file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_comm | [] | [
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Mathlib/CategoryTheory/Subobject/Limits.lean | CategoryTheory.Limits.imageSubobject_le | [
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Mathlib/Topology/Category/Compactum.lean | compactumToCompHaus.essSurj | [] | [
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Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiffAt.differentiableAt | [
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Mathlib/Probability/ProbabilityMassFunction/Uniform.lean | Pmf.uniformOfFintype_apply | [
{
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Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.support_finset_sum | [
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Mathlib/Topology/Algebra/ContinuousAffineMap.lean | ContinuousAffineMap.mk_coe | [
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Mathlib/Combinatorics/Quiver/SingleObj.lean | Quiver.SingleObj.toPrefunctor_symm_id | [] | [
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Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | Real.hasStrictDerivAt_rpow_const_of_ne | [
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Mathlib/Order/InitialSeg.lean | RelEmbedding.collapseF.lt | [
{
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Mathlib/Algebra/Hom/Units.lean | isUnit_map_of_leftInverse | [] | [
238,
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Mathlib/Algebra/GroupWithZero/Units/Basic.lean | Units.mk0_val | [] | [
202,
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Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.lipschitzOnWith | [] | [
130,
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129,
11
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Mathlib/NumberTheory/LegendreSymbol/MulCharacter.lean | MulChar.IsNontrivial.comp | [
{
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480,
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475,
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Mathlib/Algebra/Ring/BooleanRing.lean | toBoolRing_bot | [] | [
533,
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532,
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Mathlib/Analysis/Calculus/Deriv/Slope.lean | HasDerivWithinAt.limsup_slope_le | [] | [
101,
74
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99,
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Mathlib/LinearAlgebra/Dual.lean | Module.evalEquiv_toLinearMap | [] | [
616,
6
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614,
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Mathlib/GroupTheory/GroupAction/Prod.lean | Prod.smul_snd | [] | [
55,
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Mathlib/Algebra/Quaternion.lean | Quaternion.normSq_inv | [] | [
1392,
20
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1391,
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.eapprox_lt_top | [
{
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Mathlib/Data/Set/Basic.lean | Set.subset_union_of_subset_right | [] | [
850,
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Mathlib/Data/Fintype/BigOperators.lean | Finset.card_pi | [] | [
134,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/List/Chain.lean | List.chain'_iff_nthLe | [
{
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368,
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Mathlib/Topology/Basic.lean | mem_closure_iff | [] | [
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560,
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Mathlib/Order/CompleteLattice.lean | sSup_eq_iSup | [] | [
929,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Lie/Submodule.lean | LieIdeal.map_sup_ker_eq_map' | [
{
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Mathlib/Data/Set/List.lean | Set.range_list_map_coe | [
{
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"tactic": "rw [range_list_map, Subtype.range_coe]"
}
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Mathlib/Topology/Instances/NNReal.lean | NNReal.tendsto_tsum_compl_atTop_zero | [
{
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"tactic": "simp_rw [← tendsto_coe, coe_tsum, NNReal.coe_zero]"
},
