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/Algebra/Group/Units.lean | Units.mul_right_inj | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Monoid α\na✝ b✝ c✝ u a : αˣ\nb c : α\nh : ↑a * b = ↑a * c\n⊢ b = c",
"tactic": "simpa only [inv_mul_cancel_left] using congr_arg (fun x : α => ↑(a⁻¹ : αˣ) * x) h"
}
] | [
310,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.IntegrableAtFilter.inf_of_left | [] | [
414,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
Mathlib/Algebra/Group/Semiconj.lean | SemiconjBy.inv_right | [] | [
213,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.integralSum_inf_partition | [] | [
108,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | Memℓp.neg_iff | [] | [
177,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Algebra/Group/Basic.lean | inv_eq_iff_eq_inv | [] | [
265,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/Order/CompleteLattice.lean | sSup_le_sSup_of_subset_insert_bot | [] | [
515,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
514,
1
] |
Mathlib/GroupTheory/Exponent.lean | Monoid.exponent_ne_zero_iff_range_orderOf_finite | [
{
"state_after": "case refine'_1\nG : Type u\ninst✝ : Monoid G\nh : ∀ (g : G), 0 < orderOf g\nhe : exponent G ≠ 0\n⊢ Set.Finite (Set.range orderOf)\n\ncase refine'_2\nG : Type u\ninst✝ : Monoid G\nh : ∀ (g : G), 0 < orderOf g\nhe : Set.Finite (Set.range orderOf)\n⊢ exponent G ≠ 0",
"state_before": "G : Type... | [
244,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.map_comap_le | [] | [
598,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
597,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.QuasiMeasurePreserving.limsup_preimage_iterate_ae_eq | [
{
"state_after": "α : Type u_1\nβ : Type ?u.495766\nγ : Type ?u.495769\nδ : Type ?u.495772\nι : Type ?u.495775\nR : Type ?u.495778\nR' : Type ?u.495781\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set α\nμa μa' : Measure α\nμb μb' : ... | [
2557,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2549,
1
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.comap_id | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝² : CommRing R\nS : Type u\ninst✝¹ : CommRing S\nP : Type u\ninst✝ : CommRing P\nU V : Opens ↑(PrimeSpectrum.Top R)\nhUV : U = V\np : ↑(PrimeSpectrum.Top R)\nhpV : p ∈ V.carrier\n⊢ p ∈ ↑(PrimeSpectrum.comap (RingHom.id R)) ⁻¹' U.carrier",
"t... | [
1190,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1187,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.restrict_sInf_eq_sInf_restrict | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nm : Set (OuterMeasure α)\ns : Set α\nhm : Set.Nonempty m\n⊢ ↑(restrict s) (sInf m) = sInf (↑(restrict s) '' m)",
"tactic": "simp only [sInf_eq_iInf, restrict_biInf, hm, iInf_image]"
}
] | [
1289,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1287,
1
] |
Mathlib/CategoryTheory/NatIso.lean | CategoryTheory.NatIso.ofComponents.app | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nE : Type u₃\ninst✝ : Category E\nF G : C ⥤ D\nX✝ Y : C\napp' : (X : C) → F.obj X ≅ G.obj X\nnaturality : ∀ {X Y : C} (f : X ⟶ Y), F.map f ≫ (app' Y).hom = (app' X).hom ≫ G.map f\nX : C\n⊢ (ofCom... | [
237,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Data/Option/NAry.lean | Option.mem_map₂_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_3\nγ : Type u_1\nf : α → β → γ\na : Option α\nb : Option β\nc✝ : Option γ\nc : γ\n⊢ c ∈ map₂ f a b ↔ ∃ a' b', a' ∈ a ∧ b' ∈ b ∧ f a' b' = c",
"tactic": "simp [map₂]"
}
] | [
81,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | MeasureTheory.integral_integral_swap | [] | [
501,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
] |
Mathlib/Data/TwoPointing.lean | TwoPointing.prod_snd | [] | [
124,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Order/Hom/Lattice.lean | SupBotHom.sup_apply | [] | [
850,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
