"α : Type u_1\nβ : Type u_2\ns : Set α\ninst✝ : Finite ↑s\nf : α → β\n⊢ s.ncard ≤ (f '' s).ncard + 1 ↔\n ∀ a ∈ s, ∀ b ∈ s, ∀ c ∈ s, ∀ d ∈ s, f a = f b → f c = f d → ¬a = b → ¬c = d → {a, b} = {c, d}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Fin.Tuple | {
"line": 118,
"column": 24
} | {
"line": 118,
"column": 40
} | {
"line": 120,
"column": 0
} | [
{
"pp": "α : Type u_1\nn : ℕ\ninst✝ : Zero α\nv : Fin n → α\nx : α\nx✝ : x = 0 ∧ v = 0\nhx : x = 0\nhv : v = 0\n⊢ vecCons x v = 0",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"congrArg",
"Pi.instZero",
"instOfNatNat",
"instHAdd",
"Matrix.cons_zero_zero",
... | [] | by simp [hx, hv] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.GroupTheory.QuotientGroup.Basic | {
"line": 361,
"column": 2
} | {
"line": 361,
"column": 13
} | {
"line": 361,
"column": 14
} | [
{
"pp": "G : Type u\ninst✝¹ : Group G\nN : Subgroup G\ninst✝ : N.Normal\nH : Subgroup (G ⧸ N)\n⊢ N ≤ Subgroup.comap (mk' N) H",
"ppTerm": "?m.21",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"G : Type u\ninst✝¹ : Group G\nN : Subgroup G\ninst✝ : N.Normal\nH : Subgroup (G ⧸ N)\n⊢ N ≤ Subgroup.comap (mk' N) H"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Graph | {
"line": 84,
"column": 2
} | {
"line": 84,
"column": 31
} | {
"line": 84,
"column": 32
} | [
{
"pp": "case h\nG : Type u_1\nH : Type u_2\nI : Type u_3\ninst✝² : Monoid G\ninst✝¹ : Monoid H\ninst✝ : Monoid I\nf : G →* H × I\nhf₁ : Surjective (Prod.fst ∘ ⇑f)\nhf : ∀ (g₁ g₂ : G), (f g₁).1 = (f g₂).1 → (f g₁).2 = (f g₂).2\nf' : H → I\nhf' : ∀ (a : H) (b : I), (∃ y, f y = (a, b)) ↔ f' a = b\n⊢ mrange f = { ... | [
"case h\nG : Type u_1\nH : Type u_2\nI : Type u_3\ninst✝² : Monoid G\ninst✝¹ : Monoid H\ninst✝ : Monoid I\nf : G →* H × I\nhf₁ : Surjective (Prod.fst ∘ ⇑f)\nhf : ∀ (g₁ g₂ : G), (f g₁).1 = (f g₂).1 → (f g₁).2 = (f g₂).2\nf' : H → I\nhf' : ∀ (a : H) (b : I), (∃ y, f y = (a, b)) ↔ f' a = b\n⊢ ∀ (a : H) (b : I), (∃ x, ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.QuotientGroup.Basic | {
"line": 482,
"column": 4
} | {
"line": 482,
"column": 31
} | {
"line": 482,
"column": 32
} | [
{
"pp": "ι : Type u_1\nA : ι → Type u_2\ninst✝ : (i : ι) → CommGroup (A i)\nn : ℕ\nφ : ((i : ι) → A i) →* (i : ι) → A i ⧸ (powMonoidHom n).range :=\n { toFun := fun x x_1 ↦ ↑(x x_1), map_one' := ⋯, map_mul' := ⋯ }\nx : (i : ι) → A i\n⊢ x ∈ (powMonoidHom n).range ↔ x ∈ φ.ker",
"ppTerm": "?m.78",
"assign... | [
"ι : Type u_1\nA : ι → Type u_2\ninst✝ : (i : ι) → CommGroup (A i)\nn : ℕ\nφ : ((i : ι) → A i) →* (i : ι) → A i ⧸ (powMonoidHom n).range :=\n { toFun := fun x x_1 ↦ ↑(x x_1), map_one' := ⋯, map_mul' := ⋯ }\nx : (i : ι) → A i\n⊢ (∃ x_1, ∀ (x_2 : ι), x_1 x_2 ^ n = x x_2) ↔ ∀ (x_1 : ι), ∃ x_2, x_2 ^ n = x x_1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Graph | {
"line": 127,
"column": 2
} | {
"line": 127,
"column": 13
} | {
"line": 127,
"column": 14
} | [
{
"pp": "H : Type u_2\nI : Type u_3\ninst✝¹ : Monoid H\ninst✝ : Monoid I\nG : Submonoid (H × I)\nhG₁ : Bijective (Prod.fst ∘ ⇑G.subtype)\n⊢ ∃ f, G = f.mgraph",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"H : Type u_2\nI : Type u_3\ninst✝¹ : Monoid H\ninst✝ : Monoid I\nG : Submonoid (H × I)\nhG₁ : Bijective (Prod.fst ∘ ⇑G.subtype)\n⊢ ∃ f, G = f.mgraph"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Group.Graph | {
"line": 141,
"column": 2
} | {
"line": 141,
"column": 13
} | {
"line": 141,
"column": 14
} | [
{
"pp": "H : Type u_2\nI : Type u_3\ninst✝¹ : Monoid H\ninst✝ : Monoid I\nG : Submonoid (H × I)\nhG₁ : Bijective (Prod.fst ∘ ⇑G.subtype)\nhG₂ : Bijective (Prod.snd ∘ ⇑G.subtype)\n⊢ ∃ e, G = e.toMonoidHom.mgraph",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Monoid.toMulOneClass",
... | [
"H : Type u_2\nI : Type u_3\ninst✝¹ : Monoid H\ninst✝ : Monoid I\nG : Submonoid (H × I)\nhG₁ : Bijective (Prod.fst ∘ ⇑G.subtype)\nhG₂ : Bijective (Prod.snd ∘ ⇑G.subtype)\n⊢ ∃ e, G = (↑e).mgraph"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Quotient.Defs | {
"line": 98,
"column": 54
} | {
"line": 98,
"column": 65
} | {
"line": 98,
"column": 66
} | [
{
"pp": "R : Type u_1\nM : Type u_2\nx : M\ninst✝² : Ring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\np : Submodule R M\n⊢ mk x = 0 ↔ x ∈ p",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_1\nM : Type u_2\nx : M\ninst✝² : Ring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\np : Submodule R M\n⊢ mk x = 0 ↔ x ∈ p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Quotient.Defs | {
"line": 135,
"column": 30
} | {
"line": 135,
"column": 41
} | {
"line": 135,
"column": 42
} | [
{
"pp": "R : Type u_1\nM : Type u_2\nr : R\nx✝ y✝ : M\ninst✝⁵ : Ring R\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\np p' : Submodule R M\nS : Type u_3\ninst✝² : SMul S R\ninst✝¹ : SMul S M\ninst✝ : IsScalarTower S R M\nP : Submodule R M\na : S\nx y : M\nh : P.quotientRel x y\n⊢ -(a • x) + a • y ∈ P.toAddSubgr... | [
