file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Data/Nat/PartENat.lean | PartENat.get_one | [] | [
201,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/RingTheory/Ideal/Over.lean | Ideal.IsIntegralClosure.eq_bot_of_comap_eq_bot | [
{
"state_after": "R : Type u_1\ninst✝⁹ : CommRing R\nS : Type ?u.516571\ninst✝⁸ : CommRing S\nf : R →+* S\nI✝ J : Ideal S\ninst✝⁷ : Algebra R S\nA : Type u_2\ninst✝⁶ : CommRing A\ninst✝⁵ : Algebra R A\ninst✝⁴ : Algebra A S\ninst✝³ : IsScalarTower R A S\ninst✝² : IsIntegralClosure A R S\ninst✝¹ : IsDomain A\nins... | [
335,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.rightInvOn | [] | [
181,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
11
] |
Mathlib/Order/Disjoint.lean | IsCompl.sup_inf | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : DistribLattice α\ninst✝ : BoundedOrder α\na b x y z x' y' : α\nh : IsCompl x y\nh' : IsCompl x' y'\n⊢ (x ⊔ x') ⊓ (y ⊓ y') = ⊥",
"tactic": "rw [inf_sup_right, ← inf_assoc, h.inf_eq_bot, bot_inf_eq, bot_sup_eq, inf_left_comm,\nh'.inf_eq_... | [
571,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
566,
1
] |
Mathlib/Analysis/Calculus/IteratedDeriv.lean | iteratedDerivWithin_eq_iteratedFDerivWithin | [] | [
84,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Combinatorics/SimpleGraph/Coloring.lean | SimpleGraph.chromaticNumber_pos | [
{
"state_after": "V : Type u\nG : SimpleGraph V\nα : Type v\nC : Coloring G α\ninst✝ : Nonempty V\nn : ℕ\nhc : Colorable G n\n⊢ ∀ (b : ℕ), b ∈ {n | Colorable G n} → Nat.succ 0 ≤ b",
"state_before": "V : Type u\nG : SimpleGraph V\nα : Type v\nC : Coloring G α\ninst✝ : Nonempty V\nn : ℕ\nhc : Colorable G n\n⊢... | [
311,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/GroupTheory/Congruence.lean | Con.ker_eq_lift_of_injective | [] | [
1010,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1009,
1
] |
Mathlib/Algebra/GCDMonoid/Finset.lean | Finset.lcm_eq_lcm_image | [] | [
122,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Order/Ideal.lean | IsCoatom.isProper | [] | [
229,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Combinatorics/Colex.lean | Colex.mem_le_of_singleton_le | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrder α\nr : α\ns : Finset α\n⊢ ¬toColex s < toColex {r} ↔ ∃ x, x ∈ s ∧ ¬x < r",
"state_before": "α : Type u_1\ninst✝ : LinearOrder α\nr : α\ns : Finset α\n⊢ toColex {r} ≤ toColex s ↔ ∃ x, x ∈ s ∧ r ≤ x",
"tactic": "simp only [← not_lt]"
},
{
"state_... | [
296,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Disjoint.exists_cthickenings | [
{
"state_after": "case intro.intro\nι : Sort ?u.135640\nα : Type u\nβ : Type v\ninst✝ : PseudoEMetricSpace α\nδ✝ ε : ℝ\ns t : Set α\nx : α\nhst : Disjoint s t\nhs : IsCompact s\nht : IsClosed t\nδ : ℝ\nhδ : 0 < δ\nh : Disjoint (thickening δ s) (thickening δ t)\n⊢ ∃ δ, 0 < δ ∧ Disjoint (cthickening δ s) (cthicke... | [
1269,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1264,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.cof_sup_le_lift | [
{
"state_after": "α : Type ?u.29854\nr : α → α → Prop\nι : Type u\nf : ι → Ordinal\nH : (sup fun i => f i) = lsub fun i => f i\n⊢ cof (sup f) ≤ Cardinal.lift (#ι)",
"state_before": "α : Type ?u.29854\nr : α → α → Prop\nι : Type u\nf : ι → Ordinal\nH : ∀ (i : ι), f i < sup f\n⊢ cof (sup f) ≤ Cardinal.lift (#... | [
347,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/RingTheory/Congruence.lean | RingCon.refl | [] | [
