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/Order/Filter/ZeroAndBoundedAtFilter.lean | Filter.zero_zeroAtFilter | [] | [
40,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
Mathlib/RingTheory/Valuation/Quotient.lean | AddValuation.supp_quot | [] | [
134,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/ModelTheory/Satisfiability.lean | FirstOrder.Language.Theory.models_sentence_iff | [] | [
322,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_nat_cast_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np q r : R[X]\nx : R\nn : ℕ\n⊢ eval x (↑n * p) = ↑n * eval x p",
"tactic": "rw [← C_eq_nat_cast, eval_C_mul]"
}
] | [
448,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | DifferentiableWithinAt.fderivWithin_prod | [] | [
129,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.refl_apply | [] | [
272,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
9
] |
Mathlib/MeasureTheory/Group/MeasurableEquiv.lean | MeasurableEquiv.symm_smul | [] | [
67,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/RingTheory/FreeCommRing.lean | FreeRing.coe_mul | [] | [
360,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
11
] |
Mathlib/Probability/CondCount.lean | ProbabilityTheory.condCount_univ | [
{
"state_after": "Ω : Type u_1\ninst✝¹ : MeasurableSpace Ω\ninst✝ : Fintype Ω\ns : Set Ω\n⊢ ↑↑Measure.count s / ↑↑Measure.count Set.univ = ↑↑Measure.count s / ↑(Fintype.card Ω)",
"state_before": "Ω : Type u_1\ninst✝¹ : MeasurableSpace Ω\ninst✝ : Fintype Ω\ns : Set Ω\n⊢ ↑↑(condCount Set.univ) s = ↑↑Measure.c... | [
78,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Algebra/ContinuedFractions/Computation/Translations.lean | GeneralizedContinuedFraction.get?_of_eq_some_of_get?_intFractPair_stream_fr_ne_zero | [
{
"state_after": "case mk\nK : Type u_1\ninst✝¹ : LinearOrderedField K\ninst✝ : FloorRing K\nv : K\nn : ℕ\nb✝ : ℤ\nfr✝ : K\nstream_nth_eq : IntFractPair.stream v n = some { b := b✝, fr := fr✝ }\nnth_fr_ne_zero : { b := b✝, fr := fr✝ }.fr ≠ 0\n⊢ IntFractPair.stream v (n + 1) = some (IntFractPair.of { b := b✝, fr... | [
260,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/CategoryTheory/Limits/Opposites.lean | CategoryTheory.Limits.PushoutCocone.unop_fst | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nJ : Type u₂\ninst✝ : Category J\nX✝ : Type v₂\nX Y Z : Cᵒᵖ\nf : X ⟶ Y\ng : X ⟶ Z\nc : PushoutCocone f g\n⊢ PullbackCone.fst (unop c) = (inl c).unop",
"tactic": "simp"
}
] | [
482,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/Deprecated/Submonoid.lean | Monoid.closure_mono | [] | [
331,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.sumAddHom_add | [] | [
2062,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2060,
1
] |
Mathlib/Order/Disjoint.lean | Disjoint.mono | [] | [
69,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Logic/Basic.lean | eq_or_ne | [] | [
210,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | ae_of_mem_of_ae_of_mem_inter_Ioo | [
{
"state_after": "μ : MeasureTheory.Measure ℝ\ninst✝ : NoAtoms μ\ns : Set ℝ\np : ℝ → Prop\nh : ∀ (a b : ℝ), a ∈ s → b ∈ s → a < b → ∀ᵐ (x : ℝ) ∂μ, x ∈ s ∩ Ioo a b → p x\nT : ↑s × ↑s → Set ℝ := fun p => Ioo ↑p.fst ↑p.snd\n⊢ ∀ᵐ (x : ℝ) ∂μ, x ∈ s → p x",
"state_before": "μ : MeasureTheory.Measure ℝ\ninst✝ : No... | [
650,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
1
] |
Mathlib/Order/Basic.lean | exists_between | [] | [
1272,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1271,
1
] |
Mathlib/GroupTheory/Nilpotent.lean | least_descending_central_series_length_eq_nilpotencyClass | [
{