"R : Type u_1\nM : Type u_2\nr : R\nx✝ y✝ : M\ninst✝⁵ : Ring R\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\np p' : Submodule R M\nS : Type u_3\ninst✝² : SMul S R\ninst✝¹ : SMul S M\ninst✝ : IsScalarTower S R M\nP : Submodule R M\na : S\nx y : M\nh : P.quotientRel x y\n⊢ -(a • x) + a • y ∈ P"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Congruence.Basic | {
"line": 274,
"column": 2
} | {
"line": 274,
"column": 33
} | {
"line": 274,
"column": 34
} | [
{
"pp": "α : Type u_4\nM : Type u_5\ninst✝² : MulOneClass M\ninst✝¹ : SMul α M\ninst✝ : IsScalarTower α M M\nc : Con M\na : α\nw x : M\nh : c w x\n⊢ c (a • w) (a • x)",
"ppTerm": "?m.15",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_4\nM : Type u_5\ninst✝² : MulOneClass M\ninst✝¹ : SMul α M\ninst✝ : IsScalarTower α M M\nc : Con M\na : α\nw x : M\nh : c w x\n⊢ c (a • w) (a • x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Pi | {
"line": 222,
"column": 4
} | {
"line": 222,
"column": 41
} | {
"line": 224,
"column": 0
} | [
{
"pp": "case intro.convert_2\nR : Type u\nι : Type x\ninst✝⁴ : Semiring R\nφ : ι → Type i\ninst✝³ : (i : ι) → AddCommMonoid (φ i)\ninst✝² : (i : ι) → Module R (φ i)\ninst✝¹ : DecidableEq ι\ninst✝ : Finite ι\nval✝ : Fintype ι\n⊢ Set.univ ⊆ ↑Finset.univ ∪ ∅",
"ppTerm": "?intro.convert_2",
"assigned": tru... | [] | rw [Finset.coe_univ, Set.union_empty] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.LinearAlgebra.Pi | {
"line": 222,
"column": 4
} | {
"line": 222,
"column": 41
} | {
"line": 224,
"column": 0
} | [
{
"pp": "case intro.convert_2\nR : Type u\nι : Type x\ninst✝⁴ : Semiring R\nφ : ι → Type i\ninst✝³ : (i : ι) → AddCommMonoid (φ i)\ninst✝² : (i : ι) → Module R (φ i)\ninst✝¹ : DecidableEq ι\ninst✝ : Finite ι\nval✝ : Fintype ι\n⊢ Set.univ ⊆ ↑Finset.univ ∪ ∅",
"ppTerm": "?intro.convert_2",
"assigned": tru... | [] | rw [Finset.coe_univ, Set.union_empty] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Pi | {
"line": 222,
"column": 4
} | {
"line": 222,
"column": 41
} | {
"line": 224,
"column": 0
} | [
{
"pp": "case intro.convert_2\nR : Type u\nι : Type x\ninst✝⁴ : Semiring R\nφ : ι → Type i\ninst✝³ : (i : ι) → AddCommMonoid (φ i)\ninst✝² : (i : ι) → Module R (φ i)\ninst✝¹ : DecidableEq ι\ninst✝ : Finite ι\nval✝ : Fintype ι\n⊢ Set.univ ⊆ ↑Finset.univ ∪ ∅",
"ppTerm": "?intro.convert_2",
"assigned": tru... | [] | rw [Finset.coe_univ, Set.union_empty] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Field.IsField | {
"line": 57,
"column": 4
} | {
"line": 57,
"column": 45
} | {
"line": 57,
"column": 46
} | [
{
"pp": "R : Type u\ninst✝ : Semiring R\nh : IsField R\na✝ : R\nha : a✝ ≠ 0\nx✝¹ x✝ : R\nhb : (fun x ↦ a✝ * x) x✝¹ = (fun x ↦ a✝ * x) x✝\nx : R\nhx : a✝ * x = 1\n⊢ x✝¹ = x✝",
"ppTerm": "?m.32",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u\ninst✝ : Semiring R\nh : IsField R\na✝ : R\nha : a✝ ≠ 0\nx✝¹ x✝ : R\nhb : (fun x ↦ a✝ * x) x✝¹ = (fun x ↦ a✝ * x) x✝\nx : R\nhx : a✝ * x = 1\n⊢ x✝¹ = x✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Field.IsField | {
"line": 60,
"column": 4
} | {
"line": 60,
"column": 31
} | {
"line": 60,
"column": 32
} | [
{
"pp": "R : Type u\ninst✝ : Semiring R\nh : IsField R\na✝ : R\nha : a✝ ≠ 0\nx✝¹ x✝ : R\nhb : (fun x ↦ x * a✝) x✝¹ = (fun x ↦ x * a✝) x✝\nx : R\nhx : a✝ * x = 1\n⊢ x✝¹ = x✝",
"ppTerm": "?m.63",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u\ninst✝ : Semiring R\nh : IsField R\na✝ : R\nha : a✝ ≠ 0\nx✝¹ x✝ : R\nhb : (fun x ↦ x * a✝) x✝¹ = (fun x ↦ x * a✝) x✝\nx : R\nhx : a✝ * x = 1\n⊢ x✝¹ = x✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Quotient.Basic | {
"line": 81,
"column": 55
} | {
"line": 81,
"column": 66
} | {
"line": 81,
"column": 67
} | [
{
"pp": "R : Type u_1\nM : Type u_2\nr : R\nx y : M\ninst✝³ : Ring R\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\np p' p'' : Submodule R M\ninst✝ : Subsingleton M\n⊢ Subsingleton (M ⧸ p)",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Submodule",
"AddCommGrou... | [
"R : Type u_1\nM : Type u_2\nr : R\nx y : M\ninst✝³ : Ring R\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\np p' p'' : Submodule R M\ninst✝ : Subsingleton M\n⊢ p = ⊤"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Quotient.Basic | {
"line": 157,
"column": 2
} | {
"line": 157,
"column": 13
} | {
"line": 157,
"column": 14
} | [
{
"pp": "R : Type u_1\nM : Type u_2\ninst✝² : Ring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\np : Submodule R M\np' : Submodule R (M ⧸ p)\n⊢ p ≤ comap p.mkQ p'",
"ppTerm": "?m.39",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_1\nM : Type u_2\ninst✝² : Ring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\np : Submodule R M\np' : Submodule R (M ⧸ p)\n⊢ p ≤ comap p.mkQ p'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Quotient.Basic | {
