file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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|---|---|---|---|---|---|---|
Mathlib/Data/Option/Basic.lean | Option.none_bind' | [] | [
81,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_zero_map | [
{
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] | [
959,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
958,
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Mathlib/Analysis/Calculus/Deriv/Comp.lean | HasDerivAt.scomp | [] | [
99,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.toPartENat_apply_of_aleph0_le | [] | [
1861,
18
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1860,
1
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Mathlib/Order/Filter/Prod.lean | Filter.Eventually.prod_inr | [] | [
164,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
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Mathlib/Topology/Order/Basic.lean | IsOpen.exists_Ioo_subset | [
{
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"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : Top... | [
1289,
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Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.cokernel.π_of_epi | [] | [
952,
47
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951,
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Mathlib/Order/SuccPred/Limit.lean | Order.not_isSuccLimit_succ_of_not_isMax | [
{
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},
{
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80,
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Mathlib/Data/Option/Basic.lean | Option.coe_def | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.nnnorm_changeOrigin_le | [
{
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Mathlib/Geometry/Euclidean/Basic.lean | EuclideanGeometry.vsub_orthogonalProjection_mem_direction_orthogonal | [] | [
440,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
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Mathlib/Logic/Function/Basic.lean | Function.Involutive.injective | [] | [
896,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
896,
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Mathlib/Control/LawfulFix.lean | Part.Fix.approx_le_fix | [
{
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99,
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Mathlib/Data/Sym/Basic.lean | SymOptionSuccEquiv.decode_inl | [] | [
637,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Real.dist_left_le_of_mem_uIcc | [
{
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"tactic": "simpa only [dist_comm x] using abs_sub_left_of_mem_uIcc h"
}
] | [
1367,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1366,
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Mathlib/Topology/Category/Compactum.lean | Compactum.str_incl | [
{
"state_after": "X : Compactum\nx : X.A\n⊢ ((Monad.η β).app X.A ≫ X.a) x = x",
"state_before": "X : Compactum\nx : X.A\n⊢ str X (incl X x) = x",
"tactic": "change ((β ).η.app _ ≫ X.a) _ = _"
},
{
"state_after": "X : Compactum\nx : X.A\n⊢ 𝟙 X.A x = x",
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149,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
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Mathlib/Data/Finsupp/Basic.lean | Finsupp.mapRange.addEquiv_toAddMonoidHom | [] | [
284,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
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Mathlib/Computability/Partrec.lean | Nat.Partrec.of_eq | [] | [
173,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Data/Set/Basic.lean | Set.mem_of_eq_of_mem | [] | [
368,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
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Mathlib/Analysis/SpecialFunctions/Complex/Circle.lean | periodic_expMapCircle | [
{
"state_after": "no goals",
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"tactic": "rw [Int.cast_one, one_mul]"
}
] | [
97,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
