file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.le_sup_iff | [
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_mul_C' | [
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199,
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Mathlib/Order/WellFoundedSet.lean | Set.PartiallyWellOrderedOn.prod | [
{
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Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.sum_ite_self_eq_aux | [
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Mathlib/Algebra/DirectSum/Basic.lean | DirectSum.addHom_ext' | [] | [
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Mathlib/Data/Multiset/Antidiagonal.lean | Multiset.prod_map_add | [
{
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Mathlib/Computability/Partrec.lean | Computable.ofOption | [
{
"state_after": "case some\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.37095\nσ : Type ?u.37098\ninst✝³ : Primcodable α\ninst✝² : Primcodable β\ninst✝¹ : Primcodable γ\ninst✝ : Primcodable σ\nf : α → Option β\nhf : Computable f\nn : ℕ\na : α\n⊢ ↑(Nat.ppred (encode (f a))) = map encode ↑(f a)",
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Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.domCoprod.summand_eq_zero_of_smul_invariant | [
{
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Mathlib/Order/GaloisConnection.lean | GaloisConnection.u_comm_of_l_comm | [] | [
362,
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Mathlib/Data/Nat/Log.lean | Nat.log_zero_right | [] | [
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Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.prod_sum_index | [] | [
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531,
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Mathlib/RingTheory/Subsemiring/Basic.lean | RingHom.restrict_apply | [] | [
1137,
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1136,
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Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | Real.continuousAt_rpow_const | [
{
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"tactic": "change ContinuousAt ((fun p : ℝ × ℝ => p.1 ^ p.2) ∘ fun y : ℝ => (y, q)) x"
},
{
"state_after"... | [
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Std/Data/Array/Lemmas.lean | Array.back_eq_back? | [
{
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}
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Mathlib/Data/Set/Pairwise/Basic.lean | Set.PairwiseDisjoint.mono | [] | [
258,
28
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Mathlib/Combinatorics/SetFamily/Shadow.lean | Finset.upShadow_empty | [] | [
197,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Algebra/Order/Field.lean | Filter.Tendsto.atTop_mul_neg | [
{
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Mathlib/Analysis/Calculus/Deriv/Add.lean | hasDerivAtFilter_neg | [] | [
243,
50
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Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | UniformFun.hasBasis_uniformity | [] | [
313,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Pi/Algebra.lean | Pi.prod_snd_fst | [] | [
352,
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Mathlib/Data/Complex/Exponential.lean | Real.expNear_zero | [
{
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}
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Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.antilipschitz_of_norm_ge | [
{
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Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.ortho_smul_right | [
{
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Mathlib/Algebra/Hom/Group.lean | MonoidHom.mk_coe | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/List/Perm.lean | List.subset_cons_diff | [] | [
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Mathlib/Algebra/BigOperators/Finsupp.lean | MonoidHom.finsupp_prod_apply | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.trans_assoc | [] | [
