file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Algebra/ContinuedFractions/Translations.lean | GeneralizedContinuedFraction.convergent_eq_num_div_denom | [] | [
105,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Algebra/Algebra/Basic.lean | algebraMap.coe_zpow | [] | [
241,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Data/Fin/SuccPred.lean | Fin.succ_eq | [] | [
44,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/Data/List/Rotate.lean | List.rotate_length_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u\nl : List α\nn : ℕ\n⊢ rotate l (length l * n) = l",
"tactic": "rw [rotate_eq_rotate', rotate'_length_mul]"
}
] | [
173,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
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Mathlib/Data/Setoid/Basic.lean | Setoid.sSup_eq_eqvGen | [
{
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"state_before": "α : Type u_1\nβ : Type ?u.8031\nS : Set (Setoid α)\n⊢ sSup S = EqvGen.Setoid fun x y => ∃ r, r ∈ S ∧ Rel r x y",
"tactic": "rw [eqvGen_eq]"
}... | [
236,
59
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230,
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Mathlib/Data/Finset/Pointwise.lean | Finset.smul_mem_smul | [] | [
1293,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1292,
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Mathlib/Algebra/GroupPower/Basic.lean | pow_sub_mul_pow | [
{
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"tactic": "rw [← pow_add, Nat.sub_add_canc... | [
172,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
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Mathlib/Data/Nat/Parity.lean | Nat.mod_two_ne_one | [
{
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}
] | [
32,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Calculus/Deriv/Basic.lean | deriv_id'' | [] | [
663,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
662,
1
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Mathlib/Data/Finmap.lean | Finmap.union_toFinmap | [] | [
578,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
577,
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Mathlib/MeasureTheory/Measure/Regular.lean | MeasureTheory.Measure.InnerRegular.weaklyRegular_of_finite | [
{
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437,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.eq_mk_support | [
{
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"state_before": "ι : Type u\nγ : Type w\nβ : ι → Type ... | [
1129,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1126,
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Mathlib/Combinatorics/SimpleGraph/AdjMatrix.lean | SimpleGraph.transpose_adjMatrix | [
{
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"state_before": "V : Type u_2\nα : Type u_1\nβ : Type ?u.27033\nG : SimpleGraph V\ninst✝² : D... | [
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173,
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Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.SignedMeasure.singularPart_smul | [
{
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1108,
89
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.normalizer_eq_top | [
{
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"tactic": "rwa [h.mem_comm_iff, inv_mul_cancel_left] at... | [
2187,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2184,
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Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.mem_or_compl_mem | [] | [
183,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
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Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.coe_finset_sup | [] | [
212,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
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Mathlib/CategoryTheory/Iso.lean | CategoryTheory.IsIso.inv_eq_inv | [] | [
478,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.IsImage.image_eq | [] | [
503,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
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Mathlib/InformationTheory/Hamming.lean | eq_of_hammingDist_eq_zero | [
{
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"tactic": "simp_rw [hammingDist, card_... | [
97,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
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Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | ContinuousLinearMap.mulLeftRight_isBoundedBilinear | [] | [
518,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
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Mathlib/LinearAlgebra/Dimension.lean | Module.Free.rank_eq_card_chooseBasisIndex | [] | [