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Mathlib/Algebra/Support.lean | Function.mulSupport_one_add | [] | [
415,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
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Mathlib/GroupTheory/Subgroup/Basic.lean | MonoidHom.coe_comp_rangeRestrict | [] | [
2633,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2631,
1
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Mathlib/Data/Finset/Basic.lean | Finset.erase_inj | [
{
"state_after": "α : Type u_1\nβ : Type ?u.219474\nγ : Type ?u.219477\ninst✝ : DecidableEq α\ns✝ t u v : Finset α\na b x y : α\ns : Finset α\nhx : x ∈ s\nh : erase s x = erase s y\n⊢ ¬x ∈ erase s y",
"state_before": "α : Type u_1\nβ : Type ?u.219474\nγ : Type ?u.219477\ninst✝ : DecidableEq α\ns✝ t u v : Fi... | [
2013,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2010,
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] |
Mathlib/GroupTheory/Submonoid/Basic.lean | Submonoid.coe_iInf | [
{
"state_after": "no goals",
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"tactic": "simp only [iInf, coe_sInf, Set... | [
336,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
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] |
Mathlib/Order/CompleteLattice.lean | sInf_le_sSup | [] | [
464,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.zero_apply | [] | [
137,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.prod_self_lt_prod_self | [] | [
1728,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1727,
1
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Mathlib/AlgebraicTopology/SimplexCategory.lean | SimplexCategory.eq_comp_δ_of_not_surjective | [
{
"state_after": "case intro\nn : ℕ\nΔ : SimplexCategory\nθ : Δ ⟶ [n + 1]\nhθ : ¬Function.Surjective ↑(Hom.toOrderHom θ)\ni : Fin (len [n + 1] + 1)\nhi : ¬∃ a, ↑(Hom.toOrderHom θ) a = i\n⊢ ∃ i θ', θ = θ' ≫ δ i",
"state_before": "n : ℕ\nΔ : SimplexCategory\nθ : Δ ⟶ [n + 1]\nhθ : ¬Function.Surjective ↑(Hom.to... | [
710,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
705,
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.withDensity_add_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.1756534\nγ : Type ?u.1756537\nδ : Type ?u.1756540\nm : MeasurableSpace α\nμ ν : Measure α\nf g : α → ℝ≥0∞\nhg : Measurable g\n⊢ withDensity μ (f + g) = withDensity μ f + withDensity μ g",
"tactic": "simpa only [add_comm] using withD... | [
1571,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1569,
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Mathlib/Topology/Sheaves/Stalks.lean | TopCat.Presheaf.germ_res | [] | [
113,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
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Mathlib/MeasureTheory/Function/ConvergenceInMeasure.lean | MeasureTheory.TendstoInMeasure.exists_seq_tendsto_ae' | [
{
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260,
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255,
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Mathlib/Algebra/Hom/NonUnitalAlg.lean | NonUnitalAlgHom.coe_inverse | [] | [
301,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | norm_iteratedFDerivWithin_comp_le_aux | [
{
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2646,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2534,
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Mathlib/Data/List/Sort.lean | List.Sorted.le_of_lt | [] | [
50,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
11
] |
Mathlib/RingTheory/Derivation/ToSquareZero.lean | diffToIdealOfQuotientCompEq_apply | [] | [
46,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
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Mathlib/Data/Fintype/Basic.lean | Finset.not_mem_compl | [
{
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"tactic": "rw [mem_compl, not_not]"
}
] | [
173,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
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Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.Ico_filter_lt_of_le_left | [
{
