module stringlengths 16 90 | startPos dict | endPos dict | nextStartPos dict | goals listlengths 0 96 | goalsAfter listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 375
values | kind stringclasses 379
values |
|---|---|---|---|---|---|---|---|---|
Mathlib.Tactic.FieldSimp.Lemmas | {
"line": 278,
"column": 17
} | {
"line": 278,
"column": 27
} | {
"line": 278,
"column": 28
} | [
{
"pp": "M : Type u_1\ninst✝ : CommGroupWithZero M\nn : ℤ\ne : M\nL l l' : NF M\nh : L.eval * l.eval = l'.eval\n⊢ L.eval * (l.eval * zpow' (n, e).2 (n, e).1) = ((n, e) ::ᵣ l').eval",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
... | [
"M : Type u_1\ninst✝ : CommGroupWithZero M\nn : ℤ\ne : M\nL l l' : NF M\nh : L.eval * l.eval = l'.eval\n⊢ L.eval * (l.eval * zpow' (n, e).2 (n, e).1) = l'.eval * zpow' (n, e).2 (n, e).1"
] | eval_cons, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Tactic.FieldSimp.Lemmas | {
"line": 288,
"column": 6
} | {
"line": 288,
"column": 16
} | {
"line": 288,
"column": 17
} | [
{
"pp": "M : Type u_1\ninst✝ : CommGroupWithZero M\nn : ℤ\ne : M\nL l l' : NF M\nh : L.eval * l.eval = l'.eval\n⊢ ((n, e) ::ᵣ L).eval * l.eval = ((n, e) ::ᵣ l').eval",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"HMul.hMul",
... | [
"M : Type u_1\ninst✝ : CommGroupWithZero M\nn : ℤ\ne : M\nL l l' : NF M\nh : L.eval * l.eval = l'.eval\n⊢ L.eval * zpow' (n, e).2 (n, e).1 * l.eval = ((n, e) ::ᵣ l').eval"
] | eval_cons, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Tactic.FieldSimp.Lemmas | {
"line": 288,
"column": 17
} | {
"line": 288,
"column": 27
} | {
"line": 288,
"column": 28
} | [
{
"pp": "M : Type u_1\ninst✝ : CommGroupWithZero M\nn : ℤ\ne : M\nL l l' : NF M\nh : L.eval * l.eval = l'.eval\n⊢ L.eval * zpow' (n, e).2 (n, e).1 * l.eval = ((n, e) ::ᵣ l').eval",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"... | [
"M : Type u_1\ninst✝ : CommGroupWithZero M\nn : ℤ\ne : M\nL l l' : NF M\nh : L.eval * l.eval = l'.eval\n⊢ L.eval * zpow' (n, e).2 (n, e).1 * l.eval = l'.eval * zpow' (n, e).2 (n, e).1"
] | eval_cons, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Tactic.FieldSimp.Lemmas | {
"line": 374,
"column": 12
} | {
"line": 374,
"column": 22
} | {
"line": 374,
"column": 23
} | [
{
"pp": "M : Type u_1\ninst✝ : CommGroupWithZero M\nr : ℤ\nx : M\nt t' l' : NF M\nh : t.eval = t'.eval\nh' : ((r, x) ::ᵣ t').eval = l'.eval\n⊢ ((r, x) ::ᵣ t).eval = ((r, x) ::ᵣ t').eval",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
... | [
"M : Type u_1\ninst✝ : CommGroupWithZero M\nr : ℤ\nx : M\nt t' l' : NF M\nh : t.eval = t'.eval\nh' : ((r, x) ::ᵣ t').eval = l'.eval\n⊢ t.eval * zpow' (r, x).2 (r, x).1 = ((r, x) ::ᵣ t').eval"
] | eval_cons, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Tactic.FieldSimp.Lemmas | {
"line": 374,
"column": 23
} | {
"line": 374,
"column": 33
} | {
"line": 374,
"column": 34
} | [
{
"pp": "M : Type u_1\ninst✝ : CommGroupWithZero M\nr : ℤ\nx : M\nt t' l' : NF M\nh : t.eval = t'.eval\nh' : ((r, x) ::ᵣ t').eval = l'.eval\n⊢ t.eval * zpow' (r, x).2 (r, x).1 = ((r, x) ::ᵣ t').eval",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMono... | [
"M : Type u_1\ninst✝ : CommGroupWithZero M\nr : ℤ\nx : M\nt t' l' : NF M\nh : t.eval = t'.eval\nh' : ((r, x) ::ᵣ t').eval = l'.eval\n⊢ t.eval * zpow' (r, x).2 (r, x).1 = t'.eval * zpow' (r, x).2 (r, x).1"
] | eval_cons, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Ring.Rat | {
"line": 85,
"column": 2
} | {
"line": 85,
"column": 68
} | {
"line": 87,
"column": 0
} | [
{
"pp": "num den n : ℕ\n⊢ mkRat (↑num) den ^ n = mkRat (↑num ^ n) (den ^ n)",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"instPowNat",
"Eq.mpr",
"congrArg",
"Nat.instMonoid",
"Rat",
"Rat.divInt",
"Int.natCast_pow",
"Rat.instPowNat",
... | [] | rw [mkRat_eq_divInt, mkRat_eq_divInt, divInt_pow, Int.natCast_pow] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Ring.Rat | {
"line": 85,
"column": 2
} | {
"line": 85,
"column": 68
} | {
"line": 87,
"column": 0
} | [
{
"pp": "num den n : ℕ\n⊢ mkRat (↑num) den ^ n = mkRat (↑num ^ n) (den ^ n)",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"instPowNat",
"Eq.mpr",
"congrArg",
"Nat.instMonoid",
"Rat",
"Rat.divInt",
"Int.natCast_pow",
"Rat.instPowNat",
... | [] | rw [mkRat_eq_divInt, mkRat_eq_divInt, divInt_pow, Int.natCast_pow] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Ring.Rat | {
"line": 85,
"column": 2
} | {
"line": 85,
"column": 68
} | {
"line": 87,
"column": 0
} | [
{
"pp": "num den n : ℕ\n⊢ mkRat (↑num) den ^ n = mkRat (↑num ^ n) (den ^ n)",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"instPowNat",
"Eq.mpr",
"congrArg",
"Nat.instMonoid",
"Rat",
"Rat.divInt",
"Int.natCast_pow",
"Rat.instPowNat",
... | [] | rw [mkRat_eq_divInt, mkRat_eq_divInt, divInt_pow, Int.natCast_pow] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Group.Commute.Basic | {
"line": 96,
"column": 2
} | {
"line": 96,
"column": 36
} | {
"line": 98,
"column": 0
} | [
{
"pp": "G : Type u_1\ninst✝ : Group G\na b : G\nh : Commute a b\n⊢ a⁻¹ * (b * a) = b",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Semigroup.toMul",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"congrArg",
"mu... | [] | rw [← mul_assoc, h.inv_mul_cancel] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Group.Commute.Basic | {
"line": 96,
"column": 2
} | {
"line": 96,
"column": 36
} | {
"line": 98,
"column": 0
} | [
{
"pp": "G : Type u_1\ninst✝ : Group G\na b : G\nh : Commute a b\n⊢ a⁻¹ * (b * a) = b",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Semigroup.toMul",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"congrArg",
"mu... | [] | rw [← mul_assoc, h.inv_mul_cancel] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Group.Commute.Basic | {
"line": 96,
"column": 2
} | {
"line": 96,
"column": 36
} | {
"line": 98,
"column": 0
} | [
{
"pp": "G : Type u_1\ninst✝ : Group G\na b : G\nh : Commute a b\n⊢ a⁻¹ * (b * a) = b",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Semigroup.toMul",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"congrArg",
"mu... | [] | rw [← mul_assoc, h.inv_mul_cancel] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.GroupWithZero.Divisibility | {
"line": 171,
"column": 9
} | {
"line": 171,
"column": 30
} | {
"line": 171,
"column": 31
} | [
{
"pp": "case mp\nα : Type u_1\ninst✝¹ : CommMonoidWithZero α\ninst✝ : IsCancelMulZero α\na : α\nm n : ℕ\nha₀ : a ≠ 0\nha : ¬IsUnit a\nh : a ^ n ∣ a ^ m\nhmn : m < n\nthis : a ^ m * a ∣ a ^ m * 1\n⊢ IsUnit a",
"ppTerm": "?mp",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"Dvd.dvd... | [
"case mp\nα : Type u_1\ninst✝¹ : CommMonoidWithZero α\ninst✝ : IsCancelMulZero α\na : α\nm n : ℕ\nha₀ : a ≠ 0\nha : ¬IsUnit a\nh : a ^ n ∣ a ^ m\nhmn : m < n\nthis : a ∣ 1\n⊢ IsUnit a",
"case mp\nα : Type u_1\ninst✝¹ : CommMonoidWithZero α\ninst✝ : IsCancelMulZero α\na : α\nm n : ℕ\nha₀ : a ≠ 0\nha : ¬IsUnit a\nh... | mul_dvd_mul_iff_left, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Rat.Lemmas | {
"line": 59,
"column": 75
} | {
"line": 67,
"column": 65
} | {
"line": 69,
"column": 0
} | [
{
"pp": "q₁ q₂ : ℚ\n⊢ (q₁ + q₂).den ∣ q₁.den.lcm q₂.den",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Nat.gcd",
"Nat.lcm",
"Nat.dvd_gcd_iff",
"Nat.gcd_dvd_left",
"Eq.mpr",
"Nat.gcd_mul_lcm",
"Int.instDiv",
"False",
"Nat.instMulZeroCla... | [] | by
rw [add_def, normalize_eq, Nat.div_dvd_iff_dvd_mul (Nat.gcd_dvd_right _ _)
