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/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.Equalizer.map_normNoninc | [] | [
998,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
996,
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Mathlib/Analysis/Convex/Exposed.lean | exposed_point_def | [] | [
210,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
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Mathlib/Order/Bounds/Basic.lean | isLUB_empty | [] | [
896,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Data/Finset/Basic.lean | Finset.not_mem_union | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.141391\nγ : Type ?u.141394\ninst✝ : DecidableEq α\ns s₁ s₂ t t₁ t₂ u v : Finset α\na b : α\n⊢ ¬a ∈ s ∪ t ↔ ¬a ∈ s ∧ ¬a ∈ t",
"tactic": "rw [mem_union, not_or]"
}
] | [
1362,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1362,
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Mathlib/GroupTheory/QuotientGroup.lean | QuotientGroup.map_id | [] | [
260,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/MetricSpace/Basic.lean | Real.nndist_eq' | [] | [
1360,
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Mathlib/Topology/MetricSpace/Basic.lean | dist_dist_dist_le_left | [] | [
1777,
21
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Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.det_updateColumn_smul | [
{
"state_after": "m : Type ?u.1649973\nn : Type u_1\ninst✝⁴ : DecidableEq n\ninst✝³ : Fintype n\ninst✝² : DecidableEq m\ninst✝¹ : Fintype m\nR : Type v\ninst✝ : CommRing R\nM : Matrix n n R\nj : n\ns : R\nu : n → R\n⊢ s * det (updateRow Mᵀ j u) = s * det (updateColumn M j u)",
"state_before": "m : Type ?u.1... | [
410,
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Mathlib/Data/Matrix/Basic.lean | Matrix.mulVec_smul | [
{
"state_after": "case h\nl : Type ?u.867277\nm : Type u_4\nn : Type u_1\no : Type ?u.867286\nm' : o → Type ?u.867291\nn' : o → Type ?u.867296\nR : Type u_2\nS : Type u_3\nα : Type v\nβ : Type w\nγ : Type ?u.867309\ninst✝⁵ : NonUnitalNonAssocSemiring α\ninst✝⁴ : Fintype n\ninst✝³ : Monoid R\ninst✝² : NonUnitalN... | [
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.sum_add | [] | [
999,
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997,
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Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | derivWithin_rpow_const | [] | [
595,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
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Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.Ioc_self | [
{
"state_after": "no goals",
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"tactic": "rw [Ioc, Finset.Ioc_self, Finset.empty_val]"
}
] | [
108,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
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Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.add_left_neg | [
{
"state_after": "case c\nR : Type u_1\ninst✝¹ : Ring R\nS : Submonoid R\ninst✝ : OreSet S\nr : R\ns : { x // x ∈ S }\n⊢ -(r /ₒ s) + r /ₒ s = 0",
"state_before": "R : Type u_1\ninst✝¹ : Ring R\nS : Submonoid R\ninst✝ : OreSet S\nx : OreLocalization R S\n⊢ -x + x = 0",
"tactic": "induction' x using OreLo... | [
852,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
851,
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Mathlib/Data/Set/Function.lean | Function.Injective.injOn_range | [
{
"state_after": "case intro.intro\nα : Type u_1\nβ : Type u_3\nγ : Type u_2\nι : Sort ?u.34009\nπ : α → Type ?u.34014\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\np : Set γ\nf f₁ f₂ f₃ : α → β\ng g₁ g₂ : β → γ\nf' f₁' f₂' : β → α\ng' : γ → β\na : α\nb : β\nh : Injective (g ∘ f)\nx y : α\nH : g (f x) = g (f y)\n⊢ f x = f... | [
679,
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.uniformity_basis_dist_pow | [] | [
767,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
763,
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Mathlib/Data/Matrix/Basic.lean | Matrix.submatrix_diagonal | [
{
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Mathlib/Data/Finset/NAry.lean | Finset.image₂_singleton_left' | [] | [