"state_after": "α : Type u_1\ninst✝² : Preorder α\ninst✝¹ : LocallyFiniteOrder α\na b c : α\ninst✝ : DecidablePred fun x => x < c\nhca : c ≤ a\n⊢ ∅.val = ∅",
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156,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
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Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffWithinAt.comp' | [] | [
712,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
709,
1
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Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Embedding.realize_term | [] | [
236,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Algebra/BigOperators/Intervals.lean | Finset.prod_Ico_id_eq_factorial | [
{
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"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns₂ s₁ s : Finset α\na : α\ng f : α → β\ninst✝ : CommMonoid β\nn : ℕ\n⊢ ∏ x in Ico 1 (n + 1 + 1), x = (n + 1)!",
"tactic": "rw [prod_Ico_succ_top <| Nat.succ_le_succ <| Nat.zero_le n, Nat.factorial_succ,\n prod_Ico_id_eq_f... | [
191,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
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Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.nonsing_inv_nonsing_inv | [
{
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"tactic": "rw [Matrix.one_mul]"
},
{
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... | [
417,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
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Mathlib/Topology/Instances/Matrix.lean | Continuous.matrix_row | [] | [
110,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
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Mathlib/Topology/SubsetProperties.lean | isClopen_inter_of_disjoint_cover_clopen | [
{
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1634,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1627,
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Mathlib/Order/Monotone/Basic.lean | Antitone.comp | [] | [
645,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
644,
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Mathlib/Analysis/Asymptotics/AsymptoticEquivalent.lean | Asymptotics.IsEquivalent.inv | [
{
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296,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_mul_const | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.13362421\n𝕜✝ : Type ?u.13362424\nE : Type ?u.13362427\nF : Type ?u.13362430\nA : Type ?u.13362433\ninst✝³ : NormedAddCommGroup E\ninst✝² : CompleteSpace E\ninst✝¹ : NormedSpace ℝ E\na b : ℝ\nf✝ g : ℝ → E\nμ : MeasureTheory.Measure ℝ\n𝕜 : Type u_1\n... | [
625,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
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Mathlib/Topology/MetricSpace/Holder.lean | holderOnWith_empty | [] | [
65,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/RingTheory/DedekindDomain/Ideal.lean | idealFactorsEquivOfQuotEquiv_mem_normalizedFactors_of_mem_normalizedFactors | [
{
"state_after": "case pos\nR : Type u_2\nA : Type u_1\nK : Type ?u.1123265\ninst✝¹¹ : CommRing R\ninst✝¹⁰ : CommRing A\ninst✝⁹ : Field K\ninst✝⁸ : IsDomain A\ninst✝⁷ : IsDedekindDomain A\nI : Ideal R\nJ : Ideal A\nB : Type ?u.1123802\ninst✝⁶ : CommRing B\ninst✝⁵ : IsDomain B\ninst✝⁴ : IsDedekindDomain B\nL✝ : ... | [
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52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1135,
1
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Mathlib/Algebra/Algebra/Hom.lean | AlgHom.coe_toRingHom | [] | [
179,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.opow_isLimit_left | [
{
"state_after": "case inl\na b : Ordinal\nl : IsLimit a\nhb : b ≠ 0\ne : b = 0\n⊢ IsLimit (a ^ b)\n\ncase inr.inl.intro\na : Ordinal\nl : IsLimit a\nb : Ordinal\nhb : succ b ≠ 0\n⊢ IsLimit (a ^ succ b)\n\ncase inr.inr\na b : Ordinal\nl : IsLimit a\nhb : b ≠ 0\nl' : IsLimit b\n⊢ IsLimit (a ^ b)",
"state_bef... | [
136,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Topology/SubsetProperties.lean | IsOpen.dense | [] | [
