file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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|---|---|---|---|---|---|---|
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.tan_sub_int_mul_pi | [] | [
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32
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1338,
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Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.restrict | [
{
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437,
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Mathlib/Topology/VectorBundle/Basic.lean | VectorBundleCore.mem_localTrivAt_baseSet | [] | [
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48
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763,
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Mathlib/Data/Int/ModEq.lean | Int.mod_modEq | [] | [
112,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
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Mathlib/Order/OrderIsoNat.lean | Nat.orderEmbeddingOfSet_range | [] | [
153,
31
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Std/Data/List/Lemmas.lean | List.Pairwise.sublist | [] | [
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80
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Ioc_ae_eq_Icc | [] | [
3344,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3343,
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Mathlib/CategoryTheory/Generator.lean | CategoryTheory.isSeparator_op_iff | [
{
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"tactic": "rw [IsSeparator, IsCoseparator, ← isSeparating_op_iff, Set.singleton_op]"
}
] | [
407,
75
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Mathlib/Order/Max.lean | noBotOrder_iff_noMinOrder | [] | [
159,
19
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Mathlib/Analysis/NormedSpace/Pointwise.lean | smul_closedBall | [
{
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399,
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Mathlib/Data/Nat/Choose/Central.lean | Nat.two_dvd_centralBinom_of_one_le | [
{
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"state_before": "n : ℕ\nh : 0 < n\n⊢ 2 ∣ centralBinom n",
"tactic": "rw [← Nat.succ_pred_eq_of_pos h]"
},
{
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"tactic"... | [
128,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
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Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | BilinForm.toQuadraticForm_apply | [] | [
653,
6
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652,
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Mathlib/Order/WithBot.lean | WithBot.lt_toDual_iff | [] | [
1019,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1017,
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Mathlib/SetTheory/Game/PGame.lean | PGame.ofLists_moveRight' | [] | [
207,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigOWith_inv | [
{
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Mathlib/Data/Set/Intervals/Instances.lean | Set.Icc.coe_nonneg | [] | [
100,
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Mathlib/Init/Data/Nat/Bitwise.lean | Nat.div2_two | [] | [
114,
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113,
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.Dart.ext_iff | [
{
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701,
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700,
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Mathlib/Combinatorics/Additive/PluenneckeRuzsa.lean | Finset.card_mul_mul_le_card_div_mul_card_mul | [
{
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77,
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Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.cramer_eq_adjugate_mulVec | [
{
"state_after": "m : Type u\nn : Type v\nα : Type w\ninst✝⁴ : DecidableEq n\ninst✝³ : Fintype n\ninst✝² : DecidableEq m\ninst✝¹ : Fintype m\ninst✝ : CommRing α\nA : Matrix n n α\nb : n → α\n⊢ ↑(cramer A) b = mulVec (adjugate Aᵀᵀ) b",
"state_before": "m : Type u\nn : Type v\nα : Type w\ninst✝⁴ : DecidableEq... | [
283,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
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Mathlib/Data/Int/Basic.lean | Int.coe_nat_nonneg | [] | [
123,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
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Mathlib/Logic/Equiv/Defs.lean | Equiv.psigmaCongrRight_refl | [] | [
721,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
720,
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Mathlib/Analysis/Normed/Group/Basic.lean | tendsto_norm_cocompact_atTop' | [
{
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418,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
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Mathlib/Data/Nat/Prime.lean | Nat.Prime.even_iff | [
{