(Nat.gcd_pos_of_pos_right _ (by simp [Nat.pos_iff_ne_zero])), ← Nat.gcd_mul_lcm,
mul_dvd_mul_iff_right (Nat.lcm_ne_zero (by simp) (by simp)), Nat.dvd_gcd_iff]
refine ⟨?_, dvd_mul_right _ _⟩
rw [← Int.natCast_dvd_natCast, Int.dvd... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Rat.Lemmas | {
"line": 103,
"column": 65
} | {
"line": 104,
"column": 54
} | {
"line": 106,
"column": 0
} | [
{
"pp": "q : ℚ\nn : ℤ\n⊢ (q - ↑n).den = q.den",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Int.cast_neg",
"Int.cast",
"Rat.instSub",
"Eq.mpr",
"NegZeroClass.toNeg",
"AddGroupWithOne.toAddGroup",
"congrArg",
... | [] | by
rw [sub_eq_add_neg, ← Int.cast_neg, add_intCast_den] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Tactic.CancelDenoms.Core | {
"line": 66,
"column": 6
} | {
"line": 66,
"column": 11
} | {
"line": 66,
"column": 12
} | [
{
"pp": "α : Type u_1\ninst✝ : CommRing α\nn e1 t1 k l : α\ne2 : ℕ\nh1 : n * e1 = t1\nh2 : l * n ^ e2 = k\n⊢ k * e1 ^ e2 = l * t1 ^ e2",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"id",
"NP... | [
"α : Type u_1\ninst✝ : CommRing α\nn e1 t1 k l : α\ne2 : ℕ\nh1 : n * e1 = t1\nh2 : l * n ^ e2 = k\n⊢ l * n ^ e2 * e1 ^ e2 = l * t1 ^ e2"
] | ← h2, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.CompleteLattice.Basic | {
"line": 341,
"column": 33
} | {
"line": 341,
"column": 78
} | {
"line": 343,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : CompleteLattice α\ninst✝ : CompleteLattice β\ns : Set α\nf : α → β\nhf : Monotone f\n⊢ ⨆ a ∈ s, f a ≤ f (sSup s)",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"iSup",
"PartialOrder.toPreorder",
... | [] | by rw [sSup_eq_iSup]; exact hf.le_map_iSup₂ _ | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Set.Lattice | {
"line": 793,
"column": 65
} | {
"line": 793,
"column": 77
} | {
"line": 793,
"column": 77
} | [
{
"pp": "α : Type u_1\nι : Sort u_5\nκ : ι → Sort u_8\ns : (i : ι) → κ i → Set α\nt : Set α\n⊢ (⋃ i, ⋃ j, s i j) ∩ t = ⋃ i, ⋃ j, s i j ∩ t",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"congrArg",
"Set.instInter",
"Set.iUnion_inter",
"Inter.inter",
"funext",... | [] | iUnion_inter | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Data.Set.Lattice | {
"line": 970,
"column": 84
} | {
"line": 971,
"column": 44
} | {
"line": 973,
"column": 0
} | [
{
"pp": "α : Type u_1\nc : Set (Set α)\n⊢ ⋃₀ c = univ ↔ ∀ (a : α), ∃ b ∈ c, a ∈ b",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"congrArg",
"Set.univ",
"Set.sUnion",
"Membership.mem",
"Exists",
"iff_self",
"And",
"Iff",
"True",
... | [] | by
simp only [eq_univ_iff_forall, mem_sUnion] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.CompleteBooleanAlgebra | {
"line": 238,
"column": 29
} | {
"line": 238,
"column": 40
} | {
"line": 238,
"column": 41
} | [
{
"pp": "α : Type u\nι : Sort w\nκ : ι → Sort w'\ninst✝ : CompleteLattice α\nminAx : MinimalAxioms α\nf : (a : ι) → κ a → α\n⊢ ⨅ i, ⨆ j, f i j = ⨅ i ∈ range fun x ↦ range (f x), ⨆ b, ↑b",
"ppTerm": "?m.82",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"iInf",
"congrArg",
"i... | [
"α : Type u\nι : Sort w\nκ : ι → Sort w'\ninst✝ : CompleteLattice α\nminAx : MinimalAxioms α\nf : (a : ι) → κ a → α\n⊢ ⨅ i, ⨆ j, f i j = ⨅ i, ⨆ b, ↑b"
] | iInf_range, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Data.Set.Lattice | {
"line": 1341,
"column": 90
} | {
"line": 1342,
"column": 20
} | {
"line": 1344,
"column": 0
} | [
{
"pp": "α : Type u_1\nι : Sort u_5\nκ : ι → Sort u_8\ninst✝ : CompleteLattice α\nf : (i : ι) → κ i → α\n⊢ Ici (⨆ i, ⨆ j, f i j) = ⋂ i, ⋂ j, Ici (f i j)",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Set.Ici",
"congrArg",
"iSup",
"Set.iInter",
"PartialOrder.... | [] | by
simp_rw [Ici_iSup] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.CompleteBooleanAlgebra | {
"line": 766,
"column": 29
} | {
"line": 766,
"column": 40
} | {
"line": 766,
"column": 41
} | [
{
"pp": "α : Type u\nβ : Type v\ninst✝¹ : CompleteLattice α\ninst✝ : CompleteLattice β\nminAx : CompletelyDistribLattice.MinimalAxioms β\nf : α → β\nhf : Injective f\nmap_sSup : ∀ (s : Set α), f (sSup s) = ⨆ a ∈ s, f a\nmap_sInf : ∀ (s : Set α), f (sInf s) = ⨅ a ∈ s, f a\nι✝ : Type u\nκ✝ : ι✝ → Type u\ng : (a :... | [
"α : Type u\nβ : Type v\ninst✝¹ : CompleteLattice α\ninst✝ : CompleteLattice β\nminAx : CompletelyDistribLattice.MinimalAxioms β\nf : α → β\nhf : Injective f\nmap_sSup : ∀ (s : Set α), f (sSup s) = ⨆ a ∈ s, f a\nmap_sInf : ∀ (s : Set α), f (sInf s) = ⨅ a ∈ s, f a\nι✝ : Type u\nκ✝ : ι✝ → Type u\ng : (a : ι✝) → κ✝ a ... | iInf_range, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Order.CompleteBooleanAlgebra | {
"line": 766,
"column": 79
} | {
"line": 766,
"column": 90
} | {
"line": 767,
"column": 6
} | [
{
"pp": "α : Type u\nβ : Type v\ninst✝¹ : CompleteLattice α\ninst✝ : CompleteLattice β\nminAx : CompletelyDistribLattice.MinimalAxioms β\nf : α → β\nhf : Injective f\nmap_sSup : ∀ (s : Set α), f (sSup s) = ⨆ a ∈ s, f a\nmap_sInf : ∀ (s : Set α), f (sInf s) = ⨅ a ∈ s, f a\nι✝ : Type u\nκ✝ : ι✝ → Type u\ng : (a :... | [
"α : Type u\nβ : Type v\ninst✝¹ : CompleteLattice α\ninst✝ : CompleteLattice β\nminAx : CompletelyDistribLattice.MinimalAxioms β\nf : α → β\nhf : Injective f\nmap_sSup : ∀ (s : Set α), f (sSup s) = ⨆ a ∈ s, f a\nmap_sInf : ∀ (s : Set α), f (sInf s) = ⨅ a ∈ s, f a\nι✝ : Type u\nκ✝ : ι✝ → Type u\ng : (a : ι✝) → κ✝ a ... | iInf_range, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Order.CompleteBooleanAlgebra | {
"line": 785,
"column": 29
} | {
"line": 785,
"column": 40
} | {
"line": 785,
"column": 41
} | [
{
"pp": "α : Type u\nβ : Type v\nι : Sort w\nκ : ι → Sort w'\ninst✝¹² : Max α\ninst✝¹¹ : Min α\ninst✝¹⁰ : LE α\ninst✝⁹ : LT α\ninst✝⁸ : SupSet α\ninst✝⁷ : InfSet α\ninst✝⁶ : Top α\ninst✝⁵ : Bot α\ninst✝⁴ : Compl α\ninst✝³ : HImp α\ninst✝² : HNot α\ninst✝¹ : SDiff α\ninst✝ : CompletelyDistribLattice β\nf : α → β... | [
"α : Type u\nβ : Type v\nι : Sort w\nκ : ι → Sort w'\ninst✝¹² : Max α\ninst✝¹¹ : Min α\ninst✝¹⁰ : LE α\ninst✝⁹ : LT α\ninst✝⁸ : SupSet α\ninst✝⁷ : InfSet α\ninst✝⁶ : Top α\ninst✝⁵ : Bot α\ninst✝⁴ : Compl α\ninst✝³ : HImp α\ninst✝² : HNot α\ninst✝¹ : SDiff α\ninst✝ : CompletelyDistribLattice β\nf : α → β\nhf : Injec... | iInf_range, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Order.CompleteBooleanAlgebra | {
"line": 785,
"column": 79
} | {
"line": 785,
"column": 90
} | {
"line": 786,
"column": 6
} | [
{
"pp": "α : Type u\nβ : Type v\nι : Sort w\nκ : ι → Sort w'\ninst✝¹² : Max α\ninst✝¹¹ : Min α\ninst✝¹⁰ : LE α\ninst✝⁹ : LT α\ninst✝⁸ : SupSet α\ninst✝⁷ : InfSet α\ninst✝⁶ : Top α\ninst✝⁵ : Bot α\ninst✝⁴ : Compl α\ninst✝³ : HImp α\ninst✝² : HNot α\ninst✝¹ : SDiff α\ninst✝ : CompletelyDistribLattice β\nf : α → β... | [
"α : Type u\nβ : Type v\nι : Sort w\nκ : ι → Sort w'\ninst✝¹² : Max α\ninst✝¹¹ : Min α\ninst✝¹⁰ : LE α\ninst✝⁹ : LT α\ninst✝⁸ : SupSet α\ninst✝⁷ : InfSet α\ninst✝⁶ : Top α\ninst✝⁵ : Bot α\ninst✝⁴ : Compl α\ninst✝³ : HImp α\ninst✝² : HNot α\ninst✝¹ : SDiff α\ninst✝ : CompletelyDistribLattice β\nf : α → β\nhf : Injec... | iInf_range, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Order.ConditionallyCompleteLattice.Basic | {
"line": 616,
"column": 4
} | {
"line": 632,
"column": 32
} | {
"line": 633,
"column": 2
} | [
{
"pp": "case left\nβ : Type u_5\ninst✝ : ConditionallyCompleteLattice β\ns : Set (WithTop β)\nhs : BddBelow s\n⊢ sInf s ∈ lowerBounds s",
"ppTerm": "?left",
"assigned": true,
"usedConstants": [
