file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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|---|---|---|---|---|---|---|
Mathlib/Algebra/GCDMonoid/Basic.lean | Associated.gcd_eq_left | [] | [
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37
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499,
1
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Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.prod_pair | [
{
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"tactic": "rw [insert_eq_cons, prod_cons, prod_singleton]"
}
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113,
49
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Mathlib/Order/Monotone/Union.lean | MonotoneOn.union_right | [
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Std/Data/RBMap/Lemmas.lean | Std.RBNode.Stream.foldl_eq_foldl_toList | [
{
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}
] | [
383,
98
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Mathlib/GroupTheory/Sylow.lean | Sylow.prime_dvd_card_quotient_normalizer | [
{
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Mathlib/Algebra/Field/Basic.lean | div_sub' | [
{
"state_after": "no goals",
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] | [
246,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | Filter.Tendsto.liminf_eq | [] | [
207,
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Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.weightedVSubVSubWeights_self | [
{
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681,
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Mathlib/CategoryTheory/NatIso.lean | CategoryTheory.NatIso.inv_inv_app | [
{
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] | [
166,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.Equiv.map_rel | [] | [
803,
31
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Mathlib/Data/Seq/Seq.lean | Stream'.Seq1.join_nil | [] | [
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Mathlib/Topology/Connected.lean | Continuous.image_connectedComponent_subset | [] | [
712,
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Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.derivFamily_lt_ord_lift | [
{
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Mathlib/RingTheory/Ideal/Basic.lean | Ideal.span_iUnion | [] | [
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26
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Mathlib/GroupTheory/Solvable.lean | derivedSeries_normal | [
{
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Mathlib/Algebra/Star/Prod.lean | Prod.snd_star | [] | [
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Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.succ_one | [
{
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Mathlib/Logic/Equiv/Defs.lean | Equiv.permCongr_def | [] | [
432,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Monad/Algebra.lean | CategoryTheory.Monad.algebra_iso_of_iso | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\nT : Monad C\nA B : Algebra T\nf : A ⟶ B\ninst✝ : IsIso f.f\n⊢ T.map (inv f.f) ≫ T.map f.f ≫ B.a = B.a",
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215,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Group/Units.lean | Units.val_eq_one | [
{
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] | [
238,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Multiset/Basic.lean | Multiset.mem_of_mem_nsmul | [
{
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687,
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Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.join_congr | [] | [
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19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Cover.lean | Wcovby.le_and_le_iff | [
{
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"tactic": "refine' ⟨fun h2 => h.eq_or_eq h2... | [
172,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Order/Field/Basic.lean | one_lt_inv_iff | [] | [
326,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/Coprime/Lemmas.lean | IsCoprime.prod_left | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.symm_conj_apply | [] | [
2380,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Fintype/BigOperators.lean | Function.Bijective.prod_comp | [] | [
210,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Algebra/ContinuousAffineMap.lean | ContinuousAffineMap.zero_apply | [] | [
190,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