108,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
11
] |
Mathlib/Analysis/Normed/Group/BallSphere.lean | coe_neg_ball | [] | [
47,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
9
] |
Mathlib/CategoryTheory/Shift/Basic.lean | CategoryTheory.shift_shiftFunctorCompIsoId_add_neg_self_inv_app | [
{
"state_after": "no goals",
"state_before": "C : Type u\nA : Type u_1\ninst✝² : Category C\ninst✝¹ : AddGroup A\ninst✝ : HasShift C A\nX✝ Y : C\nf : X✝ ⟶ Y\nn : A\nX : C\n⊢ (shiftFunctor C n).map ((shiftFunctorCompIsoId C n (-n) (_ : n + -n = 0)).inv.app X) =\n (shiftFunctorCompIsoId C (-n) n (_ : -n + ... | [
532,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | mul_lt_of_one_lt_left | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.87941\ninst✝ : StrictOrderedRing α\na b c : α\nhb : b < 0\nh : 1 < a\n⊢ a * b < b",
"tactic": "simpa only [one_mul] using mul_lt_mul_of_neg_right h hb"
}
] | [
709,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
708,
1
] |
Mathlib/Combinatorics/SimpleGraph/Hasse.lean | SimpleGraph.pathGraph_connected | [] | [
114,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Topology/LocallyConstant/Basic.lean | IsLocallyConstant.mul | [] | [
206,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.mem_pairSep | [
{
"state_after": "p : ZFSet → ZFSet → Prop\nx y z : ZFSet\ne : ∃ a, a ∈ x ∧ ∃ b, b ∈ y ∧ z = pair a b ∧ p a b\n⊢ z ∈ powerset (powerset (x ∪ y))",
"state_before": "p : ZFSet → ZFSet → Prop\nx y z : ZFSet\n⊢ z ∈ pairSep p x y ↔ ∃ a, a ∈ x ∧ ∃ b, b ∈ y ∧ z = pair a b ∧ p a b",
"tactic": "refine' mem_sep.t... | [
1308,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1300,
1
] |
Mathlib/LinearAlgebra/Matrix/Trace.lean | Matrix.trace_neg | [] | [
127,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.abs_sub_le_of_uIcc_subset_uIcc | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\na b c d : α\nh : [[c, d]] ⊆ [[a, b]]\n⊢ max c d - min c d ≤ max a b - min a b",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\na b c d : α\nh : [[c, d]] ⊆ [[a, b]]\n⊢ abs (d - c) ≤ abs (b - a)",
"tactic": "rw [← ma... | [
484,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/Order/Bounded.lean | Set.bounded_ge_Ioi | [] | [
199,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.diam_mono | [] | [
2692,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2691,
1
] |
Mathlib/GroupTheory/Subsemigroup/Center.lean | Set.center_units_subset | [
{
"state_after": "case inl\nM : Type u_1\ninst✝ : GroupWithZero M\na : Mˣ\nha : a ∈ center Mˣ\n⊢ 0 * ↑a = ↑a * 0\n\ncase inr\nM : Type u_1\ninst✝ : GroupWithZero M\na : Mˣ\nha : a ∈ center Mˣ\nb : M\nhb : b ≠ 0\n⊢ b * ↑a = ↑a * b",
"state_before": "M : Type u_1\ninst✝ : GroupWithZero M\na : Mˣ\nha : a ∈ cen... | [
97,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_eq_of_ae_eq_trim | [] | [
4396,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4394,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | irreducible_iff_prime_of_exists_prime_factors | [
{
"state_after": "case pos\nα : Type u_1\ninst✝ : CancelCommMonoidWithZero α\npf : ∀ (a : α), a ≠ 0 → ∃ f, (∀ (b : α), b ∈ f → Prime b) ∧ Multiset.prod f ~ᵤ a\np : α\nhp0 : p = 0\n⊢ Irreducible p ↔ Prime p\n\ncase neg\nα : Type u_1\ninst✝ : CancelCommMonoidWithZero α\npf : ∀ (a : α), a ≠ 0 → ∃ f, (∀ (b : α), b ... | [
337,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.map_one_add | [