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Mathlib/Algebra/Hom/Centroid.lean | CentroidHom.coe_toAddMonoidHom | [] | [
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Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.inf_principal | [
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Mathlib/Algebra/Order/Pi.lean | Function.const_lt_one | [] | [
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Mathlib/Order/Interval.lean | Interval.coe_top | [] | [
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Mathlib/RingTheory/DedekindDomain/PID.lean | IsDedekindDomain.isPrincipalIdealRing_localization_over_prime | [
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Mathlib/Data/List/Rotate.lean | List.rotate_rotate | [
{
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}
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Mathlib/Algebra/Free.lean | FreeSemigroup.head_mul | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Filter/Lift.lean | Filter.lift'_pure | [
{
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}
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Mathlib/Logic/Embedding/Basic.lean | Function.Embedding.toFun_eq_coe | [] | [
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Mathlib/Order/Filter/Basic.lean | Filter.seq_eq_filter_seq | [] | [
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Mathlib/Dynamics/OmegaLimit.lean | mem_omegaLimit_singleton_iff_map_cluster_point | [
{
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"tactic": "simp_rw [mem_omegaLimit_iff_frequently, mapClu... | [
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Mathlib/RepresentationTheory/Action.lean | Action.id_hom | [] | [
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurable_cInf | [] | [
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Mathlib/Order/Basic.lean | lt_of_eq_of_lt' | [] | [
203,
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202,
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Mathlib/Data/Set/Pairwise/Basic.lean | Set.pairwise_insert_of_symmetric_of_not_mem | [
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Mathlib/RingTheory/IntegralClosure.lean | IsIntegral.multiset_prod | [] | [
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Mathlib/Algebra/Star/Basic.lean | star_eq_zero | [] | [
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Mathlib/Algebra/Hom/Centroid.lean | CentroidHom.nsmul_apply | [] | [
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Mathlib/Control/Functor/Multivariate.lean | MvFunctor.id_map | [] | [
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.omega_pos | [] | [
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Mathlib/Order/Atoms.lean | GaloisCoinsertion.isCoatom_of_l_top | [] | [
771,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/List/Sort.lean | List.Sorted.lt_of_le | [] | [
54,
42
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Mathlib/Topology/Constructions.lean | embedding_sigma_map | [
{
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | fderivWithin_univ | [] | [
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Mathlib/Algebra/Hom/GroupAction.lean | MulSemiringActionHom.map_sub | [] | [
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Mathlib/GroupTheory/Perm/Fin.lean | Fin.cycleRange_last | [
{
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238,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Data/Nat/Factors.lean | Nat.factors_subset_of_dvd | [] | [
238,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.tail_support_append | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v w : V\np : Walk G u v\np' : Walk G v w\n⊢ List.tail (support (append p p')) = List.tail (support p) ++ List.tail (support p')",
"tactic": "rw [support_a... | [
567,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
565,
1
] |
Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.LocalInvariantProp.liftPropOn_chart_symm | [] | [