{
... | [
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Mathlib/Data/Set/Basic.lean | Set.insert_union | [] | [
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24
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1190,
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Mathlib/Combinatorics/SimpleGraph/Clique.lean | SimpleGraph.CliqueFree.anti | [] | [
223,
44
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222,
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Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.le_ceil_map_map_zero | [] | [
509,
54
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506,
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Mathlib/CategoryTheory/Abelian/Opposite.lean | CategoryTheory.kernel.ι_op | [
{
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"state_before": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Abelian C\nX Y : C\nf : X ⟶ Y\nA B : Cᵒᵖ\ng : A ⟶ B\n⊢ (kernel.ι f.op).unop = eqToHom (_ : Y.op.unop = Y) ≫ cokernel.π f ≫ (kernelOpUnop f).inv",
"tactic": "simp [kernelOpUnop]"
}
] | [
110,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.exp_mul_I_periodic | [] | [
1363,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1362,
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Mathlib/Topology/Algebra/UniformGroup.lean | uniformContinuous_pow_const | [] | [
131,
35
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130,
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Mathlib/GroupTheory/Coset.lean | mem_leftCoset | [] | [
84,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/Matrix/DotProduct.lean | Matrix.dotProduct_self_star_eq_zero | [
{
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"tactic": "simp [Function.funext_i... | [
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Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atBot_add_left_of_ge' | [] | [
775,
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.vsub_left_mem_direction_iff_mem | [
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"state_before": "k : Type u_1\nV : Type u_2\nP : Type u... | [
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344,
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Mathlib/Algebra/Order/Monoid/Lemmas.lean | mul_lt_of_lt_of_lt_one' | [] | [
592,
35
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Mathlib/Data/ENat/Basic.lean | ENat.nat_induction | [
{
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... | [
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Mathlib/Computability/Primrec.lean | PrimrecRel.comp | [] | [
499,
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Mathlib/Data/Finsupp/Basic.lean | Finsupp.mapRange.equiv_trans | [
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Mathlib/Algebra/Module/Torsion.lean | Ideal.torsionOf_eq_bot_iff_of_noZeroSMulDivisors | [
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Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Memℒp.pos_part | [] | [
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Mathlib/GroupTheory/Submonoid/Centralizer.lean | Submonoid.centralizer_toSubsemigroup | [] | [
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_comp_neg | [
{
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862,
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861,
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Mathlib/Algebra/Quandle.lean | Rack.toEnvelGroup.univ_uniq | [] | [
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Mathlib/Data/Multiset/Basic.lean | Multiset.coe_card | [] | [
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Mathlib/LinearAlgebra/Projection.lean | Submodule.linearProjOfIsCompl_apply_eq_zero_iff | [
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174,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.TaggedPrepartition.iUnion_mk | [] | [
73,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Logic/Relation.lean | Symmetric.comap | [] | [
109,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.atBot_basis' | [] | [
148,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/LinearAlgebra/PiTensorProduct.lean | PiTensorProduct.reindex_comp_tprod | [] | [
484,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.IndepSets.inter | [] | [