"state_after": "G : Type u_1\ninst✝¹ : Group G\nH : Subgroup G\ninst✝ : Normal H\nhG : Group.IsNilpotent G\n⊢ Nat.find (_ : ∃ n H, IsDescendingCentralSeries H ∧ H n = ⊥) =\n Nat.find (_ : ∃ n H, IsAscendingCentralSeries H ∧ H n = ⊤)",
"state_before": "G : Type u_1\ninst✝¹ : Group G\nH : Subgroup G\nins... | [
415,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean | SimpleGraph.incMatrix_apply_mul_incMatrix_apply | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nα : Type u_2\nG : SimpleGraph α\ninst✝ : MulZeroOneClass R\na b : α\ne : Sym2 α\n⊢ incMatrix R G a e * incMatrix R G b e = Set.indicator (incidenceSet G a ∩ incidenceSet G b) 1 e",
"tactic": "classical simp only [incMatrix, Set.indicator_apply,... | [
84,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.exists_reduced_factors | [
{
"state_after": "α : Type ?u.947754\nR : Type u_1\ninst✝¹ : CancelCommMonoidWithZero R\ninst✝ : UniqueFactorizationMonoid R\nthis : (a : Prop) → Decidable a\n⊢ ∀ (a : R), a ≠ 0 → ∀ (b : R), ∃ a' b' c', (∀ {d : R}, d ∣ a' → d ∣ b' → IsUnit d) ∧ c' * a' = a ∧ c' * b' = b",
"state_before": "α : Type ?u.947754... | [
922,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
895,
1
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.natTrailingDegree_X | [] | [
450,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
1
] |
Mathlib/Data/Nat/Factorial/Cast.lean | Nat.cast_ascFactorial | [
{
"state_after": "no goals",
"state_before": "S : Type u_1\ninst✝ : Semiring S\na b : ℕ\n⊢ ↑(ascFactorial a b) = Polynomial.eval (↑a + 1) (pochhammer S b)",
"tactic": "rw [← pochhammer_nat_eq_ascFactorial, pochhammer_eval_cast, Nat.cast_add, Nat.cast_one]"
}
] | [
38,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | ContinuousLinearMap.add_compLpL | [
{
"state_after": "case h\nα : Type u_4\nE : Type u_2\nF : Type u_3\nG : Type ?u.7355959\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : MeasureTheory.Measure α\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedAddCommGroup G\ng : E → F\nc : ℝ≥0\n𝕜 : Type u_1\ninst✝³ : Nontrivially... | [
1051,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1050,
1
] |
Mathlib/Order/BooleanAlgebra.lean | sdiff_sdiff_eq_self | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.30279\nw x y z : α\ninst✝ : GeneralizedBooleanAlgebra α\nh : y ≤ x\n⊢ x \\ (x \\ y) = y",
"tactic": "rw [sdiff_sdiff_right_self, inf_of_le_right h]"
}
] | [
385,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
1
] |
Mathlib/Topology/FiberBundle/Basic.lean | FiberBundle.exists_trivialization_Icc_subset | [
{
"state_after": "case intro\nι : Type ?u.12142\nB : Type u_1\nF : Type u_2\nX : Type ?u.12151\ninst✝⁷ : TopologicalSpace X\ninst✝⁶ : TopologicalSpace B\ninst✝⁵ : TopologicalSpace F\nE : B → Type u_3\ninst✝⁴ : TopologicalSpace (TotalSpace E)\ninst✝³ : (b : B) → TopologicalSpace (E b)\ninst✝² : ConditionallyComp... | [
401,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_mono_set' | [] | [
158,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Order/Cover.lean | Covby.Ioc_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.37096\ninst✝ : PartialOrder α\na b c : α\nh : a ⋖ b\n⊢ Ioc a b = {b}",
"tactic": "rw [← Ioo_union_right h.lt, h.Ioo_eq, empty_union]"
}
] | [
409,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
src/lean/Init/Control/StateCps.lean | StateCpsT.runK_bind_lift | [] | [
67,
79
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
66,
9
] |
Mathlib/Order/Basic.lean | eq_or_lt_of_le | [] | [
398,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.lt_succ_iff_eq_or_lt | [] | [
494,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.smul_essSup | [