529,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
527,
1
] |
Mathlib/Data/Set/Intervals/Monotone.lean | MonotoneOn.Ici | [] | [
45,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
11
] |
Mathlib/RingTheory/NonZeroDivisors.lean | le_nonZeroDivisors_of_noZeroDivisors | [] | [
143,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Data/Rat/NNRat.lean | NNRat.coe_mk | [] | [
95,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Ordered.lean | lineMap_lt_map_iff_slope_lt_slope_left | [] | [
239,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Data/Set/Countable.lean | Set.Countable.union | [] | [
220,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Algebra/Group/Pi.lean | Pi.single_mul_right_apply | [] | [
523,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
] |
Mathlib/Topology/StoneCech.lean | denseInducing_pure | [] | [
146,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.Red.exact | [] | [
668,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
665,
1
] |
Mathlib/Order/JordanHolder.lean | CompositionSeries.toList_injective | [
{
"state_after": "X : Type u\ninst✝¹ : Lattice X\ninst✝ : JordanHolderLattice X\ns₁ s₂ : CompositionSeries X\nh : List.ofFn s₁.series = List.ofFn s₂.series\nh₁ : s₁.length = s₂.length\n⊢ s₁ = s₂",
"state_before": "X : Type u\ninst✝¹ : Lattice X\ninst✝ : JordanHolderLattice X\ns₁ s₂ : CompositionSeries X\nh ... | [
245,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.isomorphisms.iff | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\nD : Type ?u.59249\ninst✝ : Category D\nX Y : C\nf : X ⟶ Y\n⊢ isomorphisms C f ↔ IsIso f",
"tactic": "rfl"
}
] | [
404,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Analysis/ODE/PicardLindelof.lean | PicardLindelof.proj_of_mem | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nv : PicardLindelof E\nt : ℝ\nht : t ∈ Icc v.tMin v.tMax\n⊢ ↑(proj v t) = t",
"tactic": "simp only [proj, projIcc_of_mem v.tMin_le_tMax ht]"
}
] | [
152,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Std/Data/List/Lemmas.lean | List.isPrefix.filter | [
{
"state_after": "case intro\nα : Type u_1\np : α → Bool\nl₁ xs : List α\n⊢ List.filter p l₁ <+: List.filter p (l₁ ++ xs)",
"state_before": "α : Type u_1\np : α → Bool\nl₁ l₂ : List α\nh : l₁ <+: l₂\n⊢ List.filter p l₁ <+: List.filter p l₂",
"tactic": "obtain ⟨xs, rfl⟩ := h"
},
{
"state_after": ... | [
1739,
42
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1736,
1
] |
Mathlib/Algebra/Group/Semiconj.lean | SemiconjBy.units_val_iff | [] | [
165,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Order/LocallyFinite.lean | Ico_toDual | [
{
"state_after": "α : Type u_1\nβ : Type ?u.112926\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ninst✝ : LocallyFiniteOrder α\na b : α\n⊢ Ico (↑toDual a) (↑toDual b) = Ioc b a",
"state_before": "α : Type u_1\nβ : Type ?u.112926\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ninst✝ : LocallyFiniteOrder α\na b : α\n⊢... | [
838,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
834,
1
] |
Mathlib/Logic/Equiv/Fin.lean | Fin.snoc_eq_cons_rotate | [
{
"state_after": "case h.mk\nm n : ℕ\nα : Type u_1\nv : Fin n → α\na : α\ni : ℕ\nh : i < n + 1\n⊢ snoc v a { val := i, isLt := h } = cons a v (↑(finRotate (n + 1)) { val := i, isLt := h })",
"state_before": "m n : ℕ\nα : Type u_1\nv : Fin n → α\na : α\n⊢ snoc v a = fun i => cons a v (↑(finRotate (n + 1)) i)... | [
427,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.subtype_comp_ofLe | [
{
"state_after": "case h.mk\nR : Type u_1\nR₁ : Type ?u.394963\nR₂ : Type ?u.394966\nR₃ : Type ?u.394969\nR₄ : Type ?u.394972\nS : Type ?u.394975\nK : Type ?u.394978\nK₂ : Type ?u.394981\nM : Type u_2\nM' : Type ?u.394987\nM₁ : Type ?u.394990\nM₂ : Type ?u.394993\nM₃ : Type ?u.394996\nM₄ : Type ?u.394999\nN : T... | [
641,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
638,
1
] |
Mathlib/Data/Polynomial/Splits.lean | Polynomial.adjoin_rootSet_eq_range | [
{