238,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.IsPrime.mul_mem_iff_mem_or_mem | [
{
"state_after": "case inl\nα : Type u\nβ : Type v\na b : α\ninst✝ : CommSemiring α\nI✝ I : Ideal α\nhI : IsPrime I\nx y : α\nh : x ∈ I\n⊢ x * y ∈ I\n\ncase inr\nα : Type u\nβ : Type v\na b : α\ninst✝ : CommSemiring α\nI✝ I : Ideal α\nhI : IsPrime I\nx y : α\nh : y ∈ I\n⊢ x * y ∈ I",
"state_before": "α : Ty... | [
580,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
576,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.mul_div_mul_left | [
{
"state_after": "no goals",
"state_before": "m n k : Nat\nH : 0 < m\n⊢ m * n / (m * k) = n / k",
"tactic": "rw [← Nat.div_div_eq_div_mul, Nat.mul_div_cancel_left _ H]"
}
] | [
639,
93
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
638,
11
] |
Mathlib/Order/Lattice.lean | sup_congr_left | [] | [
294,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Std/Data/BinomialHeap.lean | Std.BinomialHeapImp.Heap.WellFormed.findMin | [
{
"state_after": "α : Type u_1\nle : α → α → Bool\nn : Nat\nk : Heap α → Heap α\nres : FindMin α\ns✝ : Heap α\nhr : FindMin.WellFormed le res\nhk : ∀ {s : Heap α}, WellFormed le n s → WellFormed le 0 (k s)\nr : Nat\na : α\nc : HeapNode α\ns : Heap α\nh : WellFormed le n (cons r a c s)\nh₁ : n ≤ r\nh₂ : HeapNode... | [
484,
87
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
474,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.exists_mem_closure_infDist_eq_dist | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.70605\nα : Type u\nβ : Type v\ninst✝² : PseudoMetricSpace α\ninst✝¹ : PseudoMetricSpace β\ns t u : Set α\nx✝ y : α\nΦ : α → β\ninst✝ : ProperSpace α\nhne : Set.Nonempty s\nx : α\n⊢ ∃ y, y ∈ closure s ∧ infDist x s = dist x y",
"tactic": "simpa on... | [
652,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
650,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.one_le_mulIndicator | [] | [
798,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
797,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Finset.lean | Set.Nonempty.cSup_mem | [
{
"state_after": "case intro\nα : Type u_1\nβ : Type ?u.9542\nγ : Type ?u.9545\ninst✝ : ConditionallyCompleteLinearOrder α\nt : Set α\na b : α\ns : Finset α\nh : Set.Nonempty ↑s\n⊢ sSup ↑s ∈ ↑s",
"state_before": "α : Type u_1\nβ : Type ?u.9542\nγ : Type ?u.9545\ninst✝ : ConditionallyCompleteLinearOrder α\ns... | [
63,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Topology/ContinuousFunction/Ordered.lean | ContinuousMap.inf_coe | [] | [
97,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/CategoryTheory/Limits/Types.lean | CategoryTheory.Limits.Types.Colimit.ι_desc_apply | [] | [
316,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Mathlib/Data/QPF/Univariate/Basic.lean | Qpf.Fix.dest_mk | [
{
"state_after": "F : Type u → Type u\ninst✝ : Functor F\nq : Qpf F\nx : F (Fix F)\n⊢ rec (Functor.map mk) (mk x) = x",
"state_before": "F : Type u → Type u\ninst✝ : Functor F\nq : Qpf F\nx : F (Fix F)\n⊢ dest (mk x) = x",
"tactic": "unfold Fix.dest"
},
{
"state_after": "F : Type u → Type u\nins... | [
348,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.nsmul_lt_aleph0_iff_of_ne_zero | [] | [
1551,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1550,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.and_xor_distrib_right | [
{
"state_after": "no goals",
"state_before": "a b c : Bool\n⊢ (xor a b && c) = xor (a && c) (b && c)",
"tactic": "cases a <;> cases b <;> cases c <;> simp"
}
] | [
298,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Std/Data/List/Lemmas.lean | List.mem_range' | [
{
"state_after": "no goals",
"state_before": "m s step : Nat\n⊢ m ∈ range' s 0 step ↔ ∃ i, i < 0 ∧ m = s + step * i",
"tactic": "simp [range', Nat.not_lt_zero]"
},
{
"state_after": "m s step n : Nat\nh : ∀ (i : Nat), i ≤ n ↔ i = 0 ∨ ∃ j, i = succ j ∧ j < n\n⊢ m ∈ range' s (n + 1) step ↔ ∃ i, i <... | [
1821,
71
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1816,
1
] |
Mathlib/Order/CompactlyGenerated.lean | Directed.iSup_inf_eq | [
{
"state_after": "no goals",
"state_before": "ι : Sort u_2\nα : Type u_1\ninst✝² : CompleteLattice α\nf : ι → α\ninst✝¹ : CompleteLattice α\ninst✝ : IsCompactlyGenerated α\na b : α\ns : Set α\nh : Directed (fun x x_1 => x ≤ x_1) f\n⊢ (⨆ (i : ι), f i) ⊓ a = ⨆ (i : ι), f i ⊓ a",