164,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/ContinuousFunction/Basic.lean | ContinuousMap.const_comp | [] | [
267,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
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Mathlib/Dynamics/PeriodicPts.lean | Function.IsPeriodicPt.const_mul | [
{
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"tactic": "simp only [mul_comm n, hm.mul_const n]"
}
] | [
130,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
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Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.mem_compl_zeroLocus_iff_not_mem | [
{
"state_after": "R : Type u_1\nA : Type u_2\ninst✝³ : CommSemiring R\ninst✝² : CommRing A\ninst✝¹ : Algebra R A\n𝒜 : ℕ → Submodule R A\ninst✝ : GradedAlgebra 𝒜\nf : A\nI : ProjectiveSpectrum 𝒜\n⊢ ¬f ∈ ↑I.asHomogeneousIdeal ↔ ¬f ∈ I.asHomogeneousIdeal",
"state_before": "R : Type u_1\nA : Type u_2\ninst✝³... | [
323,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/Ideal/Operations.lean | Submodule.smul_induction_on' | [
{
"state_after": "R : Type u\nM : Type v\nF : Type ?u.42169\nG : Type ?u.42172\ninst✝² : CommSemiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nI J : Ideal R\nN P : Submodule R M\nx : M\nhx : x ∈ I • N\np : (x : M) → x ∈ I • N → Prop\nHb : ∀ (r : R) (hr : r ∈ I) (n : M) (hn : n ∈ N), p (r • n) (_ : r • n... | [
134,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Summable.indicator | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Real/Pointwise.lean | Real.mul_iInf_of_nonpos | [] | [
127,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
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Mathlib/RingTheory/DedekindDomain/Factorization.lean | Ideal.finprod_not_dvd | [
{
"state_after": "R : Type u_1\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDomain R\ninst✝³ : IsDedekindDomain R\nK : Type ?u.235854\ninst✝² : Field K\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\nv : HeightOneSpectrum R\nI : Ideal R\nhI : I ≠ 0\nhf : Set.Finite (mulSupport fun v => maxPowDividing v I)\n⊢ ¬v.asIdeal ... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/MeasurableSpaceDef.lean | measurable_const | [] | [
567,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Ico_union_Ici | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type ?u.83670\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\nhab : a ≤ b\nh : c ≤ b\n⊢ Ico a b ∪ Ici c = Ici (min a c)\n\ncase inr\nα : Type u_1\nβ : Type ?u.83670\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\nhab : b ≤ a\nh : c ≤ a\n⊢ Ico a b ∪ Ici c = Ici (mi... | [
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Mathlib/Order/Filter/Pointwise.lean | Filter.map₂_vsub | [] | [
1085,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1084,
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Mathlib/Order/SuccPred/Basic.lean | Order.bot_lt_succ | [] | [
553,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
552,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infiniteNeg_mul_infinitePos | [] | [
879,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
877,
1
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Std/Data/AssocList.lean | Std.AssocList.foldlM_eq | [
{
"state_after": "no goals",
"state_before": "m : Type u_1 → Type u_2\nδ : Type u_1\nα : Type u_3\nβ : Type u_4\ninst✝ : Monad m\nf : δ → α → β → m δ\ninit : δ\nl : AssocList α β\n⊢ foldlM f init l =\n List.foldlM\n (fun d x =>\n match x with\n | (a, b) => f d a b)\n init (toList ... | [
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] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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Mathlib/Topology/Algebra/Order/LeftRightLim.lean | Monotone.rightLim_le_leftLim | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝³ : LinearOrder α\ninst✝² : ConditionallyCompleteLinearOrder β\ninst✝¹ : TopologicalSpace β\ninst✝ : OrderTopology β\nf : α → β\nhf : Monotone f\nx y : α\nh : x < y\nthis : TopologicalSpace α := Preorder.topology α\n⊢ rightLim f x ≤ leftLim f y",
"state_bef... | [
162,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