"state_after": "F : Type u\nK : Type v\nL : Type w\ninst✝⁴ : Field K\ninst✝³ : Field L\ninst✝² : Field F\ni : K →+* L\ninst✝¹ : Algebra F K\ninst✝ : Algebra F L\np : F[X]\nh : Splits (algebraMap F K) p\nf : K →ₐ[F] L\n⊢ Subalgebra.map f (Algebra.adjoin F (rootSet p K)) = Subalgebra.map f ⊤ ↔ Algebra.adjoin F ... | [
348,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
Mathlib/Algebra/Group/Commute.lean | Commute.mul_mul_mul_comm | [
{
"state_after": "no goals",
"state_before": "G : Type ?u.3529\nS : Type u_1\ninst✝ : Semigroup S\na✝ b c : S\nhbc : Commute b c\na d : S\n⊢ a * b * (c * d) = a * c * (b * d)",
"tactic": "simp only [hbc.left_comm, mul_assoc]"
}
] | [
132,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
11
] |
Mathlib/Data/Set/Intervals/Disjoint.lean | Set.biUnion_Ioc_eq_Ioi_self_iff | [
{
"state_after": "no goals",
"state_before": "ι : Sort u\nα : Type v\nβ : Type w\ninst✝ : LinearOrder α\na₁ a₂ b₁ b₂ : α\np : ι → Prop\nf : (i : ι) → p i → α\na : α\n⊢ (⋃ (i : ι) (hi : p i), Ioc a (f i hi)) = Ioi a ↔ ∀ (x : α), a < x → ∃ i hi, x ≤ f i hi",
"tactic": "simp [← Ioi_inter_Iic, ← inter_iUnio... | [
174,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_restrict_of_ae_restrict_of_subset | [] | [
2845,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2843,
1
] |
Mathlib/Data/PFunctor/Multivariate/M.lean | MvPFunctor.M.bisim' | [
{
"state_after": "case refine_3\nn : ℕ\nP : MvPFunctor (n + 1)\nα : TypeVec n\nR : M P α → M P α → Prop\nh : ∀ (x y : M P α), R x y → (TypeVec.id ::: Quot.mk R) <$$> dest P x = (TypeVec.id ::: Quot.mk R) <$$> dest P y\nx y : M P α\nr : R x y\nthis : ∀ (x y : M P α), EqvGen R x y → x = y\n⊢ x = y\n\ncase refine_... | [
365,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.toList_scanl | [] | [
348,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.Nonempty.smul | [] | [
1329,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1328,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.smul_iInter₂_subset | [] | [
290,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/Algebra/Divisibility/Basic.lean | dvd_of_mul_right_dvd | [] | [
91,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.iterate_pos_eq_iff | [
{
"state_after": "no goals",
"state_before": "f g : CircleDeg1Lift\nx : ℝ\nm : ℤ\nn : ℕ\nhn : 0 < n\n⊢ (↑f^[n]) x = x + ↑n * ↑m ↔ ↑f x = x + ↑m",
"tactic": "simpa only [nsmul_eq_mul, add_right_iterate] using\n (f.commute_add_int m).iterate_pos_eq_iff_map_eq f.monotone (strictMono_id.add_const (m : ℝ)) ... | [
603,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
600,
1
] |
Mathlib/FieldTheory/Finite/Basic.lean | FiniteField.sum_pow_lt_card_sub_one | [
{
"state_after": "case pos\nK : Type u_1\nR : Type ?u.640358\ninst✝¹ : Field K\ninst✝ : Fintype K\ni : ℕ\nh : i < q - 1\nhi : i = 0\n⊢ ∑ x : K, x ^ i = 0\n\ncase neg\nK : Type u_1\nR : Type ?u.640358\ninst✝¹ : Field K\ninst✝ : Fintype K\ni : ℕ\nh : i < q - 1\nhi : ¬i = 0\n⊢ ∑ x : K, x ^ i = 0",
"state_befor... | [
224,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Data/Fintype/Card.lean | Fintype.card_of_subtype | [
{
"state_after": "α : Type u_1\nβ : Type ?u.3349\nγ : Type ?u.3352\np : α → Prop\ns : Finset α\nH : ∀ (x : α), x ∈ s ↔ p x\ninst✝ : Fintype { x // p x }\n⊢ card { x // p x } = card { x // p x }",
"state_before": "α : Type u_1\nβ : Type ?u.3349\nγ : Type ?u.3352\np : α → Prop\ns : Finset α\nH : ∀ (x : α), x ... | [
131,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.mul_dvd_mul | [
{
"state_after": "no goals",
"state_before": "a b c d e : Nat\nhe : b = a * e\nf : Nat\nhf : d = c * f\n⊢ b * d = a * c * (e * f)",
"tactic": "simp [he, hf, Nat.mul_assoc, Nat.mul_left_comm, Nat.mul_comm]"
}
] | [
684,
78
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
682,
11
] |
Mathlib/Order/Hom/CompleteLattice.lean | FrameHom.coe_copy | [] | [
579,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
578,
1
] |
Mathlib/Data/Set/Intervals/Monotone.lean | MonotoneOn.Ioi | [] | [
