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/GroupTheory/FreeGroup.lean | FreeGroup.map.mk | [] | [
803,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
802,
1
] |
Mathlib/Data/List/Destutter.lean | List.destutter'_ne_nil | [] | [
121,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.setToL1_smul_left | [
{
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1111,
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Mathlib/Order/PrimeIdeal.lean | Order.Ideal.isPrime_iff_mem_or_mem | [] | [
145,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
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src/lean/Init/Data/Array/DecidableEq.lean | Array.eq_of_isEqvAux | [
{
"state_after": "case inl\nα : Type u_1\ninst✝ : DecidableEq α\na b : Array α\nhsz : size a = size b\ni : Nat\nhi : i ≤ size a\nheqv : isEqvAux a b hsz (fun x y => decide (x = y)) i = true\nj : Nat\nlow : i ≤ j\nhigh : j < size a\nh : i < size a\n⊢ a[j] = b[j]\n\ncase inr\nα : Type u_1\ninst✝ : DecidableEq α\n... | [
23,
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.div_nonempty | [
{
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"state_before": "α : Type ?u.224685\nβ : Type ?u.224688\nγ : Type ?u.224691\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\na b : Ordinal\nh : b ≠ 0\n⊢ succ a ≤ b * succ a",
"tactic": "simpa only [succ_zero, one_mul] using\n mul_le_mul_right' (succ_le_of_lt (Ordinal.... | [
872,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
869,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | fderiv_cosh | [] | [
1098,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1096,
1
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Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.domCoprod.summand_add_swap_smul_eq_zero | [
{
"state_after": "R : Type ?u.925959\ninst✝²¹ : Semiring R\nM : Type ?u.925965\ninst✝²⁰ : AddCommMonoid M\ninst✝¹⁹ : Module R M\nN : Type ?u.925997\ninst✝¹⁸ : AddCommMonoid N\ninst✝¹⁷ : Module R N\nP : Type ?u.926027\ninst✝¹⁶ : AddCommMonoid P\ninst✝¹⁵ : Module R P\nM' : Type ?u.926057\ninst✝¹⁴ : AddCommGroup M... | [
1006,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
993,
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.re_to_real | [] | [
839,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
838,
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Mathlib/Order/WellFoundedSet.lean | Set.IsPwo.image_of_monotone | [] | [
432,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.sub_eq_zero_iff_le | [] | [
159,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
158,
11
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Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.mk_coe' | [] | [
289,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Data/Nat/Sqrt.lean | Nat.sqrt_le' | [] | [
72,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
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Mathlib/Order/WithBot.lean | WithBot.map_le_iff | [
{
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"tactic": "simp only [map_bot, bot_le]"
... | [
380,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
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Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tsum_biUnion_le | [] | [
1012,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1010,
1
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Mathlib/RingTheory/MvPolynomial/Ideal.lean | MvPolynomial.mem_ideal_span_monomial_image_iff_dvd | [
{
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"state_before": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\nx... | [
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42,
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Mathlib/RingTheory/IntegralClosure.lean | isIntegral_of_noetherian | [
{
"state_after": "R : Type u_1\nS : Type ?u.77479\nA : Type u_2\ninst✝³ : CommRing R\ninst✝² : Ring A\ninst✝¹ : Ring S\nf : R →+* S\ninst✝ : Algebra R A\nH : IsNoetherian R A\nx : A\nleval : R[X] →ₗ[R] A := AlgHom.toLinearMap (aeval x)\n⊢ IsIntegral R x",