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Mathlib/GroupTheory/Complement.lean | Subgroup.range_mem_rightTransversals | [
{
"state_after": "case mk.intro.mk.intro\nG : Type u_1\ninst✝ : Group G\nH K : Subgroup G\nS T : Set G\nf : Quotient (QuotientGroup.rightRel H) → G\nhf : ∀ (q : Quotient (QuotientGroup.rightRel H)), Quotient.mk'' (f q) = q\nq₁ q₂ : Quotient (QuotientGroup.rightRel H)\nh :\n Set.restrict (Set.range f) Quotient.... | [
310,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
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Mathlib/Analysis/NormedSpace/Exponential.lean | exp_eq_exp | [
{
"state_after": "case h\n𝕂 : Type u_2\n𝕂' : Type u_3\n𝔸 : Type u_1\ninst✝⁶ : Field 𝕂\ninst✝⁵ : Field 𝕂'\ninst✝⁴ : Ring 𝔸\ninst✝³ : Algebra 𝕂 𝔸\ninst✝² : Algebra 𝕂' 𝔸\ninst✝¹ : TopologicalSpace 𝔸\ninst✝ : TopologicalRing 𝔸\nx : 𝔸\n⊢ exp 𝕂 x = exp 𝕂' x",
"state_before": "𝕂 : Type u_2\n𝕂' : T... | [
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41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
660,
1
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Mathlib/Order/Filter/Cofinite.lean | Filter.disjoint_cofinite_right | [] | [
139,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
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Mathlib/Data/ZMod/Basic.lean | ZMod.addOrderOf_coe | [
{
"state_after": "case zero\nn : ℕ\nn0 : n ≠ 0\n⊢ addOrderOf ↑Nat.zero = n / Nat.gcd n Nat.zero\n\ncase succ\nn : ℕ\nn0 : n ≠ 0\na : ℕ\n⊢ addOrderOf ↑(Nat.succ a) = n / Nat.gcd n (Nat.succ a)",
"state_before": "a n : ℕ\nn0 : n ≠ 0\n⊢ addOrderOf ↑a = n / Nat.gcd n a",
"tactic": "cases' a with a"
},
{... | [
114,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Std/Data/BinomialHeap.lean | Std.BinomialHeapImp.Heap.WellFormed.deleteMin | [
{
"state_after": "case cons.refl\nα : Type u_1\nle : α → α → Bool\nn r : Nat\na : α\nc : HeapNode α\ns : Heap α\nh : WellFormed le n (cons r a c s)\n⊢ WellFormed le 0\n (Heap.merge le\n (HeapNode.toHeap (Heap.findMin le (cons r a c) s { before := id, val := a, node := c, next := s }).node)\n (FindM... | [
497,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
486,
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Mathlib/Data/Finsupp/Basic.lean | Finsupp.mapDomain_mapRange | [] | [
651,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
644,
1
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Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.sum_tmul | [
{
"state_after": "case empty\nR : Type u_4\ninst✝¹⁶ : CommSemiring R\nR' : Type ?u.457403\ninst✝¹⁵ : Monoid R'\nR'' : Type ?u.457409\ninst✝¹⁴ : Semiring R''\nM : Type u_2\nN : Type u_3\nP : Type ?u.457421\nQ : Type ?u.457424\nS : Type ?u.457427\ninst✝¹³ : AddCommMonoid M\ninst✝¹² : AddCommMonoid N\ninst✝¹¹ : Ad... | [
394,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
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Mathlib/LinearAlgebra/Span.lean | Submodule.coe_iSup_of_chain | [] | [
326,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
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] |
Mathlib/Data/Matrix/Block.lean | Matrix.blockDiagonal'_zero | [
{
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697,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
695,
1
] |
Mathlib/LinearAlgebra/CrossProduct.lean | cross_self | [
{
"state_after": "R : Type u_1\ninst✝ : CommRing R\nv : Fin 3 → R\n⊢ v 1 * v 2 - v 1 * v 2 = 0 ∧ v 0 * v 2 - v 0 * v 2 = 0 ∧ v 0 * v 1 - v 0 * v 1 = 0 ∧ ![] = 0",
"state_before": "R : Type u_1\ninst✝ : CommRing R\nv : Fin 3 → R\n⊢ ↑(↑crossProduct v) v = 0",
"tactic": "simp_rw [cross_apply, mul_comm, con... | [
91,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/GroupTheory/Congruence.lean | Con.mul | [] | [
162,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
11
] |
Mathlib/Deprecated/Group.lean | Additive.isAddHom | [] | [
446,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.log_le_iff_le_exp | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\nhx : 0 < x\n⊢ log x ≤ y ↔ x ≤ exp y",
"tactic": "rw [← exp_le_exp, exp_log hx]"
}
] | [