1854,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1852,
11
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.hasFiniteIntegral_def | [] | [
116,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.zero_dotProduct | [
{
"state_after": "no goals",
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758,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
758,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | InnerProductSpace.Core.inner_sub_sub_self | [
{
"state_after": "𝕜 : Type u_1\nE : Type ?u.642770\nF : Type u_2\ninst✝² : IsROrC 𝕜\ninst✝¹ : AddCommGroup F\ninst✝ : Module 𝕜 F\nc : Core 𝕜 F\nx y : F\n⊢ inner x x - inner y x - (inner x y - inner y y) = inner x x - inner x y - inner y x + inner y y",
"state_before": "𝕜 : Type u_1\nE : Type ?u.642770\... | [
312,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.erase_sub | [] | [
1162,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1161,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.le_congr_left | [] | [
806,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
805,
1
] |
Mathlib/Algebra/Order/Floor.lean | round_sub_int | [
{
"state_after": "F : Type ?u.255284\nα : Type u_1\nβ : Type ?u.255290\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nx : α\ny : ℤ\n⊢ round (x + -↑y) = round x - y",
"state_before": "F : Type ?u.255284\nα : Type u_1\nβ : Type ?u.255290\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nx : α\ny : ℤ\n⊢... | [
1369,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1366,
1
] |
Mathlib/Order/WithBot.lean | WithTop.ne_top_iff_exists | [] | [
767,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
766,
1
] |
Mathlib/Init/Data/Ordering/Lemmas.lean | cmpUsing_eq_gt | [
{
"state_after": "α : Type u\nlt : α → α → Prop\ninst✝¹ : DecidableRel lt\ninst✝ : IsStrictOrder α lt\na b : α\n⊢ (¬lt a b ∧ lt b a) = lt b a",
"state_before": "α : Type u\nlt : α → α → Prop\ninst✝¹ : DecidableRel lt\ninst✝ : IsStrictOrder α lt\na b : α\n⊢ (cmpUsing lt a b = Ordering.gt) = lt b a",
"tac... | [
66,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Algebra/Hom/Iterate.lean | MonoidHom.iterate_map_inv | [] | [
69,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Topology/Algebra/Monoid.lean | Filter.TendstoNhdsWithinIoi.const_mul | [] | [
175,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Order/WithBot.lean | WithBot.coe_le_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.11671\nγ : Type ?u.11674\nδ : Type ?u.11677\na b : α\ninst✝ : LE α\nx : α\n⊢ ↑a ≤ Option.some x ↔ ∃ b, Option.some x = ↑b ∧ a ≤ b",
"tactic": "simp [some_eq_coe]"
},
{
"state_after": "no goals",
"state_before": "α : Type... | [
237,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | finrank_eq_one_iff' | [
{
"state_after": "no goals",
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"tactic": "rw [finrank_eq_one_iff PUnit.{u+1}, Basis.basis_singleton_iff PUnit]"
}
] | [
1283,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1280,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_union_add_inter | [
{
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"st... | [
148,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/LinearAlgebra/Ray.lean | SameRay.of_subsingleton' | [] | [
75,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.sdiff_ssubset | [] | [
2203,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2202,
1
] |
Mathlib/GroupTheory/QuotientGroup.lean | QuotientGroup.kerLift_mk | [] | [
354,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.signAux_eq_signAux2 | [
{
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"state_before": "α : Type u\nβ : Type v\ninst✝ : DecidableEq α\nn : ℕ\nf : Perm α\ne : α ≃ Fin n\nh : ∀ (x... | [
504,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.setToL1_smul_left' | [
{
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1132,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1122,
1