{
"state_after": "α : Type u_3\nβ : Type u_2\nγ : Type ?u.969961\nδ : Type ?u.969964\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝⁵ : MeasurableSpace δ\ninst✝⁴ : NormedAddCommGroup β\ninst✝³ : NormedAddCommGroup γ\n𝕜 : Type u_1\ninst✝² : NormedRing 𝕜\ninst✝¹ : Module 𝕜 β\ninst✝ : BoundedSMul 𝕜 β\nf : α → �... | [
763,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
751,
1
] |
Mathlib/Analysis/InnerProductSpace/LaxMilgram.lean | IsCoercive.antilipschitz | [
{
"state_after": "case intro.intro\nV : Type u\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace ℝ V\ninst✝ : CompleteSpace V\nB : V →L[ℝ] V →L[ℝ] ℝ\ncoercive : IsCoercive B\nC : ℝ\nC_pos : 0 < C\nbelow_bound : ∀ (v : V), C * ‖v‖ ≤ ‖↑(continuousLinearMapOfBilin B) v‖\n⊢ ∃ C, 0 < C ∧ AntilipschitzWith C... | [
79,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.affineCombinationLineMapWeights_apply_of_ne | [
{
"state_after": "no goals",
"state_before": "k : Type u_2\nV : Type ?u.441077\nP : Type ?u.441080\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\nS : AffineSpace V P\nι : Type u_1\ns : Finset ι\nι₂ : Type ?u.441736\ns₂ : Finset ι₂\ninst✝ : DecidableEq ι\ni j t : ι\nhi : t ≠ i\nhj : t ≠ j\nc... | [
734,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
732,
1
] |
Std/Data/Array/Init/Lemmas.lean | Array.foldr_push' | [] | [
90,
98
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
89,
9
] |
Mathlib/NumberTheory/BernoulliPolynomials.lean | Polynomial.sum_bernoulli | [
{
"state_after": "n : ℕ\n⊢ ∑ k in range (n + 1 - 0),\n ∑ k_1 in range (n + 1 - (0 + k)),\n ↑(Nat.choose (n + 1) (0 + k + k_1)) •\n ↑(monomial (0 + k)) (_root_.bernoulli (0 + k + k_1 - (0 + k)) * ↑(Nat.choose (0 + k + k_1) (0 + k))) =\n ↑(monomial n) (↑n + 1)",
"state_before": "n : ℕ\... | [
152,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
8
] |
Mathlib/Data/Set/Basic.lean | Set.insert_diff_of_not_mem | [
{
"state_after": "case h\nα : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns✝ s₁ s₂ t t₁ t₂ u s : Set α\nh : ¬a ∈ t\nx : α\n⊢ x ∈ insert a s \\ t ↔ x ∈ insert a (s \\ t)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns✝ s₁ s₂ t t₁ t₂ u s : Set α\nh : ¬a ∈ t\n⊢ insert a s... | [
1985,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1976,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf_eq_dif | [] | [
1128,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1126,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Real.contDiff_cosh | [] | [
664,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
663,
1
] |
Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.PositiveCompacts.coe_top | [] | [
389,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Std/Data/List/Lemmas.lean | List.suffix_append | [] | [
1561,
78
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1561,
9
] |
Mathlib/Analysis/BoxIntegral/Partition/Split.lean | BoxIntegral.Prepartition.inf_splitMany | [
{
"state_after": "case empty\nι : Type u_1\nM : Type ?u.45780\nn : ℕ\nI✝ J : Box ι\ni : ι\nx : ℝ\nI : Box ι\nπ : Prepartition I\n⊢ π ⊓ splitMany I ∅ = biUnion π fun J => splitMany J ∅\n\ncase insert\nι : Type u_1\nM : Type ?u.45780\nn : ℕ\nI✝ J : Box ι\ni : ι\nx : ℝ\nI : Box ι\nπ : Prepartition I\np : ι × ℝ\ns ... | [
278,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Topology/Connected.lean | IsPreconnected.subset_connectedComponentIn | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.54741\nπ : ι → Type ?u.54746\ninst✝ : TopologicalSpace α\ns t u v : Set α\nx : α\nF : Set α\nhs : IsPreconnected s\nhxs : x ∈ s\nhsF : s ⊆ F\nthis : IsPreconnected (Subtype.val ⁻¹' s)\n⊢ s ⊆ connectedComponentIn F x",