158,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Topology/Basic.lean | nhds_bind_nhds | [] | [
982,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
981,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tsum_eq_add_tsum_ite | [] | [
1029,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1027,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csSup_singleton | [] | [
652,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
651,
1
] |
Mathlib/RingTheory/Derivation/Lie.lean | Derivation.commutator_apply | [] | [
49,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Std/Logic.lean | Bool.eq_false_or_eq_true | [] | [
765,
22
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
763,
1
] |
Mathlib/Topology/Constructions.lean | Filter.HasBasis.prod_nhds' | [] | [
552,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
1
] |
Mathlib/Topology/Category/TopCat/OpenNhds.lean | TopologicalSpace.OpenNhds.map_id_obj_unop | [
{
"state_after": "no goals",
"state_before": "X Y : TopCat\nf : X ⟶ Y\nx : ↑X\nU : (OpenNhds x)ᵒᵖ\n⊢ (map (𝟙 X) x).obj U.unop = U.unop",
"tactic": "simp"
}
] | [
127,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.fg_of_noetherian | [] | [
942,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
941,
1
] |
Mathlib/Analysis/InnerProductSpace/l2Space.lean | IsHilbertSum.linearIsometryEquiv_symm_apply_single | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\n𝕜 : Type u_2\ninst✝⁴ : IsROrC 𝕜\nE : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ncplt : CompleteSpace E\nG : ι → Type u_4\ninst✝¹ : (i : ι) → NormedAddCommGroup (G i)\ninst✝ : (i : ι) → InnerProductSpace 𝕜 (G i)\nV ... | [
354,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
11
] |
Mathlib/Algebra/GroupPower/Ring.lean | sub_sq' | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.130363\nM : Type ?u.130366\ninst✝ : CommRing R\na b : R\n⊢ (a - b) ^ 2 = a ^ 2 + b ^ 2 - 2 * a * b",
"tactic": "rw [sub_eq_add_neg, add_sq', neg_sq, mul_neg, ← sub_eq_add_neg]"
}
] | [
291,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.mem_coe | [] | [
113,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Analysis/Convex/StrictConvexBetween.lean | Sbtw.dist_lt_max_dist | [
{
"state_after": "V : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : NormedSpace ℝ V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : NormedAddTorsor V P\ninst✝ : StrictConvexSpace ℝ V\np p₁ p₂ p₃ : P\nh : Sbtw ℝ p₁ p₂ p₃\nhp₁p₃ : p₁ -ᵥ p ≠ p₃ -ᵥ p\n⊢ dist p₂ p < max (dist p₁ p) (dist p₃ p)",
"state... | [
41,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
27,
1
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Mathlib/LinearAlgebra/Ray.lean | units_inv_smul | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝² : LinearOrderedCommRing R\nM : Type u_2\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nu : Rˣ\nv : Module.Ray R M\nthis : 0 < ↑u * ↑u\n⊢ 0 < ↑(u * u)",
"tactic": "exact this"
},
{
"state_after": "no goals",
"state_before": "R ... | [
525,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.eqLocus_toAddSubmonoid | [] | [
1274,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1272,
1
] |
Std/Data/Rat/Lemmas.lean | Rat.one_mul | [
{
"state_after": "no goals",
"state_before": "a : Rat\n⊢ 1 * a = a",
"tactic": "simp [mul_def, normalize_self]"
}
] | [
262,
93
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
262,
19
] |
Mathlib/Logic/Basic.lean | forall_true_iff | [] | [
713,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
713,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | IsDedekindDomainInv.mul_inv_eq_one | [] | [
280,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/CategoryTheory/Yoneda.lean | CategoryTheory.Functor.reprW_app_hom | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\nF : Cᵒᵖ ⥤ Type v₁\ninst✝ : Representable F\nX : Cᵒᵖ\nf : X.unop ⟶ reprX F\n⊢ (reprF F).app X f = ((reprF F).app (reprX F).op ≫ F.map f.op) (𝟙 (reprX F))",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nF : Cᵒᵖ ⥤ Type v₁\ninst✝ : Representable F\nX : C... | [
228,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | Homeomorph.transLocalHomeomorph_eq_trans | [] | [