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Mathlib/Algebra/Order/Kleene.lean | add_eq_left_iff_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.19220\nι : Type ?u.19223\nπ : ι → Type ?u.19228\ninst✝ : IdemSemiring α\na b c : α\n⊢ a + b = a ↔ b ≤ a",
"tactic": "simp"
}
] | [
153,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Asymptotics.lean | tendsto_rpow_div | [
{
"state_after": "case h.e'_3.h.h.e'_6.h.e'_6\nx✝ : ℝ\n⊢ x✝ = 1 * x✝ + 0",
"state_before": "⊢ Tendsto (fun x => x ^ (1 / x)) atTop (𝓝 1)",
"tactic": "convert tendsto_rpow_div_mul_add (1 : ℝ) _ (0 : ℝ) zero_ne_one"
},
{
"state_after": "case h.e'_3.h.h.e'_6.h.e'_6\nx✝ : ℝ\n⊢ x✝ = 1 * x✝ + 0",
... | [
81,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.succ_sub | [
{
"state_after": "m n : Nat\nh : n ≤ m\nk : Nat\nhk : n + k = m\n⊢ succ m - n = succ (m - n)",
"state_before": "m n : Nat\nh : n ≤ m\n⊢ succ m - n = succ (m - n)",
"tactic": "let ⟨k, hk⟩ := Nat.le.dest h"
},
{
"state_after": "no goals",
"state_before": "m n : Nat\nh : n ≤ m\nk : Nat\nhk : n ... | [
426,
74
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
424,
1
] |
Mathlib/Data/Set/Image.lean | Set.preimage_eq_preimage | [
{
"state_after": "no goals",
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"tactic": "rw [← image_preimage_eq s hf, ← image_preimage_eq t hf, eq]"
}
] | [
501,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | sInfHom.id_apply | [] | [
451,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.iSup_lintegral_measurable_le_eq_lintegral | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.71667\nγ : Type ?u.71670\nδ : Type ?u.71673\nm : MeasurableSpace α\nμ ν : Measure α\nf : α → ℝ≥0∞\n⊢ (⨆ (g : α → ℝ≥0∞) (_ : Measurable g) (_ : g ≤ f), ∫⁻ (a : α), g a ∂μ) ≤ ∫⁻ (a : α), f a ∂μ\n\ncase a\nα : Type u_1\nβ : Type ?u.71667\nγ : Type ?u.71670\nδ : T... | [
148,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Order/Monotone/Basic.lean | StrictMono.comp_strictAntiOn | [] | [
701,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
699,
1
] |
Mathlib/Data/List/BigOperators/Basic.lean | List.prod_isUnit_iff | [
{
"state_after": "ι : Type ?u.50139\nα✝ : Type ?u.50142\nM : Type ?u.50145\nN : Type ?u.50148\nP : Type ?u.50151\nM₀ : Type ?u.50154\nG : Type ?u.50157\nR : Type ?u.50160\ninst✝³ : Monoid M\ninst✝² : Monoid N\ninst✝¹ : Monoid P\nl l₁ l₂ : List M\na : M\nα : Type u_1\ninst✝ : CommMonoid α\nL : List α\nh : IsUnit... | [
160,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiffOn.continuousOn_iteratedFDerivWithin | [] | [
1072,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1070,
1
] |
Mathlib/Topology/ContinuousOn.lean | ContinuousOn.snd | [] | [
1292,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1290,
1
] |
Mathlib/Data/Set/MulAntidiagonal.lean | Set.MulAntidiagonal.finite_of_isPwo | [
{
"state_after": "α : Type u_1\ninst✝ : OrderedCancelCommMonoid α\ns t : Set α\na✝ : α\nx y : ↑(mulAntidiagonal s t a✝)\nhs : IsPwo s\nht : IsPwo t\na : α\nh : Set.Infinite (mulAntidiagonal s t a)\n⊢ False",
"state_before": "α : Type u_1\ninst✝ : OrderedCancelCommMonoid α\ns t : Set α\na✝ : α\nx y : ↑(mulAn... | [
132,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Data/Polynomial/Module.lean | PolynomialModule.monomial_smul_apply | [
{
"state_after": "case h0\nR : Type u_1\nM : Type u_2\ninst✝⁶ : CommRing R\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\nI : Ideal R\nS : Type ?u.247072\ninst✝³ : CommSemiring S\ninst✝² : Algebra S R\ninst✝¹ : Module S M\ninst✝ : IsScalarTower S R M\ni : ℕ\nr : R\nn : ℕ\n⊢ ↑(↑(monomial i) r • 0) n = if i ≤ n t... | [
161,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Data/List/Forall2.lean | List.rel_foldl | [] | [
283,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/Logic/Equiv/Set.lean | dite_comp_equiv_update | [
{
"state_after": "case h\nα✝ : Sort u\nβ✝ : Sort v\nγ✝ : Sort w\nα : Type u_1\nβ : Sort u_2\nγ : Sort u_3\np : α → Prop\ne : β ≃ Subtype p\nv : β → γ\nw : α → γ\nj : β\nx : γ\ninst✝² : DecidableEq β\ninst✝¹ : DecidableEq α\ninst✝ : (j : α) → Decidable (p j)\ni : α\n⊢ (if h : p i then update v j x (↑e.symm { val... | [