849,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | ciInf_subsingleton | [] | [
857,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
856,
1
] |
Mathlib/GroupTheory/Commutator.lean | commutatorSet_def | [] | [
254,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/CategoryTheory/Sites/Grothendieck.lean | CategoryTheory.GrothendieckTopology.bot_covers | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX Y : C\nS✝ R : Sieve X\nJ : GrothendieckTopology C\nS : Sieve X\nf : Y ⟶ X\n⊢ Covers ⊥ S f ↔ S.arrows f",
"tactic": "rw [covers_iff, bot_covering, ← Sieve.pullback_eq_top_iff_mem]"
}
] | [
339,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.eq_of_mem_map_const | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.125652\nb₁ b₂ : β\nl : List α\nh : b₁ ∈ map (const α b₂) ↑l\n⊢ b₁ ∈ replicate (?m.125825 h) b₂",
"tactic": "rwa [map_const] at h"
}
] | [
1304,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1302,
1
] |
Mathlib/MeasureTheory/Measure/Stieltjes.lean | rightLim_eq_sInf | [] | [
75,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Algebra/DirectSum/Basic.lean | DirectSum.induction_on | [
{
"state_after": "ι : Type v\ndec_ι : DecidableEq ι\nβ : ι → Type w\ninst✝ : (i : ι) → AddCommMonoid (β i)\nC : (⨁ (i : ι), β i) → Prop\nx : ⨁ (i : ι), β i\nH_zero : C 0\nH_basic : ∀ (i : ι) (x : β i), C (↑(of β i) x)\nH_plus : ∀ (x y : ⨁ (i : ι), β i), C x → C y → C (x + y)\n⊢ ∀ (i : ι) (b : (fun i => β i) i) ... | [
170,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
11
] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.equivOfLe_apply | [] | [
652,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
651,
1
] |
Mathlib/Algebra/Hom/GroupInstances.lean | MonoidHom.flip_apply | [] | [
147,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Algebra/Module/Torsion.lean | Submodule.mem_torsion'_iff | [] | [
612,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
611,
1
] |
Mathlib/Algebra/Group/TypeTags.lean | toAdd_one | [] | [
245,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigOWith_abs_abs | [] | [
814,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
812,
1
] |
Mathlib/Computability/Language.lean | Language.ext | [] | [
97,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Analysis/Quaternion.lean | Quaternion.tsum_coe | [
{
"state_after": "case pos\nα : Type u_1\nf : α → ℝ\nhf : Summable f\n⊢ (∑' (a : α), ↑(f a)) = ↑(∑' (a : α), f a)\n\ncase neg\nα : Type u_1\nf : α → ℝ\nhf : ¬Summable f\n⊢ (∑' (a : α), ↑(f a)) = ↑(∑' (a : α), f a)",
"state_before": "α : Type u_1\nf : α → ℝ\n⊢ (∑' (a : α), ↑(f a)) = ↑(∑' (a : α), f a)",
... | [
258,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/Algebra/Order/AbsoluteValue.lean | IsAbsoluteValue.abv_neg | [] | [
422,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/Algebra/Order/Monoid/TypeTags.lean | Additive.toMul_lt | [] | [
139,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.Prime.eq_of_factorization_pos | [
{
"state_after": "no goals",
"state_before": "p q : ℕ\nhp : Prime p\nh : ↑(Nat.factorization p) q ≠ 0\n⊢ p = q",
"tactic": "simpa [hp.factorization, single_apply] using h"
}
] | [
299,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiff.contDiffWithinAt | [] | [
1426,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1425,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.prime_three | [
{
"state_after": "no goals",
"state_before": "⊢ Prime 3",
"tactic": "decide"
}
] | [
175,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Data/Polynomial/Div.lean | Polynomial.div_modByMonic_unique | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R\nn : ℕ\ninst✝ : CommRing R\np q✝ : R[X]\nf g : R[X]\nq r : R[X]\nhg : Monic g\nh : r + g * q = f ∧ degree r < degree g\n✝ : Nontrivial R\n⊢ f /ₘ g = q ∧ f %ₘ g = r",
"state_before": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b... | [