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"tactic": "rw [even_iff_two_dvd, prime_dvd_prime_iff_eq prime_two hp, eq_comm]"
}
] | [
505,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.comp_apply | [] | [
593,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
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Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_self_re_eq_norm | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.1652408\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nx : E\n⊢ ↑re (inner x x) = ‖↑(↑re (inner x x))‖",
"state_before": "𝕜 :... | [
599,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
596,
1
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Mathlib/Order/Heyting/Basic.lean | fst_hnot | [] | [
123,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
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Mathlib/MeasureTheory/Function/SpecialFunctions/Inner.lean | AEMeasurable.inner | [
{
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39,
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Mathlib/ModelTheory/Definability.lean | Set.Definable.sdiff | [] | [
151,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.nhdsWithin_source_inter | [] | [
264,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
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Mathlib/Algebra/GroupPower/Order.lean | pow_bit0_nonneg | [
{
"state_after": "β : Type ?u.251747\nA : Type ?u.251750\nG : Type ?u.251753\nM : Type ?u.251756\nR : Type u_1\ninst✝ : LinearOrderedRing R\na : R\nn : ℕ\n⊢ 0 ≤ a ^ n * a ^ n",
"state_before": "β : Type ?u.251747\nA : Type ?u.251750\nG : Type ?u.251753\nM : Type ?u.251756\nR : Type u_1\ninst✝ : LinearOrdere... | [
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Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.norm_apply_le_norm | [
{
"state_after": "case inl\nα : Type u_1\nE : α → Type u_2\nq : ℝ≥0∞\ninst✝ : (i : α) → NormedAddCommGroup (E i)\ni : α\nhp : ⊤ ≠ 0\nf : { x // x ∈ lp E ⊤ }\n⊢ ‖↑f i‖ ≤ ‖f‖\n\ncase inr\nα : Type u_1\nE : α → Type u_2\np q : ℝ≥0∞\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nhp : p ≠ 0\nf : { x // x ∈ lp E p }\ni... | [
565,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | linearIndependent_span | [] | [
281,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/Algebra/Hom/Group.lean | MulHom.coe_inj | [] | [
731,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
730,
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Mathlib/Order/WellFounded.lean | Acc.induction_bot' | [] | [
248,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
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Mathlib/Topology/Instances/Complex.lean | Complex.uniformContinuous_ringHom_eq_id_or_conj | [
{
"state_after": "K : Subfield ℂ\nψ : { x // x ∈ K } →+* ℂ\nhc : UniformContinuous ↑ψ\nthis : TopologicalDivisionRing ℂ := TopologicalDivisionRing.mk\n⊢ ψ.toFun = ↑(Subfield.subtype K) ∨ ψ.toFun = ↑(starRingEnd ℂ) ∘ ↑(Subfield.subtype K)",
"state_before": "K : Subfield ℂ\nψ : { x // x ∈ K } →+* ℂ\nhc : Unif... | [
119,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
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Mathlib/Algebra/GroupWithZero/Units/Basic.lean | Ring.inverse_unit | [
{
"state_after": "no goals",
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"tactic": "rw [inverse, dif_pos u.isUnit, IsUnit.unit_of_val_units]"
... | [
97,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
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Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.xn_modEq_x4n_sub | [
{
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"state_before": "a : ℕ\na1 : 1 < a\nn j : ℕ\nh : j ≤ 2 * n\n⊢ 2 * n ≤ 2 * n",
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},
{
"state_after": "a : ℕ\na1 : 1 < a\nn j : ℕ\nh h' : j ≤ 2 * n\n⊢ xn a1 (4 * n - j) + xn a1 (2 * n - j) ≡ 0 [MOD xn a1 n]",
"state_before": "a : ℕ\na1 :... | [
644,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
639,
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Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.cardFactors_eq_one_iff_prime | [
{
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"state_before": "R : Type ?u.553341\nn : ℕ\n⊢ ↑Ω n = 1 ↔ Prime n",
"tactic": "refine' ⟨fun h => _, fun h => List.length_eq_one.2 ⟨n, factors_prime h⟩⟩"
},
{
"state_after": "case zero\nR : Type ?u.553341\nh : ↑Ω Nat.zero = 1\n... | [
871,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
862,
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.memℒp_congr_ae | [
{
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528,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
527,
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Std/Data/Nat/Gcd.lean | Nat.coprime.pow_right | [] | [
373,
28
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
372,
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_liminf_le' | [
{
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87