"tactic": "rw [iSup, h.dir... | [
389,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
11
] |
Mathlib/Order/Bounds/Basic.lean | IsLeast.nonempty | [] | [
349,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
src/lean/Init/Prelude.lean | Nat.le_of_ble_eq_true | [] | [
1678,
61
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1675,
1
] |
Mathlib/LinearAlgebra/Matrix/Orthogonal.lean | Matrix.transpose_hasOrthogonalCols_iff_hasOrthogonalRows | [] | [
64,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.partition_eq_of_isConj | [
{
"state_after": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ τ : Perm α\n⊢ cycleType σ = cycleType τ ↔ partition σ = partition τ",
"state_before": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ τ : Perm α\n⊢ IsConj σ τ ↔ partition σ = partition τ",
"tactic": "rw [isConj_iff_... | [
548,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
1
] |
Mathlib/Data/Set/Image.lean | Set.image_diff_preimage | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.52978\nι : Sort ?u.52981\nι' : Sort ?u.52984\nf✝ : α → β\ns✝ t✝ : Set α\nf : α → β\ns : Set α\nt : Set β\n⊢ f '' (s \\ f ⁻¹' t) = f '' s \\ t",
"tactic": "simp_rw [diff_eq, ← preimage_compl, image_inter_preimage]"
}
... | [
526,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
525,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.le_limsup_of_le | [] | [
469,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.rpow_le_rpow_of_exponent_le | [] | [
175,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioi_ssubset_Ici_self | [] | [
546,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
545,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.single_injective | [] | [
662,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
661,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_add_one | [
{
"state_after": "no goals",
"state_before": "x✝ y✝ z x : ℝ\nhx : x ≠ 0\ny : ℝ\n⊢ x ^ (y + 1) = x ^ y * x",
"tactic": "simpa using rpow_add_nat hx y 1"
}
] | [
346,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.of_c_eq_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.507248\nF : Type ?u.507251\nK : Type ?u.507254\nP Q : Cubic R\na b c d a' b' c' d' : R\ninst✝ : Semiring R\nha : P.a = 0\nhb : P.b = 0\nhc : P.c = 0\n⊢ toPoly P = ↑C P.d",
"tactic": "rw [of_b_eq_zero ha hb, hc, C_0, MulZeroClass.zer... | [
157,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
src/lean/Init/SizeOfLemmas.lean | UInt16.sizeOf | [
{
"state_after": "case mk\nval✝ : Fin size\n⊢ SizeOf.sizeOf { val := val✝ } = toNat { val := val✝ } + 2",
"state_before": "a : UInt16\n⊢ SizeOf.sizeOf a = toNat a + 2",
"tactic": "cases a"
},
{
"state_after": "no goals",
"state_before": "case mk\nval✝ : Fin size\n⊢ SizeOf.sizeOf { val := val... | [
18,
37
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
17,
9
] |
Mathlib/Topology/MetricSpace/Basic.lean | nndist_pi_const_le | [] | [
2024,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2023,
1
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.prod_eq_top | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.176800\nι : Sort ?u.176803\nκ : ι → Sort ?u.176808\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ns s₁ s₂ : UpperSet α\nt t₁ t₂ : UpperSet β\nx : α × β\n⊢ ↑(s ×ˢ t) = ↑⊤ ↔ ↑s = ↑⊤ ∨ ↑t = ↑⊤",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.176800... | [
1631,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1629,
1
] |
Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.prod_eq_zero_iff | [
{
"state_after": "ι : Type ?u.90765\nα : Type u_1\nβ : Type ?u.90771\nγ : Type ?u.90774\ninst✝² : CommMonoidWithZero α\ninst✝¹ : NoZeroDivisors α\ninst✝ : Nontrivial α\ns : Multiset α\nl : List α\n⊢ List.prod l = 0 ↔ 0 ∈ ↑l",
"state_before": "ι : Type ?u.90765\nα : Type u_1\nβ : Type ?u.90771\nγ : Type ?u.9... | [
293,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.tan_neg | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ tan (-x) = -tan x",
"tactic": "simp [tan, neg_div]"
}
] | [
1238,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1238,
1
] |
Mathlib/RingTheory/MvPolynomial/Homogeneous.lean | MvPolynomial.IsHomogeneous.mul | [] | [