"WithTop.instInfSet",
"Iff.mpr",
"Eq.mpr",
"instDecidableNot",
"False",
... | [] | change ite _ _ _ ∈ _
simp only [hs, not_true_eq_false, or_false]
split_ifs with h
· intro a ha
exact top_le_iff.2 (Set.mem_singleton_iff.1 (h ha))
· rintro (⟨⟩ | a) ha
· exact le_top
refine coe_le_coe.2 (csInf_le ?_ ha)
rcases hs with ⟨⟨⟩ | b, hb⟩
· exfalso
apply h
... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.ConditionallyCompleteLattice.Basic | {
"line": 616,
"column": 4
} | {
"line": 632,
"column": 32
} | {
"line": 633,
"column": 2
} | [
{
"pp": "case left\nβ : Type u_5\ninst✝ : ConditionallyCompleteLattice β\ns : Set (WithTop β)\nhs : BddBelow s\n⊢ sInf s ∈ lowerBounds s",
"ppTerm": "?left",
"assigned": true,
"usedConstants": [
"WithTop.instInfSet",
"Iff.mpr",
"Eq.mpr",
"instDecidableNot",
"False",
... | [] | change ite _ _ _ ∈ _
simp only [hs, not_true_eq_false, or_false]
split_ifs with h
· intro a ha
exact top_le_iff.2 (Set.mem_singleton_iff.1 (h ha))
· rintro (⟨⟩ | a) ha
· exact le_top
refine coe_le_coe.2 (csInf_le ?_ ha)
rcases hs with ⟨⟨⟩ | b, hb⟩
· exfalso
apply h
... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.ConditionallyCompleteLattice.Basic | {
"line": 650,
"column": 10
} | {
"line": 650,
"column": 27
} | {
"line": 651,
"column": 10
} | [
{
"pp": "case neg.some.refine_2\nβ : Type u_5\ninst✝ : ConditionallyCompleteLattice β\ns : Set (WithTop β)\nhs : BddBelow s\nh : ¬s ⊆ {⊤}\na : β\nha : Option.some a ∈ lowerBounds s\nb : β\nhb : b ∈ (fun a ↦ ↑a) ⁻¹' s\n⊢ a ≤ b",
"ppTerm": "?neg.some.refine_2✝",
"assigned": true,
"usedConstants": [
... | [
"case neg.some.refine_2\nβ : Type u_5\ninst✝ : ConditionallyCompleteLattice β\ns : Set (WithTop β)\nhs : BddBelow s\nh : ¬s ⊆ {⊤}\na : β\nha : Option.some a ∈ lowerBounds s\nb : β\nhb : b ∈ (fun a ↦ ↑a) ⁻¹' s\n⊢ ↑a ≤ ↑b"
] | rw [← coe_le_coe] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Order.Interval.Set.UnorderedInterval | {
"line": 229,
"column": 2
} | {
"line": 229,
"column": 13
} | {
"line": 230,
"column": 2
} | [
{
"pp": "case mpr\nα : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrder α\ninst✝ : LinearOrder β\nf : α → β\n⊢ (∀ (a b c : α), c ∈ [[a, b]] → f c ∈ [[f a, f b]]) → Monotone f ∨ Antitone f",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"Mathlib.Tactic.Push.not_forall_eq",
"Eq.mpr",
... | [
"case mpr\nα : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrder α\ninst✝ : LinearOrder β\nf : α → β\n⊢ ¬Monotone f ∧ ¬Antitone f → ∃ a b, ∃ c ∈ [[a, b]], f c ∉ [[f a, f b]]"
] | contrapose! | Mathlib.Tactic.Contrapose._aux_Mathlib_Tactic_Contrapose___macroRules_Mathlib_Tactic_Contrapose_contrapose!_1 | Mathlib.Tactic.Contrapose.contrapose! |
Mathlib.Order.Interval.Set.UnorderedInterval | {
"line": 287,
"column": 2
} | {
"line": 287,
"column": 59
} | {
"line": 289,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : LinearOrder α\na b c : α\n⊢ b ∈ Ι a c → c ∈ Ι a b → b = c",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Set.uIoc",
"Set.uIoc_comm",
"Membership.mem",
"id",
"implies_congr",
"Eq.refl",
... | [] | simpa only [uIoc_comm a] using eq_of_mem_uIoc_of_mem_uIoc | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Order.Interval.Set.UnorderedInterval | {
"line": 287,
"column": 2
} | {
"line": 287,
"column": 59
} | {
"line": 289,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : LinearOrder α\na b c : α\n⊢ b ∈ Ι a c → c ∈ Ι a b → b = c",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Set.uIoc",
"Set.uIoc_comm",
"Membership.mem",
"id",
"implies_congr",
"Eq.refl",
... | [] | simpa only [uIoc_comm a] using eq_of_mem_uIoc_of_mem_uIoc | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Interval.Set.UnorderedInterval | {
"line": 287,
"column": 2
} | {
"line": 287,
"column": 59
} | {
"line": 289,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : LinearOrder α\na b c : α\n⊢ b ∈ Ι a c → c ∈ Ι a b → b = c",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Set.uIoc",
"Set.uIoc_comm",
"Membership.mem",
"id",
"implies_congr",
"Eq.refl",
... | [] | simpa only [uIoc_comm a] using eq_of_mem_uIoc_of_mem_uIoc | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Antichain | {
"line": 90,
"column": 31
} | {
"line": 92,
"column": 46
} | {
"line": 94,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nr : α → α → Prop\nr' : β → β → Prop\ns : Set α\nhs : IsAntichain r s\nf : α → β\nh : ∀ ⦃a b : α⦄, r' (f a) (f b) → r a b\n⊢ IsAntichain r' (f '' s)",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Compl.compl",
"Prop.instCompl",
"Member... | [] | by
rintro _ ⟨b, hb, rfl⟩ _ ⟨c, hc, rfl⟩ hbc hr
exact hs hb hc (ne_of_apply_ne _ hbc) (h hr) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Order.Ring.InjSurj | {
"line": 31,
"column": 4
} | {
"line": 31,
"column": 89
} | {
"line": 32,
"column": 2
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝⁴ : Semiring R\ninst✝³ : PartialOrder R\ninst✝² : IsOrderedRing R\ninst✝¹ : Semiring S\ninst✝ : PartialOrder S\nf : S → R\nzero : f 0 = 0\none : f 1 = 1\nadd : ∀ (x y : S), f (x + y) = f x + f y\nmul : ∀ (x y : S), f (x * y) = f x * f y\nle : ∀ {x y : S}, f x ≤ f y ↔ x ... | [] | rw [← le, mul, mul]; refine mul_le_mul_of_nonneg_left (le.2 hbc) ?_; rwa [← zero, le] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Ring.InjSurj | {
"line": 31,
"column": 4
} | {
"line": 31,
"column": 89
} | {
"line": 32,
"column": 2
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝⁴ : Semiring R\ninst✝³ : PartialOrder R\ninst✝² : IsOrderedRing R\ninst✝¹ : Semiring S\ninst✝ : PartialOrder S\nf : S → R\nzero : f 0 = 0\none : f 1 = 1\nadd : ∀ (x y : S), f (x + y) = f x + f y\nmul : ∀ (x y : S), f (x * y) = f x * f y\nle : ∀ {x y : S}, f x ≤ f y ↔ x ... | [] | rw [← le, mul, mul]; refine mul_le_mul_of_nonneg_left (le.2 hbc) ?_; rwa [← zero, le] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Nat.Factorial.Basic | {
"line": 232,
"column": 13
} | {
"line": 234,
"column": 88
} | {
"line": 236,
"column": 0
} | [
{
"pp": "n k : ℕ\n⊢ n ! * (n + 1).ascFactorial (k + 1) = (n + (k + 1))!",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"congrArg",
"Nat.factorial_succ",
"Nat.ascFactorial",
"Nat.ascFactorial_succ",
"id",
"instMulNat",
... | [] | by
rw [ascFactorial_succ, ← Nat.add_assoc, factorial_succ, Nat.mul_comm (n + 1 + k),
← Nat.mul_assoc, factorial_mul_ascFactorial n k, Nat.mul_comm, Nat.add_right_comm] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Order.Hom.Basic | {
"line": 215,
"column": 22
} | {
"line": 215,
"column": 42
} | {
"line": 215,
"column": 42
} | [
{
"pp": "F : Type u_2\nα : Type u_3\nβ : Type u_4\ninst✝⁴ : FunLike F α β\ninst✝³ : Group α\ninst✝² : AddCommMonoid β\ninst✝¹ : PartialOrder β\ninst✝ : GroupSeminormClass F α β\nf : F\nx y : α\n⊢ f (x * y⁻¹) ≤ f x + f y",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"F : Type u_2\nα : Type u_3\nβ : Type u_4\ninst✝⁴ : FunLike F α β\ninst✝³ : Group α\ninst✝² : AddCommMonoid β\ninst✝¹ : PartialOrder β\ninst✝ : GroupSeminormClass F α β\nf : F\nx y : α\n⊢ f (x * y⁻¹) ≤ f x + f y⁻¹"
] | ← map_inv_eq_map f y | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Nat.Factorial.Basic | {
"line": 389,
"column": 4
} | {
"line": 391,
"column": 25
} | {
"line": 393,
"column": 0
} | [
{
"pp": "n k : ℕ\n⊢ (n + k.succ - 1).descFactorial k.succ = n.ascFactorial k.succ",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"congrArg",
"Nat.succ_add_sub_one",
"HSub.hSub",
"Nat.ascFactorial",
"Nat.ascFactorial_succ",