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1003,
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Std/Data/String/Lemmas.lean | String.Iterator.ValidFor.pos | [] | [
536,
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535,
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Mathlib/Order/BooleanAlgebra.lean | disjoint_inf_sdiff | [] | [
126,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
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Mathlib/Control/Traversable/Instances.lean | Sum.traverse_map | [
{
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"tactic": "cases x <;> simp [Sum.traverse, id_map, functor_norm] <;> rf... | [
162,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
11
] |
Mathlib/Algebra/Hom/Units.lean | IsUnit.one_div_mul_cancel | [
{
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"tactic": "simp [h]"
}
] | [
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83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
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Mathlib/Analysis/Calculus/FDeriv/Add.lean | HasStrictFDerivAt.const_smul | [] | [
68,
51
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66,
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Mathlib/LinearAlgebra/Basis.lean | nonzero_span_atom | [
{
"state_after": "case left\nι : Type ?u.1166402\nι' : Type ?u.1166405\nR : Type ?u.1166408\nR₂ : Type ?u.1166411\nK : Type u_1\nM : Type ?u.1166417\nM' : Type ?u.1166420\nM'' : Type ?u.1166423\nV : Type u\nV' : Type ?u.1166428\ninst✝⁴ : DivisionRing K\ninst✝³ : AddCommGroup V\ninst✝² : AddCommGroup V'\ninst✝¹ ... | [
1534,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1521,
1
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Mathlib/Order/Iterate.lean | Monotone.seq_pos_lt_seq_of_le_of_lt | [] | [
67,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Data/PEquiv.lean | PEquiv.refl_apply | [] | [
129,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.cast_zero | [] | [
1076,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1074,
1
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Mathlib/Algebra/Hom/Group.lean | OneHom.one_apply | [] | [
1401,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1401,
1
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Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.coeff_zero_mul_X | [
{
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"tactic": "simp"
}
] | [
1566,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1566,
1
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_le_add_measure_right | [] | [
670,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
668,
1
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Mathlib/GroupTheory/Perm/Fin.lean | support_finRotate | [
{
"state_after": "case a\nn : ℕ\na✝ : Fin (n + 2)\n⊢ a✝ ∈ support (finRotate (n + 2)) ↔ a✝ ∈ Finset.univ",
"state_before": "n : ℕ\n⊢ support (finRotate (n + 2)) = Finset.univ",
"tactic": "ext"
},
{
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"state_before": "case a\nn : ℕ\na✝ : Fin (n + 2)\n⊢ a✝ ∈ support (f... | [
117,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Algebra/AlgebraicCard.lean | Algebraic.cardinal_mk_lift_le_mul | [
{
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"state_before": "R : Type u\nA : Type v\ninst✝⁴ : CommRing R\ninst✝³ : CommRing A\ninst✝² ... | [
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37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
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Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.LHom.id_onBoundedFormula | [
{
"state_after": "case h\nL : Language\nL' : Language\nM : Type w\nN : Type ?u.143751\nP : Type ?u.143754\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nγ : Type ?u.143782\nn : ℕ\nf : BoundedFormula L α n\n⊢ onBoundedFormula (LHom.id L) f = id f",
"state_be... | [
898,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
889,
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Mathlib/Data/Finset/Pointwise.lean | Set.toFinset_vsub | [] | [
2266,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2264,
1
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Mathlib/Data/Ordmap/Ordset.lean | Ordnode.dual_insert | [
{
"state_after": "α : Type u_1\ninst✝² : Preorder α\ninst✝¹ : IsTotal α fun x x_1 => x ≤ x_1\ninst✝ : DecidableRel fun x x_1 => x ≤ x_1\nx : α\nsize✝ : ℕ\nl : Ordnode α\ny : α\nr : Ordnode α\nthis : cmpLE x y = cmpLE y x\n⊢ dual (Ordnode.insert x (node size✝ l y r)) = Ordnode.insert x (dual (node size✝ l y r))"... | [
667,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
660,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.iterate_mono | [] | [
441,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
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Mathlib/Data/Set/Image.lean | Set.image_preimage_eq_iff | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.74585\nι : Sort ?u.74588\nι' : Sort ?u.74591\nf✝ : ι → α\ns✝ t : Set α\nf : α → β\ns : Set β\nh : f '' (f ⁻¹' s) = s\n⊢ s ⊆ range f",
