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/SetTheory/Game/PGame.lean | PGame.le_iff_sub_nonneg | [] | [
1804,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1796,
1
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Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.cast_neg | [
{
"state_after": "no goals",
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"tactic": "simp [e]"
}
] | [
838,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
837,
1
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Mathlib/Algebra/Ring/BooleanRing.lean | toBoolAlg_one | [] | [
337,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
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Mathlib/Data/List/Count.lean | List.count_le_count_cons | [] | [
218,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
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Mathlib/Algebra/Order/Interval.lean | NonemptyInterval.fst_mul | [] | [
183,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
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Mathlib/Data/Finset/Basic.lean | Finset.sdiff_insert | [
{
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"tactic": "simp_rw [← sdiff_singleton_eq_erase, insert_eq, sdiff_sdiff_left', sdiff_unio... | [
2308,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2306,
1
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Mathlib/Data/List/Cycle.lean | List.next_getLast_cons | [
{
"state_after": "case h\nα : Type u_1\ninst✝ : DecidableEq α\nl : List α\nx : α\nh✝ : x ∈ l\ny : α\nh : x ∈ y :: l\nhy : x ≠ y\nhx : x = getLast (y :: l) (_ : y :: l ≠ [])\nhl : Nodup l\n⊢ ¬getLast (y :: l) (_ : y :: l ≠ []) ∈ dropLast (y :: l)",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\nl : Li... | [
206,
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184,
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Mathlib/Analysis/InnerProductSpace/Calculus.lean | contDiffWithinAt_euclidean | [
{
"state_after": "𝕜 : Type u_1\nι : Type u_3\nH : Type u_2\ninst✝³ : IsROrC 𝕜\ninst✝² : NormedAddCommGroup H\ninst✝¹ : NormedSpace 𝕜 H\ninst✝ : Fintype ι\nf : H → EuclideanSpace 𝕜 ι\nf' : H →L[𝕜] EuclideanSpace 𝕜 ι\nt : Set H\ny : H\nn : ℕ∞\n⊢ (∀ (i : ι), ContDiffWithinAt 𝕜 n (fun x => (↑(EuclideanSpace.... | [
339,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
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Mathlib/Algebra/Order/Floor.lean | Int.ceil_nonneg | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.221444\nα : Type u_1\nβ : Type ?u.221450\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na : α\nha : 0 ≤ a\n⊢ 0 ≤ ⌈a⌉",
"tactic": "exact_mod_cast ha.trans (le_ceil a)"
}
] | [
1203,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1203,
1
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Mathlib/CategoryTheory/Limits/Shapes/Types.lean | CategoryTheory.Limits.Types.productIso_hom_comp_eval | [] | [
339,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.roots_monomial | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\na b : R\nn✝ : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np q : R[X]\nha : a ≠ 0\nn : ℕ\n⊢ roots (↑(monomial n) a) = n • {0}",
"tactic": "rw [← C_mul_X_pow_eq_monomial, roots_C_mul_X_pow ha]"
}
] | [
729,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
728,
1
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Mathlib/Data/Finset/Functor.lean | Finset.seqRight_def | [] | [
90,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
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Mathlib/Topology/Instances/NNReal.lean | NNReal.sum_add_tsum_nat_add | [] | [
225,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
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Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.kernel.lift_zero | [
{