"line": 175,
"column": 31
} | {
"line": 175,
"column": 53
} | {
"line": 175,
"column": 54
} | [
{
"pp": "R : Type u_1\nM : Type u_2\nr : R\nx y : M\ninst✝⁵ : Ring R\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\np p' p'' : Submodule R M\nR₂ : Type u_3\nM₂ : Type u_4\ninst✝² : Ring R₂\ninst✝¹ : AddCommGroup M₂\ninst✝ : Module R₂ M₂\nτ₁₂ : R →+* R₂\nq : Submodule R₂ M₂\nf : M →ₛₗ[τ₁₂] M₂\nh : p ≤ comap f q\... | [
"R : Type u_1\nM : Type u_2\nr : R\nx y : M\ninst✝⁵ : Ring R\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\np p' p'' : Submodule R M\nR₂ : Type u_3\nM₂ : Type u_4\ninst✝² : Ring R₂\ninst✝¹ : AddCommGroup M₂\ninst✝ : Module R₂ M₂\nτ₁₂ : R →+* R₂\nq : Submodule R₂ M₂\nf : M →ₛₗ[τ₁₂] M₂\nh : p ≤ comap f q\n⊢ p ≤ comap... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.SuccPred | {
"line": 52,
"column": 22
} | {
"line": 52,
"column": 33
} | {
"line": 52,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : SuccOrder α\na b : α\n⊢ ↑(Ico (succ a) b) = ↑(Ioo a b)",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.coe_Ico",
"Order.succ",
"congrArg",
"Finset",
"... | [
"α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : SuccOrder α\na b : α\n⊢ Set.Ico (succ a) b = Set.Ioo a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.SuccPred | {
"line": 55,
"column": 22
} | {
"line": 55,
"column": 33
} | {
"line": 55,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : SuccOrder α\na : α\nha : ¬IsMax a\nb : α\n⊢ ↑(Icc (succ a) b) = ↑(Ioc a b)",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ioc",
"Order.succ",
"congrArg",
"Fin... | [
"α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : SuccOrder α\na : α\nha : ¬IsMax a\nb : α\n⊢ Set.Icc (succ a) b = Set.Ioc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.SuccPred | {
"line": 58,
"column": 22
} | {
"line": 58,
"column": 33
} | {
"line": 58,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : SuccOrder α\nb : α\nhb : ¬IsMax b\na : α\n⊢ ↑(Ico a (succ b)) = ↑(Icc a b)",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.coe_Ico",
"Order.succ",
"congrArg",
... | [
"α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : SuccOrder α\nb : α\nhb : ¬IsMax b\na : α\n⊢ Set.Ico a (succ b) = Set.Icc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.SuccPred | {
"line": 61,
"column": 22
} | {
"line": 61,
"column": 33
} | {
"line": 61,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : SuccOrder α\nb : α\nhb : ¬IsMax b\na : α\n⊢ ↑(Ioo a (succ b)) = ↑(Ioc a b)",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ioc",
"Order.succ",
"congrArg",
"Fin... | [
"α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : SuccOrder α\nb : α\nhb : ¬IsMax b\na : α\n⊢ Set.Ioo a (succ b) = Set.Ioc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.SuccPred | {
"line": 65,
"column": 22
} | {
"line": 65,
"column": 33
} | {
"line": 65,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : SuccOrder α\nb : α\nhb : ¬IsMax b\na : α\n⊢ ↑(Ico (succ a) (succ b)) = ↑(Ioc a b)",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ioc",
"Finset.coe_Ico",
"Order.succ... | [
"α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : SuccOrder α\nb : α\nhb : ¬IsMax b\na : α\n⊢ Set.Ico (succ a) (succ b) = Set.Ioc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.SuccPred | {
"line": 70,
"column": 22
} | {
"line": 70,
"column": 33
} | {
"line": 70,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : SuccOrder α\na b : α\nh : a ≤ b\n⊢ ↑(insert a (Icc (succ a) b)) = ↑(Icc a b)",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Order.succ",
"LinearOrder.toDecidableEq",
"c... | [
"α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : SuccOrder α\na b : α\nh : a ≤ b\n⊢ insert a (Set.Icc (succ a) b) = Set.Icc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.SuccPred | {
"line": 73,
"column": 22
} | {
"line": 73,
"column": 33
} | {
"line": 73,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : SuccOrder α\na b : α\nh : a ≤ succ b\n⊢ ↑(insert (succ b) (Icc a b)) = ↑(Icc a (succ b))",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Order.succ",
"LinearOrder.toDecidableE... | [
"α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : SuccOrder α\na b : α\nh : a ≤ succ b\n⊢ insert (succ b) (Set.Icc a b) = Set.Icc a (succ b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.SuccPred | {
"line": 77,
"column": 22
} | {
"line": 77,
"column": 33
} | {
"line": 77,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : SuccOrder α\na b : α\nh : a ≤ b\nhb : ¬IsMax b\n⊢ ↑(insert b (Ico a b)) = ↑(Ico a (succ b))",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.coe_Ico",
"Order.succ",
... | [