... | [] | rw [descFactorial_succ, ascFactorial_succ, ← succ_add_eq_add_succ,
add_descFactorial_eq_ascFactorial' _ k, ← succ_ascFactorial, succ_add_sub_one,
Nat.add_sub_cancel] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Nat.Factorial.Basic | {
"line": 389,
"column": 4
} | {
"line": 391,
"column": 25
} | {
"line": 393,
"column": 0
} | [
{
"pp": "n k : ℕ\n⊢ (n + k.succ - 1).descFactorial k.succ = n.ascFactorial k.succ",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"congrArg",
"Nat.succ_add_sub_one",
"HSub.hSub",
"Nat.ascFactorial",
"Nat.ascFactorial_succ",
... | [] | rw [descFactorial_succ, ascFactorial_succ, ← succ_add_eq_add_succ,
add_descFactorial_eq_ascFactorial' _ k, ← succ_ascFactorial, succ_add_sub_one,
Nat.add_sub_cancel] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Nat.Factorial.Basic | {
"line": 389,
"column": 4
} | {
"line": 391,
"column": 25
} | {
"line": 393,
"column": 0
} | [
{
"pp": "n k : ℕ\n⊢ (n + k.succ - 1).descFactorial k.succ = n.ascFactorial k.succ",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"congrArg",
"Nat.succ_add_sub_one",
"HSub.hSub",
"Nat.ascFactorial",
"Nat.ascFactorial_succ",
... | [] | rw [descFactorial_succ, ascFactorial_succ, ← succ_add_eq_add_succ,
add_descFactorial_eq_ascFactorial' _ k, ← succ_ascFactorial, succ_add_sub_one,
Nat.add_sub_cancel] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.PNat.Basic | {
"line": 335,
"column": 6
} | {
"line": 337,
"column": 50
} | {
"line": 339,
"column": 0
} | [
{
"pp": "case neg\nk m : ℕ+\nh : m.mod k = k\nh' : ¬↑m % ↑k = 0\n⊢ ↑m % ↑k = 0",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"PNat.mod_coe",
"PNat.val",
"congrArg",
"False.elim",
"Eq.mp",
"Nat.instMod",
"instHMod",
"PNat.mod",
"instOf... | [] | replace h : (mod m k : ℕ) = (k : ℕ) := congr_arg _ h
rw [mod_coe, if_neg h'] at h
exact ((Nat.mod_lt (m : ℕ) k.pos).ne h).elim | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.PNat.Basic | {
"line": 335,
"column": 6
} | {
"line": 337,
"column": 50
} | {
"line": 339,
"column": 0
} | [
{
"pp": "case neg\nk m : ℕ+\nh : m.mod k = k\nh' : ¬↑m % ↑k = 0\n⊢ ↑m % ↑k = 0",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"PNat.mod_coe",
"PNat.val",
"congrArg",
"False.elim",
"Eq.mp",
"Nat.instMod",
"instHMod",
"PNat.mod",
"instOf... | [] | replace h : (mod m k : ℕ) = (k : ℕ) := congr_arg _ h
rw [mod_coe, if_neg h'] at h
exact ((Nat.mod_lt (m : ℕ) k.pos).ne h).elim | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Floor.Ring | {
"line": 176,
"column": 40
} | {
"line": 176,
"column": 70
} | {
"line": 178,
"column": 0
} | [
{
"pp": "R : Type u_2\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : FloorRing R\ninst✝ : IsOrderedRing R\n⊢ ⌊1⌋ = 1",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Int.cast",
"Eq.mpr",
"Int.floor",
"Int.floor_intCast",
"congrArg",
"AddGroupWithOne.... | [] | rw [← cast_one, floor_intCast] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Order.Floor.Ring | {
"line": 176,
"column": 40
} | {
"line": 176,
"column": 70
} | {
"line": 178,
"column": 0
} | [
{
"pp": "R : Type u_2\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : FloorRing R\ninst✝ : IsOrderedRing R\n⊢ ⌊1⌋ = 1",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Int.cast",
"Eq.mpr",
"Int.floor",
"Int.floor_intCast",
"congrArg",
"AddGroupWithOne.... | [] | rw [← cast_one, floor_intCast] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Floor.Ring | {
"line": 176,
"column": 40
} | {
"line": 176,
"column": 70
} | {
"line": 178,
"column": 0
} | [
{
"pp": "R : Type u_2\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : FloorRing R\ninst✝ : IsOrderedRing R\n⊢ ⌊1⌋ = 1",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Int.cast",
"Eq.mpr",
"Int.floor",
"Int.floor_intCast",
"congrArg",
"AddGroupWithOne.... | [] | rw [← cast_one, floor_intCast] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Floor.Ring | {
"line": 261,
"column": 4
} | {
"line": 261,
"column": 49
} | {
"line": 261,
"column": 49
} | [
{
"pp": "R : Type u_4\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : IsStrictOrderedRing R\ninst✝ : FloorRing R\nn : ℤ\nhn : 0 < n\na : R\nm : ℤ\n⊢ ↑m * ↑n ≤ a * ↑n ↔ ↑m ≤ a",
"ppTerm": "?m.60",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Int.cast",
"Eq.mpr",
"Preord... | [
"R : Type u_4\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : IsStrictOrderedRing R\ninst✝ : FloorRing R\nn : ℤ\nhn : 0 < n\na : R\nm : ℤ\n⊢ ↑m ≤ a ↔ ↑m ≤ a"
] | mul_le_mul_iff_of_pos_right (cast_pos.mpr hn) | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Floor.Ring | {
"line": 280,
"column": 6
} | {
"line": 280,
"column": 20
} | {
"line": 280,
"column": 21
} | [
{
"pp": "R : Type u_4\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : IsStrictOrderedRing R\ninst✝ : FloorRing R\nn : ℕ\nhn : n ≠ 0\na : R\n⊢ ⌊↑n * a⌋ / ↑n = ⌊a⌋",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Nat.cast_comm",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoi... | [
"R : Type u_4\ninst✝³ : Ring R\ninst✝² : LinearOrder R\ninst✝¹ : IsStrictOrderedRing R\ninst✝ : FloorRing R\nn : ℕ\nhn : n ≠ 0\na : R\n⊢ ⌊a * ↑n⌋ / ↑n = ⌊a⌋"
] | Nat.cast_comm, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Rat.Floor | {
"line": 181,
"column": 2
} | {
"line": 186,
"column": 89
} | {
"line": 188,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝³ : Field α\ninst✝² : LinearOrder α\ninst✝¹ : IsStrictOrderedRing α\ninst✝ : FloorRing α\nr : α\nn d : ℕ\n⊢ IsNNRat r n d → IsNat ⌈r⌉ (-(-↑n / ↑d)).toNat",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Int.cast",
"Eq.mpr",
"No... | [] | rintro ⟨inv, rfl⟩
constructor
simp only [invOf_eq_inv, ← div_eq_mul_inv]
rw [← ceil_intCast_div_natCast n d, ← ceil_cast (α := α), Rat.cast_div,
cast_intCast, cast_natCast, Int.cast_natCast,
Int.natCast_toNat_eq_self.mpr (ceil_nonneg (div_nonneg n.cast_nonneg d.cast_nonneg))] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Rat.Floor | {
"line": 181,
"column": 2
} | {
"line": 186,
"column": 89
} | {
"line": 188,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝³ : Field α\ninst✝² : LinearOrder α\ninst✝¹ : IsStrictOrderedRing α\ninst✝ : FloorRing α\nr : α\nn d : ℕ\n⊢ IsNNRat r n d → IsNat ⌈r⌉ (-(-↑n / ↑d)).toNat",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Int.cast",
"Eq.mpr",
"No... | [] | rintro ⟨inv, rfl⟩
constructor
simp only [invOf_eq_inv, ← div_eq_mul_inv]
rw [← ceil_intCast_div_natCast n d, ← ceil_cast (α := α), Rat.cast_div,
cast_intCast, cast_natCast, Int.cast_natCast,
Int.natCast_toNat_eq_self.mpr (ceil_nonneg (div_nonneg n.cast_nonneg d.cast_nonneg))] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Rat.Floor | {
"line": 409,
"column": 8
} | {
"line": 409,
"column": 17
} | {
"line": 409,
"column": 17
} | [
{
"pp": "q : ℚ\nq_pos : 0 < q\nq_num_pos : 0 < q.num\nq_num_abs_eq_q_num : ↑q.num.natAbs = q.num\nq_inv : ℚ := ↑q.den / ↑q.num\nq_inv_def : q_inv = ↑q.den / ↑q.num\nq_inv_eq : q⁻¹ = q_inv\nq_inv_num_denom_ineq : q⁻¹.num - ⌊q⁻¹⌋ * ↑q⁻¹.den < ↑q⁻¹.den\ncoprime_q_denom_q_num : (↑q.den).natAbs.Coprime q.num.natAbs\... | [
"q : ℚ\nq_pos : 0 < q\nq_num_pos : 0 < q.num\nq_num_abs_eq_q_num : ↑q.num.natAbs = q.num\nq_inv : ℚ := ↑q.den / ↑q.num\nq_inv_def : q_inv = ↑q.den / ↑q.num\nq_inv_eq : q⁻¹ = q_inv\nq_inv_num_denom_ineq : q⁻¹.num - ⌊q⁻¹⌋ * ↑q⁻¹.den < ↑q⁻¹.den\ncoprime_q_denom_q_num : (↑q.den).natAbs.Coprime q.num.natAbs\nthis : (↑q.... | q_inv_def | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Torsor.Defs | {