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Mathlib/Data/Multiset/Basic.lean | Multiset.pmap_eq_map_attach | [] | [
1530,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Instances/ENNReal.lean | ENNReal.Tendsto.mul_const | [
{
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"tactic"... | [
384,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.coeff_sub | [
{
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"state_before": "R : Type u\na b : R\nm n✝ : ℕ\ninst✝ : Ring R\np q : R[X]\nn :... | [
1168,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/BooleanAlgebra.lean | disjoint_compl_right_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.60077\nw x y z : α\ninst✝ : BooleanAlgebra α\n⊢ Disjoint x (yᶜ) ↔ x ≤ y",
"tactic": "rw [← le_compl_iff_disjoint_right, compl_compl]"
}
] | [
739,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
738,
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Iic_union_Ioo_eq_Iio | [] | [
1431,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1429,
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Mathlib/Order/Disjoint.lean | Disjoint.sup_right | [] | [
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32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
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Mathlib/Data/Set/Image.lean | Set.preimage_comp | [] | [
150,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
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Mathlib/Data/List/Cycle.lean | Cycle.card_toMultiset | [
{
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"state_before": "α : Type u_1\ns : Cycle α\n⊢ ∀ (a : List α), ↑Multiset.card (toMultiset (Quotient.mk'' a)) = length (Quotient.mk'' a)",
"tactic": "simp"
}
] | [
704,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometry.isometry | [] | [
160,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
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Mathlib/Analysis/Convex/Star.lean | StarConvex.mem_smul | [
{
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"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.156386\ninst✝² ... | [
411,
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Mathlib/Algebra/Free.lean | FreeMagma.toFreeSemigroup_map | [] | [
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51
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736,
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Mathlib/Order/Hom/Set.lean | OrderIso.image_preimage | [] | [
60,
29
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59,
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Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.map_ne_zero | [] | [
146,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
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Mathlib/FieldTheory/SplittingField/IsSplittingField.lean | Polynomial.IsSplittingField.splits | [] | [
62,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
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Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.map_zero | [] | [
98,
22
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97,
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.sum_monomial_eq | [] | [
361,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
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Mathlib/RingTheory/Ideal/LocalRing.lean | LocalRing.of_isUnit_or_isUnit_one_sub_self | [] | [
167,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
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Mathlib/CategoryTheory/Shift/Basic.lean | CategoryTheory.shift_shiftFunctorCompIsoId_neg_add_self_inv_app | [
{
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Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean | HasFDerivAt.restrictScalars | [] | [
67,
4
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65,
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Mathlib/Analysis/NormedSpace/Exponential.lean | hasFPowerSeriesAt_exp_zero_of_radius_pos | [] | [
248,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
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Mathlib/Combinatorics/SimpleGraph/Density.lean | Rel.card_interedges_finpartition_right | [
{
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Mathlib/LinearAlgebra/Basic.lean | LinearMap.pow_apply | [
{
"state_after": "case zero\nR : Type u_1\nR₁ : Type ?u.141510\nR₂ : Type ?u.141513\nR₃ : Type ?u.141516\nR₄ : Type ?u.141519\nS : Type ?u.141522\nK : Type ?u.141525\nK₂ : Type ?u.141528\nM : Type u_2\nM' : Type ?u.141534\nM₁ : Type ?u.141537\nM₂ : Type ?u.141540\nM₃ : Type ?u.141543\nM₄ : Type ?u.141546\nN : T... | [