357,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/Logic/Function/Iterate.lean | Function.iterate_id | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nf : α → α\nn✝ n : ℕ\nihn : id^[n] = id\n⊢ id^[Nat.succ n] = id",
"tactic": "rw [iterate_succ, ihn, comp.left_id]"
}
] | [
64,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.log_mul | [] | [
506,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.max_of_succ_le | [] | [
221,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | sum_add_tsum_nat_add | [] | [
970,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
968,
1
] |
Mathlib/Init/Algebra/Order.lean | lt_of_lt_of_le | [] | [
122,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Order/Cover.lean | Wcovby.covby_of_lt | [] | [
293,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioc_subset_Ioc_union_Icc | [] | [
1682,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1681,
1
] |
Mathlib/Order/Monotone/Basic.lean | StrictAnti.lt_iff_lt | [] | [
819,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
818,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.Iso.trans_symm | [] | [
184,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Std/Data/Int/Lemmas.lean | Int.lt_of_le_sub_one | [] | [
1266,
93
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1266,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.range_eq_top | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nR₁ : Type ?u.1083452\nR₂ : Type u_2\nR₃ : Type ?u.1083458\nR₄ : Type ?u.1083461\nS : Type ?u.1083464\nK : Type ?u.1083467\nK₂ : Type ?u.1083470\nM : Type u_4\nM' : Type ?u.1083476\nM₁ : Type ?u.1083479\nM₂ : Type u_3\nM₃ : Type ?u.1083485\nM₄ : Typ... | [
1240,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1239,
1
] |
Mathlib/Data/Fintype/Lattice.lean | Finset.sup_univ_eq_iSup | [] | [
33,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.toRingHom_comp_symm_toRingHom | [
{
"state_after": "case a\nF : Type ?u.100208\nα : Type ?u.100211\nβ : Type ?u.100214\nR : Type u_1\nS : Type u_2\nS' : Type ?u.100223\ninst✝² : NonAssocSemiring R\ninst✝¹ : NonAssocSemiring S\ninst✝ : NonAssocSemiring S'\ne : R ≃+* S\nx✝ : S\n⊢ ↑(RingHom.comp (toRingHom e) (toRingHom (RingEquiv.symm e))) x✝ = ↑... | [
769,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
766,
1
] |
Mathlib/Data/Set/Pointwise/Iterate.lean | smul_eq_self_of_preimage_zpow_eq_self | [
{
"state_after": "G : Type u_1\ninst✝ : CommGroup G\nn : ℤ\ns : Set G\nhs : (fun x => x ^ n) ⁻¹' s = s\ng : G\nj : ℕ\nhg : g ^ n ^ j = 1\n⊢ ∀ {g' : G}, g' ^ n ^ j = 1 → g' • (fun x => x ^ n)^[j] ⁻¹' s ⊆ (fun x => x ^ n)^[j] ⁻¹' s",
"state_before": "G : Type u_1\ninst✝ : CommGroup G\nn : ℤ\ns : Set G\nhs : (... | [
47,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
] |
Mathlib/Data/List/Cycle.lean | Cycle.nontrivial_coe_nodup_iff | [
{
"state_after": "α : Type u_1\nl : List α\nhl : Nodup l\n⊢ (∃ x y _h, x ∈ ↑l ∧ y ∈ ↑l) ↔ 2 ≤ List.length l",
"state_before": "α : Type u_1\nl : List α\nhl : Nodup l\n⊢ Nontrivial ↑l ↔ 2 ≤ List.length l",
"tactic": "rw [Nontrivial]"
},
{
"state_after": "case nil\nα : Type u_1\nhl : Nodup []\n⊢ (... | [
633,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
1
] |
Mathlib/Algebra/Algebra/Basic.lean | Algebra.smul_mul_assoc | [] | [
400,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
11
] |
Mathlib/Analysis/Complex/ReImTopology.lean | Complex.quotientMap_im | [] | [
69,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Data/Dfinsupp/Lex.lean | Dfinsupp.lt_of_forall_lt_of_lt | [] | [
144,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.lex_acc_inr | [
{
"state_after": "case intro\nα : Type u\nα' : Type w\nβ : Type v\nβ' : Type x\nγ : Type ?u.32484\nδ : Type ?u.32487\nr r₁ r₂ : α → α → Prop\ns s₁ s₂ : β → β → Prop\na a₁ a₂ : α\nb✝¹ b₁ b₂ : β\nx y : α ⊕ β\naca : ∀ (a : α), Acc (Lex r s) (inl a)\nb✝ b : β\nh✝ : ∀ (y : β), s y b → Acc s y\nIH : ∀ (y : β), s y b ... | [
542,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.le_of_dvd | [
{