726,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
709,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.Red.antisymm | [] | [
442,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
1
] |
Mathlib/Order/UpperLower/Basic.lean | Set.OrdConnected.upperClosure_inter_lowerClosure | [] | [
1465,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1462,
1
] |
Mathlib/Order/JordanHolder.lean | CompositionSeries.forall_mem_eq_of_length_eq_zero | [] | [
379,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.inter_subset_union | [] | [
1711,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1710,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.nat_cast_imK | [] | [
425,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/Topology/Order.lean | isOpen_induced_iff | [] | [
370,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Mathlib/Analysis/Convex/Function.lean | ConcaveOn.sub | [] | [
892,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
891,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.le_inv_iff_mul_le | [
{
"state_after": "case ht.h\nα : Type ?u.294981\nβ : Type ?u.294984\na b c d : ℝ≥0∞\nr p q : ℝ≥0\n⊢ 1 ≠ ⊤",
"state_before": "case ht\nα : Type ?u.294981\nβ : Type ?u.294984\na b c d : ℝ≥0∞\nr p q : ℝ≥0\n⊢ b ≠ ⊤ ∨ 1 ≠ ⊤",
"tactic": "right"
},
{
"state_after": "no goals",
"state_before": "case... | [
1634,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1631,
1
] |
Mathlib/LinearAlgebra/Matrix/SpecialLinearGroup.lean | Matrix.SpecialLinearGroup.ext_iff | [] | [
104,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.of_nonpos_disjoint_union_eq_zero | [
{
"state_after": "α : Type u_1\nβ : Type ?u.43464\nm : MeasurableSpace α\nM : Type ?u.43470\ninst✝² : AddCommMonoid M\ninst✝¹ : TopologicalSpace M\ninst✝ : T2Space M\nv : VectorMeasure α M\nf : ℕ → Set α\ns : SignedMeasure α\nA B : Set α\nh : Disjoint A B\nhA₁ : MeasurableSet A\nhB₁ : MeasurableSet B\nhA₂ : ↑s ... | [
247,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.map_le_of_le_comap | [] | [
282,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/Data/Finset/Prod.lean | Finset.subset_product_image_fst | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.1583\ns s' : Finset α\nt t' : Finset β\na : α\nb : β\ninst✝ : DecidableEq α\ni : α\n⊢ i ∈ image Prod.fst (s ×ˢ t) → i ∈ s",
"tactic": "simp (config := { contextual := true }) [mem_image]"
}
] | [
71,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/GroupTheory/Complement.lean | Subgroup.isComplement_singleton_left | [
{
"state_after": "G : Type u_1\ninst✝ : Group G\nH K : Subgroup G\nS T : Set G\ng : G\nh : IsComplement {g} S\nx : G\nx✝ : x ∈ ⊤\n⊢ x ∈ S",
"state_before": "G : Type u_1\ninst✝ : Group G\nH K : Subgroup G\nS T : Set G\ng : G\n⊢ IsComplement {g} S ↔ S = ⊤",
"tactic": "refine'\n ⟨fun h => top_le_iff.mp f... | [
131,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.map_prod_map_coprod_le | [
{
"state_after": "α : Type ?u.62585\nβ : Type ?u.62588\nγ : Type ?u.62591\nδ : Type ?u.62594\nι : Sort ?u.62597\nf : Filter α\ng : Filter β\nα₁ : Type u\nα₂ : Type v\nβ₁ : Type w\nβ₂ : Type x\nf₁ : Filter α₁\nf₂ : Filter α₂\nm₁ : α₁ → β₁\nm₂ : α₂ → β₂\ns : Set (β₁ × β₂)\n⊢ s ∈ Filter.coprod (map m₁ f₁) (map m₂ ... | [
531,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
525,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.sum_inl | [] | [
997,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
996,
1
] |
Mathlib/Order/Height.lean | Set.chainHeight_dual | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.31224\ninst✝¹ : LT α\ninst✝ : LT β\ns t : Set α\nl : List α\na : α\n⊢ ∀ (l : List α), l ∈ subchain s → ∃ l', l' ∈ subchain (↑ofDual ⁻¹' s) ∧ length l = length l'",
"state_before": "case a\nα : Type u_1\nβ : Type ?u.31224\ninst✝¹ : LT α\ninst✝ : LT β\ns t :... | [
251,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Combinatorics/SetFamily/Shadow.lean | Finset.insert_mem_upShadow | [] | [
213,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
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