"state_before": "α : Type u\nβ : Typ... | [
655,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
644,
1
] |
Mathlib/Algebra/CharZero/Defs.lean | charZero_of_inj_zero | [
{
"state_after": "case zero\nR : Type u_1\ninst✝ : AddGroupWithOne R\nH : ∀ (n : ℕ), ↑n = 0 → n = 0\nm n✝ : ℕ\nh✝ : ↑m = ↑n✝\nn : ℕ\nh : ↑Nat.zero = ↑n\n⊢ Nat.zero = n\n\ncase succ\nR : Type u_1\ninst✝ : AddGroupWithOne R\nH : ∀ (n : ℕ), ↑n = 0 → n = 0\nm✝ n✝ : ℕ\nh✝ : ↑m✝ = ↑n✝\nm : ℕ\nih : ∀ (n : ℕ), ↑m = ↑n ... | [
60,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Data/Set/Pairwise/Basic.lean | Set.Nonempty.pairwise_iff_exists_forall | [
{
"state_after": "case mp\nα : Type u_1\nβ : Type ?u.5561\nγ : Type ?u.5564\nι : Type u_2\nι' : Type ?u.5570\nr p q : α → α → Prop\nf g : ι → α\ns✝ t u : Set α\na b : α\ninst✝ : IsEquiv α r\ns : Set ι\nhs : Set.Nonempty s\n⊢ Set.Pairwise s (r on f) → ∃ z, ∀ (x : ι), x ∈ s → r (f x) z\n\ncase mpr\nα : Type u_1\n... | [
112,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | inv_lt_inv_of_neg | [] | [
772,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
771,
1
] |
Mathlib/GroupTheory/GroupAction/Basic.lean | MulAction.mem_fixedPoints | [] | [
137,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Data/List/Basic.lean | List.takeWhile_eq_nil_iff | [
{
"state_after": "case nil\nι : Type ?u.412046\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\np : α → Bool\nl : List α\n⊢ takeWhile p [] = [] ↔ ∀ (hl : 0 < length []), ¬p (nthLe [] 0 hl) = true\n\ncase cons\nι : Type ?u.412046\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\np ... | [
3648,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3643,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | AEMeasurable.is_lub_of_nonempty | [
{
"state_after": "α : Type u_3\nβ : Type ?u.1096180\nγ : Type ?u.1096183\nγ₂ : Type ?u.1096186\nδ : Type u_2\nι✝ : Sort y\ns t u : Set α\ninst✝¹³ : TopologicalSpace α\ninst✝¹² : MeasurableSpace α\ninst✝¹¹ : BorelSpace α\ninst✝¹⁰ : TopologicalSpace β\ninst✝⁹ : MeasurableSpace β\ninst✝⁸ : BorelSpace β\ninst✝⁷ : T... | [
1109,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1085,
9
] |
Mathlib/Logic/Equiv/Functor.lean | Bifunctor.mapEquiv_refl_refl | [
{
"state_after": "case H\nα β : Type u\nα' β' : Type v\nF : Type u → Type v → Type w\ninst✝¹ : Bifunctor F\ninst✝ : LawfulBifunctor F\nx : F α α'\n⊢ ↑(mapEquiv F (Equiv.refl α) (Equiv.refl α')) x = ↑(Equiv.refl (F α α')) x",
"state_before": "α β : Type u\nα' β' : Type v\nF : Type u → Type v → Type w\ninst✝¹... | [
95,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Data/Real/Basic.lean | Real.cauchy_zero | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ Real.zero.cauchy = 0",
"tactic": "rw [zero_def]"
}
] | [
145,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | Continuous.integrableOn_Ioc | [] | [
286,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Data/List/Join.lean | List.nthLe_join | [
{
"state_after": "α : Type u_1\nβ : Type ?u.15601\nL : List (List α)\ni j : ℕ\nhi : i < length L\nhj : j < length (nthLe L i hi)\nthis :\n nthLe (join L) (sum (take i (map length L)) + j) (_ : sum (take i (map length L)) + j < length (join L)) =\n nthLe (take (sum (take (i + 1) (map length L))) (join L)) (s... | [
187,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/SetTheory/Ordinal/Topology.lean | Ordinal.nhdsBasis_Ioc | [] | [
72,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Topology/SubsetProperties.lean | disjoint_nhds_cocompact | [] | [
1096,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1094,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.map_one' | [] | [