"state_after": "m n k : Nat\ne : n = m * k\n⊢ 0 < n → m ≤ n",
"state_before": "m n : Nat\nh : 0 < n\nk : Nat\ne : n = m * k\n⊢ m ≤ n",
"tactic": "revert h"
},
{
"state_after": "m n k : Nat\ne : n = m * k\n⊢ 0 < m * k → m ≤ m * k",
"state_before": "m n k : Nat\ne : n = m * k\n⊢ 0 < n → m ≤ ... | [
705,
32
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
696,
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] |
Mathlib/Algebra/Field/Defs.lean | Rat.cast_mk' | [] | [
139,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.zpow_apply_mem_support | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\nn : ℤ\nx : α\n⊢ ↑(f ^ n) x ∈ support f ↔ x ∈ support f",
"tactic": "simp only [mem_support, ne_eq, apply_zpow_apply_eq_iff]"
}
] | [
382,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/Logic/Encodable/Lattice.lean | Encodable.iSup_decode₂ | [
{
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"state_before": "α : Type u_1\nβ : Type u_2\ninst✝¹ : Encodable β\ninst✝ : CompleteLattice α\nf : β → α\n⊢ (⨆ (i : ℕ) (b : β) (_ : b ∈... | [
35,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
] |
Mathlib/Topology/PartitionOfUnity.lean | BumpCovering.toPouFun_eq_mul_prod | [
{
"state_after": "ι : Type u\nX : Type v\ninst✝ : TopologicalSpace X\ns : Set X\nf : BumpCovering ι X s\ni : ι\nx : X\nt : Finset ι\nht : ∀ (j : ι), WellOrderingRel j i → ↑(toFun s f j) x ≠ 0 → j ∈ t\nj : ι\nhj : 1 - ↑(toFun s f j) x ≠ 1\n⊢ WellOrderingRel j i ↔ j ∈ Finset.filter (fun j => WellOrderingRel j i) ... | [
395,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
] |
Mathlib/Analysis/Normed/Group/Pointwise.lean | inv_ball | [] | [
94,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Metrizable.lean | measurable_of_tendsto_metrizable | [] | [
92,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Topology/Order/Hom/Esakia.lean | PseudoEpimorphism.comp_id | [] | [
204,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.dual_Ioi | [] | [
241,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.star_snd | [] | [
446,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
] |
Mathlib/Order/Filter/Partial.lean | Filter.rtendsto_def | [] | [
100,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | EMetric.infEdist_smul | [] | [
203,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Data/List/Perm.lean | List.cons_subperm_of_mem | [
{
"state_after": "case intro.intro\nα : Type uu\nβ : Type vv\nl₁✝ l₂✝ : List α\na : α\nl₁ l₂ : List α\nd₁ : Nodup l₁\nh₁ : ¬a ∈ l₁\nh₂ : a ∈ l₂\nl : List α\np : l ~ l₁\ns : l <+ l₂\n⊢ a :: l₁ <+~ l₂",
"state_before": "α : Type uu\nβ : Type vv\nl₁✝ l₂✝ : List α\na : α\nl₁ l₂ : List α\nd₁ : Nodup l₁\nh₁ : ¬a ... | [
708,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.support_onFinset | [
{
"state_after": "α : Type u_2\nβ : Type ?u.176434\nγ : Type ?u.176437\nι : Type ?u.176440\nM : Type u_1\nM' : Type ?u.176446\nN : Type ?u.176449\nP : Type ?u.176452\nG : Type ?u.176455\nH : Type ?u.176458\nR : Type ?u.176461\nS : Type ?u.176464\ninst✝¹ : Zero M\ninst✝ : DecidableEq M\ns : Finset α\nf : α → M\n... | [
719,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
716,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.coe_mul | [
{
"state_after": "no goals",
"state_before": "S : Type ?u.120411\nT : Type ?u.120414\nR : Type u_1\ninst✝ : CommRing R\nc₁ c₂ r x y z : R\na b c : ℍ[R,c₁,c₂]\n⊢ ↑(x * y) = ↑x * ↑y",
"tactic": "ext <;> simp"
}
] | [
479,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
1
] |
Mathlib/RingTheory/Algebraic.lean | isAlgebraic_algHom_of_isAlgebraic | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type ?u.133744\nA : Type v\ninst✝⁸ : CommRing R\ninst✝⁷ : CommRing S\ninst✝⁶ : Ring A\ninst✝⁵ : Algebra R A\ninst✝⁴ : Algebra R S\ninst✝³ : Algebra S A\ninst✝² : IsScalarTower R S A\nB : Type u_1\ninst✝¹ : Ring B\ninst✝ : Algebra R B\nf : A →ₐ[R]... | [
152,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Balanced.dual | [