928,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
927,
1
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Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.equalizerComparison_comp_π | [] | [
1127,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1125,
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Mathlib/Algebra/DirectSum/Decomposition.lean | DirectSum.Decomposition.isInternal | [] | [
72,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
11
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Mathlib/Data/Fin/Tuple/Basic.lean | Fin.snoc_castSucc | [
{
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461,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
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Mathlib/Dynamics/PeriodicPts.lean | Function.iterate_minimalPeriod | [] | [
286,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
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Mathlib/Data/Finset/LocallyFinite.lean | Finset.image_add_right_Ico | [
{
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"state_before": "ι : Type ?u.247963\nα : Type ... | [
1130,
6
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Mathlib/Algebra/Lie/Solvable.lean | LieAlgebra.derivedSeriesOfIdeal_mono | [] | [
114,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Sigma/Lex.lean | Sigma.lex_iff | [
{
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Mathlib/Order/Filter/Pointwise.lean | Filter.vsub_pure | [] | [
1135,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/GroupTheory/SpecificGroups/Cyclic.lean | card_pow_eq_one_eq_orderOf_aux | [
{
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335,
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Mathlib/Data/Set/Lattice.lean | Set.iUnion_diff | [] | [
565,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
564,
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Mathlib/Analysis/Calculus/ContDiffDef.lean | contDiffOn_iff_continuousOn_differentiableOn | [] | [
1106,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1100,
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Mathlib/Data/Multiset/Nodup.lean | Multiset.Nodup.map | [] | [
140,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
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Mathlib/Order/Height.lean | Set.chainHeight_union_le | [
{
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"state_before": "α : Type u_1\nβ : Type ?u.37990\ns t : Set α\ninst✝ : Preorder α\n⊢ chainHeight (s ∪ t) ≤ chainHeight s + chainHeight t"... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
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Mathlib/CategoryTheory/Limits/Lattice.lean | CategoryTheory.Limits.CompleteLattice.finite_colimit_eq_finset_univ_sup | [] | [
83,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Polynomial/Div.lean | Polynomial.dvd_iff_modByMonic_eq_zero | [
{
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Mathlib/Algebra/DirectSum/Basic.lean | DirectSum.IsInternal.addSubmonoid_iSup_eq_top | [
{
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Std/Data/List/Lemmas.lean | List.get?_range' | [
{
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}
] | [
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55
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.prod_induction_nonempty | [
{
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm'_le_snormEssSup_mul_rpow_measure_univ | [
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Mathlib/Data/Complex/Exponential.lean | Real.one_le_exp | [
{
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"tactic": "linarith [add_one_le_exp_of_nonneg hx]"
}
] | [
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97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Algebra.iInf_toSubmodule | [
{
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888,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Cover.lean | covby_congr_right | [] | [
326,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
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Mathlib/Topology/ShrinkingLemma.lean | exists_iUnion_eq_closed_subset | [] | [
265,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/GroupTheory/Subsemigroup/Membership.lean | Subsemigroup.coe_sSup_of_directed_on | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.4507\nM : Type u_1\nA : Type ?u.4513\nB : Type ?u.4516\ninst✝ : Mul M\nS : Set (Subsemigroup M)\nhS : DirectedOn (fun x x_1 => x ≤ x_1) S\nx : M\n⊢ x ∈ ↑(sSup S) ↔ x ∈ ⋃ (s : Subsemigroup M) (_ : s ∈ S), ↑s",
"tactic": "simp [mem_sSup_of_directed... | [