{
"state_after": "no goals",
"state_before": "f g : CircleDeg1Lift\nx : ℝ\n⊢ ↑f (1 + x) = 1 + ↑f x",
"tactic": "rw [add_comm, map_add_one, add_comm 1]"
}
] | [
167,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Data/List/Lattice.lean | List.count_bagInter | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl l₁ l₂✝ : List α\np : α → Prop\na✝ : α\ninst✝ : DecidableEq α\na : α\nl₂ : List α\n⊢ count a (List.bagInter [] l₂) = min (count a []) (count a l₂)",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl ... | [
264,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | abs_lt_of_sq_lt_sq' | [] | [
714,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
713,
1
] |
Mathlib/Algebra/Homology/Augment.lean | ChainComplex.chainComplex_d_succ_succ_zero | [
{
"state_after": "case a\nV : Type u\ninst✝¹ : Category V\ninst✝ : HasZeroMorphisms V\nC : ChainComplex V ℕ\ni : ℕ\n⊢ ¬ComplexShape.Rel (ComplexShape.down ℕ) (i + 2) 0",
"state_before": "V : Type u\ninst✝¹ : Category V\ninst✝ : HasZeroMorphisms V\nC : ChainComplex V ℕ\ni : ℕ\n⊢ d C (i + 2) 0 = 0",
"tact... | [
136,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | MulEquiv.map_finprod | [] | [
331,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.coeff_C_mul_X_pow | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nx : R\nk n : ℕ\n⊢ ↑(coeff R n) (↑(C R) x * X ^ k) = if n = k then x else 0",
"tactic": "simp [X_pow_eq, coeff_monomial]"
}
] | [
1580,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1578,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.ofReal_ofNat | [] | [
653,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
652,
1
] |
Std/Data/String/Lemmas.lean | Substring.prev_zero | [
{
"state_after": "no goals",
"state_before": "s : Substring\n⊢ prev s 0 = 0",
"tactic": "simp [prev, Pos.add_eq]"
}
] | [
765,
87
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
765,
9
] |
Mathlib/Order/Hom/Lattice.lean | SupBotHom.dual_comp | [] | [
1458,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1456,
1
] |
Mathlib/Analysis/Normed/Field/InfiniteSum.lean | summable_norm_sum_mul_range_of_summable_norm | [
{
"state_after": "R : Type u_1\nι : Type ?u.10189\nι' : Type ?u.10192\ninst✝ : NormedRing R\nf g : ℕ → R\nhf : Summable fun x => ‖f x‖\nhg : Summable fun x => ‖g x‖\n⊢ Summable fun n => ‖∑ ij in antidiagonal n, f ij.fst * g ij.snd‖",
"state_before": "R : Type u_1\nι : Type ?u.10189\nι' : Type ?u.10192\ninst... | [
105,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.nat_lt_card | [
{
"state_after": "α : Type ?u.236919\nβ : Type ?u.236922\nγ : Type ?u.236925\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\no : Ordinal\nn : ℕ\n⊢ ↑(Nat.succ n) ≤ o ↔ succ ↑n ≤ o",
"state_before": "α : Type ?u.236919\nβ : Type ?u.236922\nγ : Type ?u.236925\nr : α → α → Prop\ns : β → β → Prop\nt : γ →... | [
1567,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1565,
1
] |
Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.casesOn_one | [] | [
192,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Analysis/SpecialFunctions/Exponential.lean | hasFDerivAt_exp_of_mem_ball | [
{
"state_after": "𝕂 : Type u_1\n𝔸 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕂\ninst✝³ : NormedCommRing 𝔸\ninst✝² : NormedAlgebra 𝕂 𝔸\ninst✝¹ : CompleteSpace 𝔸\ninst✝ : CharZero 𝕂\nx : 𝔸\nhx : x ∈ EMetric.ball 0 (FormalMultilinearSeries.radius (expSeries 𝕂 𝔸))\nhpos : 0 < FormalMultilinearSeries.ra... | [