"state_after": "case h\nC : Type u\ninst✝² : Category C\ninst✝¹ : HasZeroMorphisms C\nX Y : C\nf : X ⟶ Y\ninst✝ : HasKernel f\nW : C\nh : 0 ≫ f = 0\n⊢ lift f 0 h ≫ equalizer.ι f 0 = 0 ≫ equalizer.ι f 0",
"state_before": "C : Type u\ninst✝² : Category C\ninst✝¹ : HasZeroMorphisms C\nX Y : C\nf : X ⟶ Y\nins... | [
261,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
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Mathlib/Probability/ProbabilityMassFunction/Monad.lean | Pmf.support_bind | [
{
"state_after": "no goals",
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"tactic": "simp [mem_support_iff, ENNReal.tsum_eq_zero, not_or]"
}
] | [
125,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
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Mathlib/Order/WithBot.lean | WithBot.map_ofDual | [] | [
959,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
957,
1
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Mathlib/Algebra/Lie/Nilpotent.lean | coe_lowerCentralSeries_ideal_quot_eq | [
{
"state_after": "case zero\nR : Type u\nL : Type v\nL' : Type w\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\ninst✝¹ : LieRing L'\ninst✝ : LieAlgebra R L'\nI : LieIdeal R L\n⊢ ↑(lowerCentralSeries R L (L ⧸ I) Nat.zero) = ↑(lowerCentralSeries R (L ⧸ I) (L ⧸ I) Nat.zero)\n\ncase succ\nR : Ty... | [
572,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
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Mathlib/Data/Nat/ModEq.lean | Nat.ModEq.add_left_cancel' | [] | [
163,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
11
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Mathlib/Order/UpperLower/Basic.lean | IsUpperSet.bot_mem | [] | [
308,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_add_eq_left_of_degree_lt | [
{
"state_after": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q : R[X]\nι : Type ?u.529420\nh : degree q < degree p\n⊢ coeff p (natDegree p) ≠ 0",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q : R[X]\nι : Type ?u.529420\nh : degree q < degree ... | [
694,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
690,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | div_pos_of_neg_of_neg | [] | [
701,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
1
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Mathlib/Data/Real/GoldenRatio.lean | goldConj_ne_zero | [] | [
127,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Order/Ideal.lean | Order.Ideal.IsProper.ne_top | [] | [
225,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Analysis/InnerProductSpace/Adjoint.lean | LinearMap.adjoint_eq_toClm_adjoint | [] | [
388,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
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Mathlib/LinearAlgebra/Matrix/ToLinearEquiv.lean | Matrix.nondegenerate_iff_det_ne_zero | [
{
"state_after": "R : Type ?u.534603\nM✝ : Type ?u.534606\ninst✝⁶ : CommRing R\ninst✝⁵ : AddCommGroup M✝\ninst✝⁴ : Module R M✝\nn : Type u_2\ninst✝³ : Fintype n\nA : Type u_1\ninst✝² : DecidableEq n\ninst✝¹ : CommRing A\ninst✝ : IsDomain A\nM : Matrix n n A\n⊢ Nondegenerate M ↔ ¬∃ v x, vecMul v M = 0",
"sta... | [
193,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
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Mathlib/Data/Finset/Card.lean | Finset.card_image_of_injective | [] | [
243,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.uIcc_eq_union | [
{
"state_after": "ι : Type ?u.199082\nα : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : LocallyFiniteOrder α\na a₁ a₂ b b₁ b₂ c x : α\n⊢ Set.uIcc a b = Set.Icc a b ∪ Set.Icc b a",
"state_before": "ι : Type ?u.199082\nα : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : LocallyFiniteOrder α\na a₁ a₂ b b₁ b₂ c x : α\n⊢ ... | [
1006,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1003,
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Mathlib/Data/Matrix/Basic.lean | Matrix.col_vecMul | [
{