"line": 292,
"column": 2
} | {
"line": 292,
"column": 52
} | {
"line": 293,
"column": 0
} | [
{
"pp": "G : Type u_1\nP : Type u_2\ninst✝¹ : Group G\ninst✝ : Torsor G P\ninhabited_h : Inhabited P\n⊢ Subsingleton G ↔ Subsingleton P",
"ppTerm": "?m.4",
"assigned": true,
"usedConstants": [
"Inhabited.default",
"Equiv.subsingleton_congr",
"Equiv.smulConst"
],
"usedFVars"... | [] | exact (Equiv.smulConst default).subsingleton_congr | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Algebra.Group.Action.Basic | {
"line": 103,
"column": 4
} | {
"line": 103,
"column": 43
} | {
"line": 104,
"column": 4
} | [
{
"pp": "G✝ : Type u_1\nM : Type u_2\nA✝ : Type u_3\nB✝ : Type u_4\nα : Type u_5\nβ : Type u_6\nG : Type u_7\nA : Type u_8\nB : Type u_9\ninst✝¹ : DivisionMonoid G\ninst✝ : MulAction G A\nf : A → B\n⊢ 1 • f = f",
"ppTerm": "?m.50",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"in... | [
"G✝ : Type u_1\nM : Type u_2\nA✝ : Type u_3\nB✝ : Type u_4\nα : Type u_5\nβ : Type u_6\nG : Type u_7\nA : Type u_8\nB : Type u_9\ninst✝¹ : DivisionMonoid G\ninst✝ : MulAction G A\nf : A → B\n⊢ (fun x ↦ f (1⁻¹ • x)) = f"
] | change (fun x => f ((1 : G)⁻¹ • x)) = f | Lean.Elab.Tactic.evalChange | Lean.Parser.Tactic.change |
Mathlib.Algebra.Order.Archimedean.Basic | {
"line": 386,
"column": 4
} | {
"line": 386,
"column": 64
} | {
"line": 387,
"column": 4
} | [
{
"pp": "case refine_1\nK : Type u_4\ninst✝³ : Field K\ninst✝² : LinearOrder K\ninst✝¹ : IsStrictOrderedRing K\ninst✝ : Archimedean K\nn : ℕ\nhn : n ≠ 0\nx y : K\nh : x < y\nhy : 0 < y\nδ : K\nδ_pos : δ > 0\ncont : ∀ (q r : K), |r| ≤ max 1 y → |q - r| ≤ δ → |q ^ n - r ^ n| < y - max x 0\nm : ℕ\nhm : y / δ + 1 /... | [
"case refine_2\nK : Type u_4\ninst✝³ : Field K\ninst✝² : LinearOrder K\ninst✝¹ : IsStrictOrderedRing K\ninst✝ : Archimedean K\nn : ℕ\nhn : n ≠ 0\nx y : K\nh : x < y\nhy : 0 < y\nδ : K\nδ_pos : δ > 0\ncont : ∀ (q r : K), |r| ≤ max 1 y → |q - r| ≤ δ → |q ^ n - r ^ n| < y - max x 0\nm : ℕ\nhm : y / δ + 1 / δ ≤ ↑m\n⊢ 1... | · exact (lt_add_of_pos_right _ <| by positivity).le.trans hm | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Data.Multiset.Defs | {
"line": 260,
"column": 65
} | {
"line": 261,
"column": 34
} | {
"line": 262,
"column": 6
} | [
{
"pp": "α : Type u_1\nβ : Type v\nγ : Type u_2\np : α → Prop\nf : (a : α) → p a → β\ns : Multiset α\nl₁ l₂ : List α\npp : l₁ ~ l₂\nH₂ : ∀ (a : α), a ∈ l₂ → p a\nH₁ : ∀ (a : α), a ∈ l₁ → p a\n⊢ ∀ {s₂ : Multiset α} {e : ↑l₁ = s₂} {H : ∀ (a : α), a ∈ s₂ → p a},\n Eq.ndrec (motive := fun s ↦ (∀ (a : α), a ∈ s →... | [] | by
intro s₂ e _; subst e; rfl | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Multiset.MapFold | {
"line": 478,
"column": 4
} | {
"line": 478,
"column": 11
} | {
"line": 479,
"column": 4
} | [
{
"pp": "α : Type u_1\nβ : Type v\nγ : Type u_2\nf : α → γ\ng : β → γ\ns : Multiset α\nt : Multiset β\nhs : s.Nodup\nht : t.Nodup\ni : (a : α) → a ∈ s → β\nhi : ∀ (a : α) (ha : a ∈ s), i a ha ∈ t\ni_inj : ∀ (a₁ : α) (ha₁ : a₁ ∈ s) (a₂ : α) (ha₂ : a₂ ∈ s), i a₁ ha₁ = i a₂ ha₂ → a₁ = a₂\ni_surj : ∀ (b : β), b ∈ t... | [
"α : Type u_1\nβ : Type v\nγ : Type u_2\nf : α → γ\ng : β → γ\ns : Multiset α\nt : Multiset β\nhs : s.Nodup\nht : t.Nodup\ni : (a : α) → a ∈ s → β\nhi : ∀ (a : α) (ha : a ∈ s), i a ha ∈ t\ni_inj : ∀ (a₁ : α) (ha₁ : a₁ ∈ s) (a₂ : α) (ha₂ : a₂ ∈ s), i a₁ ha₁ = i a₂ ha₂ → a₁ = a₂\ni_surj : ∀ (b : β), b ∈ t → ∃ a ha, i... | · aesop | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Data.List.Lattice | {
"line": 250,
"column": 31
} | {
"line": 250,
"column": 61
} | {
"line": 250,
"column": 61
} | [
{
"pp": "α : Type u_1\nl₁ l₂ : List α\ninst✝ : DecidableEq α\nh : l₁.Nodup\nx : α\n⊢ List.count x (l₁.bagInter l₂) ≤ 1",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Data.List.Lattice.0.List.Nodup.bagInter_right._proof_1_1"
],
"usedFVars": [
"α",
... | [] | by grind [List.count_bagInter] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.List.Lattice | {
"line": 253,
"column": 31
} | {
"line": 253,
"column": 61
} | {
"line": 253,
"column": 61
} | [
{
"pp": "α : Type u_1\nl₁ l₂ : List α\ninst✝ : DecidableEq α\nh : l₂.Nodup\nx : α\n⊢ List.count x (l₁.bagInter l₂) ≤ 1",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Data.List.Lattice.0.List.Nodup.bagInter_left._proof_1_1"
],
"usedFVars": [
"α",
... | [] | by grind [List.count_bagInter] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.List.Dedup | {
"line": 162,
"column": 2
} | {
"line": 162,
"column": 43
} | {
"line": 163,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\nxs ys : List α\nh : xs.Disjoint ys\n⊢ (xs ++ ys).dedup = xs.dedup ++ ys.dedup",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"List.dedup",
"id",
"instBEqOfDecidableEq",
"instHAppendOfAp... | [
"α : Type u_1\ninst✝ : DecidableEq α\nxs ys : List α\nh : xs.Disjoint ys\n⊢ xs.Disjoint ys.dedup"
] | rw [List.dedup_append, Disjoint.union_eq] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Multiset.Dedup | {
"line": 122,
"column": 2
} | {
"line": 122,
"column": 43
} | {
"line": 124,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Multiset α\nh : t ⊆ s\n⊢ (s + t).dedup = s.dedup",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Multiset.dedup",
"Multiset.add_comm",
"Multiset",
"id",
"instHAdd",
"H... | [] | rw [s.add_comm, Subset.dedup_add_right h] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Multiset.Dedup | {
"line": 122,
"column": 2
} | {
"line": 122,
"column": 43
} | {
"line": 124,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Multiset α\nh : t ⊆ s\n⊢ (s + t).dedup = s.dedup",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Multiset.dedup",
"Multiset.add_comm",
"Multiset",
"id",
"instHAdd",
"H... | [] | rw [s.add_comm, Subset.dedup_add_right h] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Multiset.Dedup | {
"line": 122,
"column": 2
} | {
"line": 122,
"column": 43
} | {
"line": 124,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Multiset α\nh : t ⊆ s\n⊢ (s + t).dedup = s.dedup",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Multiset.dedup",
"Multiset.add_comm",
"Multiset",
"id",
"instHAdd",
"H... | [] | rw [s.add_comm, Subset.dedup_add_right h] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Multiset.Filter | {
"line": 170,
"column": 4
} | {
"line": 170,
"column": 15
} | {
"line": 171,
"column": 4
} | [
{
"pp": "case mpr\nα : Type u_1\ns : Multiset α\nP : α → Prop\ninst✝ : DecidablePred P\nn : ℕ\n⊢ (∀ (s' : Multiset α), s' ≤ s → n < s'.card → ∃ a, a ∈ s' ∧ ¬P a) → (filter P s).card ≤ n",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"Mathlib.Tactic.Push.not_forall_eq",
"Mathlib... | [
"case mpr\nα : Type u_1\ns : Multiset α\nP : α → Prop\ninst✝ : DecidablePred P\nn : ℕ\n⊢ n < (filter P s).card → ∃ s', s' ≤ s ∧ n < s'.card ∧ ∀ (a : α), a ∈ s' → P a"
] | contrapose! | Mathlib.Tactic.Contrapose._aux_Mathlib_Tactic_Contrapose___macroRules_Mathlib_Tactic_Contrapose_contrapose!_1 | Mathlib.Tactic.Contrapose.contrapose! |
Mathlib.Data.Multiset.UnionInter | {
"line": 297,
"column": 2
} | {
"line": 297,
"column": 53
} | {
"line": 299,
"column": 0
} | [
{
"pp": "α : Type u_1\ns t u : Multiset α\n⊢ _root_.Disjoint s (t + u) ↔ _root_.Disjoint s t ∧ _root_.Disjoint s u",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Multiset.disjoint_add_left",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