110,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.div_left_inj | [
{
"state_after": "m n k a b d : ℕ\nhda : d ∣ a\nhdb : d ∣ b\nh : a / d = b / d\n⊢ a = b",
"state_before": "m n k a b d : ℕ\nhda : d ∣ a\nhdb : d ∣ b\n⊢ a / d = b / d ↔ a = b",
"tactic": "refine ⟨fun h => ?_, congr_arg fun n => n / d⟩"
},
{
"state_after": "no goals",
"state_before": "m n k a ... | [
687,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
11
] |
Mathlib/RingTheory/Nilpotent.lean | Commute.isNilpotent_mul_right | [
{
"state_after": "R S : Type u\nx y : R\ninst✝ : Semiring R\nh_comm : Commute x y\nh : IsNilpotent y\n⊢ IsNilpotent (y * x)",
"state_before": "R S : Type u\nx y : R\ninst✝ : Semiring R\nh_comm : Commute x y\nh : IsNilpotent y\n⊢ IsNilpotent (x * y)",
"tactic": "rw [h_comm.eq]"
},
{
"state_after"... | [
166,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Data/Set/Basic.lean | Set.strictMonoOn_singleton | [] | [
2704,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2703,
1
] |
Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.kernel_sum_seq | [] | [
288,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Algebra/Field/Basic.lean | one_div_mul_sub_mul_one_div_eq_one_div_add_one_div | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.42728\nβ : Type ?u.42731\nK : Type u_1\ninst✝ : DivisionRing K\na b c d : K\nha : a ≠ 0\nhb : b ≠ 0\n⊢ 1 / a * (b - a) * (1 / b) = 1 / a - 1 / b",
"tactic": "rw [mul_sub_left_distrib (1 / a), one_div_mul_cancel ha, mul_sub_right_distrib, one_mul,... | [
184,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | Ideal.fg_of_isUnit | [
{
"state_after": "R : Type u_1\ninst✝⁶ : CommRing R\nS : Submonoid R\nP : Type u_2\ninst✝⁵ : CommRing P\ninst✝⁴ : Algebra R P\nloc : IsLocalization S P\nP' : Type ?u.763155\ninst✝³ : CommRing P'\ninst✝² : Algebra R P'\nloc' : IsLocalization S P'\nP'' : Type ?u.763608\ninst✝¹ : CommRing P''\ninst✝ : Algebra R P'... | [
890,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
887,
1
] |
Mathlib/RingTheory/Derivation/Basic.lean | Derivation.coe_injective | [] | [
102,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | gcd_dvd_gcd | [] | [
426,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/Analysis/Calculus/BumpFunctionInner.lean | ContDiffBump.sub | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\nX : Type ?u.74038\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : NormedAddCommGroup X\ninst✝¹ : NormedSpace ℝ X\ninst✝ : HasContDiffBump E\nc : E\nf : ContDiffBump c\nx✝ : E\nn : ℕ∞\nx : E\n⊢ ↑f (c - x) = ↑f (c + x)",
"tacti... | [
376,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
11
] |
Mathlib/Order/CompleteLattice.lean | Monotone.iSup_comp_eq | [] | [
996,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
994,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioo_union_Ioi' | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.77673\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\nh₁ : c < b\nx : α\n⊢ x ∈ Ioo a b ∪ Ioi c ↔ x ∈ Ioi (min a c)",
"state_before": "α : Type u_1\nβ : Type ?u.77673\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\nh₁ : c < b\n⊢ Ioo a b ∪ Ioi c = Ioi (min... | [
1247,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1241,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.IsRadical.comap | [
{