"state_after": "case a.h\nl : Type ?u.1215363\nm : Type u_1\nn : Type u_2\no : Type ?u.1215372\nm' : o → Type ?u.1215377\nn' : o → Type ?u.1215382\nR : Type ?u.1215385\nS : Type ?u.1215388\nα : Type v\nβ : Type w\nγ : Type ?u.1215395\ninst✝¹ : Fintype m\ninst✝ : NonUnitalNonAssocSemiring α\nM : Matrix m n α\n... | [
2711,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2708,
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Mathlib/LinearAlgebra/Projection.lean | LinearMap.linearProjOfIsCompl_of_proj | [
{
"state_after": "case h.a\nR : Type u_1\ninst✝⁹ : Ring R\nE : Type u_2\ninst✝⁸ : AddCommGroup E\ninst✝⁷ : Module R E\nF : Type ?u.361842\ninst✝⁶ : AddCommGroup F\ninst✝⁵ : Module R F\nG : Type ?u.362358\ninst✝⁴ : AddCommGroup G\ninst✝³ : Module R G\np q : Submodule R E\nS : Type ?u.363321\ninst✝² : Semiring S\... | [
316,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
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] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Formula.realize_relabel_sum_inr | [
{
"state_after": "no goals",
"state_before": "L : Language\nL' : Language\nM : Type w\nN : Type ?u.239536\nP : Type ?u.239539\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nn : ℕ\nφ✝ ψ : Formula L α\nv✝ : α → M\nφ : Formula L (Fin n)\nv : Empty → M\nx : Fin... | [
684,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
680,
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Mathlib/Data/Real/Hyperreal.lean | Hyperreal.exists_st_of_not_infinite | [] | [
321,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
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Mathlib/Data/Set/Enumerate.lean | Set.enumerate_inj | [
{
"state_after": "case inl\nα : Type u_1\nsel : Set α → Option α\nn₁ n₂ : ℕ\na : α\ns : Set α\nh_sel : ∀ (s : Set α) (a : α), sel s = some a → a ∈ s\nh₁ : enumerate sel s n₁ = some a\nh₂ : enumerate sel s n₂ = some a\nhn : n₁ ≤ n₂\n⊢ n₁ = n₂\n\ncase inr\nα : Type u_1\nsel : Set α → Option α\nn₁ n₂ : ℕ\na : α\ns... | [
102,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.graph_eq_empty | [] | [
123,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Topology/Instances/AddCircle.lean | AddCircle.liftIco_zero_coe_apply | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nB : Type u_2\ninst✝³ : LinearOrderedAddCommGroup 𝕜\ninst✝² : TopologicalSpace 𝕜\ninst✝¹ : OrderTopology 𝕜\np a : 𝕜\nhp : Fact (0 < p)\ninst✝ : Archimedean 𝕜\nf : 𝕜 → B\nx : 𝕜\nhx : x ∈ Ico 0 p\n⊢ x ∈ Ico 0 (0 + p)",
"tactic": "rwa [zero... | [
659,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
658,
1
] |
Mathlib/Analysis/Asymptotics/AsymptoticEquivalent.lean | Asymptotics.isEquivalent_zero_iff_eventually_zero | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝ : NormedAddCommGroup β\nu v w : α → β\nl : Filter α\n⊢ u =o[l] 0 ↔ u =ᶠ[l] 0",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝ : NormedAddCommGroup β\nu v w : α → β\nl : Filter α\n⊢ u ~[l] 0 ↔ u =ᶠ[l] 0",
"tactic": "rw [IsEquivalent, sub_zero]"
},... | [
126,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Data/List/Cycle.lean | Cycle.toMultiset_eq_nil | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns : Cycle α\n⊢ ∀ (a : List α), toMultiset (Quotient.mk'' a) = 0 ↔ Quotient.mk'' a = nil",
"tactic": "simp"
}
] | [
709,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
708,
1
] |
Mathlib/Analysis/Fourier/FourierTransform.lean | Real.fourierChar_apply | [
{
"state_after": "no goals",
"state_before": "x : ℝ\n⊢ ↑(↑fourierChar (↑Multiplicative.ofAdd x)) = Complex.exp (↑(2 * π * x) * Complex.I)",
"tactic": "rfl"
}
] | [
244,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
src/lean/Init/SimpLemmas.lean | false_or | [] | [
91,
91
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
91,
9
] |
Mathlib/Order/Antisymmetrization.lean | antisymmetrization_fibration | [
{