924,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
922,
1
] |
Mathlib/Data/MvPolynomial/Equiv.lean | MvPolynomial.finSuccEquiv_coeff_coeff | [
{
"state_after": "case h1\nR : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type ?u.1032018\na a' a₁ a₂ : R\ne : ℕ\ns : σ →₀ ℕ\ninst✝ : CommSemiring R\nn : ℕ\nm✝ : Fin n →₀ ℕ\ni✝ : ℕ\nj : Fin (n + 1) →₀ ℕ\nr : R\nm : Fin n →₀ ℕ\ni : ℕ\n⊢ coeff m (Polynomial.coeff (↑(finSuccEquiv R n) (↑(monomial j) r)) i)... | [
389,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Mathlib/Algebra/GroupRingAction/Basic.lean | toRingHom_injective | [] | [
69,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/MeasureTheory/Function/AEEqOfIntegral.lean | MeasureTheory.ae_eq_zero_of_forall_dual | [] | [
117,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Logic/Function/Conjugate.lean | Function.Semiconj₂.isIdempotent_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.3984\nf : α → β\nga : α → α → α\ngb : β → β → β\ninst✝ : IsIdempotent β gb\nh : Semiconj₂ f ga gb\nh_inj : Injective f\nx : α\n⊢ f (ga x x) = f x",
"tactic": "rw [h.eq, @IsIdempotent.idempotent _ gb]"
}
] | [
181,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Algebra/Ring/Aut.lean | RingAut.smul_def | [] | [
130,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
11
] |
Mathlib/Analysis/Convex/Hull.lean | convexHull_mono | [] | [
85,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Topology/Basic.lean | mem_closure_iff_clusterPt | [] | [
1291,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1290,
1
] |
Mathlib/Algebra/ContinuedFractions/Computation/Translations.lean | GeneralizedContinuedFraction.of_s_tail | [] | [
322,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.floor_add_nat | [
{
"state_after": "F : Type ?u.78159\nα : Type u_1\nβ : Type ?u.78165\ninst✝¹ : LinearOrderedSemiring α\ninst✝ : FloorSemiring α\na : α\nn✝ : ℕ\nha : 0 ≤ a\nn b : ℕ\n⊢ ↑b ≤ a + ↑n ↔ b ≤ ⌊a⌋₊ + n",
"state_before": "F : Type ?u.78159\nα : Type u_1\nβ : Type ?u.78165\ninst✝¹ : LinearOrderedSemiring α\ninst✝ : F... | [
448,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
1
] |
Mathlib/Analysis/Convex/Function.lean | neg_convexOn_iff | [
{
"state_after": "case mp\n𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.627009\nα : Type ?u.627012\nβ : Type u_3\nι : Type ?u.627018\ninst✝⁵ : OrderedSemiring 𝕜\ninst✝⁴ : AddCommMonoid E\ninst✝³ : AddCommMonoid F\ninst✝² : OrderedAddCommGroup β\ninst✝¹ : SMul 𝕜 E\ninst✝ : Module 𝕜 β\ns : Set E\nf g : E → β\n⊢ Co... | [
845,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
835,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.le_radius_of_bound | [] | [
136,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/GroupTheory/FreeAbelianGroup.lean | FreeAbelianGroup.map_id | [] | [
376,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.succ_succAbove_succ | [
{
"state_after": "n✝ m n : ℕ\ni : Fin (n + 1)\nj : Fin n\nh : ↑castSucc j < i\nh' : ↑castSucc (succ j) < succ i\n⊢ ↑(succAbove (succ i)) (succ j) = succ (↑(succAbove i) j)",
"state_before": "n✝ m n : ℕ\ni : Fin (n + 1)\nj : Fin n\nh : ↑castSucc j < i\n⊢ ↑(succAbove (succ i)) (succ j) = succ (↑(succAbove i) ... | [
2226,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2216,
1
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.ofReal_tsum | [] | [
603,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
602,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.incl_coe | [] | [
566,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
565,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.piecewise_le_piecewise' | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.310085\nγ : Type ?u.310088\nδ✝ : α → Sort ?u.310093\ns : Finset α\nf✝ g✝ : (i : α) → δ✝ i\ninst✝¹ : (j : α) → Decidable (j ∈ s)\nδ : α → Type u_1\ninst✝ : (i : α) → Preorder (δ i)\nf g f' g' : (i : α) → δ i\nHf : ∀ (x : α), x ∈ s → f x ... | [
2569,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2567,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_iUnion_decode₂ | [] | [
726,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
724,
1
] |