"state_before": "R : Type u_1\nS : Type ?u.77479\nA ... | [
101,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
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Mathlib/Data/Set/Intervals/Disjoint.lean | Set.biUnion_Ico_eq_Iio_self_iff | [
{
"state_after": "no goals",
"state_before": "ι : Sort u\nα : Type v\nβ : Type w\ninst✝ : LinearOrder α\na₁ a₂ b₁ b₂ : α\np : ι → Prop\nf : (i : ι) → p i → α\na : α\n⊢ (⋃ (i : ι) (hi : p i), Ico (f i hi) a) = Iio a ↔ ∀ (x : α), x < a → ∃ i hi, f i hi ≤ x",
"tactic": "simp [← Ici_inter_Iio, ← iUnion_inte... | [
168,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
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Mathlib/FieldTheory/Subfield.lean | Subfield.mem_comap | [] | [
496,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
495,
1
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Mathlib/Data/Quot.lean | Trunc.induction_on₂ | [] | [
510,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
11
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Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.natTrailingDegree_le_trailingDegree | [
{
"state_after": "case pos\nR : Type u\nS : Type v\na b : R\nn m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nhp : p = 0\n⊢ ↑(natTrailingDegree p) ≤ trailingDegree p\n\ncase neg\nR : Type u\nS : Type v\na b : R\nn m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nhp : ¬p = 0\n⊢ ↑(natTrailingDegree p) ≤ trailingDegree p",
... | [
148,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
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Mathlib/Topology/Order.lean | isOpen_coinduced | [] | [
393,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
1
] |
Mathlib/Data/List/Perm.lean | List.Subperm.length_le | [] | [
439,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
1
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.lipschitz_equivRealProd | [
{
"state_after": "no goals",
"state_before": "E : Type ?u.231205\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\n⊢ LipschitzWith 1 ↑equivRealProd",
"tactic": "simpa using AddMonoidHomClass.lipschitz_of_bound equivRealProdLm 1 equivRealProd_apply_le'"
}
] | [
217,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
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] |
Mathlib/Topology/Algebra/Group/Basic.lean | IsClosed.inv | [] | [
364,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/Algebra/Hom/Group.lean | AddMonoid.coe_mul | [] | [
1370,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1370,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.inv_smul_integral_comp_add_div | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.14905629\n𝕜 : Type ?u.14905632\nE : Type u_1\nF : Type ?u.14905638\nA : Type ?u.14905641\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\na b c✝ d✝ : ℝ\nf : ℝ → E\nc d : ℝ\n⊢ (c⁻¹ • ∫ (x : ℝ) in a..b, f (d + x / c))... | [
797,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
795,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.tan_nat_mul_pi_sub | [] | [
1051,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1050,
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Mathlib/Analysis/BoxIntegral/Partition/Filter.lean | BoxIntegral.IntegrationParams.gp_le | [] | [
287,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
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] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.comp₂Measurable_mk_mk | [] | [
348,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
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Mathlib/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.mk_eq_mk_of_comm | [
{
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"state_before": "C : Type u₁\ninst✝³ : Category C\nX Y Z : C\nD : Type u₂\ninst✝² : Category D\nB A₁ A₂ : C\nf : A₁ ⟶ B\ng : A₂ ⟶ B\ninst✝¹ : Mono f\ninst✝ : Mono g\ni : A₁ ≅ A₂\nw : i.hom ≫ g = f\n⊢ (underlyingIso f ≪≫ i).hom ≫ g = arrow (mk f)",
"tactic": "simp [w]"
}
] | [