"state_after": "case mk\nα : Type u_1\nβ : Type ?u.3549\ninst✝¹ : Preorder α\ninst✝ : Preorder β\na✝ b✝¹ a : α\nb✝ : Antisymmetrization α fun x x_1 => x ≤ x_1\nb : α\nh : Quot.mk Setoid.r b < toAntisymmetrization (fun x x_1 => x ≤ x_1) a\n⊢ ∃ a', (fun x x_1 => x < x_1) a' a ∧ toAntisymmetrization (fun x x_1 =... | [
159,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.isFiniteMeasure_of_le | [] | [
3122,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3121,
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Mathlib/Topology/LocalExtr.lean | IsLocalMax.min | [] | [
511,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
8
] |
Mathlib/Topology/Basic.lean | IsOpen.closure_inter | [
{
"state_after": "no goals",
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"tactic": "simpa only [inter_comm t] using h.inter_closure"
}
] | [
1394,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1393,
1
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Mathlib/Init/CcLemmas.lean | false_of_a_eq_not_a | [] | [
80,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Algebra/Ring/Prod.lean | RingHom.prod_apply | [] | [
227,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Analysis/InnerProductSpace/GramSchmidtOrtho.lean | gramSchmidt_pairwise_orthogonal | [] | [
120,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Algebra/Order/Sub/Defs.lean | add_tsub_le_tsub_add | [
{
"state_after": "α : Type u_1\nβ : Type ?u.8408\ninst✝⁴ : Preorder α\ninst✝³ : AddCommSemigroup α\ninst✝² : Sub α\ninst✝¹ : OrderedSub α\na b c d : α\ninst✝ : CovariantClass α α (fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1\n⊢ b + a - c ≤ b + (a - c)",
"state_before": "α : Type u_1\nβ : Type ?u.8408\ninst✝⁴ ... | [
144,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
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Mathlib/Algebra/BigOperators/Order.lean | Finset.prod_eq_one_iff' | [] | [
402,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/Logic/Basic.lean | xor_true | [
{
"state_after": "no goals",
"state_before": "⊢ Xor' True = Not",
"tactic": "simp [Xor']"
}
] | [
284,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
9
] |
Mathlib/GroupTheory/SemidirectProduct.lean | SemidirectProduct.lift_inr | [
{
"state_after": "no goals",
"state_before": "N : Type u_2\nG : Type u_3\nH : Type u_1\ninst✝² : Group N\ninst✝¹ : Group G\ninst✝ : Group H\nφ : G →* MulAut N\nf₁ : N →* H\nf₂ : G →* H\nh :\n ∀ (g : G),\n MonoidHom.comp f₁ (MulEquiv.toMonoidHom (↑φ g)) = MonoidHom.comp (MulEquiv.toMonoidHom (↑MulAut.con... | [
240,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Algebra/Homology/HomotopyCategory.lean | HomotopyCategory.quot_mk_eq_quotient_map | [] | [
89,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Std/Classes/Order.lean | Std.TransCmp.ge_trans | [
{
"state_after": "cmp✝ : ?m.1112 → ?m.1112 → Ordering\ninst✝¹ : TransCmp cmp✝\nx✝ : Sort ?u.1110\ncmp : x✝ → x✝ → Ordering\ninst✝ : TransCmp cmp\nx y z : x✝\nh₁ : cmp x y ≠ Ordering.lt\nh₂ : cmp y z ≠ Ordering.lt\nthis : cmp z y ≠ Ordering.gt → cmp y x ≠ Ordering.gt → cmp z x ≠ Ordering.gt\n⊢ cmp x z ≠ Ordering... | [
56,
42
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
54,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.image₂_right_identity | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.99320\nα' : Type ?u.99323\nβ : Type u_2\nβ' : Type ?u.99329\nγ : Type u_1\nγ' : Type ?u.99335\nδ : Type ?u.99338\nδ' : Type ?u.99341\nε : Type ?u.99344\nε' : Type ?u.99347\nζ : Type ?u.99350\nζ' : Type ?u.99353\nν : Type ?u.99356\ninst✝⁷ : DecidableE... | [
518,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.sup_mem_sups | [] | [
85,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Init/Data/Nat/Bitwise.lean | Nat.shiftr_zero | [
{
"state_after": "n : ℕ\n⊢ shiftr 0 n = 0",
"state_before": "⊢ ∀ (n : ℕ), shiftr 0 n = 0",
"tactic": "intro n"
},
{
"state_after": "case zero\n\n⊢ shiftr 0 zero = 0\n\ncase succ\nn : ℕ\nIH : shiftr 0 n = 0\n⊢ shiftr 0 (succ n) = 0",