... | [] | rw [_root_.disjoint_comm, disjoint_add_left]; tauto | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Multiset.UnionInter | {
"line": 297,
"column": 2
} | {
"line": 297,
"column": 53
} | {
"line": 299,
"column": 0
} | [
{
"pp": "α : Type u_1\ns t u : Multiset α\n⊢ _root_.Disjoint s (t + u) ↔ _root_.Disjoint s t ∧ _root_.Disjoint s u",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Multiset.disjoint_add_left",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
... | [] | rw [_root_.disjoint_comm, disjoint_add_left]; tauto | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.Infix | {
"line": 50,
"column": 2
} | {
"line": 50,
"column": 60
} | {
"line": 52,
"column": 0
} | [
{
"pp": "α : Type u_1\nl₁ l₂ : List α\nh : l₁ <+: l₂\nn : ℕ\n⊢ List.drop n l₁ <+: List.drop n l₂",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"List.prefix_iff_eq_take",
"HSub.hSub",
"List.drop_take",
"id",
"instSubNat",
... | [] | rw [prefix_iff_eq_take.mp h, drop_take]; apply take_prefix | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.List.Infix | {
"line": 50,
"column": 2
} | {
"line": 50,
"column": 60
} | {
"line": 52,
"column": 0
} | [
{
"pp": "α : Type u_1\nl₁ l₂ : List α\nh : l₁ <+: l₂\nn : ℕ\n⊢ List.drop n l₁ <+: List.drop n l₂",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"List.prefix_iff_eq_take",
"HSub.hSub",
"List.drop_take",
"id",
"instSubNat",
... | [] | rw [prefix_iff_eq_take.mp h, drop_take]; apply take_prefix | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Finset.BooleanAlgebra | {
"line": 56,
"column": 2
} | {
"line": 56,
"column": 13
} | {
"line": 56,
"column": 13
} | [
{
"pp": "α : Type u_1\ninst✝ : Fintype α\n⊢ univ = ∅ ↔ IsEmpty α",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Mathlib.Tactic.Contrapose.contrapose_iff₁",
"Finset.univ",
"congrArg",
"Finset",
"id",
"IsEmpty",
"Finset.instEmptyColl... | [
"α : Type u_1\ninst✝ : Fintype α\n⊢ univ.Nonempty ↔ Nonempty α"
] | contrapose! | Mathlib.Tactic.Contrapose._aux_Mathlib_Tactic_Contrapose___macroRules_Mathlib_Tactic_Contrapose_contrapose!_1 | Mathlib.Tactic.Contrapose.contrapose! |
Mathlib.Data.Finset.Basic | {
"line": 646,
"column": 84
} | {
"line": 646,
"column": 98
} | {
"line": 646,
"column": 98
} | [
{
"pp": "ι : Type u_5\ninst✝ : DecidableEq ι\nα : ι → Type u_4\ns t : Finset ι\nh : Disjoint s t\nf : (i : ↥s) → α ↑i\ng : (i : ↥t) → α ↑i\ni : ι\nhi : i ∈ s\nhi' : i ∈ s ∪ t\n⊢ { toFun := fun f x ↦ f ((Finset.union s t h).symm.symm x), invFun := fun f x ↦ ⋯ ▸ f ((Finset.union s t h).symm x),\n left_in... | [
"ι : Type u_5\ninst✝ : DecidableEq ι\nα : ι → Type u_4\ns t : Finset ι\nh : Disjoint s t\nf : (i : ↥s) → α ↑i\ng : (i : ↥t) → α ↑i\ni : ι\nhi : i ∈ s\nhi' : i ∈ s ∪ t\n⊢ ⋯ ▸ Sum.rec f g ((Finset.union s t h).symm ⟨i, hi'⟩) = f ⟨i, hi⟩"
] | coe_fn_symm_mk | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Data.Finset.Basic | {
"line": 654,
"column": 84
} | {
"line": 654,
"column": 98
} | {
"line": 654,
"column": 98
} | [
{
"pp": "ι : Type u_5\ninst✝ : DecidableEq ι\nα : ι → Type u_4\ns t : Finset ι\nh : Disjoint s t\nf : (i : ↥s) → α ↑i\ng : (i : ↥t) → α ↑i\ni : ι\nhi : i ∈ t\nhi' : i ∈ s ∪ t\n⊢ { toFun := fun f x ↦ f ((Finset.union s t h).symm.symm x), invFun := fun f x ↦ ⋯ ▸ f ((Finset.union s t h).symm x),\n left_in... | [
"ι : Type u_5\ninst✝ : DecidableEq ι\nα : ι → Type u_4\ns t : Finset ι\nh : Disjoint s t\nf : (i : ↥s) → α ↑i\ng : (i : ↥t) → α ↑i\ni : ι\nhi : i ∈ t\nhi' : i ∈ s ∪ t\n⊢ ⋯ ▸ Sum.rec f g ((Finset.union s t h).symm ⟨i, hi'⟩) = g ⟨i, hi⟩"
] | coe_fn_symm_mk | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Data.Finset.Image | {
"line": 788,
"column": 17
} | {
"line": 792,
"column": 9
} | {
"line": 794,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\np : α → Prop\ns : { s // ∀ a ∈ s, p a }\n⊢ (fun s ↦ ⟨Finset.map { toFun := fun a ↦ ↑a, inj' := ⋯ } s, ⋯⟩)\n ((fun s ↦ Finset.map (Subtype.impEmbedding (Membership.mem ↑s) p ⋯) (↑s).attach) s) =\n s",
"ppTerm": "?m.113",
"assigned": true,
"us... | [] | by
ext a; constructor <;> intro h <;>
simp only [Finset.mem_map, Finset.mem_attach, Subtype.exists, Embedding.coeFn_mk,
Subtype.impEmbedding] at * <;>
grind | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Fin.SuccPred | {
"line": 348,
"column": 2
} | {
"line": 349,
"column": 24
} | {
"line": 351,
"column": 0
} | [
{
"pp": "n : ℕ\ni : Fin (n + 1)\nh : i ≠ last n\n⊢ (i.castPred h).castSucc = i",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Eq.mpr",
"Fin.ext_iff",
"Fin.castPred_castSucc",
"congrArg",
"Exists",
"id",
"Iff.not",
"Fin.cast... | [] | rcases exists_castSucc_eq.mpr h with ⟨y, rfl⟩
rw [castPred_castSucc] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Fin.SuccPred | {
"line": 348,
"column": 2
} | {
"line": 349,
"column": 24
} | {
"line": 351,
"column": 0
} | [
{
"pp": "n : ℕ\ni : Fin (n + 1)\nh : i ≠ last n\n⊢ (i.castPred h).castSucc = i",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Eq.mpr",
"Fin.ext_iff",
"Fin.castPred_castSucc",
"congrArg",
"Exists",
"id",
"Iff.not",
"Fin.cast... | [] | rcases exists_castSucc_eq.mpr h with ⟨y, rfl⟩
rw [castPred_castSucc] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Finset.Card | {
"line": 494,
"column": 2
} | {
"line": 494,
"column": 83
} | {
"line": 496,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ns : Finset α\nt : Finset β\nf : α → β\nhf : Set.MapsTo f ↑s ↑t\nhinj : Set.InjOn f ↑s\nhst : #t ≤ #s\nthis : image f s ⊆ t\n⊢ image f s = t",
"ppTerm": "?m.42",
"assigned": true,
"usedConstants": [
"LE.le.trans_eq",
"Classical.propDecidable",
"i... | [] | exact eq_of_subset_of_card_le this (hst.trans_eq (card_image_of_injOn hinj).symm) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Data.Fin.SuccPred | {
"line": 652,
"column": 9
} | {
"line": 652,
"column": 36
} | {
"line": 652,
"column": 37
} | [
{
"pp": "case inr\nn : ℕ\np : Fin (n + 1)\ni : Fin n\nH : p < i.succ\n⊢ p < p.succAbove i ↔ p ≤ i.castSucc",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"Fin.succAbove",
"Eq.mpr",
"Fin.succ",
"congrArg",
"id",
"instOfNatNat",
"LE.le",
"instL... | [
"case inr\nn : ℕ\np : Fin (n + 1)\ni : Fin n\nH : p < i.succ\n⊢ p < i.succ ↔ p ≤ i.castSucc"
] | succAbove_of_lt_succ _ _ H, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Fin.SuccPred | {
"line": 702,
"column": 4
} | {
"line": 702,
"column": 63
} | {
"line": 703,
"column": 2
} | [
{
"pp": "case inl\nn : ℕ\ni : Fin (n + 1)\nj : Fin n\nh : i < j.succ\n⊢ i.succ.succAbove j.succ = (i.succAbove j).succ",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Fin.succAbove",
"Eq.mpr",
"Fin.succ",
"congrArg",
"id",
"instOfNatNat",
"Fin.succ... | [] | rw [succAbove_of_lt_succ _ _ h, succAbove_succ_of_lt _ _ h] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Fin.SuccPred | {
"line": 702,
"column": 4
} | {
"line": 702,
"column": 63
} | {
"line": 703,
"column": 2
} | [
{
"pp": "case inl\nn : ℕ\ni : Fin (n + 1)\nj : Fin n\nh : i < j.succ\n⊢ i.succ.succAbove j.succ = (i.succAbove j).succ",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Fin.succAbove",
"Eq.mpr",
"Fin.succ",
"congrArg",
"id",
"instOfNatNat",
"Fin.succ... | [] | rw [succAbove_of_lt_succ _ _ h, succAbove_succ_of_lt _ _ h] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Fin.SuccPred | {
"line": 702,
"column": 4
} | {
"line": 702,
"column": 63
} | {
"line": 703,
"column": 2
} | [
{
"pp": "case inl\nn : ℕ\ni : Fin (n + 1)\nj : Fin n\nh : i < j.succ\n⊢ i.succ.succAbove j.succ = (i.succAbove j).succ",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Fin.succAbove",