Mathlib/Algebra/DirectSum/Module.lean | DirectSum.apply_eq_component | [] | [
206,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.le_iff_exists_add | [] | [
662,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
657,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.ListBlank.induction_on | [] | [
208,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
11
] |
Mathlib/GroupTheory/Congruence.lean | Con.refl | [] | [
144,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
11
] |
Mathlib/LinearAlgebra/Quotient.lean | Submodule.mkQ_surjective | [
{
"state_after": "case mk\nR : Type u_1\nM : Type u_2\nr : R\nx✝ y : M\ninst✝⁴ : Ring R\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\np p' : Submodule R M\nM₂ : Type ?u.182338\ninst✝¹ : AddCommGroup M₂\ninst✝ : Module R M₂\nA : Submodule R M\nb✝ : M ⧸ A\nx : M\n⊢ ∃ a, ↑(mkQ A) a = Quot.mk Setoid.r x",
"sta... | [
331,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mul_le_max | [
{
"state_after": "case inl\nb : Cardinal\n⊢ 0 * b ≤ max (max 0 b) ℵ₀\n\ncase inr\na b : Cardinal\nha0 : a ≠ 0\n⊢ a * b ≤ max (max a b) ℵ₀",
"state_before": "a b : Cardinal\n⊢ a * b ≤ max (max a b) ℵ₀",
"tactic": "rcases eq_or_ne a 0 with (rfl | ha0)"
},
{
"state_after": "case inr.inl\na : Cardin... | [
648,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
639,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPushout.unop | [] | [
864,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
859,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiff.hasStrictDerivAt | [] | [
1987,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1985,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.sum_lt_top_iff | [] | [
1227,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1226,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.coequalizer_as_cokernel | [] | [
692,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
] |
Mathlib/MeasureTheory/Measure/ProbabilityMeasure.lean | MeasureTheory.ProbabilityMeasure.tendsto_nhds_iff_toFiniteMeasure_tendsto_nhds | [] | [
270,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Data/Nat/Parity.lean | Nat.Odd.of_mul_right | [] | [
169,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Data/Nat/Fib.lean | Nat.fib_mono | [] | [
102,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.degreeOf_rename_of_injective | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nσ : Type u_1\nτ : Type u_2\nr : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝ : CommSemiring R\np✝ q p : MvPolynomial σ R\nf : σ → τ\nh : Injective f\ni : σ\n⊢ degreeOf (f i) (↑(rename f) p) = degreeOf i p",
"tactic": "classical\nsimp only [de... | [
582,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
] |
Mathlib/Order/CompleteLattice.lean | sSup_univ | [] | [
495,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
1
] |
Mathlib/Logic/Equiv/Set.lean | Equiv.symm_preimage_preimage | [] | [
108,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Std/Data/Int/DivMod.lean | Int.mod_zero | [] | [
256,
18
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
254,
9
] |
Mathlib/Order/Basic.lean | Preorder.ext | [
{
"state_after": "case a.le.h.h.a\nι : Type ?u.19676\nα✝ : Type u\nβ : Type v\nγ : Type w\nπ : ι → Type ?u.19687\nr : α✝ → α✝ → Prop\nα : Type u_1\nA B : Preorder α\nH : ∀ (x y : α), x ≤ y ↔ x ≤ y\nx y : α\n⊢ x ≤ y ↔ x ≤ y",
"state_before": "ι : Type ?u.19676\nα✝ : Type u\nβ : Type v\nγ : Type w\nπ : ι → Ty... | [
653,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
650,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.inter_smul_union_subset_union | [] | [
220,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
src/lean/Init/SizeOfLemmas.lean | Subtype.sizeOf | [
{
"state_after": "case mk\nα : Sort u_1\np : α → Prop\nval✝ : α\nproperty✝ : p val✝\n⊢ SizeOf.sizeOf { val := val✝, property := property✝ } = SizeOf.sizeOf { val := val✝, property := property✝ }.val + 1",
"state_before": "α : Sort u_1\np : α → Prop\ns : Subtype p\n⊢ SizeOf.sizeOf s = SizeOf.sizeOf s.val + 1... | [
33,
22
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
32,
9
] |
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