312,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | InnerProductGeometry.norm_add_eq_add_norm_of_angle_eq_zero | [
{
"state_after": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx✝ y✝ x y : V\nh : angle x y = 0\n⊢ ‖x‖ ^ 2 + 2 * (‖x‖ * ‖y‖) + ‖y‖ ^ 2 = (‖x‖ + ‖y‖) ^ 2",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx✝ y✝ x y : V\nh : angle x y ... | [
283,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.coe_inj | [] | [
102,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.lt_iff_cons_le | [] | [
780,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
777,
1
] |
Mathlib/Logic/IsEmpty.lean | not_isEmpty_iff | [] | [
141,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.tail_cons | [] | [
54,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.neighborSet_top | [] | [
507,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.coe_iInf | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.686964\nR : Type u_2\nA : Type u_3\nB : Type ?u.686973\ninst✝⁹ : CommSemiring R\ninst✝⁸ : StarRing R\ninst✝⁷ : Semiring A\ninst✝⁶ : Algebra R A\ninst✝⁵ : StarRing A\ninst✝⁴ : StarModule R A\ninst✝³ : Semiring B\ninst✝² : Algebra R B\ninst✝¹ : StarRin... | [
686,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
1
] |
Mathlib/CategoryTheory/Monoidal/Mod_.lean | Mod_.comp_hom' | [] | [
93,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Std/Data/String/Lemmas.lean | String.split_of_valid | [
{
"state_after": "no goals",
"state_before": "s : String\np : Char → Bool\n⊢ split s p = List.map mk (List.splitOnP p s.data)",
"tactic": "simpa [split] using splitAux_of_valid p [] [] s.1 []"
}
] | [
466,
55
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
465,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.getLeft_map | [
{
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"tactic": "cases x <;> rfl"
}
] | [
266,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.iterate_mem_periodicOrbit | [] | [
530,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
528,
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Mathlib/Algebra/Opposites.lean | MulOpposite.unop_eq_zero_iff | [] | [
335,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
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] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.X_mul | [
{
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"state_before": "R : Type u\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q : R[X]\n⊢ X * p = p * X",
"tactic"... | [
576,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
570,
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Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.copy_eq | [] | [
233,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.HasIntegral.sub | [
{
"state_after": "no goals",
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303,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
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Mathlib/Computability/Partrec.lean | Nat.rfind_dom | [] | [
93,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Std/Data/RBMap/WF.lean | Std.RBNode.Balanced.erase | [] | [
463,
42
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
461,
11
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Mathlib/Order/Interval.lean | NonemptyInterval.mem_mk | [] | [
139,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Analysis/NormedSpace/Extr.lean | IsMaxFilter.norm_add_sameRay | [] | [
45,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | PSet.mk_func | [] | [
142,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.sups_singleton | [] | [
156,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Analysis/Quaternion.lean | Quaternion.continuous_imJ | [] | [
219,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.Dart.symm_symm | [] | [
762,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
761,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.coeff_X_pow_self | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nn : ℕ\n⊢ ↑(coeff R n) (X ^ n) = 1",