78,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
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Mathlib/Algebra/Ring/BooleanRing.lean | ofBoolRing_inj | [] | [
429,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearEquiv.nnnorm_symm_pos | [] | [
1967,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1965,
1
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Mathlib/Data/Polynomial/Reverse.lean | Polynomial.reverse_leadingCoeff | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nf✝ f : R[X]\n⊢ leadingCoeff (reverse f) = trailingCoeff f",
"tactic": "rw [leadingCoeff, reverse_natDegree, ← revAt_le f.natTrailingDegree_le_natDegree,\n coeff_reverse, revAt_invol, trailingCoeff]"
}
] | [
300,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/Data/PNat/Factors.lean | PNat.factorMultiset_ofPrime | [
{
"state_after": "case a\np : Nat.Primes\n⊢ ↑factorMultisetEquiv.symm (factorMultiset ↑p) = ↑factorMultisetEquiv.symm (PrimeMultiset.ofPrime p)",
"state_before": "p : Nat.Primes\n⊢ factorMultiset ↑p = PrimeMultiset.ofPrime p",
"tactic": "apply factorMultisetEquiv.symm.injective"
},
{
"state_afte... | [
322,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Mathlib/Order/Bounds/Basic.lean | isLUB_lt_iff | [] | [
1051,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1050,
1
] |
Mathlib/Topology/Algebra/Ring/Basic.lean | TopologicalSemiring.toTopologicalRing | [] | [
76,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.support_subset_verts | [] | [
206,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Algebra/Algebra/Unitization.lean | Unitization.inr_add | [] | [
291,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/Data/List/Duplicate.lean | List.Duplicate.ne_nil | [] | [
67,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Data/Int/GCD.lean | Int.dvd_of_mul_dvd_mul_left | [
{
"state_after": "i j k : ℤ\nk_non_zero : k ≠ 0\nH : k * i ∣ k * j\nl : ℤ\nH1 : k * j = k * (i * l)\n⊢ i ∣ j",
"state_before": "i j k : ℤ\nk_non_zero : k ≠ 0\nH : k * i ∣ k * j\nl : ℤ\nH1 : k * j = k * i * l\n⊢ i ∣ j",
"tactic": "rw [mul_assoc] at H1"
},
{
"state_after": "no goals",
"state_b... | [
226,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Topology/Separation.lean | SeparatedNhds.comm | [] | [
127,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.div_union | [] | [
668,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
667,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Filter.le_iff_ultrafilter | [] | [
442,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
1
] |
Std/Data/Int/Lemmas.lean | Int.le_of_sub_one_lt | [] | [
1262,
51
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1261,
1
] |
Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.multiset_prod_mem | [
{
"state_after": "case intro\nM✝ : Type ?u.27146\nA : Type ?u.27149\nB : Type ?u.27152\ninst✝³ : Monoid M✝\ninst✝² : SetLike B M✝\ninst✝¹ : SubmonoidClass B M✝\nS✝ : B\ns : Submonoid M✝\nM : Type u_1\ninst✝ : CommMonoid M\nS : Submonoid M\nm : Multiset { x // x ∈ S }\n⊢ Multiset.prod (Multiset.map Subtype.val m... | [
149,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.eq | [] | [
145,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
11
] |
Mathlib/CategoryTheory/EqToHom.lean | CategoryTheory.congrArg_cast_hom_right | [
{
"state_after": "case refl\nC : Type u₁\ninst✝ : Category C\nX Y : C\np : X ⟶ Y\n⊢ cast (_ : (X ⟶ Y) = (X ⟶ Y)) p = p ≫ eqToHom (_ : Y = Y)",
"state_before": "C : Type u₁\ninst✝ : Category C\nX Y Z : C\np : X ⟶ Y\nq : Z = Y\n⊢ cast (_ : (X ⟶ Y) = (X ⟶ Z)) p = p ≫ eqToHom (_ : Y = Z)",
"tactic": "cases ... | [
104,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.sumFinsuppEquivProdFinsupp_symm_inr | [] | [
1365,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1363,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderEmbedding.lt_iff_lt | [] | [
657,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
656,
1
] |
Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | WithSeminorms.image_isVonNBounded_iff_seminorm_bounded | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\n𝕜₂ : Type ?u.493266\n𝕝 : Type ?u.493269\n𝕝₂ : Type ?u.493272\nE : Type u_3\nF : Type ?u.493278\nG : Type u_1\nι : Type u_4\nι' : Type ?u.493287\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : AddCommGroup E\ninst✝² : Module 𝕜 E\ninst✝¹ : Nonemp... | [
583,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
580,
1
] |
Mathlib/NumberTheory/LegendreSymbol/MulCharacter.lean | MulChar.coe_toUnitHom | [] | [
199,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Constructions.lean | Pmf.ofFinset_apply | [] | [