"α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : SuccOrder α\na b : α\nh : a ≤ b\nhb : ¬IsMax b\n⊢ insert b (Set.Ico a b) = Set.Ico a (succ b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.SuccPred | {
"line": 80,
"column": 22
} | {
"line": 80,
"column": 33
} | {
"line": 80,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : SuccOrder α\na b : α\nh : a < b\n⊢ ↑(insert a (Ico (succ a) b)) = ↑(Ico a b)",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.coe_Ico",
"Order.succ",
"LinearOrder.... | [
"α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : SuccOrder α\na b : α\nh : a < b\n⊢ insert a (Set.Ico (succ a) b) = Set.Ico a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.SuccPred | {
"line": 84,
"column": 22
} | {
"line": 84,
"column": 33
} | {
"line": 84,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : SuccOrder α\na b : α\nh : a ≤ b\nhb : ¬IsMax b\n⊢ ↑(insert (succ b) (Ioc a b)) = ↑(Ioc a (succ b))",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ioc",
"Order.succ",
... | [
"α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : SuccOrder α\na b : α\nh : a ≤ b\nhb : ¬IsMax b\n⊢ insert (succ b) (Set.Ioc a b) = Set.Ioc a (succ b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.SuccPred | {
"line": 87,
"column": 22
} | {
"line": 87,
"column": 33
} | {
"line": 87,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : SuccOrder α\na b : α\nh : a < b\n⊢ ↑(insert (succ a) (Ioc (succ a) b)) = ↑(Ioc a b)",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ioc",
"Order.succ",
"LinearOrder.... | [
"α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : SuccOrder α\na b : α\nh : a < b\n⊢ insert (succ a) (Set.Ioc (succ a) b) = Set.Ioc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.SuccPred | {
"line": 105,
"column": 22
} | {
"line": 105,
"column": 33
} | {
"line": 105,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝³ : LinearOrder α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : SuccOrder α\na b : α\ninst✝ : NoMaxOrder α\nh : a ≤ b\n⊢ ↑(insert b (Ico a b)) = ↑(Ico a (succ b))",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.coe_Ico",
"Order.suc... | [
"α : Type u_1\ninst✝³ : LinearOrder α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : SuccOrder α\na b : α\ninst✝ : NoMaxOrder α\nh : a ≤ b\n⊢ insert b (Set.Ico a b) = Set.Icc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.SuccPred | {
"line": 108,
"column": 22
} | {
"line": 108,
"column": 33
} | {
"line": 108,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝³ : LinearOrder α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : SuccOrder α\na b : α\ninst✝ : NoMaxOrder α\nh : a ≤ b\n⊢ ↑(insert (succ b) (Ioc a b)) = ↑(Ioc a (succ b))",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ioc",
"Order.suc... | [
"α : Type u_1\ninst✝³ : LinearOrder α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : SuccOrder α\na b : α\ninst✝ : NoMaxOrder α\nh : a ≤ b\n⊢ insert (succ b) (Set.Ioc a b) = Set.Ioc a (succ b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.SuccPred | {
"line": 122,
"column": 22
} | {
"line": 122,
"column": 33
} | {
"line": 122,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : PredOrder α\na b : α\n⊢ ↑(Ioc a (pred b)) = ↑(Ioo a b)",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ioc",
"congrArg",
"Finset",
"PartialOrder.toPreorder",
... | [
"α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : PredOrder α\na b : α\n⊢ Set.Ioc a (pred b) = Set.Ioo a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.SuccPred | {
"line": 125,
"column": 22
} | {
"line": 125,
"column": 33
} | {
"line": 125,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : PredOrder α\nb : α\nhb : ¬IsMin b\na : α\n⊢ ↑(Icc a (pred b)) = ↑(Ico a b)",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.coe_Ico",
"congrArg",
"Finset",
"... | [
"α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : PredOrder α\nb : α\nhb : ¬IsMin b\na : α\n⊢ Set.Icc a (pred b) = Set.Ico a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.SuccPred | {
"line": 128,
"column": 22
} | {
"line": 128,
"column": 33
} | {
"line": 128,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : PredOrder α\na : α\nha : ¬IsMin a\nb : α\n⊢ ↑(Ioc (pred a) b) = ↑(Icc a b)",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ioc",
"congrArg",
"Finset",
"Partial... | [
"α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : PredOrder α\na : α\nha : ¬IsMin a\nb : α\n⊢ Set.Ioc (pred a) b = Set.Icc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.SuccPred | {
"line": 131,
"column": 22
} | {
"line": 131,
"column": 33
} | {
"line": 131,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : PredOrder α\na : α\nha : ¬IsMin a\nb : α\n⊢ ↑(Ioo (pred a) b) = ↑(Ico a b)",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.coe_Ico",
"congrArg",
"Finset",
"... | [
