file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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|---|---|---|---|---|---|---|
Mathlib/Logic/Relation.lean | Relation.reflTransGen_of_equivalence | [] | [
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67
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662,
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Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.fp_iff_derivBFamily | [
{
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387,
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Mathlib/Order/MinMax.lean | max_eq_iff | [] | [
181,
26
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180,
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Mathlib/Analysis/Calculus/LocalExtr.lean | IsLocalExtr.hasDerivAt_eq_zero | [] | [
253,
69
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252,
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.C_eq_smul_one | [
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281,
25
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280,
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Mathlib/Algebra/Order/Monoid/MinMax.lean | lt_or_le_of_mul_le_mul | [
{
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Mathlib/SetTheory/Ordinal/Basic.lean | Cardinal.gc_ord_card | [] | [
1373,
69
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1373,
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Mathlib/Algebra/Order/Field/Power.lean | zpow_le_of_le | [
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"tactic": "have ha₀ : 0 < a :=... | [
39,
86
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Mathlib/GroupTheory/Transfer.lean | MonoidHom.transfer_def | [
{
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120,
84
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Mathlib/Order/Heyting/Hom.lean | HeytingHom.coe_id | [] | [
306,
6
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305,
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Mathlib/Data/Real/Cardinality.lean | Cardinal.cantorFunctionAux_succ | [
{
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Mathlib/Order/Basic.lean | Prod.mk_le_mk_iff_right | [] | [
1225,
23
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.lsub_le_of_range_subset | [
{
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"tactic": "convert Se... | [
1693,
97
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1691,
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Mathlib/Order/Filter/Basic.lean | Filter.le_map | [] | [
2557,
68
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Mathlib/RingTheory/Subring/Basic.lean | Subring.coe_top | [] | [
555,
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554,
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Mathlib/Data/Set/Countable.lean | Set.countable_range | [] | [
93,
41
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92,
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.affineSpan_eq_top_iff_vectorSpan_eq_top_of_nontrivial | [
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809,
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805,
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Mathlib/NumberTheory/VonMangoldt.lean | Nat.ArithmeticFunction.vonMangoldt_le_log | [
{
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{
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{
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169,
43
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Mathlib/Analysis/Seminorm.lean | Seminorm.closedBall_eq_biInter_ball | [
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Mathlib/Algebra/Lie/Abelian.lean | Function.Surjective.isLieAbelian | [
{
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Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | Seminorm.continuous_iff_continuous_comp | [] | [
625,
85
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Mathlib/Data/TypeVec.lean | TypeVec.repeat_eq_nil | [
{
"state_after": "case a.h\nn : ℕ\nα : TypeVec 0\ni : Fin2 0\nx✝ : (α ⊗ α) i\n⊢ repeatEq α i x✝ = nilFun i x✝",
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_nonneg_of_nonneg_of_le_pi | [] | [
425,
35
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424,
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Mathlib/GroupTheory/PGroup.lean | IsPGroup.of_injective | [
{
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Mathlib/Topology/SubsetProperties.lean | exists_compact_superset | [] | [
1183,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1180,
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Mathlib/Algebra/Group/TypeTags.lean | Additive.toMul_symm_eq | [] | [
70,
6
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Mathlib/Control/Basic.lean | fish_pure | [] | [
116,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
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Mathlib/Algebra/Order/Sub/Canonical.lean | AddLECancellable.tsub_tsub_assoc | [