331,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/Data/Finite/Basic.lean | Finite.sum_right | [] | [
94,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/MeasureTheory/Integral/ExpDecay.lean | exp_neg_integrableOn_Ioi | [
{
"state_after": "a b : ℝ\nh : 0 < b\nthis : Tendsto (fun x => -exp (-b * x) / b) atTop (𝓝 (-0 / b))\n⊢ IntegrableOn (fun x => exp (-b * x)) (Ioi a)",
"state_before": "a b : ℝ\nh : 0 < b\n⊢ IntegrableOn (fun x => exp (-b * x)) (Ioi a)",
"tactic": "have : Tendsto (fun x => -exp (-b * x) / b) atTop (𝓝 (... | [
38,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
] |
Mathlib/Topology/Algebra/Order/Compact.lean | ContinuousOn.exists_forall_le' | [] | [
286,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/CategoryTheory/Limits/Cones.lean | CategoryTheory.Limits.CoconeMorphism.ext | [
{
"state_after": "case mk\nJ : Type u₁\ninst✝³ : Category J\nK : Type u₂\ninst✝² : Category K\nC : Type u₃\ninst✝¹ : Category C\nD : Type u₄\ninst✝ : Category D\nF : J ⥤ C\nc c' : Cocone F\ng : c ⟶ c'\nHom✝ : c.pt ⟶ c'.pt\nw✝ : ∀ (j : J), c.ι.app j ≫ Hom✝ = c'.ι.app j\nw : (mk Hom✝).Hom = g.Hom\n⊢ mk Hom✝ = g",... | [
505,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
1
] |
Mathlib/Data/W/Basic.lean | WType.elim_injective | [
{
"state_after": "case intro\nα : Type u_2\nβ : α → Type u_3\nγ : Type u_1\nfγ : (a : α) × (β a → γ) → γ\nfγ_injective : Function.Injective fγ\na₁ : α\nf₁ f₂ : β a₁ → WType fun a => β a\nh✝ : elim γ fγ (mk a₁ f₁) = elim γ fγ (mk a₁ f₂)\nh : HEq (fun b => elim γ fγ (f₁ b)) fun b => elim γ fγ (f₂ b)\n⊢ mk a₁ f₁ =... | [
101,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Data/PFun.lean | PFun.dom_prodMap | [] | [
670,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
668,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | ofAdd_multiset_prod | [
{
"state_after": "ι : Type ?u.999738\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf g : α → β\ninst✝ : AddCommMonoid α\ns : Multiset α\n⊢ Multiset.sum s = Multiset.prod s",
"state_before": "ι : Type ?u.999738\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf g : α → β\ni... | [
2350,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2349,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.partiallyWellOrderedOn_singleton | [] | [
307,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/Combinatorics/Colex.lean | Colex.colex_lt_of_ssubset | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrder α\nA B : Finset α\nh : A ⊂ B\n⊢ toColex ∅ < toColex (B \\ A)",
"state_before": "α : Type u_1\ninst✝ : LinearOrder α\nA B : Finset α\nh : A ⊂ B\n⊢ toColex A < toColex B",
"tactic": "rw [← sdiff_lt_sdiff_iff_lt, sdiff_eq_empty_iff_subset.2 h.1]"
},
{... | [
351,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioi_inj | [] | [
1124,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1123,
1
] |
Mathlib/RingTheory/Coprime/Lemmas.lean | IsCoprime.of_prod_right | [] | [
80,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | sInfHom.cancel_right | [] | [
489,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
487,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.set_biUnion_singleton | [] | [
2007,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2006,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_quadratic_le | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q : R[X]\nι : Type ?u.936788\n⊢ degree (↑C a * X ^ 2 + ↑C b * X + ↑C c) ≤ 2",
"tactic": "simpa only [add_assoc] using\n degree_add_le_of_degree_le (degree_C_mul_X_pow_le 2 a)\n (le_trans... | [
1176,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1173,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.finrank_adjoin_eq_one_iff | [] | [
740,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
739,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_const_add_Ioc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\n⊢ (fun x => a + x) ⁻¹' Ioc b c = Ioc (b - a) (c - a)",
"tactic": "simp [← Ioi_inter_Iic]"
}
] | [
74,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisInsertion.u_injective | [] | [
530,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.eq_pow_of_mul_eq_pow | [
{
"state_after": "case pos\nα : Type u_1\ninst✝² : CancelCommMonoidWithZero α\ndec_irr : (p : Associates α) → Decidable (Irreducible p)\ninst✝¹ : UniqueFactorizationMonoid α\ndec : DecidableEq α\ndec' : DecidableEq (Associates α)\ninst✝ : Nontrivial α\na b c : Associates α\nha : a ≠ 0\nhb : b ≠ 0\nhab : ∀ (d : ... | [