"Eq.mpr",
"Fin.succ",
"congrArg",
"id",
"instOfNatNat",
"Fin.succ... | [] | rw [succAbove_of_lt_succ _ _ h, succAbove_succ_of_lt _ _ h] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Fintype.Basic | {
"line": 60,
"column": 2
} | {
"line": 60,
"column": 21
} | {
"line": 62,
"column": 0
} | [
{
"pp": "α : Type u_1\nn : ℕ\ninst✝ : DecidableEq α\nf : Fin n → α\n⊢ image f univ = (List.ofFn f).toFinset",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Multiset.toFinset",
"Finset.univ",
"Multiset.map",
"congrArg",
"Finset",
"List.ofFn",
"Mult... | [] | simp [Finset.image] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Fintype.Basic | {
"line": 60,
"column": 2
} | {
"line": 60,
"column": 21
} | {
"line": 62,
"column": 0
} | [
{
"pp": "α : Type u_1\nn : ℕ\ninst✝ : DecidableEq α\nf : Fin n → α\n⊢ image f univ = (List.ofFn f).toFinset",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Multiset.toFinset",
"Finset.univ",
"Multiset.map",
"congrArg",
"Finset",
"List.ofFn",
"Mult... | [] | simp [Finset.image] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Fintype.Basic | {
"line": 60,
"column": 2
} | {
"line": 60,
"column": 21
} | {
"line": 62,
"column": 0
} | [
{
"pp": "α : Type u_1\nn : ℕ\ninst✝ : DecidableEq α\nf : Fin n → α\n⊢ image f univ = (List.ofFn f).toFinset",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Multiset.toFinset",
"Finset.univ",
"Multiset.map",
"congrArg",
"Finset",
"List.ofFn",
"Mult... | [] | simp [Finset.image] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Finset.Card | {
"line": 735,
"column": 2
} | {
"line": 735,
"column": 13
} | {
"line": 735,
"column": 13
} | [
{
"pp": "α : Type u_1\ns : Finset α\n⊢ 1 < #s ↔ ∃ a ∈ s, ∃ b ∈ s, a ≠ b",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Mathlib.Tactic.Push.not_exists._simp_1",
"Eq.mpr",
"Mathlib.Tactic.Push.not_and_eq",
"Mathlib.Tactic.Contrapose.contrapose_iff₁",
"congrArg... | [
"α : Type u_1\ns : Finset α\n⊢ #s ≤ 1 ↔ ∀ a ∈ s, ∀ b ∈ s, a = b"
] | contrapose! | Mathlib.Tactic.Contrapose._aux_Mathlib_Tactic_Contrapose___macroRules_Mathlib_Tactic_Contrapose_contrapose!_1 | Mathlib.Tactic.Contrapose.contrapose! |
Mathlib.Data.Fin.Tuple.Basic | {
"line": 359,
"column": 4
} | {
"line": 360,
"column": 28
} | {
"line": 361,
"column": 4
} | [
{
"pp": "case refine_1.refine_1\nm n : ℕ\nα : Sort u_1\np : ℕ\na : Fin m → α\nb : Fin n → α\nc : Fin p → α\ni : Fin (m + n + p)\nl : Fin (m + n)\nll : Fin m\n⊢ append a b (castAdd n ll) = append a (append b c) (Fin.cast ⋯ (castAdd p (castAdd n ll)))",
"ppTerm": "?refine_1.refine_1",
"assigned": true,
... | [
"case refine_1.refine_2\nm n : ℕ\nα : Sort u_1\np : ℕ\na : Fin m → α\nb : Fin n → α\nc : Fin p → α\ni : Fin (m + n + p)\nl : Fin (m + n)\nlr : Fin n\n⊢ append a b (natAdd m lr) = append a (append b c) (Fin.cast ⋯ (castAdd p (natAdd m lr)))"
] | · rw [append_left]
simp [castAdd_castAdd] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Data.List.Duplicate | {
"line": 79,
"column": 2
} | {
"line": 85,
"column": 28
} | {
"line": 87,
"column": 0
} | [
{
"pp": "α : Type u_1\nl : List α\nx y : α\n⊢ x ∈+ y :: l ↔ y = x ∧ x ∈ l ∨ x ∈+ l",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"List.Duplicate.cons_duplicate",
"Eq.mpr",
"List.Duplicate.cons_mem",
"HEq.refl",
"List.duplicate_cons_self_iff._simp_1",
"M... | [] | refine ⟨fun h => ?_, fun h => ?_⟩
· obtain hm | hm := h
· exact Or.inl ⟨rfl, hm⟩
· exact Or.inr hm
· rcases h with (⟨rfl | h⟩ | h)
· simpa
· exact h.cons_duplicate | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.List.Duplicate | {
"line": 79,
"column": 2
} | {
"line": 85,
"column": 28
} | {
"line": 87,
"column": 0
} | [
{
"pp": "α : Type u_1\nl : List α\nx y : α\n⊢ x ∈+ y :: l ↔ y = x ∧ x ∈ l ∨ x ∈+ l",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"List.Duplicate.cons_duplicate",
"Eq.mpr",
"List.Duplicate.cons_mem",
"HEq.refl",
"List.duplicate_cons_self_iff._simp_1",
"M... | [] | refine ⟨fun h => ?_, fun h => ?_⟩
· obtain hm | hm := h
· exact Or.inl ⟨rfl, hm⟩
· exact Or.inr hm
· rcases h with (⟨rfl | h⟩ | h)
· simpa
· exact h.cons_duplicate | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Fin.Tuple.Basic | {
"line": 520,
"column": 43
} | {
"line": 523,
"column": 28
} | {
"line": 525,
"column": 0
} | [
{
"pp": "n : ℕ\nα : Fin (n + 1) → Sort u_1\nx : α (last n)\np : (i : Fin n) → α i.castSucc\n⊢ init (snoc p x) = p",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"dite_congr",
"instDecidableTrue",
"_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.init_snoc._sim... | [] | by
ext i
simp only [init, snoc, val_castSucc, is_lt, dite_true]
convert! cast_eq rfl (p i) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Fin.Tuple.Basic | {
"line": 675,
"column": 6
} | {
"line": 675,
"column": 22
} | {
"line": 675,
"column": 22
} | [
{
"pp": "n m : ℕ\nα : Sort u_2\nxs : Fin n → α\ny : α\nys : Fin m → α\n⊢ append xs (cons y ys) = append (snoc xs y) ys ∘ Fin.cast ⋯",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Fin.cons",
"Function.comp",
"Fin.append_left_snoc",
... | [
"n m : ℕ\nα : Sort u_2\nxs : Fin n → α\ny : α\nys : Fin m → α\n⊢ append xs (cons y ys) = (append xs (cons y ys) ∘ Fin.cast ⋯) ∘ Fin.cast ⋯"
] | append_left_snoc | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Fin.Tuple.Basic | {
"line": 687,
"column": 6
} | {
"line": 687,
"column": 46
} | {
"line": 688,
"column": 6
} | [
{
"pp": "case pos\nm n : ℕ\nα : Sort u_2\na : α\nas : Fin n → α\nbs : Fin m → α\ni : ℕ\nisLt✝ : i + 1 < n + 1 + m\nh : i + 1 < n + 1\n⊢ cases a as ⟨i + 1, ⋯⟩ = cases a (addCases as bs) (Fin.cast ⋯ ⟨i + 1, isLt✝⟩)",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Nat",
"LT.lt",
... | [
"case pos\nm n : ℕ\nα : Sort u_2\na : α\nas : Fin n → α\nbs : Fin m → α\ni : ℕ\nisLt✝ : i + 1 < n + 1 + m\nh : i + 1 < n + 1\nthis : i < n\n⊢ cases a as ⟨i + 1, ⋯⟩ = cases a (addCases as bs) (Fin.cast ⋯ ⟨i + 1, isLt✝⟩)"
] | have : i < n := Nat.lt_of_succ_lt_succ h | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Data.Fin.Tuple.Basic | {
"line": 702,
"column": 4
} | {
"line": 703,
"column": 37
} | {
"line": 704,
"column": 2
} | [
{
"pp": "case neg\nm n : ℕ\nα : Sort u_2\nas : Fin n → α\nbs : Fin m → α\nb : α\ni : ℕ\nisLt : i < n + (m + 1)\nlt_n : ¬i < n\nsub_lt : i - n < m\nnlt_add : ¬i < n + m\n⊢ bs ⟨i - n, ⋯⟩ = b",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"False",
"Nat.sub_lt_right_of_lt_add",
... | [] | obtain rfl := Nat.eq_of_le_of_lt_succ (Nat.not_lt.mp nlt_add) isLt
simp [Nat.add_comm n m] at sub_lt | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Fin.Tuple.Basic | {
"line": 702,
"column": 4
} | {
"line": 703,
"column": 37
} | {
"line": 704,
"column": 2
} | [
{
"pp": "case neg\nm n : ℕ\nα : Sort u_2\nas : Fin n → α\nbs : Fin m → α\nb : α\ni : ℕ\nisLt : i < n + (m + 1)\nlt_n : ¬i < n\nsub_lt : i - n < m\nnlt_add : ¬i < n + m\n⊢ bs ⟨i - n, ⋯⟩ = b",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"False",
"Nat.sub_lt_right_of_lt_add",
... | [] | obtain rfl := Nat.eq_of_le_of_lt_succ (Nat.not_lt.mp nlt_add) isLt
simp [Nat.add_comm n m] at sub_lt | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Fintype.EquivFin | {
"line": 244,
"column": 2
} | {
"line": 244,
"column": 13
} | {
"line": 244,
"column": 13
} | [
{
"pp": "α : Type u_1\ninst✝ : Fintype α\n⊢ 1 < card α ↔ Nontrivial α",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Nontrivial",