{
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Mathlib/Order/Partition/Equipartition.lean | Finpartition.IsEquipartition.card_parts_eq_average | [] | [
53,
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Mathlib/LinearAlgebra/Determinant.lean | LinearMap.detAux_def' | [
{
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151,
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Mathlib/FieldTheory/Separable.lean | Polynomial.Separable.squarefree | [
{
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165,
99
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163,
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Mathlib/Data/Nat/Squarefree.lean | Nat.squarefree_mul | [
{
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"tactic": "simp only [squarefree_iff_prime_squarefree, ← sq, ← forall_a... | [
375,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
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Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.toLinAlgEquiv_apply | [
{
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Mathlib/Data/Multiset/Basic.lean | Multiset.le_zero | [] | [
558,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | deriv_ccosh | [] | [
259,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
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Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.memℒp_add_of_disjoint | [
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Mathlib/Analysis/Calculus/FDeriv/Mul.lean | Differentiable.smul_const | [] | [
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70
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Mathlib/Data/Fin/Basic.lean | Fin.castSucc_injective | [] | [
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Mathlib/Topology/ContinuousFunction/Basic.lean | ContinuousMap.copy_eq | [] | [
132,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.empty_of_count_eq_zero' | [
{
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Std/Data/List/Basic.lean | List.modifyNth_eq_modifyNthTR | [
{
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Mathlib/Data/Num/Lemmas.lean | Num.bitwise'_to_nat | [
{
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Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.kernelComparison_comp_kernel_map | [
{
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Mathlib/Analysis/Normed/Group/Basic.lean | norm_div_rev | [
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424,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/Order/JordanHolder.lean | CompositionSeries.strictMono | [] | [
175,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
11
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.sub_self_equiv | [] | [
1702,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1701,
1
] |
Mathlib/Order/RelClasses.lean | subset_of_ssubset | [] | [
726,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
725,
1
] |
Mathlib/Logic/Encodable/Basic.lean | Encodable.mem_decode₂' | [
{
"state_after": "α : Type u_1\nβ : Type ?u.4397\ninst✝ : Encodable α\nn : ℕ\na : α\n⊢ (∃ a_1, decode n = some a_1 ∧ a_1 = a ∧ encode a_1 = n) ↔ decode n = some a ∧ encode a = n",
"state_before": "α : Type u_1\nβ : Type ?u.4397\ninst✝ : Encodable α\nn : ℕ\na : α\n⊢ a ∈ decode₂ α n ↔ a ∈ decode n ∧ encode a ... | [
197,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.equiv_refl | [
{
"state_after": "no goals",
"state_before": "ι : Type u_3\nι' : Type ?u.552010\nR : Type u_2\nR₂ : Type ?u.552016\nK : Type ?u.552019\nM : Type u_1\nM' : Type ?u.552025\nM'' : Type ?u.552028\nV : Type u\nV' : Type ?u.552033\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\ninst✝³ : AddCo... | [
682,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
681,
1
] |
Mathlib/GroupTheory/GroupAction/Basic.lean | MulAction.orbit.coe_smul | [] | [
106,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | PSet.Resp.Equiv.trans | [] | [
580,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
578,
11
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.ratio_le_op_norm | [] | [
223,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | le_mul_inv_iff_mul_le | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : Group α\ninst✝¹ : LE α\ninst✝ : CovariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b c : α\n⊢ c * b ≤ a * b⁻¹ * b ↔ c * b ≤ a",
"tactic": "rw [inv_mul_cancel_right]"
}
] | [
252,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Topology/Basic.lean | ContinuousAt.tendsto | [] | [
1589,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1587,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.self_comp_symm | [] | [
201,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.coe_prodMap | [] | [
1125,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1123,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.succ_inj' | [] | [
314,
25
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
313,
1
] |