118,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
11
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | MonoidHom.mem_mrange | [] | [
1052,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1051,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_of_im_nonneg_of_ne_zero | [
{
"state_after": "no goals",
"state_before": "z : ℂ\nh₁ : 0 ≤ z.im\nh₂ : z ≠ 0\n⊢ arg z = arccos (z.re / ↑abs z)",
"tactic": "rw [← cos_arg h₂, Real.arccos_cos (arg_nonneg_iff.2 h₁) (arg_le_pi _)]"
}
] | [
292,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.L1.stronglyMeasurable_coeFn | [] | [
1283,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1282,
1
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | isPreconnected_Icc | [
{
"state_after": "case intro.intro\nα : Type u\nβ : Type v\nγ : Type w\ninst✝⁷ : ConditionallyCompleteLinearOrder α\ninst✝⁶ : TopologicalSpace α\ninst✝⁵ : OrderTopology α\ninst✝⁴ : ConditionallyCompleteLinearOrder β\ninst✝³ : TopologicalSpace β\ninst✝² : OrderTopology β\ninst✝¹ : Nonempty γ\ninst✝ : DenselyOrde... | [
421,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
Mathlib/Combinatorics/Additive/SalemSpencer.lean | mulSalemSpencer_mul_right_iff₀ | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.106147\nα : Type u_1\nβ : Type ?u.106153\n𝕜 : Type ?u.106156\nE : Type ?u.106159\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : NoZeroDivisors α\ns : Set α\na : α\nha : a ≠ 0\nhs : MulSalemSpencer ((fun x => x * a) '' s)\nb c d : α\nhb : b ∈ s\nhc : ... | [
266,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Std/Data/String/Lemmas.lean | String.Pos.zero_addString_eq | [
{
"state_after": "no goals",
"state_before": "s : String\n⊢ 0 + s = { byteIdx := utf8ByteSize s }",
"tactic": "rw [← zero_addString_byteIdx]"
}
] | [
137,
32
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
136,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.Normal.comap | [
{
"state_after": "no goals",
"state_before": "G : Type u_2\nG' : Type ?u.669539\ninst✝³ : Group G\ninst✝² : Group G'\nA : Type ?u.669548\ninst✝¹ : AddGroup A\nN : Type u_1\ninst✝ : Group N\nH : Subgroup N\nhH : Normal H\nf : G →* N\nx✝ : G\n⊢ x✝ ∈ Subgroup.comap f H → ∀ (g : G), g * x✝ * g⁻¹ ∈ Subgroup.coma... | [
3386,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3385,
1
] |
Mathlib/Order/Monotone/Monovary.lean | Antivary.comp_monotone_left | [] | [
172,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.pointReflection_midpoint_right | [] | [
837,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
836,
1
] |
Mathlib/Order/Filter/Cofinite.lean | Filter.cofinite_eq_bot | [] | [
67,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Std/Data/Nat/Gcd.lean | Nat.gcd_mul_right_left | [
{
"state_after": "no goals",
"state_before": "m n : Nat\n⊢ gcd (n * m) n = n",
"tactic": "rw [Nat.mul_comm, gcd_mul_left_left]"
}
] | [
156,
39
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
155,
9
] |
Mathlib/Topology/UniformSpace/Basic.lean | SymmetricRel.mk_mem_comm | [] | [
232,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.eq_zero_or_eq_zero_of_mul_eq_zero | [
{
"state_after": "d : ℕ\ndnsq : Nonsquare d\nx y z w : ℤ\nh1 : { re := x, im := y }.re * { re := z, im := w }.re + ↑d * { re := x, im := y }.im * { re := z, im := w }.im = 0\nh2 : { re := x, im := y }.re * { re := z, im := w }.im + { re := x, im := y }.im * { re := z, im := w }.re = 0\n⊢ { re := x, im := y } = ... | [
983,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
956,
11