"state_after": "R : Type u\nS : Type v\nF : Type u_1\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nrc : RingHomClass F R S\nf : F\nI J : Ideal R\nK L : Ideal S\nhK : IsRadical K\n⊢ IsRadical (Ideal.radical (Ideal.comap f K))",
"state_before": "R : Type u\nS : Type v\nF : Type u_1\ninst✝¹ : CommRing R\ninst✝ :... | [
1815,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1813,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.succ_ne_zero | [] | [
1089,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1088,
1
] |
Std/Data/String/Lemmas.lean | String.default_eq | [] | [
20,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
20,
9
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.bijective | [] | [
172,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
11
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.Memℒp.of_le_mul | [] | [
1327,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1323,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | CommGroup.center_eq_top | [
{
"state_after": "G✝ : Type ?u.362185\nG' : Type ?u.362188\ninst✝³ : Group G✝\ninst✝² : Group G'\nA : Type ?u.362197\ninst✝¹ : AddGroup A\nH K : Subgroup G✝\nG : Type u_1\ninst✝ : CommGroup G\n⊢ ∀ (x : G), x ∈ center G",
"state_before": "G✝ : Type ?u.362185\nG' : Type ?u.362188\ninst✝³ : Group G✝\ninst✝² : ... | [
2102,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2099,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.lt_one_add_iff | [
{
"state_after": "no goals",
"state_before": "m n k a b : ℕ\n⊢ a < 1 + b ↔ a ≤ b",
"tactic": "simp only [add_comm, lt_succ_iff]"
}
] | [
224,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Data/Fintype/Sum.lean | infinite_sum | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nH : Infinite (α ⊕ β)\n⊢ Infinite α ∨ Infinite β",
"state_before": "α : Type u_2\nβ : Type u_1\n⊢ Infinite (α ⊕ β) ↔ Infinite α ∨ Infinite β",
"tactic": "refine' ⟨fun H => _, fun H => H.elim (@Sum.infinite_of_left α β) (@Sum.infinite_of_right α β)⟩"
},
{
... | [
145,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Topology/Basic.lean | clusterPt_iff_not_disjoint | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\na : α\ns s₁ s₂ t : Set α\np p₁ p₂ : α → Prop\ninst✝ : TopologicalSpace α\nx : α\nF : Filter α\n⊢ ClusterPt x F ↔ ¬Disjoint (𝓝 x) F",
"tactic": "rw [disjoint_iff, ClusterPt, neBot_iff]"
}
] | [
1100,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1098,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.one_mul | [
{
"state_after": "no goals",
"state_before": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na : R\n⊢ Nat.rawCast 1 * a = a",
"tactic": "simp [Nat.rawCast]"
}
] | [
354,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieModuleHom.coe_injective | [
{
"state_after": "case mk.mk.mk.mk.mk.mk\nR : Type u\nL : Type v\nM : Type w\nN : Type w₁\nP : Type w₂\ninst✝¹⁴ : CommRing R\ninst✝¹³ : LieRing L\ninst✝¹² : LieAlgebra R L\ninst✝¹¹ : AddCommGroup M\ninst✝¹⁰ : AddCommGroup N\ninst✝⁹ : AddCommGroup P\ninst✝⁸ : Module R M\ninst✝⁷ : Module R N\ninst✝⁶ : Module R P\... | [
799,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
797,
1
] |
Mathlib/Probability/CondCount.lean | ProbabilityTheory.condCount_disjoint_union | [
{
"state_after": "case inl.inl\nΩ : Type u_1\ninst✝¹ : MeasurableSpace Ω\ninst✝ : MeasurableSingletonClass Ω\nu : Set Ω\nhs ht : Set.Finite ∅\nhst : Disjoint ∅ ∅\n⊢ ↑↑(condCount ∅) u * ↑↑(condCount (∅ ∪ ∅)) ∅ + ↑↑(condCount ∅) u * ↑↑(condCount (∅ ∪ ∅)) ∅ = ↑↑(condCount (∅ ∪ ∅)) u\n\ncase inl.inr\nΩ : Type u_1\n... | [