"tactic": "rw [coeff_X_pow, if_pos rfl]"
}
] | [
1463,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1462,
1
] |
Mathlib/Data/FunLike/Embedding.lean | EmbeddingLike.apply_eq_iff_eq | [] | [
152,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Data/Holor.lean | Holor.cprankMax_add | [
{
"state_after": "no goals",
"state_before": "α : Type\nd : ℕ\nds ds₁ ds₂ ds₃ : List ℕ\ninst✝¹ : Monoid α\ninst✝ : AddMonoid α\nn : ℕ\nx y : Holor α ds\nhx : CPRankMax 0 x\nhy : CPRankMax n y\n⊢ CPRankMax (0 + n) (x + y)",
"tactic": "match hx with\n| CPRankMax.zero => simp only [zero_add, hy]"
},
{
... | [
350,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.neBot_of_le | [] | [
509,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Antiperiodic.const_sub | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.170605\nf g : α → β\nc c₁ c₂ x✝ : α\ninst✝¹ : AddCommGroup α\ninst✝ : InvolutiveNeg β\nh : Antiperiodic f c\na x : α\n⊢ (fun x => f (a - x)) (x + c) = -(fun x => f (a - x)) x",
"tactic": "simp only [← sub_sub, h.sub_eq... | [
446,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.star_im | [] | [
1105,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1105,
9
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.sub.elim | [
{
"state_after": "no goals",
"state_before": "motive : Nat → Prop\nx y : Nat\nh₁ : y ≤ x → ∀ (k : Nat), x = y + k → motive k\nh₂ : x < y → motive 0\n⊢ motive (x - y)",
"tactic": "cases Nat.lt_or_ge x y with\n| inl hlt => rw [Nat.sub_eq_zero_of_le (Nat.le_of_lt hlt)]; exact h₂ hlt\n| inr hle => exact h₁ ... | [
696,
65
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
689,
1
] |
Mathlib/Topology/Order.lean | TopologicalSpace.leftInverse_generateFrom | [] | [
225,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Combinatorics/Quiver/Push.lean | Quiver.Push.lift_comp | [
{
"state_after": "case h_obj\nV : Type u_1\ninst✝¹ : Quiver V\nW : Type u_5\nσ : V → W\nW' : Type u_3\ninst✝ : Quiver W'\nφ : V ⥤q W'\nτ : W → W'\nh : ∀ (x : V), φ.obj x = τ (σ x)\n⊢ ∀ (X : V), (of σ ⋙q lift σ φ τ h).obj X = φ.obj X\n\ncase h_map\nV : Type u_1\ninst✝¹ : Quiver V\nW : Type u_5\nσ : V → W\nW' : T... | [
92,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | Valuation.zero_iff | [] | [
234,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.snd_inl | [] | [
125,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.destruct_append | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ns t : WSeq α\n⊢ Computation.IsBisimulation fun c1 c2 =>\n ∃ s t, c1 = destruct (append s t) ∧ c2 = Computation.bind (destruct s) (destruct_append.aux t)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns t : WSeq α\n⊢ destruct (append s t) = Com... | [
1534,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1523,
1
] |
Mathlib/Order/Interval.lean | NonemptyInterval.coe_pure_interval | [] | [
640,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
639,
1
] |
Mathlib/Analysis/Convex/Segment.lean | Convex.mem_Ico | [
{
"state_after": "case refine'_1\n𝕜 : Type u_1\nE : Type ?u.298826\nF : Type ?u.298829\nG : Type ?u.298832\nι : Type ?u.298835\nπ : ι → Type ?u.298840\ninst✝ : LinearOrderedField 𝕜\nx y z : 𝕜\nh : x < y\nhz : z ∈ Ico x y\n⊢ ∃ a b, 0 < a ∧ 0 ≤ b ∧ a + b = 1 ∧ a * x + b * y = z\n\ncase refine'_2\n𝕜 : Type u_1... | [
583,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
570,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | DifferentiableOn.sinh | [] | [
1150,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1149,
1
] |
Mathlib/Data/Dfinsupp/WellFounded.lean | Dfinsupp.Lex.acc_of_single_erase | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : ι → Type u_2\ninst✝¹ : (i : ι) → Zero (α i)\nr : ι → ι → Prop\ns : (i : ι) → α i → α i → Prop\ninst✝ : DecidableEq ι\nx : Π₀ (i : ι), α i\ni : ι\nhs : Acc (Dfinsupp.Lex r s) (single i (↑x i))\nhu : Acc (Dfinsupp.Lex r s) (erase i x)\n⊢ Acc (Dfi... | [
111,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Data/Sigma/Lex.lean | Sigma.Lex.mono | [
{