191,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.coe_comap | [] | [
529,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
528,
1
] |
Mathlib/RingTheory/Ideal/IdempotentFG.lean | Ideal.isIdempotentElem_iff_of_fg | [
{
"state_after": "case mp\nR : Type u_1\ninst✝ : CommRing R\nI : Ideal R\nh : FG I\n⊢ IsIdempotentElem I → ∃ e, IsIdempotentElem e ∧ I = Submodule.span R {e}\n\ncase mpr\nR : Type u_1\ninst✝ : CommRing R\nI : Ideal R\nh : FG I\n⊢ (∃ e, IsIdempotentElem e ∧ I = Submodule.span R {e}) → IsIdempotentElem I",
"s... | [
37,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
22,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.nonempty_mk_iff | [
{
"state_after": "x : PSet\n⊢ ZFSet.Nonempty (mk x) → PSet.Nonempty x",
"state_before": "x : PSet\n⊢ ZFSet.Nonempty (mk x) ↔ PSet.Nonempty x",
"tactic": "refine' ⟨_, fun ⟨a, h⟩ => ⟨mk a, h⟩⟩"
},
{
"state_after": "case intro\nx : PSet\na : ZFSet\nh : a ∈ toSet (mk x)\n⊢ PSet.Nonempty x",
"sta... | [
849,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
845,
1
] |
Mathlib/Topology/PathConnected.lean | Path.continuous_symm | [] | [
495,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.commonNeighbors_top_eq | [
{
"state_after": "case h\nι : Sort ?u.148498\n𝕜 : Type ?u.148501\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u✝ v✝ w✝ : V\ne : Sym2 V\nv w u : V\n⊢ u ∈ commonNeighbors ⊤ v w ↔ u ∈ Set.univ \\ {v, w}",
"state_before": "ι : Sort ?u.148498\n𝕜 : Type ?u.148501\nV : Type u... | [
1050,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1047,
1
] |
Mathlib/Data/Polynomial/Reverse.lean | Polynomial.natDegree_eq_reverse_natDegree_add_natTrailingDegree | [
{
"state_after": "case pos\nR : Type u_1\ninst✝ : Semiring R\nf✝ f : R[X]\nhf : f = 0\n⊢ natDegree f = natDegree (reverse f) + natTrailingDegree f\n\ncase neg\nR : Type u_1\ninst✝ : Semiring R\nf✝ f : R[X]\nhf : ¬f = 0\n⊢ natDegree f = natDegree (reverse f) + natTrailingDegree f",
"state_before": "R : Type ... | [
291,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Data/Set/Pairwise/Basic.lean | Set.pairwise_bot_iff | [] | [
209,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/RingTheory/Adjoin/Basic.lean | Algebra.adjoin_adjoin_coe_preimage | [
{
"state_after": "case refine'_1\nR : Type u\nA : Type v\nB : Type w\ninst✝⁴ : CommSemiring R\ninst✝³ : Semiring A\ninst✝² : Semiring B\ninst✝¹ : Algebra R A\ninst✝ : Algebra R B\ns✝ t s : Set A\nx : { x // x ∈ ↑(adjoin R s) }\na : A\nha : a ∈ s\n⊢ (fun y => y ∈ adjoin R (Subtype.val ⁻¹' s)) { val := a, propert... | [
141,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/Algebra/Lie/Character.lean | LieAlgebra.lieCharacter_apply_of_mem_derived | [
{
"state_after": "R : Type u\nL : Type v\ninst✝² : CommRing R\ninst✝¹ : LieRing L\ninst✝ : LieAlgebra R L\nχ : LieCharacter R L\nx : L\nh : x ∈ Submodule.span R {m | ∃ x n, ⁅↑x, ↑n⁆ = m}\n⊢ ↑χ x = 0",
"state_before": "R : Type u\nL : Type v\ninst✝² : CommRing R\ninst✝¹ : LieRing L\ninst✝ : LieAlgebra R L\nχ... | [
63,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Order/SupIndep.lean | CompleteLattice.Independent.map_orderIso | [] | [
341,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
src/lean/Init/Core.lean | decide_true_eq_true | [] | [
695,
36
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
692,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | differentiableOn_add_const_iff | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.214809\ninst✝³ : NormedAddCommGroup G\ninst✝² : Normed... | [
226,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Topology/Algebra/Monoid.lean | le_nhds_mul | [
{
"state_after": "ι : Type ?u.8420\nα : Type ?u.8423\nX : Type ?u.8426\nM : Type u_1\nN : Type ?u.8432\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace M\ninst✝¹ : Mul M\ninst✝ : ContinuousMul M\na b : M\n⊢ map (Function.uncurry fun x x_1 => x * x_1) (𝓝 (a, b)) ≤ 𝓝 (a * b)",
"state_before": "ι : Ty... | [
146,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | summable_extend_zero | [] | [
150,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
9
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.IsPeriodicPt.trans_dvd | [] | [
135,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
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