{
"state_after": "α : Type u_1\nsize✝ : ℕ\nl : Ordnode α\nx✝ : α\nr : Ordnode α\nb : BalancedSz (size l) (size r)\nbl : Balanced l\nbr : Balanced r\n⊢ BalancedSz (size r) (size l)",
"state_before": "α : Type u_1\nsize✝ : ℕ\nl : Ordnode α\nx✝ : α\nr : Ordnode α\nb : BalancedSz (size l) (size r)\nbl : Balance... | [
222,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.coe_repr_symm | [] | [
177,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | ULift.norm_up | [] | [
2111,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2110,
1
] |
Mathlib/CategoryTheory/Monoidal/Types/Basic.lean | CategoryTheory.tensor_apply | [] | [
36,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
] |
Mathlib/Data/Multiset/Nodup.lean | Multiset.map_eq_map_of_bij_of_nodup | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nr : α → α → Prop\ns✝ t✝ : Multiset α\na : α\nf : α → γ\ng : β → γ\ns : Multiset α\nt : Multiset β\nhs : Nodup s\nht : Nodup t\ni : (a : α) → a ∈ s → β\nhi : ∀ (a : α) (ha : a ∈ s), i a ha ∈ t\nh : ∀ (a : α) (ha : a ∈ s), f a = g (i a ha)\ni_inj : ∀ (a₁... | [
273,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.permCongr_refl | [
{
"state_after": "no goals",
"state_before": "α : Sort u\nβ : Sort v\nγ : Sort w\nα' : Type u_2\nβ' : Type u_1\ne : α' ≃ β'\n⊢ ↑(permCongr e) (Equiv.refl α') = Equiv.refl β'",
"tactic": "simp [permCongr_def]"
}
] | [
436,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
9
] |
Mathlib/Data/Vector/Basic.lean | Vector.get_set_eq_if | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nα : Type u_1\nβ : Type ?u.60181\nγ : Type ?u.60184\nv : Vector α n\ni j : Fin n\na : α\n⊢ get (set v i a) j = if i = j then a else get v j",
"tactic": "split_ifs <;> try simp [*] <;> try rw [get_set_of_ne] ; assumption"
},
{
"state_after": "no... | [
609,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
607,
1
] |
Mathlib/Analysis/SpecificLimits/Normed.lean | isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt | [
{
"state_after": "case pos\nα : Type ?u.98739\nβ : Type ?u.98742\nι : Type ?u.98745\nR : Type u_1\ninst✝ : NormedRing R\nk : ℕ\nr₁ : R\nr₂ : ℝ\nh : ‖r₁‖ < r₂\nh0 : r₁ = 0\n⊢ (fun n => ↑n ^ k * r₁ ^ n) =o[atTop] fun n => r₂ ^ n\n\ncase neg\nα : Type ?u.98739\nβ : Type ?u.98742\nι : Type ?u.98745\nR : Type u_1\ni... | [
227,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup_bool_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.162120\nβ₂ : Type ?u.162123\nγ : Type ?u.162126\nι : Sort ?u.162129\nι' : Sort ?u.162132\nκ : ι → Sort ?u.162137\nκ' : ι' → Sort ?u.162142\ninst✝ : CompleteLattice α\nf✝ g s t : ι → α\na b : α\nf : Bool → α\n⊢ (⨆ (b : Bool), f b) = f tr... | [
1515,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1514,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.direction_affineSpan_insert | [
{
"state_after": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\ns : AffineSubspace k P\np1 p2 : P\nhp1 : p1 ∈ s\n⊢ direction (affineSpan k (↑s ∪ ↑(affineSpan k {p2}))) = direction s ⊔ Submodule.span k {p2 -ᵥ p1}",
"state_bef... | [
1452,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1446,
1
] |
Mathlib/Order/Basic.lean | le_implies_le_of_le_of_le | [] | [
573,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
1
] |
Mathlib/Order/Closure.lean | LowerAdjoint.closure_sup_closure_le | [] | [
443,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | HasFDerivWithinAt.fderivWithin | [] | [
559,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
11
] |
Mathlib/Order/Heyting/Regular.lean | Heyting.Regular.coe_bot | [] | [
155,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_eq_zero_iff_of_lt_of_lt | [
{
"state_after": "no goals",
"state_before": "x : ℝ\nhx₁ : -π < x\nhx₂ : x < π\nh : x = 0\n⊢ sin x = 0",
"tactic": "simp [h]"
}
] | [
506,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/Algebra/Regular/Basic.lean | isRegular_one | [] | [