"state_after": "case left\nι : Type u_1\nα : ι → Type u_2\nr r₁ r₂ : ι → ι → Prop\ns s₁ s₂ : (i : ι) → α i → α i → Prop\na✝ b✝ : (i : ι) × α i\nhr : ∀ (a b : ι), r₁ a b → r₂ a b\nhs : ∀ (i : ι) (a b : α i), s₁ i a b → s₂ i a b\ni✝ j✝ : ι\na : α i✝\nb : α j✝\nhij : r₁ i✝ j✝\n⊢ Lex r₂ s₂ { fst := i✝, snd := a }... | [
71,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.card_support_eq_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q : R[X]\n⊢ Finset.card (support p) = 0 ↔ p = 0",
"tactic": "simp"
}
] | [
409,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_apply_ne_one | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.6623\nι : Type ?u.6626\nM : Type u_1\nN : Type ?u.6632\ninst✝¹ : One M\ninst✝ : One N\ns t : Set α\nf g : α → M\na✝ a : α\n⊢ mulIndicator s f a ≠ 1 ↔ a ∈ s ∩ mulSupport f",
"tactic": "simp only [Ne.def, mulIndicator_apply_eq_one, no... | [
144,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.enumOrd_def | [
{
"state_after": "S : Set Ordinal\no : Ordinal\n⊢ sInf (S ∩ Ici (blsub o fun a x => enumOrd S a)) = sInf (S ∩ {b | ∀ (c : Ordinal), c < o → enumOrd S c < b})",
"state_before": "S : Set Ordinal\no : Ordinal\n⊢ enumOrd S o = sInf (S ∩ {b | ∀ (c : Ordinal), c < o → enumOrd S c < b})",
"tactic": "rw [enumOr... | [
2194,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2191,
1
] |
Mathlib/Topology/Basic.lean | DenseRange.closure_range | [] | [
1811,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1810,
1
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.smul_mem_iff' | [] | [
258,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.finTwoProd_zero | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.1076425\nι' : Type ?u.1076428\nR✝ : Type ?u.1076431\nR₂ : Type ?u.1076434\nK : Type ?u.1076437\nM : Type ?u.1076440\nM' : Type ?u.1076443\nM'' : Type ?u.1076446\nV : Type u\nV' : Type ?u.1076451\nv : ι → M\ninst✝⁹ : Ring R✝\ninst✝⁸ : CommRing R₂\nins... | [
1340,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1339,
1
] |
Mathlib/Topology/MetricSpace/GromovHausdorffRealized.lean | GromovHausdorff.candidates_dist_bound | [
{
"state_after": "X : Type u\nY : Type v\ninst✝⁵ : MetricSpace X\ninst✝⁴ : CompactSpace X\ninst✝³ : Nonempty X\ninst✝² : MetricSpace Y\ninst✝¹ : CompactSpace Y\ninst✝ : Nonempty Y\nf : GromovHausdorff.ProdSpaceFun X Y\nx✝ y✝ z t : X ⊕ Y\nfA : f ∈ candidates X Y\nx y : X\n⊢ dist x y = Sum.dist (inl x) (inl y)",
... | [
180,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
9
] |
Mathlib/Data/Subtype.lean | Subtype.mk_eq_mk | [] | [
111,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | real_inner_eq_norm_mul_self_add_norm_mul_self_sub_norm_sub_mul_self_div_two | [] | [
1456,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1453,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | ContinuousLinearMap.toSesqForm_apply_coe | [] | [
1834,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1833,
1
] |
Mathlib/Algebra/Order/Sub/Defs.lean | antitone_const_tsub | [] | [
132,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.fst_list_prod | [] | [
671,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
669,
1
] |
Mathlib/FieldTheory/ChevalleyWarning.lean | char_dvd_card_solutions_of_sum_lt | [
{
"state_after": "K : Type u_3\nσ : Type u_2\nι : Type u_1\ninst✝⁵ : Fintype K\ninst✝⁴ : Field K\ninst✝³ : Fintype σ\ninst✝² : DecidableEq σ\ninst✝¹ : DecidableEq K\np : ℕ\ninst✝ : CharP K p\ns : Finset ι\nf : ι → MvPolynomial σ K\nh : ∑ i in s, totalDegree (f i) < Fintype.card σ\nhq : 0 < q - 1\n⊢ p ∣ Fintype.... | [
165,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Algebra/Quandle.lean | Rack.self_act_invAct_eq | [
{
"state_after": "R : Type u_1\ninst✝ : Rack R\nx y : R\n⊢ (x ◃ x) ◃ (x ◃ x) ◃⁻¹ y = (x ◃ x) ◃ x ◃⁻¹ y",
"state_before": "R : Type u_1\ninst✝ : Rack R\nx y : R\n⊢ (x ◃ x) ◃⁻¹ y = x ◃⁻¹ y",
"tactic": "rw [← left_cancel (x ◃ x)]"
},
{
"state_after": "R : Type u_1\ninst✝ : Rack R\nx y : R\n⊢ y = (x... | [
301,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/Algebra/Lie/Abelian.lean | commutative_ring_iff_abelian_lie_ring | [