165,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.coe_npowRec | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.1196548\nα : Type u\nβ : Type v\nγ : Type w\ninst✝¹ : TopologicalSpace α\nR : Type u_1\ninst✝ : SeminormedRing R\nf : α →ᵇ R\n⊢ ↑(npowRec 0 f) = ↑f ^ 0",
"tactic": "rw [npowRec, pow_zero, coe_one]"
},
{
"state_after": "no goals",
"sta... | [
1269,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1267,
1
] |
Mathlib/RingTheory/Coprime/Basic.lean | IsCoprime.mul_left | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : CommSemiring R\nx y z : R\nH1 : IsCoprime x z\nH2 : IsCoprime y z\na b : R\nh1 : a * x + b * z = 1\nc d : R\nh2 : c * y + d * z = 1\n⊢ a * c * (x * y) + (a * x * d + b * c * y + b * d * z) * z = (a * x + b * z) * (c * y + d * z)",
"tactic... | [
111,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Function.update_apply_equiv_apply | [] | [
1926,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1924,
1
] |
Mathlib/Tactic/Abel.lean | Mathlib.Tactic.Abel.const_add_termg | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : AddCommGroup α\nk : α\nn : ℤ\nx a a' : α\nh : k + a = a'\n⊢ k + termg n x a = termg n x a'",
"tactic": "simp [h.symm, termg, add_comm, add_assoc]"
}
] | [
132,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | inv_mul_lt_iff' | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.36563\nα : Type u_1\nβ : Type ?u.36569\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nh : 0 < b\n⊢ b⁻¹ * a < c ↔ a < c * b",
"tactic": "rw [inv_mul_lt_iff h, mul_comm]"
}
] | [
201,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Algebra/Module/LocalizedModule.lean | IsLocalizedModule.lift_unique | [
{
"state_after": "R : Type u_1\ninst✝⁷ : CommRing R\nS : Submonoid R\nM : Type u_2\nM' : Type u_4\nM'' : Type u_3\ninst✝⁶ : AddCommMonoid M\ninst✝⁵ : AddCommMonoid M'\ninst✝⁴ : AddCommMonoid M''\ninst✝³ : Module R M\ninst✝² : Module R M'\ninst✝¹ : Module R M''\nf : M →ₗ[R] M'\ng✝ : M →ₗ[R] M''\ninst✝ : IsLocali... | [
871,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
861,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_iff_exists_eq_mul | [
{
"state_after": "case mp\nα : Type u_1\nβ : Type ?u.633212\nE : Type ?u.633215\nF : Type ?u.633218\nG : Type ?u.633221\nE' : Type ?u.633224\nF' : Type ?u.633227\nG' : Type ?u.633230\nE'' : Type ?u.633233\nF'' : Type ?u.633236\nG'' : Type ?u.633239\nR : Type ?u.633242\nR' : Type ?u.633245\n𝕜 : Type u_2\n𝕜' : ... | [
1963,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1955,
1
] |
Mathlib/LinearAlgebra/Matrix/ZPow.lean | Matrix.zpow_mul | [
{
"state_after": "no goals",
"state_before": "n' : Type u_1\ninst✝² : DecidableEq n'\ninst✝¹ : Fintype n'\nR : Type u_2\ninst✝ : CommRing R\nA : M\nh : IsUnit (det A)\nm n : ℕ\n⊢ A ^ (↑m * ↑n) = (A ^ ↑m) ^ ↑n",
"tactic": "rw [zpow_ofNat, zpow_ofNat, ← pow_mul, ← zpow_ofNat, Int.ofNat_mul]"
},
{
... | [
279,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Log.lean | Complex.countable_preimage_exp | [
{
"state_after": "case refine'_1\ns : Set ℂ\nhs : Set.Countable (exp ⁻¹' s)\n⊢ Set.Countable s\n\ncase refine'_2\ns : Set ℂ\nhs : Set.Countable s\n⊢ Set.Countable (exp ⁻¹' s)",
"state_before": "s : Set ℂ\n⊢ Set.Countable (exp ⁻¹' s) ↔ Set.Countable s",
"tactic": "refine' ⟨fun hs => _, fun hs => _⟩"
},... | [
176,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Std/Logic.lean | not_imp_of_and_not | [] | [
308,
30
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
307,
1
] |
Mathlib/Algebra/Order/WithZero.lean | zero_le' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na b c d x y z : α\ninst✝ : LinearOrderedCommMonoidWithZero α\n⊢ 0 ≤ a",
"tactic": "simpa only [mul_zero, mul_one] using mul_le_mul_left' zero_le_one a"
}
] | [
94,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Data/Int/Bitwise.lean | Int.testBit_bitwise | [
{
"state_after": "case ofNat.ofNat\nf : Bool → Bool → Bool\nk a✝¹ a✝ : ℕ\n⊢ (match bif f false false then -[Nat.bitwise' (fun x y => !f x y) a✝¹ a✝+1] else ↑(Nat.bitwise' f a✝¹ a✝), k with\n | ofNat m, n => Nat.testBit m n\n | -[m+1], n => !Nat.testBit m n) =\n f (Nat.testBit a✝¹ k) (Nat.testBit a✝ k)\... | [
341,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm'_const' | [
{
"state_after": "α : Type u_1\nE : Type ?u.1031162\nF : Type u_2\nG : Type ?u.1031168\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : IsFiniteMeasure μ\nc : F\nhc_ne_zero : c ≠ 0\nhq_ne_zero : q ≠ ... | [
280,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Std/Data/Int/Lemmas.lean | Int.sub_lt_sub_left | [] | [
1120,
43
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1119,
11
] |