"state_before": "n : ℕ\n⊢ shiftr 0 n = 0",
"tactic": "i... | [
222,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.forall_mem_insert | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.438931\nγ : Type ?u.438934\ninst✝ : DecidableEq α\na : α\ns : Finset α\np : α → Prop\n⊢ (∀ (x : α), x ∈ insert a s → p x) ↔ p a ∧ ∀ (x : α), x ∈ s → p x",
"tactic": "simp only [mem_insert, or_imp, forall_and, forall_eq]"
}
] | [
3082,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3080,
1
] |
Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.lift_apply | [] | [
252,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Init/Data/Bool/Lemmas.lean | Bool.bool_iff_false | [
{
"state_after": "no goals",
"state_before": "b : Bool\n⊢ ¬b = true ↔ b = false",
"tactic": "cases b <;> exact by decide"
},
{
"state_after": "no goals",
"state_before": "⊢ ¬true = true ↔ true = false",
"tactic": "decide"
}
] | [
136,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/CategoryTheory/Monoidal/Opposite.lean | CategoryTheory.unmop_id | [] | [
140,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Topology/UniformSpace/Completion.lean | UniformSpace.Completion.induction_on | [] | [
497,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
495,
1
] |
Mathlib/Algebra/Order/Sub/WithTop.lean | WithTop.coe_sub | [] | [
39,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.norm_int_cast | [
{
"state_after": "no goals",
"state_before": "d n : ℤ\n⊢ norm ↑n = n * n",
"tactic": "simp [norm]"
}
] | [
538,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
1
] |
Std/Data/List/Lemmas.lean | List.tail_eq_of_cons_eq | [] | [
26,
81
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
26,
1
] |
Mathlib/Order/Disjoint.lean | Codisjoint.symm | [] | [
237,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | extChartAt_prod | [
{
"state_after": "𝕜 : Type u_5\nE : Type u_3\nM : Type u_1\nH : Type u_6\nE' : Type u_4\nM' : Type u_2\nH' : Type u_7\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\ninst✝⁷ : TopologicalSpace H\ninst✝⁶ : TopologicalSpace M\nf f' : LocalHomeomorph M H\nI : ModelW... | [
1297,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1292,
1
] |
Mathlib/Topology/Algebra/Order/Compact.lean | Continuous.exists_forall_le_of_hasCompactMulSupport | [
{
"state_after": "case intro.intro.intro\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.55513\ninst✝⁶ : ConditionallyCompleteLinearOrder α\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : OrderTopology α\ninst✝³ : TopologicalSpace β\ninst✝² : TopologicalSpace γ\ninst✝¹ : Nonempty β\ninst✝ : One α\nf : β → α\nhf : Continuous f\... | [
354,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.count_eq_card | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.359485\nγ : Type ?u.359488\ninst✝ : DecidableEq α\na : α\ns : Multiset α\n⊢ count a s = ↑card s ↔ ∀ (x : α), x ∈ s → a = x",
"tactic": "simp [countp_eq_card, count, @eq_comm _ a]"
}
] | [
2429,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2428,
1
] |
Mathlib/Data/Sigma/Interval.lean | Sigma.Ioc_mk_mk | [] | [
95,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/RingTheory/Coprime/Basic.lean | isCoprime_comm | [] | [
53,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Order/Bounds/OrderIso.lean | OrderIso.isGLB_image' | [] | [
51,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/Algebra/Support.lean | Pi.mulSupport_mulSingle_one | [
{
"state_after": "no goals",
"state_before": "A : Type u_1\nB : Type u_2\ninst✝¹ : DecidableEq A\ninst✝ : One B\na : A\nb : B\n⊢ mulSupport (mulSingle a 1) = ∅",
"tactic": "simp"
}
] | [
472,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
Mathlib/GroupTheory/GroupAction/Defs.lean | SMul.comp.smulCommClass | [] | [
384,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | RelIso.cof_le | [] | [