"α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : PredOrder α\na : α\nha : ¬IsMin a\nb : α\n⊢ Set.Ioo (pred a) b = Set.Ico a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Pi | {
"line": 320,
"column": 6
} | {
"line": 320,
"column": 54
} | {
"line": 320,
"column": 55
} | [
{
"pp": "R : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nι' : Type x'\ninst✝⁸ : Semiring R\ninst✝⁷ : AddCommMonoid M₂\ninst✝⁶ : Module R M₂\ninst✝⁵ : AddCommMonoid M₃\ninst✝⁴ : Module R M₃\nφ : ι → Type i\ninst✝³ : (i : ι) → AddCom... | [
"R : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nι' : Type x'\ninst✝⁸ : Semiring R\ninst✝⁷ : AddCommMonoid M₂\ninst✝⁶ : Module R M₂\ninst✝⁵ : AddCommMonoid M₃\ninst✝⁴ : Module R M₃\nφ : ι → Type i\ninst✝³ : (i : ι) → AddCommMonoid (φ i... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.SuccPred | {
"line": 135,
"column": 22
} | {
"line": 135,
"column": 33
} | {
"line": 135,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : PredOrder α\na : α\nha : ¬IsMin a\nb : α\n⊢ ↑(Ioc (pred a) (pred b)) = ↑(Ico a b)",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ioc",
"Finset.coe_Ico",
"congrArg",... | [
"α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : PredOrder α\na : α\nha : ¬IsMin a\nb : α\n⊢ Set.Ioc (pred a) (pred b) = Set.Ico a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.SuccPred | {
"line": 140,
"column": 22
} | {
"line": 140,
"column": 33
} | {
"line": 140,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : PredOrder α\na b : α\nh : a ≤ b\n⊢ ↑(insert b (Icc a (pred b))) = ↑(Icc a b)",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"LinearOrder.toDecidableEq",
"congrArg",
"Fin... | [
"α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : PredOrder α\na b : α\nh : a ≤ b\n⊢ insert b (Set.Icc a (pred b)) = Set.Icc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.SuccPred | {
"line": 143,
"column": 22
} | {
"line": 143,
"column": 33
} | {
"line": 143,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : PredOrder α\na b : α\nh : pred a ≤ b\n⊢ ↑(insert (pred a) (Icc a b)) = ↑(Icc (pred a) b)",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"LinearOrder.toDecidableEq",
"congrArg"... | [
"α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : PredOrder α\na b : α\nh : pred a ≤ b\n⊢ insert (pred a) (Set.Icc a b) = Set.Icc (pred a) b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.SuccPred | {
"line": 147,
"column": 22
} | {
"line": 147,
"column": 33
} | {
"line": 147,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : PredOrder α\na b : α\nh : a ≤ b\nha : ¬IsMin a\n⊢ ↑(insert a (Ioc a b)) = ↑(Ioc (pred a) b)",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ioc",
"LinearOrder.toDecidableE... | [
"α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : PredOrder α\na b : α\nh : a ≤ b\nha : ¬IsMin a\n⊢ insert a (Set.Ioc a b) = Set.Ioc (pred a) b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.SuccPred | {
"line": 150,
"column": 22
} | {
"line": 150,
"column": 33
} | {
"line": 150,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : PredOrder α\na b : α\nh : a < b\n⊢ ↑(insert b (Ioc a (pred b))) = ↑(Ioc a b)",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ioc",
"LinearOrder.toDecidableEq",
"cong... | [
"α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : PredOrder α\na b : α\nh : a < b\n⊢ insert b (Set.Ioc a (pred b)) = Set.Ioc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.SuccPred | {
"line": 154,
"column": 22
} | {
"line": 154,
"column": 33
} | {
"line": 154,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : PredOrder α\na b : α\nh : a ≤ b\nha : ¬IsMin a\n⊢ ↑(insert (pred a) (Ico a b)) = ↑(Ico (pred a) b)",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.coe_Ico",
"LinearOrde... | [
"α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : PredOrder α\na b : α\nh : a ≤ b\nha : ¬IsMin a\n⊢ insert (pred a) (Set.Ico a b) = Set.Ico (pred a) b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.SuccPred | {
"line": 157,
"column": 22
} | {
"line": 157,
"column": 33
} | {
"line": 157,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : PredOrder α\na b : α\nh : a < b\n⊢ ↑(insert (pred b) (Ico a (pred b))) = ↑(Ico a b)",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.coe_Ico",
"LinearOrder.toDecidableEq... | [
"α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : PredOrder α\na b : α\nh : a < b\n⊢ insert (pred b) (Set.Ico a (pred b)) = Set.Ico a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.SuccPred | {
"line": 175,
"column": 22
} | {
"line": 175,
"column": 33
} | {
"line": 175,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝³ : LinearOrder α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : PredOrder α\na b : α\ninst✝ : NoMinOrder α\nh : a ≤ b\n⊢ ↑(insert a (Ioc a b)) = ↑(Ioc (pred a) b)",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ioc",