1885,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1870,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.type_uLift | [
{
"state_after": "α : Type u\nβ : Type ?u.103331\nγ : Type ?u.103334\nr✝ : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nr : α → α → Prop\ninst✝ : IsWellOrder α r\n⊢ (type fun x y => r x.down y.down) = lift (type r)",
"state_before": "α : Type u\nβ : Type ?u.103331\nγ : Type ?u.103334\nr✝ : α → α → Prop... | [
659,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
656,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.Infinite.not_infinitesimal | [] | [
486,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
485,
1
] |
Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.monotone_upper | [] | [
236,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.and_xor_distrib_left | [
{
"state_after": "no goals",
"state_before": "a b c : Bool\n⊢ (a && xor b c) = xor (a && b) (a && c)",
"tactic": "cases a <;> simp"
}
] | [
294,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.replicate_left_injective | [] | [
949,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
947,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.codeSupp_fix | [
{
"state_after": "no goals",
"state_before": "f : Code\nk : Cont'\n⊢ codeSupp (Code.fix f) k = trStmts₁ (trNormal (Code.fix f) k) ∪ codeSupp f (Cont'.fix f k)",
"tactic": "simp [codeSupp, codeSupp', contSupp, Finset.union_assoc, Finset.union_left_comm,\n Finset.union_left_idem]"
}
] | [
1859,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1856,
1
] |
Mathlib/Analysis/InnerProductSpace/GramSchmidtOrtho.lean | gramSchmidt_orthogonal | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_3\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : InnerProductSpace 𝕜 E\nι : Type u_1\ninst✝² : LinearOrder ι\ninst✝¹ : LocallyFiniteOrderBot ι\ninst✝ : IsWellOrder ι fun x x_1 => x < x_1\nf : ι → E\n⊢ ∀ (a b : ι), a < b → inner (gramSchmidt 𝕜 f a) (gra... | [
114,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/LinearAlgebra/Matrix/Charpoly/LinearMap.lean | Matrix.Represents.eq | [] | [
154,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/RingTheory/AlgebraicIndependent.lean | AlgHom.algebraicIndependent_iff | [] | [
176,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/InverseDeriv.lean | Real.hasStrictDerivAt_arcsin | [] | [
57,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.Eventually.diag_of_prod | [
{
"state_after": "case intro.intro.intro.intro\nα : Type u_1\nβ : Type ?u.9533\nγ : Type ?u.9536\nδ : Type ?u.9539\nι : Sort ?u.9542\ns✝ : Set α\nt✝ : Set β\nf✝ : Filter α\ng : Filter β\nf : Filter α\np : α × α → Prop\nh : ∀ᶠ (i : α × α) in f ×ˢ f, p i\nt : α → Prop\nht : ∀ᶠ (x : α) in f, t x\ns : α → Prop\nhs ... | [
195,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
src/lean/Init/SimpLemmas.lean | eq_true | [] | [
15,
41
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
14,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | RingHom.mem_range | [] | [
659,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
658,
1
] |
Mathlib/LinearAlgebra/Matrix/Polynomial.lean | Polynomial.coeff_det_X_add_C_zero | [
{
"state_after": "n : Type u_1\nα : Type u_2\ninst✝² : DecidableEq n\ninst✝¹ : Fintype n\ninst✝ : CommRing α\nA B : Matrix n n α\n⊢ ∑ b : Equiv.Perm n, coeff (↑sign b • ∏ i : n, (X • Matrix.map A ↑C + Matrix.map B ↑C) (↑b i) i) 0 =\n ∑ σ : Equiv.Perm n, ↑sign σ • ∏ i : n, B (↑σ i) i",
"state_before": "n ... | [
80,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Data/Set/Image.lean | Set.preimage_compl_eq_image_compl | [] | [
365,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.ncard_eq_ofBijective | [
{
"state_after": "α : Type u_1\nβ : Type ?u.71917\ns t : Set α\na b x y : α\nf✝ : α → β\nn : ℕ\nf : (i : ℕ) → i < n → α\nhf : ∀ (a : α), a ∈ s → ∃ i h, f i h = a\nhf' : ∀ (i : ℕ) (h : i < n), f i h ∈ s\nf_inj : ∀ (i j : ℕ) (hi : i < n) (hj : j < n), f i hi = f j hj → i = j\nhs : autoParam (Set.Finite s) _auto✝\... | [
360,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/Topology/Algebra/FilterBasis.lean | GroupFilterBasis.conj | [] | [
118,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_add_mul_meas_add_le_le_lintegral | [
{
"state_after": "case intro.intro.intro\nα : Type u_1\nβ : Type ?u.953853\nγ : Type ?u.953856\nδ : Type ?u.953859\nm : MeasurableSpace α\nμ ν : Measure α\nf g : α → ℝ≥0∞\nhle : f ≤ᵐ[μ] g\nhg : AEMeasurable g\nε : ℝ≥0∞\nφ : α → ℝ≥0∞\nhφm : Measurable φ\nhφ_le : φ ≤ f\nhφ_eq : (∫⁻ (a : α), f a ∂μ) = ∫⁻ (a : α), ... | [