114,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Data/Pi/Interval.lean | Pi.card_Ioo | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : ι → Type u_2\ninst✝⁴ : DecidableEq ι\ninst✝³ : Fintype ι\ninst✝² : (i : ι) → DecidableEq (α i)\ninst✝¹ : (i : ι) → PartialOrder (α i)\ninst✝ : (i : ι) → LocallyFiniteOrder (α i)\na b : (i : ι) → α i\n⊢ Finset.card (Ioo a b) = ∏ i : ι, Finset.ca... | [
58,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Data/Fintype/Pi.lean | Finset.univ_pi_univ | [
{
"state_after": "case a\nα✝ : Type ?u.22866\nα : Type u_1\nβ : α → Type u_2\ninst✝² : DecidableEq α\ninst✝¹ : Fintype α\ninst✝ : (a : α) → Fintype (β a)\na✝ : (a : α) → a ∈ univ → β a\n⊢ (a✝ ∈ pi univ fun a => univ) ↔ a✝ ∈ univ",
"state_before": "α✝ : Type ?u.22866\nα : Type u_1\nβ : α → Type u_2\ninst✝² :... | [
113,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Algebra/DirectSum/Internal.lean | SetLike.int_cast_mem_graded | [
{
"state_after": "case ofNat\nι : Type u_1\nσ : Type u_3\nS : Type ?u.28560\nR : Type u_2\ninst✝⁴ : Zero ι\ninst✝³ : AddGroupWithOne R\ninst✝² : SetLike σ R\ninst✝¹ : AddSubgroupClass σ R\nA : ι → σ\ninst✝ : GradedOne A\na✝ : ℕ\n⊢ ↑(Int.ofNat a✝) ∈ A 0\n\ncase negSucc\nι : Type u_1\nσ : Type u_3\nS : Type ?u.28... | [
80,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.integral_fintype_iUnion | [
{
"state_after": "case h.e'_2.h.e'_7.h.e'_4.h.e'_3.h\nα : Type u_2\nβ : Type ?u.19521\nE : Type u_3\nF : Type ?u.19527\ninst✝⁴ : MeasurableSpace α\ninst✝³ : NormedAddCommGroup E\nf g : α → E\ns✝ t : Set α\nμ ν : Measure α\nl l' : Filter α\ninst✝² : CompleteSpace E\ninst✝¹ : NormedSpace ℝ E\nι : Type u_1\ninst✝ ... | [
148,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/MeasureTheory/MeasurableSpaceDef.lean | Finset.measurableSet_biUnion | [] | [
147,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Topology/SubsetProperties.lean | IsIrreducible.nonempty | [] | [
1695,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1694,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.lowerClosure | [] | [
1322,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1321,
11
] |
Mathlib/Probability/ProbabilityMassFunction/Monad.lean | Pmf.bind_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\np✝ : Pmf α\nf✝ : α → Pmf β\ng : β → Pmf γ\np : Pmf α\nq : Pmf β\nf : α → β → Pmf γ\nb : γ\n⊢ ↑(bind p fun a => bind q (f a)) b = ↑(bind q fun b => bind p fun a => f a b) b",
"tactic": "simpa only [ENNReal.coe_eq_coe.... | [
164,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | Class.sUnion_apply | [
{
"state_after": "case mp\nx : Class\ny : ZFSet\n⊢ (⋃₀ x) y → ∃ z, x z ∧ y ∈ z\n\ncase mpr\nx : Class\ny : ZFSet\n⊢ (∃ z, x z ∧ y ∈ z) → (⋃₀ x) y",
"state_before": "x : Class\ny : ZFSet\n⊢ (⋃₀ x) y ↔ ∃ z, x z ∧ y ∈ z",
"tactic": "constructor"
},
{
"state_after": "case mp.intro.intro.intro.intro\... | [
1682,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1678,
1
] |
Mathlib/Data/Rat/Cast.lean | Rat.cast_abs | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.64717\nι : Type ?u.64720\nα : Type ?u.64723\nβ : Type ?u.64726\nK : Type u_1\ninst✝ : LinearOrderedField K\nq : ℚ\n⊢ ↑(abs q) = abs ↑q",
"tactic": "simp [abs_eq_max_neg]"
}
] | [
363,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/Topology/Order.lean | continuous_of_discreteTopology | [] | [
292,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/Analysis/SpecialFunctions/Exp.lean | Real.comap_exp_atTop | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.117205\nx y z : ℝ\nl : Filter α\n⊢ comap exp atTop = atTop",
"tactic": "rw [← map_exp_atTop, comap_map exp_injective, map_exp_atTop]"
}
] | [
307,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.mrange_inl_sup_mrange_inr | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\nN : Type u_2\nP : Type ?u.157882\ninst✝³ : MulOneClass M\ninst✝² : MulOneClass N\ninst✝¹ : MulOneClass P\nS : Submonoid M\nA : Type ?u.157903\ninst✝ : SetLike A M\nhA : SubmonoidClass A M\nS' : A\n⊢ mrange (inl M N) ⊔ mrange (inr M N) = ⊤",