Mathlib/Analysis/NormedSpace/Banach.lean | ContinuousLinearEquiv.ofBijective_symm_apply_apply | [] | [
389,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean | MeasureTheory.Measure.add_haar_ball_of_pos | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : MeasurableSpace E\ninst✝⁵ : BorelSpace E\ninst✝⁴ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝³ : IsAddHaarMeasure μ\nF : Type ?u.1980009\ninst✝² : NormedAddCommGroup F\ninst✝¹ : Nor... | [
425,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/CategoryTheory/FintypeCat.lean | FintypeCat.id_apply | [] | [
78,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Std/Data/Option/Lemmas.lean | Option.isNone_some | [] | [
59,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
59,
9
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.comap_le_comap_iff_of_surjective | [] | [
1704,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1702,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.mapBilinear_apply | [] | [
840,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
839,
1
] |
Mathlib/LinearAlgebra/Matrix/Charpoly/LinearMap.lean | Matrix.Represents.zero | [
{
"state_after": "ι : Type u_1\ninst✝⁴ : Fintype ι\nM : Type u_2\ninst✝³ : AddCommGroup M\nR : Type u_3\ninst✝² : CommRing R\ninst✝¹ : Module R M\nI : Ideal R\nb : ι → M\nhb : Submodule.span R (Set.range b) = ⊤\ninst✝ : DecidableEq ι\n⊢ ↑(PiToModule.fromMatrix R b) 0 = ↑(PiToModule.fromEnd R b) 0",
"state_b... | [
143,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.rpow_neg_one | [
{
"state_after": "no goals",
"state_before": "x : ℝ≥0∞\n⊢ x ^ (-1) = x⁻¹",
"tactic": "simp [rpow_neg]"
}
] | [
452,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
Std/Data/Int/Lemmas.lean | Int.le_of_sub_nonneg | [
{
"state_after": "a b : Int\nh✝ : 0 ≤ a - b\nh : 0 + b ≤ a - b + b\n⊢ b ≤ a",
"state_before": "a b : Int\nh : 0 ≤ a - b\n⊢ b ≤ a",
"tactic": "have h := Int.add_le_add_right h b"
},
{
"state_after": "no goals",
"state_before": "a b : Int\nh✝ : 0 ≤ a - b\nh : 0 + b ≤ a - b + b\n⊢ b ≤ a",
"... | [
924,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
922,
11
] |
Mathlib/Algebra/Hom/Group.lean | MonoidHom.one_apply | [] | [
1406,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1406,
1
] |
Mathlib/Algebra/CharP/ExpChar.lean | char_zero_of_expChar_one | [
{
"state_after": "case zero\nR : Type u\ninst✝² : Semiring R\ninst✝¹ : Nontrivial R\np : ℕ\nhp : CharP R p\ninst✝ : CharZero R\n⊢ p = 0\n\ncase prime\nR : Type u\ninst✝¹ : Semiring R\ninst✝ : Nontrivial R\np : ℕ\nhp : CharP R p\nhprime✝ : Nat.Prime 1\nhchar✝ : CharP R 1\n⊢ p = 0",
"state_before": "R : Type ... | [
74,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Algebra/Hom/Units.lean | IsUnit.mul_inv_eq_iff_eq_mul | [] | [
338,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
11
] |
Std/Data/Int/Lemmas.lean | Int.neg_of_sign_eq_neg_one | [] | [
1285,
35
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1282,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Icc_diff_Ioc_self | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.97854\nα : Type u_1\ninst✝² : PartialOrder α\ninst✝¹ : LocallyFiniteOrder α\na b c : α\ninst✝ : DecidableEq α\nh : a ≤ b\n⊢ Icc a b \\ Ioc a b = {a}",
"tactic": "simp [← coe_inj, h]"
}
] | [
589,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
589,
1
] |
Mathlib/Analysis/MeanInequalities.lean | Real.Lp_add_le_tsum_of_nonneg' | [] | [
693,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
690,
1
] |
Mathlib/RepresentationTheory/Action.lean | Action.functorCategoryMonoidalEquivalence.inverse_map | [] | [
704,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
702,
1
] |
Mathlib/Data/Set/Basic.lean | Set.subset_compl_iff_disjoint_right | [] | [
1743,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1742,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.summable_norm_apply | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.211235\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\np✝ : FormalMultilinea... | [
296,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/RingTheory/PowerBasis.lean | PowerBasis.constr_pow_algebraMap | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.236266\nS : Type u_2\nT : Type ?u.236272\ninst✝¹⁰ : CommRing R\ninst✝⁹ : Ring S\ninst✝⁸ : Algebra R S\nA : Type u_1\nB : Type ?u.236578\ninst✝⁷ : CommRing A\ninst✝⁶ : CommRing B\ninst✝⁵ : IsDomain B\ninst✝⁴ : Algebra A B\nK : Type ?u.237000\ninst✝³ :... | [
278,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Topology/PathConnected.lean | Path.refl_symm | [
{
"state_after": "case a.h\nX : Type u_1\nY : Type ?u.114429\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx y z : X\nι : Type ?u.114444\nγ : Path x y\na : X\nx✝ : ↑I\n⊢ ↑(symm (refl a)) x✝ = ↑(refl a) x✝",
"state_before": "X : Type u_1\nY : Type ?u.114429\ninst✝¹ : TopologicalSpace X\ninst✝ : T... | [
188,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/LinearAlgebra/Matrix/GeneralLinearGroup.lean | Matrix.GLPos.coe_neg_apply | [] | [