191,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.size_balanceL | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : Ordnode α\nx : α\nr : Ordnode α\nhl : Balanced l\nhr : Balanced r\nsl : Sized l\nsr : Sized r\nH : (∃ l', Raised l' (size l) ∧ BalancedSz l' (size r)) ∨ ∃ r', Raised (size r) r' ∧ BalancedSz (size l) r'\n⊢ size (balanceL l x r) = size l + size ... | [
852,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
848,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.le_def | [] | [
333,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.Poly.of_denote_le_cancelAux | [
{
"state_after": "no goals",
"state_before": "case zero\nctx : Context\nm₁ m₂ r₁ r₂ : Poly\nh : denote_le ctx (cancelAux zero m₁ m₂ r₁ r₂)\n⊢ denote_le ctx (List.reverse r₁ ++ m₁, List.reverse r₂ ++ m₂)",
"tactic": "assumption"
},
{
"state_after": "case succ\nctx : Context\nfuel : Nat\nih :\n ∀... | [
494,
23
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
463,
1
] |
Mathlib/Data/Set/Basic.lean | Set.bot_eq_empty | [] | [
108,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Data/Multiset/Fintype.lean | Multiset.coe_eq | [
{
"state_after": "case mk\nα : Type u_1\ninst✝ : DecidableEq α\nm : Multiset α\ny : ToType m\nfst✝ : α\nsnd✝ : Fin (count fst✝ m)\n⊢ { fst := fst✝, snd := snd✝ }.fst = y.fst ↔ { fst := fst✝, snd := snd✝ }.fst = y.fst",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\nm : Multiset α\nx y : ToType m\n⊢ x... | [
82,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.absorbent_ball | [
{
"state_after": "R : Type ?u.1242330\nR' : Type ?u.1242333\n𝕜 : Type u_2\n𝕜₂ : Type ?u.1242339\n𝕜₃ : Type ?u.1242342\n𝕝 : Type ?u.1242345\nE : Type u_1\nE₂ : Type ?u.1242351\nE₃ : Type ?u.1242354\nF : Type ?u.1242357\nG : Type ?u.1242360\nι : Type ?u.1242363\ninst✝² : NormedField 𝕜\ninst✝¹ : AddCommGroup ... | [
998,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
995,
11
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_le_degree | [
{
"state_after": "case pos\nR : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nh : coeff q (natDegree p) ≠ 0\nhp : p = 0\n⊢ degree p ≤ degree q\n\ncase neg\nR : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nh : coeff q (natDegree p) ≠ 0\nhp : ¬p = 0\n⊢ ... | [
215,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.span_closure | [] | [
145,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.compl_mem_comap | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.227630\nι : Sort x\nf : α → β\nl : Filter β\np : α → Prop\ns : Set α\n⊢ sᶜ ∈ comap f l ↔ (f '' s)ᶜ ∈ l",
"tactic": "rw [mem_comap_iff_compl, compl_compl]"
}
] | [
1928,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1928,
1
] |
Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.signBijAux_inj | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝ : DecidableEq α\nn : ℕ\nf : Perm (Fin n)\nx✝¹ x✝ : (_ : Fin n) × Fin n\na₁ a₂ : Fin n\nha : { fst := a₁, snd := a₂ } ∈ finPairsLT n\nb₁ b₂ : Fin n\nhb : { fst := b₁, snd := b₂ } ∈ finPairsLT n\nh :\n (if x : ↑f { fst := a₁, snd := a₂ }.snd < ↑f { fst := a₁, snd :... | [
343,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/Algebra/Algebra/Hom.lean | AlgHom.one_apply | [] | [
441,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
Std/Data/String/Lemmas.lean | String.atEnd_of_valid | [
{