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795,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
790,
1
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | borel_eq_generateFrom_Iic | [
{
"state_after": "α : Type u_1\nβ : Type ?u.119737\nγ : Type ?u.119740\nγ₂ : Type ?u.119743\nδ : Type ?u.119746\nι : Sort y\ns t u : Set α\ninst✝³ : TopologicalSpace α\ninst✝² : SecondCountableTopology α\ninst✝¹ : LinearOrder α\ninst✝ : OrderTopology α\n⊢ MeasurableSpace.generateFrom (range Ioi) = MeasurableSpa... | [
171,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
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Mathlib/Data/Real/NNReal.lean | NNReal.mul_iInf | [
{
"state_after": "no goals",
"state_before": "ι : Sort u_1\nf✝ f : ι → ℝ≥0\na : ℝ≥0\n⊢ a * iInf f = ⨅ (i : ι), a * f i",
"tactic": "simpa only [mul_comm] using iInf_mul f a"
}
] | [
959,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
958,
1
] |
Mathlib/Analysis/NormedSpace/LpEquiv.lean | coe_addEquiv_lpPiLp_symm | [] | [
97,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
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Mathlib/Data/BinaryHeap.lean | BinaryHeap.size_heapifyDown | [] | [
40,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
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Mathlib/Data/List/Destutter.lean | List.destutter'_nil | [] | [
40,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.StronglyMeasurable.norm | [] | [
824,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
822,
11
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.image_add_right_Ioc | [
{
"state_after": "ι : Type ?u.250798\nα : Type u_1\ninst✝³ : OrderedCancelAddCommMonoid α\ninst✝² : ExistsAddOfLE α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : DecidableEq α\na b c : α\n⊢ image (fun x => x + c) (Ioc a b) = image (↑(addRightEmbedding c)) (Ioc a b)",
"state_before": "ι : Type ?u.250798\nα : Type ... | [
1135,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1133,
1
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Mathlib/RingTheory/Finiteness.lean | Submodule.FG.pow | [
{
"state_after": "no goals",
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"tactic": "simp [one_eq_span]"
},
{
"state_after": "no goals",
"state_before": "R ... | [
456,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
1
] |
Mathlib/Init/Algebra/Order.lean | le_not_le_of_lt | [] | [
73,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Data/PFun.lean | PFun.prodLift_apply | [] | [
651,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
649,
1
] |
Mathlib/Computability/Reduce.lean | manyOneEquiv_toNat | [
{
"state_after": "no goals",
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"tactic... | [
362,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/Data/Finite/Card.lean | Finite.card_le_one_iff_subsingleton | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1557\nγ : Type ?u.1560\ninst✝ : Finite α\nthis : Fintype α\n⊢ Nat.card α ≤ 1 ↔ Subsingleton α",
"state_before": "α : Type u_1\nβ : Type ?u.1557\nγ : Type ?u.1560\ninst✝ : Finite α\n⊢ Nat.card α ≤ 1 ↔ Subsingleton α",
"tactic": "haveI := Fintype.ofFinite α"
}... | [
83,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.QuasiMeasurePreserving.preimage_ae_eq | [] | [
2522,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2520,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.Injective.eq_iff' | [] | [
107,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Std/Data/Int/DivMod.lean | Int.div_neg | [
{
"state_after": "m : Nat\n⊢ ofNat 0 = -↑0",
"state_before": "m : Nat\n⊢ ofNat (m / 0) = -↑(m / 0)",
"tactic": "rw [Nat.div_zero]"
},
{
"state_after": "no goals",
"state_before": "m : Nat\n⊢ ofNat 0 = -↑0",
"tactic": "rfl"
}
] | [
69,
56
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
66,
19
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.asIso_hom | [] | [
320,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/NumberTheory/PythagoreanTriples.lean | Int.sq_ne_two_mod_four | [
{
"state_after": "z : ℤ\n⊢ ¬z * z % ↑4 = 2 % ↑4",
"state_before": "z : ℤ\n⊢ z * z % 4 ≠ 2",
"tactic": "suffices ¬z * z % (4 : ℕ) = 2 % (4 : ℕ) by exact this"
},
{
"state_after": "z : ℤ\n⊢ ¬↑(z * z) = ↑2",
"state_before": "z : ℤ\n⊢ ¬z * z % ↑4 = 2 % ↑4",
"tactic": "rw [← ZMod.int_cast_eq_... | [
41,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.inf'_mem | [] | [
971,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
969,
1
] |
Mathlib/Order/Basic.lean | le_rfl | [] | [
166,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_comp_sub_div | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.14946556\n𝕜 : Type ?u.14946559\nE : Type u_1\nF : Type ?u.14946565\nA : Type ?u.14946568\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\na b c d✝ : ℝ\nf : ℝ → E\nhc : c ≠ 0\nd : ℝ\n⊢ (∫ (x : ℝ) in a..b, f (d - x / ... | [