"Lattice.toSemila... | [
"α : Type u_1\ninst✝³ : LinearOrder α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : PredOrder α\na b : α\ninst✝ : NoMinOrder α\nh : a ≤ b\n⊢ insert a (Set.Ioc a b) = Set.Icc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.SuccPred | {
"line": 186,
"column": 22
} | {
"line": 186,
"column": 33
} | {
"line": 186,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝⁴ : LinearOrder α\ninst✝³ : LocallyFiniteOrder α\ninst✝² : SuccOrder α\ninst✝¹ : PredOrder α\ninst✝ : Nontrivial α\na b : α\n⊢ ↑(Icc (succ a) (pred b)) = ↑(Ioo a b)",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Order.succ",
"congrA... | [
"α : Type u_1\ninst✝⁴ : LinearOrder α\ninst✝³ : LocallyFiniteOrder α\ninst✝² : SuccOrder α\ninst✝¹ : PredOrder α\ninst✝ : Nontrivial α\na b : α\n⊢ Set.Icc (succ a) (pred b) = Set.Ioo a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.SuccPred | {
"line": 200,
"column": 22
} | {
"line": 200,
"column": 33
} | {
"line": 200,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrderBot α\ninst✝ : SuccOrder α\nb : α\nhb : ¬IsMax b\n⊢ ↑(Iio (succ b)) = ↑(Iic b)",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Order.succ",
"Finset.coe_Iic",
"congrArg",
"Fins... | [
"α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrderBot α\ninst✝ : SuccOrder α\nb : α\nhb : ¬IsMax b\n⊢ Set.Iio (succ b) = Set.Iic b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.SuccPred | {
"line": 212,
"column": 22
} | {
"line": 212,
"column": 33
} | {
"line": 212,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrderBot α\ninst✝ : PredOrder α\nb : α\nhb : ¬IsMin b\n⊢ ↑(Iic (pred b)) = ↑(Iio b)",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.coe_Iic",
"congrArg",
"Finset",
"PartialO... | [
"α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrderBot α\ninst✝ : PredOrder α\nb : α\nhb : ¬IsMin b\n⊢ Set.Iic (pred b) = Set.Iio b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.SuccPred | {
"line": 230,
"column": 22
} | {
"line": 230,
"column": 33
} | {
"line": 230,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrderTop α\ninst✝ : SuccOrder α\na : α\nha : ¬IsMax a\n⊢ ↑(Ici (succ a)) = ↑(Ioi a)",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ioi",
"Order.succ",
"Set.Ici",
"Finset.Ioi",... | [
"α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrderTop α\ninst✝ : SuccOrder α\na : α\nha : ¬IsMax a\n⊢ Set.Ici (succ a) = Set.Ioi a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Finset.SuccPred | {
"line": 242,
"column": 22
} | {
"line": 242,
"column": 33
} | {
"line": 242,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrderTop α\ninst✝ : PredOrder α\na : α\nha : ¬IsMin a\n⊢ ↑(Ioi (pred a)) = ↑(Ici a)",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ioi",
"Set.Ici",
"Finset.Ioi",
"congrArg",
... | [
"α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : LocallyFiniteOrderTop α\ninst✝ : PredOrder α\na : α\nha : ¬IsMin a\n⊢ Set.Ioi (pred a) = Set.Ici a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Pi | {
"line": 431,
"column": 2
} | {
"line": 431,
"column": 59
} | {
"line": 433,
"column": 0
} | [
{
"pp": "case intro\nR : Type u\nι : Type x\ninst✝⁴ : Semiring R\nφ : ι → Type u_1\ninst✝³ : (i : ι) → AddCommMonoid (φ i)\ninst✝² : (i : ι) → Module R (φ i)\np : (i : ι) → Submodule R (φ i)\ninst✝¹ : DecidableEq ι\ninst✝ : Finite ι\nval✝ : Fintype ι\nx : (i : ι) → φ i\nhx : x ∈ pi Set.univ p\n⊢ ∑ i, Pi.single ... | [] | exact sum_mem_iSup fun i => mem_map_of_mem (hx i trivial) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.LinearAlgebra.Pi | {
"line": 653,
"column": 31
} | {
"line": 653,
"column": 42
} | {
"line": 653,
"column": 43
} | [
{
"pp": "R : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nι' : Type x'\nη : Type u_1\ninst✝ : Semiring R\ns : ι → η\nr : R\nf : ι → R\n⊢ extend s (r • f) 0 = (RingHom.id R) r • extend s f 0",
"ppTerm": "?m.36",
"assigned": t... | [
"R : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nι' : Type x'\nη : Type u_1\ninst✝ : Semiring R\ns : ι → η\nr : R\nf : ι → R\n⊢ extend s (r • f) 0 = r • extend s f 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 53,
"column": 2
} | {
"line": 53,
"column": 31
} | {
"line": 53,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\na b : α\n⊢ Ico (a + 1) b = Ioo a b",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\na b : α\n⊢ Ico (a + 1) b = Ioo a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 56,
"column": 2
} | {
"line": 56,
"column": 31
} | {
"line": 56,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\na : α\nha : ¬IsMax a\nb : α\n⊢ Icc (a + 1) b = Ioc a b",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\na : α\nha : ¬IsMax a\nb : α\n⊢ Icc (a + 1) b = Ioc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 59,