"Eq.mpr",
"Mathlib.Tactic.Contrapose.contrapose_iff₁",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Finty... | [
"α : Type u_1\ninst✝ : Fintype α\n⊢ card α ≤ 1 ↔ Subsingleton α"
] | contrapose! | Mathlib.Tactic.Contrapose._aux_Mathlib_Tactic_Contrapose___macroRules_Mathlib_Tactic_Contrapose_contrapose!_1 | Mathlib.Tactic.Contrapose.contrapose! |
Mathlib.Data.Fintype.EquivFin | {
"line": 558,
"column": 35
} | {
"line": 558,
"column": 63
} | {
"line": 558,
"column": 63
} | [
{
"pp": "α : Type u_4\ninst✝ : Infinite α\nn : ℕ\n⊢ #(map (natEmbedding α) (range n)) = n",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Finset.card_map",
"Finset.card_range",
"Finset.map",
"id",
"Finset.range",
"Nat",
... | [] | by rw [card_map, card_range] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Fin.Tuple.Basic | {
"line": 955,
"column": 2
} | {
"line": 962,
"column": 23
} | {
"line": 964,
"column": 0
} | [
{
"pp": "n : ℕ\nα : Fin (n + 1) → Sort u_1\nx : α (last n)\np : (j : Fin n) → α ((last n).succAbove j)\n⊢ (last n).insertNth x p = snoc (fun j ↦ cast ⋯ (p j)) x",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Fin.succAbove_last",
"Fin.succAbove",
"Eq.mpr... | [] | refine insertNth_eq_iff.2 ⟨by simp, ?_⟩
ext j
apply eq_of_heq
trans snoc (fun j ↦ _root_.cast (congr_arg α (succAbove_last_apply j)) (p j)) x j.castSucc
· rw [snoc_castSucc]
exact (cast_heq _ _).symm
· apply congr_arg_heq
rw [succAbove_last] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Fin.Tuple.Basic | {
"line": 955,
"column": 2
} | {
"line": 962,
"column": 23
} | {
"line": 964,
"column": 0
} | [
{
"pp": "n : ℕ\nα : Fin (n + 1) → Sort u_1\nx : α (last n)\np : (j : Fin n) → α ((last n).succAbove j)\n⊢ (last n).insertNth x p = snoc (fun j ↦ cast ⋯ (p j)) x",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Fin.succAbove_last",
"Fin.succAbove",
"Eq.mpr... | [] | refine insertNth_eq_iff.2 ⟨by simp, ?_⟩
ext j
apply eq_of_heq
trans snoc (fun j ↦ _root_.cast (congr_arg α (succAbove_last_apply j)) (p j)) x j.castSucc
· rw [snoc_castSucc]
exact (cast_heq _ _).symm
· apply congr_arg_heq
rw [succAbove_last] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Finset.Fold | {
"line": 110,
"column": 8
} | {
"line": 110,
"column": 24
} | {
"line": 110,
"column": 24
} | [
{
"pp": "case pos\nα : Type u_1\nβ : Type u_2\nop : β → β → β\nhc : Std.Commutative op\nha : Std.Associative op\nf : α → β\nb : β\ns : Finset α\na : α\ninst✝ : DecidableEq α\nhi : Std.IdempotentOp op\nh : a ∈ s\n⊢ fold op b f (insert a s) = op (f a) (fold op b f s)",
"ppTerm": "?pos✝",
"assigned": true,... | [
"case pos\nα : Type u_1\nβ : Type u_2\nop : β → β → β\nhc : Std.Commutative op\nha : Std.Associative op\nf : α → β\nb : β\ns : Finset α\na : α\ninst✝ : DecidableEq α\nhi : Std.IdempotentOp op\nh : a ∈ s\n⊢ fold op b f (insert a (insert a (s.erase a))) = op (f a) (fold op b f (insert a (s.erase a)))"
] | ← insert_erase h | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Finset.Fold | {
"line": 161,
"column": 4
} | {
"line": 165,
"column": 10
} | {
"line": 167,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nop : β → β → β\nhc : Std.Commutative op\nha : Std.Associative op\nf : α → β\nb : β\ns : Finset α\nr : β → β → Prop\nhr : ∀ {x y z : β}, r x (op y z) ↔ r x y ∨ r x z\nc : β\n⊢ r c (fold op b f s) ↔ r c b ∨ ∃ x ∈ s, r c (f x)",
"ppTerm": "?m.15",
"assigned": true,
... | [] | induction s using Finset.induction_on with
| empty => simp
| insert a s ha IH =>
rw [Finset.fold_insert ha, hr, IH, ← or_assoc, @or_comm (r c (f a)), or_assoc]
simp | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | Lean.Parser.Tactic.induction |
Mathlib.Data.Finset.Fold | {
"line": 161,
"column": 4
} | {
"line": 165,
"column": 10
} | {
"line": 167,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nop : β → β → β\nhc : Std.Commutative op\nha : Std.Associative op\nf : α → β\nb : β\ns : Finset α\nr : β → β → Prop\nhr : ∀ {x y z : β}, r x (op y z) ↔ r x y ∨ r x z\nc : β\n⊢ r c (fold op b f s) ↔ r c b ∨ ∃ x ∈ s, r c (f x)",
"ppTerm": "?m.15",
"assigned": true,
... | [] | induction s using Finset.induction_on with
| empty => simp
| insert a s ha IH =>
rw [Finset.fold_insert ha, hr, IH, ← or_assoc, @or_comm (r c (f a)), or_assoc]
simp | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Finset.Fold | {
"line": 161,
"column": 4
} | {
"line": 165,
"column": 10
} | {
"line": 167,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nop : β → β → β\nhc : Std.Commutative op\nha : Std.Associative op\nf : α → β\nb : β\ns : Finset α\nr : β → β → Prop\nhr : ∀ {x y z : β}, r x (op y z) ↔ r x y ∨ r x z\nc : β\n⊢ r c (fold op b f s) ↔ r c b ∨ ∃ x ∈ s, r c (f x)",
"ppTerm": "?m.15",
"assigned": true,
... | [] | induction s using Finset.induction_on with
| empty => simp
| insert a s ha IH =>
rw [Finset.fold_insert ha, hr, IH, ← or_assoc, @or_comm (r c (f a)), or_assoc]
simp | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Finset.Union | {
"line": 114,
"column": 77
} | {
"line": 115,
"column": 24
} | {
"line": 117,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝ : DecidableEq β\ns : Finset α\nt : Finset β\nf : α → β\nh : ∀ x ∈ s, f x ∈ t\n⊢ t.disjiUnion (fun a ↦ {x ∈ s | f x = a}) ⋯ = s",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.disjiUnion_filter_eq",
"congrArg",
... | [] | by
simpa [filter_eq_self] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Nat.Choose.Basic | {
"line": 114,
"column": 8
} | {
"line": 114,
"column": 24
} | {
"line": 114,
"column": 25
} | [
{
"pp": "case succ\nn : ℕ\nih : n.choose 2 = n * (n - 1) / 2\n⊢ (n + 1).choose 2 = (n + 1) * (n + 1 - 1) / 2",
"ppTerm": "?succ",
"assigned": true,
"usedConstants": [
"Nat.triangle_succ",
"Eq.mpr",
"Nat.choose",
"instHDiv",
"HMul.hMul",
"congrArg",
"HSub.hSu... | [
"case succ\nn : ℕ\nih : n.choose 2 = n * (n - 1) / 2\n⊢ (n + 1).choose 2 = n * (n - 1) / 2 + n"
] | triangle_succ n, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.List.OffDiag | {
"line": 115,
"column": 2
} | {
"line": 121,
"column": 62
} | {
"line": 123,
"column": 0
} | [
{
"pp": "α : Type u_1\nl : List α\nh : l.Nodup\nx : α × α\n⊢ x ∈ l.offDiag ↔ x.fst ∈ l ∧ x.snd ∈ l ∧ x.fst ≠ x.snd",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Eq.mpr",
"Iff.of_eq",
"_private.Mathlib.Data.List.OffDiag.0.List.Nodup.mem_offDiag._simp_1_... | [] | rcases x with ⟨x, y⟩
simp_rw [mem_offDiag_iff_getElem, mem_iff_getElem, Ne]
constructor
· rintro ⟨i, hi, j, hj, hne, rfl, rfl⟩
exact ⟨⟨i, hi, rfl⟩, ⟨j, hj, rfl⟩, mt h.getElem_inj_iff.1 hne⟩
· rintro ⟨⟨i, hi, rfl⟩, ⟨j, hj, rfl⟩, hne⟩
exact ⟨i, hi, j, hj, mt h.getElem_inj_iff.2 hne, rfl, rfl⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.List.OffDiag | {
"line": 115,
"column": 2
} | {
"line": 121,
"column": 62
} | {
"line": 123,
"column": 0
} | [
{
"pp": "α : Type u_1\nl : List α\nh : l.Nodup\nx : α × α\n⊢ x ∈ l.offDiag ↔ x.fst ∈ l ∧ x.snd ∈ l ∧ x.fst ≠ x.snd",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Eq.mpr",
"Iff.of_eq",
"_private.Mathlib.Data.List.OffDiag.0.List.Nodup.mem_offDiag._simp_1_... | [] | rcases x with ⟨x, y⟩
simp_rw [mem_offDiag_iff_getElem, mem_iff_getElem, Ne]
constructor
· rintro ⟨i, hi, j, hj, hne, rfl, rfl⟩
exact ⟨⟨i, hi, rfl⟩, ⟨j, hj, rfl⟩, mt h.getElem_inj_iff.1 hne⟩
· rintro ⟨⟨i, hi, rfl⟩, ⟨j, hj, rfl⟩, hne⟩
exact ⟨i, hi, j, hj, mt h.getElem_inj_iff.2 hne, rfl, rfl⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.