822,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
807,
1
] |
Mathlib/Algebra/Order/Module.lean | smul_le_smul_iff_of_neg | [
{
"state_after": "k : Type u_1\nM : Type u_2\nN : Type ?u.89573\ninst✝³ : LinearOrderedField k\ninst✝² : OrderedAddCommGroup M\ninst✝¹ : Module k M\ninst✝ : OrderedSMul k M\na b : M\nc : k\nhc : c < 0\n⊢ -c • b ≤ -c • a ↔ b ≤ a",
"state_before": "k : Type u_1\nM : Type u_2\nN : Type ?u.89573\ninst✝³ : Linea... | [
163,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.cast_ofZNum | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : AddGroupWithOne α\nn : ZNum\n⊢ ↑(ofZNum n) = ↑(toNat ↑n)",
"tactic": "rw [← cast_to_nat, ofZNum_toNat]"
}
] | [
1307,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1306,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.coeff_eq_zero | [] | [
101,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.zero_lt_one | [] | [
1882,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1881,
11
] |
Std/Data/Int/Lemmas.lean | Int.lt_of_add_lt_add_left | [
{
"state_after": "a b c : Int\nh : a + b < a + c\nthis : -a + (a + b) < -a + (a + c)\n⊢ b < c",
"state_before": "a b c : Int\nh : a + b < a + c\n⊢ b < c",
"tactic": "have : -a + (a + b) < -a + (a + c) := Int.add_lt_add_left h _"
},
{
"state_after": "a b c : Int\nh : a + b < a + c\nthis : b < c\n... | [
771,
13
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
768,
11
] |
Mathlib/Data/Int/Cast/Lemmas.lean | toLex_intCast | [] | [
409,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/Data/Int/ConditionallyCompleteOrder.lean | Int.csInf_of_not_bdd_below | [
{
"state_after": "no goals",
"state_before": "s : Set ℤ\nh : ¬BddBelow s\n⊢ ¬(Set.Nonempty s ∧ BddBelow s)",
"tactic": "simp [h]"
}
] | [
96,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/CategoryTheory/Yoneda.lean | CategoryTheory.yonedaSectionsSmall_hom | [] | [
416,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
] |
Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.prod_hom₂ | [
{
"state_after": "no goals",
"state_before": "ι : Type u_3\nα : Type u_4\nβ : Type u_1\nγ : Type u_2\ninst✝² : CommMonoid α\ns✝ t : Multiset α\na : α\nm : Multiset ι\nf✝ g : ι → α\ninst✝¹ : CommMonoid β\ninst✝ : CommMonoid γ\ns : Multiset ι\nf : α → β → γ\nhf : ∀ (a b : α) (c d : β), f (a * b) (c * d) = f a... | [
178,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_insert | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1731961\nγ : Type ?u.1731964\nδ : Type ?u.1731967\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝ : MeasurableSingletonClass α\na : α\ns : Set α\nh : ¬a ∈ s\nf : α → ℝ≥0∞\n⊢ Disjoint s {a}",
"state_before": "α : Type u_1\nβ : Type ?u.1731961\nγ : Type ?u.1731964\nδ... | [
1474,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1470,
1
] |
Std/Data/PairingHeap.lean | Std.PairingHeapImp.Heap.size_tail?_lt | [
{
"state_after": "α : Type u_1\nle : α → α → Bool\ns' s : Heap α\n⊢ Option.map (fun x => x.snd) (deleteMin le s) = some s' → size s' < size s",
"state_before": "α : Type u_1\nle : α → α → Bool\ns' s : Heap α\n⊢ tail? le s = some s' → size s' < size s",
"tactic": "simp only [Heap.tail?]"
},
{
"st... | [
163,
53
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
159,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.mul_equiv_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝² : LinearOrderedField α\ninst✝¹ : Ring β\nabv : β → α\ninst✝ : IsAbsoluteValue abv\ng f : CauSeq β abv\nhf : f ≈ 0\nthis : LimZero (f - 0)\n⊢ LimZero f",
"tactic": "simpa"
},
{
"state_after": "no goals",
"state_b... | [
531,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
528,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.exists_update_iff | [
{
"state_after": "α : Sort u\nβ : α → Sort v\nα' : Sort w\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq α'\nf✝ g : (a : α) → β a\na✝ : α\nb✝ : β a✝\nf : (a : α) → β a\na : α\nb : β a\np : (a : α) → β a → Prop\n⊢ ¬(¬p a b ∧ ∀ (x : α), x ≠ a → ¬p x (f x)) ↔ p a b ∨ ∃ x x_1, p x (f x)",
"state_before": "α : Sor... | [
591,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
1
] |
Mathlib/Data/Semiquot.lean | Semiquot.ext_s | [
{
"state_after": "α : Type u_1\nβ : Type ?u.885\nq₁ q₂ : Semiquot α\nh : q₁.s = q₂.s\n⊢ q₁ = q₂",
"state_before": "α : Type u_1\nβ : Type ?u.885\nq₁ q₂ : Semiquot α\n⊢ q₁ = q₂ ↔ q₁.s = q₂.s",
"tactic": "refine' ⟨congr_arg _, fun h => _⟩"
},
{
"state_after": "case mk'\nα : Type u_1\nβ : Type ?u.8... | [
53,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
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