"column": 2
} | {
"line": 59,
"column": 31
} | {
"line": 59,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\nb : α\nhb : ¬IsMax b\na : α\n⊢ Ico a (b + 1) = Icc a b",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\nb : α\nhb : ¬IsMax b\na : α\n⊢ Ico a (b + 1) = Icc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fintype.Order | {
"line": 195,
"column": 2
} | {
"line": 195,
"column": 13
} | {
"line": 196,
"column": 4
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\ninst✝² : IsTrans α r\nι : Sort u_4\nκ : Sort u_5\ninst✝¹ : Nonempty ι\ninst✝ : Finite κ\nf : ι → α\nhf : Directed r f\ng : κ → ι\n⊢ ∃ z, ∀ (i : κ), r (f (g i)) (f z)",
"ppTerm": "?m.6",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoa... | [
"α : Type u_1\nr : α → α → Prop\ninst✝² : IsTrans α r\nι : Sort u_4\nκ : Sort u_5\ninst✝¹ : Nonempty ι\ninst✝ : Finite κ\nf : ι → α\nhf : Directed r f\ng : κ → ι\n⊢ ∃ z, ∀ (i : κ), r (f (g i)) (f z)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 62,
"column": 2
} | {
"line": 62,
"column": 31
} | {
"line": 62,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\nb : α\nhb : ¬IsMax b\na : α\n⊢ Ioo a (b + 1) = Ioc a b",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\nb : α\nhb : ¬IsMax b\na : α\n⊢ Ioo a (b + 1) = Ioc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 66,
"column": 2
} | {
"line": 66,
"column": 31
} | {
"line": 66,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\nb : α\nhb : ¬IsMax b\na : α\n⊢ Ico (a + 1) (b + 1) = Ioc a b",
"ppTerm": "?m.26",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}... | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\nb : α\nhb : ¬IsMax b\na : α\n⊢ Ico (a + 1) (b + 1) = Ioc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 71,
"column": 2
} | {
"line": 71,
"column": 31
} | {
"line": 71,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\na b : α\nh : a ≤ b\n⊢ insert a (Icc (a + 1) b) = Icc a b",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\na b : α\nh : a ≤ b\n⊢ insert a (Icc (a + 1) b) = Icc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 75,
"column": 2
} | {
"line": 75,
"column": 33
} | {
"line": 75,
"column": 34
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\na b : α\nh : a ≤ b + 1\n⊢ insert (b + 1) (Icc a b) = Icc a (b + 1)",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Order.succ",
... | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\na b : α\nh : a ≤ b + 1\n⊢ insert (succ b) (Icc a b) = Icc a (succ b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 79,
"column": 2
} | {
"line": 79,
"column": 31
} | {
"line": 79,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\na b : α\nh : a ≤ b\nhb : ¬IsMax b\n⊢ insert b (Ico a b) = Ico a (b + 1)",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoa... | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\na b : α\nh : a ≤ b\nhb : ¬IsMax b\n⊢ insert b (Ico a b) = Ico a (b + 1)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 82,
"column": 2
} | {
"line": 82,
"column": 31
} | {
"line": 82,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\na b : α\nh : a < b\n⊢ insert a (Ico (a + 1) b) = Ico a b",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\na b : α\nh : a < b\n⊢ insert a (Ico (a + 1) b) = Ico a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 86,
"column": 2
} | {
"line": 86,
"column": 31
} | {
"line": 86,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\na b : α\nh : a ≤ b\nhb : ¬IsMax b\n⊢ insert (b + 1) (Ioc a b) = Ioc a (b + 1)",
"ppTerm": "?m.31",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"u... | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\na b : α\nh : a ≤ b\nhb : ¬IsMax b\n⊢ insert (b + 1) (Ioc a b) = Ioc a (b + 1)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 89,
"column": 2
} | {
"line": 89,
"column": 31
} | {
"line": 89,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\na b : α\nh : a < b\n⊢ insert (a + 1) (Ioc (a + 1) b) = Ioc a b",
"ppTerm": "?m.29",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Add α\ninst✝ : SuccAddOrder α\na b : α\nh : a < b\n⊢ insert (a + 1) (Ioc (a + 1) b) = Ioc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 100,
"column": 2
} | {
"line": 100,
"column": 31
} | {
"line": 100,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : One α\ninst✝³ : LocallyFiniteOrder α\ninst✝² : Add α\ninst✝¹ : SuccAddOrder α\ninst✝ : NoMaxOrder α\na b : α\n⊢ Icc (a + 1) b = Ioc a b",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : One α\ninst✝³ : LocallyFiniteOrder α\ninst✝² : Add α\ninst✝¹ : SuccAddOrder α\ninst✝ : NoMaxOrder α\na b : α\n⊢ Icc (a + 1) b = Ioc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 103,
"column": 2
} | {
"line": 103,
"column": 31
} | {