282,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.WSameSide.trans_wOppSide | [
{
"state_after": "case intro.intro.intro.intro\nR : Type u_1\nV : Type u_2\nV' : Type ?u.282975\nP : Type u_3\nP' : Type ?u.282981\ninst✝⁶ : LinearOrderedField R\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module R V\ninst✝³ : AddTorsor V P\ninst✝² : AddCommGroup V'\ninst✝¹ : Module R V'\ninst✝ : AddTorsor V' P'\ns : Af... | [
549,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
1
] |
Mathlib/Data/Nat/Sqrt.lean | Nat.sqrt_eq' | [] | [
160,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Memℒp.snorm_mk_lt_top | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.230952\nE✝ : Type ?u.230955\nF : Type ?u.230958\nG : Type ?u.230961\nm m0 : MeasurableSpace α✝\np✝ : ℝ≥0∞\nq : ℝ\nμ✝ ν : Measure α✝\ninst✝⁴ : NormedAddCommGroup E✝\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedAddCommGroup G\nα : Type u_1\nE : Type... | [
96,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Algebra/DirectSum/Module.lean | DirectSum.isInternal_submodule_of_independent_of_iSup_eq_top | [] | [
403,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
] |
Mathlib/Data/Complex/Module.lean | Complex.rank_real_complex | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.167857\nS : Type ?u.167860\n⊢ Module.rank ℝ ℂ = 2",
"tactic": "simp [← finrank_eq_rank, finrank_real_complex]"
}
] | [
191,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.HasBasis.mem_lift_iff | [
{
"state_after": "case refine'_1\nα : Type u_2\nβ✝ : Type ?u.2792\nγ : Type u_4\nι✝ : Sort ?u.2798\nf✝ f₁ f₂ : Filter α\ng✝ g₁ g₂ : Set α → Filter β✝\nι : Sort u_1\np : ι → Prop\ns✝ : ι → Set α\nf : Filter α\nhf : HasBasis f p s✝\nβ : ι → Type u_3\npg : (i : ι) → β i → Prop\nsg : (i : ι) → β i → Set γ\ng : Set ... | [
55,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Std/Data/AssocList.lean | Std.AssocList.mapVal_toList | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nδ : Type u_3\nf : α → β → δ\nl : AssocList α β\n⊢ toList (mapVal f l) =\n List.map\n (fun x =>\n match x with\n | (a, b) => (a, f a b))\n (toList l)",
"tactic": "induction l <;> simp [*]"
}
] | [
96,
27
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
94,
9
] |
Mathlib/Logic/Embedding/Basic.lean | Function.Embedding.arrowCongrRight_apply | [] | [
354,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.isPairSelfAdjoint_equiv | [
{
"state_after": "R : Type u_1\nR₁ : Type ?u.395006\nR₂ : Type ?u.395009\nR₃ : Type ?u.395012\nM : Type u_3\nM₁ : Type u_2\nM₂ : Type ?u.395021\nMₗ₁ : Type ?u.395024\nMₗ₁' : Type ?u.395027\nMₗ₂ : Type ?u.395030\nMₗ₂' : Type ?u.395033\nK : Type ?u.395036\nK₁ : Type ?u.395039\nK₂ : Type ?u.395042\nV : Type ?u.395... | [
585,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
569,
1
] |
Mathlib/Data/Set/Function.lean | Set.Subsingleton.injOn | [] | [
597,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
596,
1
] |
Mathlib/Dynamics/Flow.lean | Flow.map_zero_apply | [] | [
135,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.pow_sup_eq_top | [
{
"state_after": "R : Type u\nι : Type ?u.281942\ninst✝ : CommSemiring R\nI J K L : Ideal R\nn : ℕ\nh : I ⊔ J = ⊤\n⊢ (∏ _x in Finset.range n, I) ⊔ J = ⊤",
"state_before": "R : Type u\nι : Type ?u.281942\ninst✝ : CommSemiring R\nI J K L : Ideal R\nn : ℕ\nh : I ⊔ J = ⊤\n⊢ I ^ n ⊔ J = ⊤",
"tactic": "rw [← ... | [
734,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
732,
1
] |
Mathlib/Data/List/Permutation.lean | List.map_permutationsAux2' | [
{
"state_after": "case nil\nα✝ : Type ?u.3849\nβ✝ : Type ?u.3852\nα : Type u_1\nβ : Type u_2\nα' : Type u_3\nβ' : Type u_4\ng : α → α'\ng' : β → β'\nt : α\nts : List α\nr : List β\nf✝ : List α → β\nf'✝ : List α' → β'\nH✝ : ∀ (a : List α), g' (f✝ a) = f'✝ (map g a)\nf : List α → β\nf' : List α' → β'\nH : ∀ (a : ... | [
101,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
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