Mathlib/Data/Set/Lattice.lean | Set.union_iInter₂ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.116945\nγ : Type ?u.116948\nι : Sort u_2\nι' : Sort ?u.116954\nι₂ : Sort ?u.116957\nκ : ι → Sort u_3\nκ₁ : ι → Sort ?u.116967\nκ₂ : ι → Sort ?u.116972\nκ' : ι' → Sort ?u.116977\ns : Set α\nt : (i : ι) → κ i → Set α\n⊢ (s ∪ ⋂ (i : ι) (j ... | [
1020,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1019,
1
] |
Mathlib/GroupTheory/Sylow.lean | Sylow.exists_comap_subtype_eq | [] | [
188,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Data/Sum/Order.lean | Sum.Lex.inl_lt_inr | [] | [
368,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.mem_insert_of_mem | [] | [
1069,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1068,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Module.DualBases.mem_of_mem_span | [
{
"state_after": "R : Type u_3\nM : Type u_2\nι : Type u_1\ninst✝³ : CommRing R\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\ne : ι → M\nε : ι → Dual R M\ninst✝ : DecidableEq ι\nh : DualBases e ε\nH : Set ι\nx : M\nhmem : x ∈ Submodule.span R (e '' H)\ni : ι\nhi : ↑(ε i) x ≠ 0\n⊢ i ∈ H",
"state_before": "R... | [
760,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
755,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_neg | [
{
"state_after": "case pos\nα : Type u_1\nE : Type ?u.3178601\nF : Type u_2\nG : Type ?u.3178607\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 : α → F\nh0 : p = 0\n⊢ snorm (-f) p μ = snorm f p μ\n\ncase ... | [
1021,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1016,
1
] |
Mathlib/Algebra/Symmetrized.lean | SymAlg.unsym_surjective | [] | [
115,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Analysis/Normed/Field/Basic.lean | NNReal.nnnorm_eq | [] | [
834,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
833,
1
] |
Mathlib/Data/Int/Cast/Basic.lean | Int.cast_one | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : AddGroupWithOne R\n⊢ ↑1 = 1",
"tactic": "erw [cast_ofNat, Nat.cast_one]"
}
] | [
80,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.mem_map_iff_of_surjective | [] | [
1606,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1604,
1
] |
Mathlib/Topology/Maps.lean | Inducing.image_mem_nhdsWithin | [] | [
121,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/CategoryTheory/Arrow.lean | CategoryTheory.Arrow.comp_left | [] | [
73,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Data/Set/Intervals/OrderIso.lean | OrderIso.image_Ico | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ne : α ≃o β\na b : α\n⊢ ↑e '' Ico a b = Ico (↑e a) (↑e b)",
"tactic": "rw [e.image_eq_preimage, e.symm.preimage_Ico, e.symm_symm]"
}
] | [
101,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.pos_part | [] | [
1006,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1003,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.dichotomy | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.832980\nβ : Type ?u.832983\na b c d : ℝ≥0∞\nr p✝ q : ℝ≥0\np : ℝ≥0∞\ninst✝ : Fact (1 ≤ p)\n⊢ p = ⊤ ∨ 0 < ENNReal.toReal p ∧ 1 ≤ ENNReal.toReal p",
"tactic": "simpa using ENNReal.trichotomy₂ (Fact.out : 1 ≤ p)"
}
] | [
2301,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2298,
11
] |
Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | MeasureTheory.integral_fn_integral_add | [
{
"state_after": "α : Type u_1\nα' : Type ?u.2415704\nβ : Type u_2\nβ' : Type ?u.2415710\nγ : Type ?u.2415713\nE : Type u_3\ninst✝¹² : MeasurableSpace α\ninst✝¹¹ : MeasurableSpace α'\ninst✝¹⁰ : MeasurableSpace β\ninst✝⁹ : MeasurableSpace β'\ninst✝⁸ : MeasurableSpace γ\nμ μ' : Measure α\nν ν' : Measure β\nτ : Me... | [
364,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
Mathlib/Topology/Semicontinuous.lean | lowerSemicontinuousAt_ciSup | [
{
"state_after": "α : Type u_1\ninst✝³ : TopologicalSpace α\nβ : Type ?u.117874\ninst✝² : Preorder β\nf✝ g : α → β\nx : α\ns t : Set α\ny z : β\nι : Sort u_3\nδ : Type ?u.117903\nδ' : Type u_2\ninst✝¹ : CompleteLinearOrder δ\ninst✝ : ConditionallyCompleteLinearOrder δ'\nf : ι → α → δ'\nbdd : ∀ᶠ (y : α) in 𝓝 x,... | [
581,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
576,
1
] |
Mathlib/Dynamics/PeriodicPts.lean | MulAction.pow_smul_eq_iff_minimalPeriod_dvd | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\ninst✝¹ : Group α\ninst✝ : MulAction α β\na : α\nb : β\nn : ℕ\n⊢ a ^ n • b = b ↔ minimalPeriod ((fun x x_1 => x • x_1) a) b ∣ n",
"tactic": "rw [← isPeriodicPt_iff_minimalPeriod_dvd, IsPeriodicPt, IsFixedPt, smul_iterate]"
}
] | [
602,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
600,
1
] |
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