"state_after": "cs cs' : List Char\n⊢ utf8Len cs + utf8Len cs' ≤ utf8Len cs ↔ cs' = []",
"state_before": "cs cs' : List Char\n⊢ atEnd { data := cs ++ cs' } { byteIdx := utf8Len cs } = true ↔ cs' = []",
"tactic": "simp [atEnd_iff]"
},
{
"state_after": "no goals",
"state_before": "cs cs' : L... | [
307,
73
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
304,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Iio_union_Ico_eq_Iio | [] | [
1380,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1378,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | HasDerivWithinAt.rpow_const | [
{
"state_after": "case h.e'_7\nf g : ℝ → ℝ\nf' g' x y p : ℝ\ns : Set ℝ\nhf : HasDerivWithinAt f f' s x\nhx : f x ≠ 0 ∨ 1 ≤ p\n⊢ f' * p * f x ^ (p - 1) = p * f x ^ (p - 1) * f'",
"state_before": "f g : ℝ → ℝ\nf' g' x y p : ℝ\ns : Set ℝ\nhf : HasDerivWithinAt f f' s x\nhx : f x ≠ 0 ∨ 1 ≤ p\n⊢ HasDerivWithinAt... | [
583,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
580,
1
] |
Mathlib/Algebra/Regular/Basic.lean | IsLeftRegular.mul | [] | [
103,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | ContinuousLinearEquiv.comp_differentiableWithinAt_iff | [
{
"state_after": "𝕜 : Type u_2\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_4\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type u_1\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.60346\ninst✝¹... | [
103,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/MeasureTheory/Measure/Content.lean | MeasureTheory.Content.outerMeasure_lt_top_of_isCompact | [
{
"state_after": "case intro.intro\nG : Type w\ninst✝² : TopologicalSpace G\nμ : Content G\ninst✝¹ : T2Space G\ninst✝ : LocallyCompactSpace G\nK : Set G\nhK : IsCompact K\nF : Set G\nh1F : IsCompact F\nh2F : K ⊆ interior F\n⊢ ↑(Content.outerMeasure μ) K < ⊤",
"state_before": "G : Type w\ninst✝² : Topologica... | [
318,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.bddBelow_range_add | [
{
"state_after": "case intro\nR : Type ?u.587125\nR' : Type ?u.587128\n𝕜 : Type u_2\n𝕜₂ : Type ?u.587134\n𝕜₃ : Type ?u.587137\n𝕝 : Type ?u.587140\nE : Type u_1\nE₂ : Type ?u.587146\nE₃ : Type ?u.587149\nF : Type ?u.587152\nG : Type ?u.587155\nι : Type ?u.587158\ninst✝² : NormedField 𝕜\ninst✝¹ : AddCommGrou... | [
463,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
460,
1
] |
Mathlib/GroupTheory/Perm/List.lean | List.mem_of_formPerm_apply_mem | [
{
"state_after": "case nil\nα : Type u_1\nβ : Type ?u.47566\ninst✝ : DecidableEq α\nl : List α\nx✝ x : α\nh : ↑(formPerm []) x ∈ []\n⊢ x ∈ []\n\ncase cons\nα : Type u_1\nβ : Type ?u.47566\ninst✝ : DecidableEq α\nl✝ : List α\nx✝ x y : α\nl : List α\nh : ↑(formPerm (y :: l)) x ∈ y :: l\n⊢ x ∈ y :: l",
"state_... | [
120,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/GroupTheory/Subgroup/Finite.lean | Subgroup.eq_top_of_le_card | [] | [
144,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPolynomial.coe_inj | [] | [
1146,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1145,
1
] |
Mathlib/MeasureTheory/Measure/MutuallySingular.lean | MeasureTheory.Measure.MutuallySingular.add_right_iff | [] | [
110,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | ofMul_prod | [] | [
2333,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2332,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.isometry | [] | [
334,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
11
] |
Mathlib/Topology/Algebra/Order/Floor.lean | tendsto_ceil_right_pure_floor_add_one | [