77,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
11
] |
Mathlib/Data/Multiset/Fintype.lean | Multiset.coe_mk | [] | [
87,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Data/Semiquot.lean | Semiquot.isPure_iff | [] | [
237,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.DominatedFinMeasAdditive.eq_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nE : Type ?u.102358\nF : Type ?u.102361\nF' : Type ?u.102364\nG : Type ?u.102367\n𝕜 : Type ?u.102370\np : ℝ≥0∞\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace ℝ F\ninst✝⁴ : NormedAddComm... | [
217,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_sub_const_Ico | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\n⊢ (fun x => x - a) '' Ico b c = Ico (b - a) (c - a)",
"tactic": "simp [sub_eq_neg_add]"
}
] | [
396,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.coprod.inr_desc | [] | [
651,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
649,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.norm_ofSubsingleton | [
{
"state_after": "case a\n𝕜 : Type u\nι : Type v\nι' : Type v'\nn : ℕ\nE : ι → Type wE\nE₁ : ι → Type wE₁\nE' : ι' → Type wE'\nEi : Fin (Nat.succ n) → Type wEi\nG : Type wG\nG' : Type wG'\ninst✝¹⁹ : Fintype ι\ninst✝¹⁸ : Fintype ι'\ninst✝¹⁷ : NontriviallyNormedField 𝕜\ninst✝¹⁶ : (i : ι) → NormedAddCommGroup (E... | [
518,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
510,
1
] |
Mathlib/RingTheory/Localization/Integer.lean | IsLocalization.exist_integer_multiples_of_finite | [
{
"state_after": "case intro\nR : Type u_2\ninst✝⁵ : CommRing R\nM : Submonoid R\nS : Type u_3\ninst✝⁴ : CommRing S\ninst✝³ : Algebra R S\nP : Type ?u.28129\ninst✝² : CommRing P\ninst✝¹ : IsLocalization M S\nι : Type u_1\ninst✝ : Finite ι\nf : ι → S\nval✝ : Fintype ι\n⊢ ∃ b, ∀ (i : ι), IsInteger R (↑b • f i)",
... | [
117,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.disjoint_span_singleton' | [] | [
469,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
467,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.LHom.realize_onBoundedFormula | [
{
"state_after": "case falsum\nL : Language\nL' : Language\nM : Type w\nN : Type ?u.231167\nP : Type ?u.231170\ninst✝⁴ : Structure L M\ninst✝³ : Structure L N\ninst✝² : Structure L P\nα : Type u'\nβ : Type v'\nn✝¹ : ℕ\ninst✝¹ : Structure L' M\nφ : L →ᴸ L'\ninst✝ : IsExpansionOn φ M\nn : ℕ\nv : α → M\nxs✝ : Fin ... | [
595,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
584,
1
] |
Mathlib/LinearAlgebra/Matrix/IsDiag.lean | Matrix.IsDiag.diagonal_diag | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type ?u.560\nR : Type ?u.563\nn : Type u_2\nm : Type ?u.569\ninst✝¹ : Zero α\ninst✝ : DecidableEq n\nA : Matrix n n α\nh : IsDiag A\ni : n\n⊢ diagonal (diag A) i i = A i i\n\ncase inr\nα : Type u_1\nβ : Type ?u.560\nR : Type ?u.563\nn : Type u_2\nm : Type ?u.569\nin... | [
54,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/MeasureTheory/Measure/GiryMonad.lean | MeasureTheory.Measure.bind_zero_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\ninst✝¹ : MeasurableSpace α\ninst✝ : MeasurableSpace β\nf : α → Measure β\n⊢ bind 0 f = 0",
"tactic": "simp [bind]"
}
] | [
160,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Logic/Encodable/Lattice.lean | Encodable.iUnion_decode₂_disjoint_on | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝ : Encodable β\nf : β → Set α\nhd : Pairwise (Disjoint on f)\ni j : ℕ\nij : i ≠ j\n⊢ (Disjoint on fun i => ⋃ (b : β) (_ : b ∈ decode₂ β i), f b) i j",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝ : Encodable β\nf : β → Set α\nhd : Pairwise (Disjoint o... | [
61,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Data/Finmap.lean | Finmap.insert_toFinmap | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\nb : β a\ns : AList β\n⊢ insert a b ⟦s⟧ = ⟦AList.insert a b s⟧",
"tactic": "simp [insert]"
}
] | [
485,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
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