"line": 103,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : One α\ninst✝³ : LocallyFiniteOrder α\ninst✝² : Add α\ninst✝¹ : SuccAddOrder α\ninst✝ : NoMaxOrder α\na b : α\n⊢ Ico a (b + 1) = Icc a b",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : One α\ninst✝³ : LocallyFiniteOrder α\ninst✝² : Add α\ninst✝¹ : SuccAddOrder α\ninst✝ : NoMaxOrder α\na b : α\n⊢ Ico a (b + 1) = Icc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 106,
"column": 2
} | {
"line": 106,
"column": 31
} | {
"line": 106,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : One α\ninst✝³ : LocallyFiniteOrder α\ninst✝² : Add α\ninst✝¹ : SuccAddOrder α\ninst✝ : NoMaxOrder α\na b : α\n⊢ Ioo a (b + 1) = Ioc a b",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : One α\ninst✝³ : LocallyFiniteOrder α\ninst✝² : Add α\ninst✝¹ : SuccAddOrder α\ninst✝ : NoMaxOrder α\na b : α\n⊢ Ioo a (b + 1) = Ioc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 109,
"column": 2
} | {
"line": 109,
"column": 31
} | {
"line": 109,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : One α\ninst✝³ : LocallyFiniteOrder α\ninst✝² : Add α\ninst✝¹ : SuccAddOrder α\ninst✝ : NoMaxOrder α\na b : α\n⊢ Ico (a + 1) (b + 1) = Ioc a b",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"α : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : One α\ninst✝³ : LocallyFiniteOrder α\ninst✝² : Add α\ninst✝¹ : SuccAddOrder α\ninst✝ : NoMaxOrder α\na b : α\n⊢ Ico (a + 1) (b + 1) = Ioc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 114,
"column": 2
} | {
"line": 114,
"column": 31
} | {
"line": 114,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : One α\ninst✝³ : LocallyFiniteOrder α\ninst✝² : Add α\ninst✝¹ : SuccAddOrder α\na b : α\ninst✝ : NoMaxOrder α\nh : a ≤ b\n⊢ insert b (Ico a b) = Ico a (b + 1)",
"ppTerm": "?m.24",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"α : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : One α\ninst✝³ : LocallyFiniteOrder α\ninst✝² : Add α\ninst✝¹ : SuccAddOrder α\na b : α\ninst✝ : NoMaxOrder α\nh : a ≤ b\n⊢ insert b (Ico a b) = Ico a (b + 1)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 131,
"column": 2
} | {
"line": 131,
"column": 31
} | {
"line": 131,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na b : α\n⊢ Ioc a (b - 1) = Ioo a b",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na b : α\n⊢ Ioc a (b - 1) = Ioo a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 134,
"column": 2
} | {
"line": 134,
"column": 31
} | {
"line": 134,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\nb : α\nhb : ¬IsMin b\na : α\n⊢ Icc a (b - 1) = Ico a b",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\nb : α\nhb : ¬IsMin b\na : α\n⊢ Icc a (b - 1) = Ico a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 137,
"column": 2
} | {
"line": 137,
"column": 31
} | {
"line": 137,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na : α\nha : ¬IsMin a\nb : α\n⊢ Ioc (a - 1) b = Icc a b",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na : α\nha : ¬IsMin a\nb : α\n⊢ Ioc (a - 1) b = Icc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 140,
"column": 2
} | {
"line": 140,
"column": 31
} | {
"line": 140,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na : α\nha : ¬IsMin a\nb : α\n⊢ Ioo (a - 1) b = Ico a b",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na : α\nha : ¬IsMin a\nb : α\n⊢ Ioo (a - 1) b = Ico a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 144,
"column": 2
} | {
"line": 144,
"column": 31
} | {
"line": 144,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na : α\nha : ¬IsMin a\nb : α\n⊢ Ioc (a - 1) (b - 1) = Ico a b",
"ppTerm": "?m.26",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}... | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na : α\nha : ¬IsMin a\nb : α\n⊢ Ioc (a - 1) (b - 1) = Ico a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 149,
"column": 2
} | {
"line": 149,
"column": 31
} | {
"line": 149,
"column": 32
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na b : α\nh : a ≤ b\n⊢ insert b (Icc a (b - 1)) = Icc a b",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na b : α\nh : a ≤ b\n⊢ insert b (Icc a (b - 1)) = Icc a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Interval.Finset.SuccPred | {
"line": 153,
"column": 2
} | {
"line": 153,
"column": 33
} | {
"line": 153,
"column": 34
} | [
{
"pp": "α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na b : α\nh : a - 1 ≤ b\n⊢ insert (a - 1) (Icc a b) = Icc (a - 1) b",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"PredSubOrder.toPre... | [
"α : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : One α\ninst✝² : LocallyFiniteOrder α\ninst✝¹ : Sub α\ninst✝ : PredSubOrder α\na b : α\nh : a - 1 ≤ b\n⊢ insert (pred a) (Icc a b) = Icc (pred a) b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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