{
"state_after": "A : Type v\ninst✝ : Ring A\nh₁ : (IsCommutative A fun x x_1 => x * x_1) ↔ ∀ (a b : A), a * b = b * a\nh₂ : IsLieAbelian A ↔ ∀ (a b : A), ⁅a, b⁆ = 0\n⊢ (IsCommutative A fun x x_1 => x * x_1) ↔ IsLieAbelian A",
"state_before": "A : Type v\ninst✝ : Ring A\nh₁ : (IsCommutative A fun x x_1 => x... | [
90,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.tmpTopologicalAddGroup | [] | [
348,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
11
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.homothety_zero | [
{
"state_after": "case h\nR : Type ?u.815526\nk : Type u_3\nV1 : Type u_1\nP1 : Type u_2\nV2 : Type ?u.815538\ninst✝⁵ : CommRing k\ninst✝⁴ : AddCommGroup V1\ninst✝³ : AffineSpace V1 P1\ninst✝² : AddCommGroup V2\ninst✝¹ : Module k V1\ninst✝ : Module k V2\nc p : P1\n⊢ ↑(homothety c 0) p = ↑(const k P1 c) p",
... | [
828,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
826,
1
] |
Mathlib/Order/WithBot.lean | WithTop.coe_min | [] | [
1241,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1240,
1
] |
Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.Measure.LebesgueDecomposition.iSup_le_le | [] | [
536,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
] |
Mathlib/Data/Set/Prod.lean | Set.prod_union | [
{
"state_after": "case h.mk\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.12021\nδ : Type ?u.12024\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\na : α\nb : β\nx : α\ny : β\n⊢ (x, y) ∈ s ×ˢ (t₁ ∪ t₂) ↔ (x, y) ∈ s ×ˢ t₁ ∪ s ×ˢ t₂",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.12021\nδ : Type ?u.12024\ns s₁ s₂ : S... | [
158,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Subspace.dualAnnihilator_le_dualAnnihilator_iff | [] | [
998,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
996,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.ediam_thickening_le | [] | [
1211,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1210,
1
] |
Mathlib/Topology/Order.lean | le_generateFrom | [] | [
561,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
559,
1
] |
Mathlib/InformationTheory/Hamming.lean | hammingNorm_comp | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.28287\nι : Type u_3\nβ : ι → Type u_2\ninst✝⁴ : Fintype ι\ninst✝³ : (i : ι) → DecidableEq (β i)\nγ : ι → Type u_1\ninst✝² : (i : ι) → DecidableEq (γ i)\ninst✝¹ : (i : ι) → Zero (β i)\ninst✝ : (i : ι) → Zero (γ i)\nf : (i : ι) → γ i → β i\nx : (i : ι)... | [
222,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Topology/UniformSpace/UniformEmbedding.lean | UniformInducing.cauchy_map_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝² : UniformSpace α\ninst✝¹ : UniformSpace β\ninst✝ : UniformSpace γ\nf : α → β\nhf : UniformInducing f\nF : Filter α\n⊢ Cauchy (map f F) ↔ Cauchy F",
"tactic": "simp only [Cauchy, map_neBot_iff, prod_map_map_eq, map_l... | [
84,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Analysis/InnerProductSpace/PiL2.lean | OrthonormalBasis.repr_injective | [
{
"state_after": "case ofRepr\nι : Type u_1\nι' : Type ?u.731886\n𝕜 : Type u_2\ninst✝⁹ : IsROrC 𝕜\nE : Type u_3\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : InnerProductSpace 𝕜 E\nE' : Type ?u.731915\ninst✝⁶ : NormedAddCommGroup E'\ninst✝⁵ : InnerProductSpace 𝕜 E'\nF : Type ?u.731933\ninst✝⁴ : NormedAddCommGrou... | [
351,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
1
] |
Mathlib/Data/Set/Prod.lean | Set.preimage_pi | [] | [
746,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
744,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.mk'_one | [] | [
257,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.iInf_le_liminf | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.105503\nι : Type ?u.105506\ninst✝ : CompleteLattice α\nf : Filter β\nu : β → α\n⊢ IsCoboundedUnder (fun x x_1 => x ≥ x_1) f u",
"tactic": "isBoundedDefault"
}
] | [
690,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
689,
1
] |
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