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.span_empty | [] | [
687,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
686,
1
] |
Mathlib/CategoryTheory/Idempotents/Karoubi.lean | CategoryTheory.Idempotents.Karoubi.ext | [
{
"state_after": "case mk\nC : Type u_1\ninst✝ : Category C\nQ : Karoubi C\nX✝ : C\np✝ : X✝ ⟶ X✝\nidem✝ : p✝ ≫ p✝ = p✝\nh_X : (mk X✝ p✝).X = Q.X\nh_p : (mk X✝ p✝).p ≫ eqToHom h_X = eqToHom h_X ≫ Q.p\n⊢ mk X✝ p✝ = Q",
"state_before": "C : Type u_1\ninst✝ : Category C\nP Q : Karoubi C\nh_X : P.X = Q.X\nh_p : ... | [
69,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Data/List/Perm.lean | List.Perm.cons_inv | [] | [
645,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
644,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Ring.lean | Summable.div_const | [] | [
89,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Data/Finset/Sym.lean | Finset.diag_mem_sym2_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\na b : α\nm : Sym2 α\n⊢ Sym2.diag a ∈ Finset.sym2 s ↔ a ∈ s",
"tactic": "simp [diag_mem_sym2_mem_iff]"
}
] | [
108,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.relMap_sum_inr | [] | [
936,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
934,
1
] |
Mathlib/Topology/Order/LowerTopology.lean | WithLowerTopology.isOpen_preimage_ofLower | [] | [
127,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | nnnorm_multiset_prod_le | [
{
"state_after": "𝓕 : Type ?u.1102052\n𝕜 : Type ?u.1102055\nα : Type ?u.1102058\nι : Type ?u.1102061\nκ : Type ?u.1102064\nE : Type u_1\nF : Type ?u.1102070\nG : Type ?u.1102073\ninst✝¹ : SeminormedCommGroup E\ninst✝ : SeminormedCommGroup F\na a₁ a₂ b b₁ b₂ : E\nr r₁ r₂ : ℝ\nm : Multiset E\n⊢ ‖Multiset.prod m... | [
1682,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1678,
1
] |
Mathlib/Analysis/Complex/AbsMax.lean | Complex.norm_eventually_eq_of_isLocalMax | [
{
"state_after": "case intro.intro\nE : Type u\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℂ E\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℂ F\nf : E → F\nc : E\nhd : ∀ᶠ (z : E) in 𝓝 c, DifferentiableAt ℂ f z\nhc : IsLocalMax (norm ∘ f) c\nr : ℝ\nhr₀ : 0 < r\nhr : ∀ ⦃x : E⦄, x ∈ cl... | [
221,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Algebra/Star/Basic.lean | RingHom.star_def | [] | [
417,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Std/Data/String/Lemmas.lean | String.mapAux_of_valid | [
{
"state_after": "f : Char → Char\nl : List Char\n⊢ (if h : atEnd { data := l ++ [] } { byteIdx := utf8Len l } = true then { data := l ++ [] }\n else\n let c := f (get { data := l ++ [] } { byteIdx := utf8Len l });\n let_fun this :=\n (_ :\n (endPos (set { data := l ++ [] } { byteId... | [
738,
47
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
731,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | DifferentiableWithinAt.cosh | [] | [
1072,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1070,
1
] |
Mathlib/GroupTheory/NielsenSchreier.lean | IsFreeGroupoid.ext_functor | [] | [
104,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.norm_eq_pow_val | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\nx : ℤ_[p]\nhx : x ≠ 0\n⊢ ↑x ≠ 0",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nx : ℤ_[p]\nhx : x ≠ 0\n⊢ ‖x‖ = ↑p ^ (-valuation x)",
"tactic": "refine @Padic.norm_eq_pow_val p hp x ?_"
},
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\nx : ℤ... | [
382,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean | CategoryTheory.Limits.IsInitial.hom_ext | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝ : Category C\nX Y : C\nt : IsInitial X\nf g : X ⟶ Y\n⊢ ∀ (j : Discrete PEmpty), (asEmptyCocone X).ι.app j ≫ f = (asEmptyCocone X).ι.app j ≫ g",