841,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
839,
1
] |
Mathlib/Data/Real/Basic.lean | Real.mk_add | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\nf g : CauSeq ℚ abs\n⊢ mk (f + g) = mk f + mk g",
"tactic": "simp [mk, ← ofCauchy_add]"
}
] | [
334,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.forall_eventually_of_eventually_forall | [] | [
1137,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1135,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.isCaratheodory_iff_le | [] | [
1056,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1054,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.lt_congr | [] | [
854,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
853,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.ext_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type u_2\nF : Type ?u.359353\nG : Type ?u.359356\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf g : { x // x ∈ Lp E p }\nh : f = g\n⊢ ↑↑... | [
170,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.coe_count | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.349078\nγ : Type ?u.349081\ninst✝ : DecidableEq α\na : α\nl : List α\n⊢ List.countp (fun b => decide (b = a)) l = List.countp (fun x => x == a) l",
"tactic": "rfl"
}
] | [
2344,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2342,
1
] |
Mathlib/ModelTheory/Satisfiability.lean | FirstOrder.Language.Theory.Model.isSatisfiable | [] | [
80,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.map_smulₛₗ | [] | [
502,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
11
] |
Mathlib/Order/SymmDiff.lean | bihimp_iff_iff | [] | [
96,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Topology/Instances/Int.lean | Int.cofinite_eq | [
{
"state_after": "no goals",
"state_before": "⊢ cofinite = atBot ⊔ atTop",
"tactic": "rw [← cocompact_eq_cofinite, cocompact_eq]"
}
] | [
83,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Topology/Algebra/Module/CharacterSpace.lean | WeakDual.CharacterSpace.union_zero | [
{
"state_after": "case inl\n𝕜 : Type u_1\nA : Type u_2\ninst✝⁶ : CommSemiring 𝕜\ninst✝⁵ : TopologicalSpace 𝕜\ninst✝⁴ : ContinuousAdd 𝕜\ninst✝³ : ContinuousConstSMul 𝕜 𝕜\ninst✝² : NonUnitalNonAssocSemiring A\ninst✝¹ : TopologicalSpace A\ninst✝ : Module 𝕜 A\nφ : WeakDual 𝕜 A\nhφ : φ ∈ characterSpace 𝕜 A\... | [
124,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Data/Holor.lean | Holor.holor_index_cons_decomp | [
{
"state_after": "α : Type\nd : ℕ\nds ds₁ ds₂ ds₃ : List ℕ\np : HolorIndex (d :: ds) → Prop\nt : HolorIndex (d :: ds)\ni : ℕ\nis : List ℕ\nh : ↑t = i :: is\n⊢ Forall₂ (fun x x_1 => x < x_1) (↑t) (d :: ds)",
"state_before": "α : Type\nd : ℕ\nds ds₁ ds₂ ds₃ : List ℕ\np : HolorIndex (d :: ds) → Prop\nt : Holor... | [
249,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.ncard_inter_add_ncard_union | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.120169\ns✝ t✝ : Set α\na b x y : α\nf : α → β\ns t : Set α\nhs : autoParam (Set.Finite s) _auto✝\nht : autoParam (Set.Finite t) _auto✝\n⊢ ncard (s ∩ t) + ncard (s ∪ t) = ncard s + ncard t",
"tactic": "rw [add_comm, ncard_union_add_n... | [
470,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
1
] |
Mathlib/Algebra/Ring/Commute.lean | Commute.neg_right | [] | [
95,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | tendstoLocallyUniformlyOn_TFAE | [
{
"state_after": "case tfae_1_to_2\nα : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝² : UniformSpace β\nF : ι → α → β\nf : α → β\ns s' : Set α\nx : α\np✝ : Filter ι\np' : Filter α\ng✝ : ι → α\ninst✝¹ : TopologicalSpace α\ninst✝ : LocallyCompactSpace α\nG : ι → α → β\ng : α → β\np : Filter ι\nhs : IsOpen s\... | [
748,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
731,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.add_pos_iff_pos_or_pos | [
{
"state_after": "m✝ n✝ k l m n : ℕ\nh : 0 < m + n\n⊢ 0 < m ∨ 0 < n",
"state_before": "m✝ n✝ k l m n : ℕ\n⊢ 0 < m + n → 0 < m ∨ 0 < n",
"tactic": "intro h"
},
{
"state_after": "case zero\nm n✝ k l n : ℕ\nh : 0 < zero + n\n⊢ 0 < zero ∨ 0 < n\n\ncase succ\nm✝ n✝ k l n m : ℕ\nh : 0 < succ m + n\n⊢ ... | [
192,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
src/lean/Init/SizeOf.lean | Unit.sizeOf | [] | [
85,
61
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
85,
9
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tendsto_nhds_top_iff_nnreal | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.39319\nγ : Type ?u.39322\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nx y z ε ε₁ ε₂ : ℝ≥0∞\ns : Set ℝ≥0∞\nm : α → ℝ≥0∞\nf : Filter α\n⊢ Tendsto m f (𝓝 ⊤) ↔ ∀ (x : ℝ≥0), ∀ᶠ (a : α) in f, ↑x < m a",
"tactic": "simp only [nhds_top', tendsto_iInf, te... | [
165,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Logic/Equiv/Fin.lean | finSumFinEquiv_apply_left | [] | [
332,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
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