"ta... | [
1338,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1337,
1
] |
Mathlib/CategoryTheory/Bicategory/Basic.lean | CategoryTheory.Bicategory.whisker_assoc_symm | [
{
"state_after": "no goals",
"state_before": "B : Type u\ninst✝ : Bicategory B\na b c d e : B\nf : a ⟶ b\ng g' : b ⟶ c\nη : g ⟶ g'\nh : c ⟶ d\n⊢ f ◁ η ▷ h = (α_ f g h).inv ≫ (f ◁ η) ▷ h ≫ (α_ f g' h).hom",
"tactic": "simp"
}
] | [
370,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.set_support_apply_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\np✝ q p : Perm α\na : α\n⊢ ↑p a ∈ {x | ↑p x ≠ x} ↔ a ∈ {x | ↑p x ≠ x}",
"tactic": "simp"
}
] | [
267,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Std/Data/Fin/Lemmas.lean | USize.mod_lt | [
{
"state_after": "a b : USize\nh : 0 < toNat b\n⊢ b.1.val > 0",
"state_before": "a b : USize\nh : 0 < b\n⊢ b.1.val > 0",
"tactic": "simp at h"
},
{
"state_after": "no goals",
"state_before": "a b : USize\nh : 0 < toNat b\n⊢ b.1.val > 0",
"tactic": "exact h"
}
] | [
39,
96
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
39,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.toWithTop_add | [
{
"state_after": "case refine_1.refine_1\nx y : PartENat\n⊢ toWithTop (⊤ + ⊤) = toWithTop ⊤ + toWithTop ⊤\n\ncase refine_1.refine_2\nx y : PartENat\n⊢ ∀ (n : ℕ), toWithTop (↑n + ⊤) = toWithTop ↑n + toWithTop ⊤\n\ncase refine_2.refine_1\nx y : PartENat\n⊢ ∀ (n : ℕ), toWithTop (⊤ + ↑n) = toWithTop ⊤ + toWithTop ↑... | [
668,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
662,
1
] |
Mathlib/Order/Lattice.lean | sup_le_iff | [] | [
175,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Topology/Order/Basic.lean | pi_Iio_mem_nhds' | [] | [
1492,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1491,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_ne_zero_iff | [] | [
395,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/Topology/Algebra/Module/FiniteDimension.lean | Basis.constrL_basis | [] | [
473,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
Mathlib/Computability/Primrec.lean | Nat.Primrec'.prec' | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nf g : Vector ℕ n → ℕ\nh : Vector ℕ (n + 2) → ℕ\nhf : Primrec' f\nhg : Primrec' g\nhh : Primrec' h\n⊢ Primrec' fun v => Nat.rec (g v) (fun y IH => h (y ::ᵥ IH ::ᵥ v)) (f v)",
"tactic": "simpa using comp' (prec hg hh) (hf.cons idv)"
}
] | [
1447,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1445,
1
] |
Mathlib/Data/Analysis/Topology.lean | Ctop.Realizer.isOpen_iff | [] | [
142,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/GroupTheory/Subsemigroup/Center.lean | Set.one_mem_center | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\ninst✝ : MulOneClass M\n⊢ 1 ∈ center M",
"tactic": "simp [mem_center_iff]"
}
] | [
54,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/CategoryTheory/Monad/Algebra.lean | CategoryTheory.Monad.algebra_mono_of_mono | [] | [
235,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Order/Directed.lean | directed_id | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nr r' s : α → α → Prop\ninst✝ : IsDirected α r\n⊢ Directed r id",
"tactic": "convert directed_of r"
}
] | [
181,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Analysis/Convex/Between.lean | Wbtw.sameRay_vsub_right | [
{
"state_after": "case intro.intro.intro\nR : Type u_1\nV : Type u_2\nV' : Type ?u.367054\nP : Type u_3\nP' : Type ?u.367060\ninst✝³ : StrictOrderedCommRing R\ninst✝² : AddCommGroup V\ninst✝¹ : Module R V\ninst✝ : AddTorsor V P\nx z : P\nt : R\nleft✝ : 0 ≤ t\nht1 : t ≤ 1\n⊢ SameRay R (z -ᵥ x) (z -ᵥ ↑(lineMap x ... | [
579,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
576,
1
] |
Std/Data/Int/Lemmas.lean | Int.zero_ne_negSucc | [] | [
78,
63
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
78,
9
] |
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