"tactic": "aesop_cat"
}
] | [
159,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | MulPosMonoRev.toMulPosStrictMono | [] | [
292,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/NumberTheory/ADEInequality.lean | ADEInequality.admissible_of_one_lt_sumInv_aux' | [
{
"state_after": "p q r : ℕ+\nhpq : p ≤ q\nhqr : q ≤ r\nH : 1 < sumInv {p, q, r}\nhp3 : p < 3\n⊢ Admissible {p, q, r}",
"state_before": "p q r : ℕ+\nhpq : p ≤ q\nhqr : q ≤ r\nH : 1 < sumInv {p, q, r}\n⊢ Admissible {p, q, r}",
"tactic": "have hp3 : p < 3 := lt_three hpq hqr H"
},
{
"state_after":... | [
252,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Order/CompleteLattice.lean | ofDual_iInf | [] | [
460,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
Mathlib/Topology/LocallyConstant/Algebra.lean | LocallyConstant.coe_algebraMap | [] | [
292,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/Order/CompleteLatticeIntervals.lean | subset_sSup_def | [] | [
56,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Data/Set/Image.lean | Set.range_diff_image | [] | [
1123,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1121,
1
] |
Mathlib/Topology/Algebra/UniformGroup.lean | uniformGroup_iInf | [
{
"state_after": "α : Type ?u.118853\nβ : Type u_2\ninst✝³ : UniformSpace α\ninst✝² : Group α\ninst✝¹ : UniformGroup α\ninst✝ : Group β\nι : Sort u_1\nus' : ι → UniformSpace β\nh' : ∀ (i : ι), UniformGroup β\n⊢ UniformGroup β",
"state_before": "α : Type ?u.118853\nβ : Type u_2\ninst✝³ : UniformSpace α\ninst... | [
233,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/Algebra/GroupPower/Basic.lean | inv_zpow | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝ : DivisionMonoid α\na✝ b a : α\nn : ℕ\n⊢ a⁻¹ ^ ↑n = (a ^ ↑n)⁻¹",
"tactic": "rw [zpow_ofNat, zpow_ofNat, inv_pow]"
},
{
"state_after"... | [
353,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Std/Data/Int/Lemmas.lean | Int.exists_eq_neg_ofNat | [] | [
1241,
35
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1239,
1
] |
Mathlib/Combinatorics/SimpleGraph/DegreeSum.lean | SimpleGraph.odd_card_odd_degree_vertices_ne | [
{
"state_after": "case intro\nV : Type u\nG : SimpleGraph V\ninst✝² : Fintype V\ninst✝¹ : DecidableEq V\ninst✝ : DecidableRel G.Adj\nv : V\nh : Odd (degree G v)\nk : ℕ\nhg : card (filter (fun v => Odd (degree G v)) univ) = k + k\n⊢ Odd (card (filter (fun w => w ≠ v ∧ Odd (degree G w)) univ))",
"state_before... | [
158,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.mul_univ_of_one_mem | [] | [
936,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
935,
1
] |
Mathlib/Topology/Category/TopCat/Opens.lean | TopologicalSpace.Opens.map_comp_obj_unop | [] | [
212,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.coe_imK | [] | [
156,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Deprecated/Group.lean | IsGroupHom.map_div | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : Group α\ninst✝ : Group β\nf : α → β\nhf✝ hf : IsGroupHom f\na b : α\n⊢ f (a / b) = f a / f b",
"tactic": "simp_rw [div_eq_mul_inv, hf.map_mul, hf.map_inv]"
}
] | [
308,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/Data/Set/Intervals/Monotone.lean | MonotoneOn.Iic | [] | [
61,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
11
] |
Mathlib/Analysis/InnerProductSpace/Calculus.lean | ContDiffOn.inner | [] | [
90,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.image_smul_distrib | [] | [
766,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
764,
1
] |
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