{
"state_after": "α : Type u_1\nβ : Type ?u.10951\nγ : Type ?u.10954\ninst✝³ : LinearOrderedRing α\ninst✝² : FloorRing α\ninst✝¹ : TopologicalSpace α\ninst✝ : OrderClosedTopology α\nx : α\n⊢ ↑⌊x⌋ ≤ x",
"state_before": "α : Type u_1\nβ : Type ?u.10951\nγ : Type ?u.10954\ninst✝³ : LinearOrderedRing α\ninst✝² ... | [
107,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/RingTheory/Localization/Integral.lean | integralClosure.isFractionRing_of_algebraic | [] | [
370,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Mathlib/GroupTheory/GroupAction/SubMulAction.lean | SubMulAction.zero_mem | [] | [
338,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Std/Data/List/Lemmas.lean | List.isPrefix.eq_of_length | [] | [
1654,
25
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1653,
1
] |
Mathlib/CategoryTheory/Closed/Monoidal.lean | CategoryTheory.MonoidalClosed.uncurry_curry | [] | [
203,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Data/Finsupp/NeLocus.lean | Finsupp.mapRange_neLocus_eq | [
{
"state_after": "case a\nα : Type u_3\nM : Type u_2\nN : Type u_1\nP : Type ?u.12674\ninst✝⁴ : DecidableEq α\ninst✝³ : DecidableEq N\ninst✝² : DecidableEq M\ninst✝¹ : Zero M\ninst✝ : Zero N\nf g : α →₀ N\nF : N → M\nF0 : F 0 = 0\nhF : Function.Injective F\na✝ : α\n⊢ a✝ ∈ neLocus (mapRange F F0 f) (mapRange F F... | [
116,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Data/Rat/NNRat.lean | NNRat.coe_multiset_prod | [] | [
271,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/Data/Nat/Totient.lean | Nat.card_units_zmod_lt_sub_one | [
{
"state_after": "p : ℕ\nhp : 1 < p\ninst✝ : Fintype (ZMod p)ˣ\nthis : NeZero p\n⊢ Fintype.card (ZMod p)ˣ ≤ p - 1",
"state_before": "p : ℕ\nhp : 1 < p\ninst✝ : Fintype (ZMod p)ˣ\n⊢ Fintype.card (ZMod p)ˣ ≤ p - 1",
"tactic": "haveI : NeZero p := ⟨(pos_of_gt hp).ne'⟩"
},
{
"state_after": "p : ℕ\nh... | [
251,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Algebra/Lie/Free.lean | FreeLieAlgebra.liftAux_map_mul | [] | [
202,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.bliminf_sup_le_inf_aux_right | [] | [
903,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
901,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | subset_Icc_csInf_csSup | [] | [
577,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
576,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.normal_subgroupOf_iff | [] | [
3543,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3540,
1
] |
Mathlib/CategoryTheory/Bicategory/Basic.lean | CategoryTheory.Bicategory.pentagon_hom_inv_inv_inv_inv | [
{
"state_after": "no goals",
"state_before": "B : Type u\ninst✝ : Bicategory B\na b c d e : B\nf : a ⟶ b\ng : b ⟶ c\nh : c ⟶ d\ni : d ⟶ e\n⊢ f ◁ (α_ g h i).hom ≫ (α_ f g (h ≫ i)).inv ≫ (α_ (f ≫ g) h i).inv = (α_ f (g ≫ h) i).inv ≫ (α_ f g h).inv ▷ i",
"tactic": "simp [← cancel_epi (f ◁ (α_ g h i).inv)]"... | [
282,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Data/List/Basic.lean | List.findIdx_cons | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.75547\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\ninst✝ : DecidableEq α\np : α → Bool\nb : α\nl : List α\n⊢ findIdx p (b :: l) = bif p b then 0 else findIdx p l + 1",
"tactic": "cases H : p b with\n | true => simp [H, findId... | [
1158,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1145,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.