237,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/RingTheory/LaurentSeries.lean | PowerSeries.coe_add | [] | [
199,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/MeasureTheory/MeasurableSpaceDef.lean | MeasurableSpace.mkOfClosure_sets | [] | [
414,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
src/lean/Init/Control/Lawful.lean | ExceptT.run_bind_lift | [
{
"state_after": "no goals",
"state_before": "m : Type u_1 → Type u_2\nα ε β : Type u_1\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nx : m α\nf : α → ExceptT ε m β\n⊢ run (ExceptT.lift x >>= f) = do\n let a ← x\n run (f a)",
"tactic": "simp[ExceptT.run, ExceptT.lift, bind, ExceptT.bind, ExceptT.mk, E... | [
115,
102
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
114,
9
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | Ideal.Quotient.algebraMap_eq | [] | [
213,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Data/PEquiv.lean | Equiv.toPEquiv_trans | [] | [
487,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
485,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.coe_inf | [] | [
417,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieModuleHom.map_smul | [] | [
731,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
730,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ico_subset_Ici_self | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.45288\nα : Type u_1\ninst✝² : Preorder α\ninst✝¹ : LocallyFiniteOrder α\na a₁ a₂ b b₁ b₂ c x : α\ninst✝ : LocallyFiniteOrderTop α\n⊢ Ico a b ⊆ Ici a",
"tactic": "simpa [← coe_subset] using Set.Ico_subset_Ici_self"
}
] | [
401,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
] |
Mathlib/Algebra/Order/Kleene.lean | add_le | [] | [
169,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.top_add_top | [] | [
659,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
658,
1
] |
Mathlib/Order/CompleteLattice.lean | Prod.swap_sInf | [] | [
1841,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1839,
1
] |
Mathlib/Topology/PartitionOfUnity.lean | PartitionOfUnity.le_one | [] | [
177,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.ite_subset_union | [] | [
1819,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1818,
1
] |
Std/Data/Array/Init/Lemmas.lean | Array.map_data | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nf : α → β\narr : Array α\n⊢ (List.foldl (fun bs a => push bs (f a)) #[] arr.data).data = List.map f arr.data",
"state_before": "α : Type u_1\nβ : Type u_2\nf : α → β\narr : Array α\n⊢ (map f arr).data = List.map f arr.data",
"tactic": "apply congrArg data (f... | [
177,
11
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
173,
9
] |
Mathlib/Data/Set/Lattice.lean | Set.nonempty_biUnion | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.83587\nι : Sort ?u.83590\nι' : Sort ?u.83593\nι₂ : Sort ?u.83596\nκ : ι → Sort ?u.83601\nκ₁ : ι → Sort ?u.83606\nκ₂ : ι → Sort ?u.83611\nκ' : ι' → Sort ?u.83616\ns✝ : ι → Set α\nt : Set α\ns : α → Set β\n⊢ Set.Nonempty (⋃ ... | [
726,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
725,
1
] |
Mathlib/CategoryTheory/Preadditive/Biproducts.lean | CategoryTheory.Limits.biprod.add_eq_lift_desc_id | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝³ : Category C\ninst✝² : Preadditive C\nJ : Type\ninst✝¹ : Fintype J\nX Y : C\nf g : X ⟶ Y\ninst✝ : HasBinaryBiproduct Y Y\n⊢ f + g = lift f g ≫ desc (𝟙 Y) (𝟙 Y)",
"tactic": "simp"
}
] | [
636,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
635,
1
] |
Mathlib/Data/Int/Interval.lean | Int.card_Icc_of_le | [
{
"state_after": "no goals",
"state_before": "a b : ℤ\nh : a ≤ b + 1\n⊢ ↑(card (Icc a b)) = b + 1 - a",
"tactic": "rw [card_Icc, toNat_sub_of_le h]"
}
] | [
131,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/RingTheory/FiniteType.lean | AddMonoidAlgebra.mem_adjoin_support | [
{
"state_after": "R : Type u_1\nM : Type u_2\ninst✝¹ : CommSemiring R\ninst✝ : AddMonoid M\nf : AddMonoidAlgebra R M\n⊢ span R (of' R M '' ↑f.support) ≤ ↑Subalgebra.toSubmodule (adjoin R (of' R M '' ↑f.support))",
"state_before": "R : Type u_1\nM : Type u_2\ninst✝¹ : CommSemiring R\ninst✝ : AddMonoid M\nf :... | [
345,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.le_mul_right | [
{
"state_after": "a b : Cardinal\nh : b ≠ 0\n⊢ a ≤ b * a",
"state_before": "a b : Cardinal\nh : b ≠ 0\n⊢ a ≤ a * b",
"tactic": "rw [mul_comm]"
},
{
"state_after": "no goals",
"state_before": "a b : Cardinal\nh : b ≠ 0\n⊢ a ≤ b * a",
"tactic": "exact le_mul_left h"
}
] | [
666,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
664,
1
] |
Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.HomotopyWith.apply_zero | [] | [
455,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/Data/PNat/Xgcd.lean | PNat.XgcdType.reduce_b | [
{
"state_after": "u✝ u : XgcdType\nh : r u ≠ 0\n⊢ (if x : r u = 0 then finish u else flip (reduce (step u))) = flip (reduce (step u))",
"state_before": "u✝ u : XgcdType\nh : r u ≠ 0\n⊢ reduce u = flip (reduce (step u))",
"tactic": "rw [reduce]"
},
{
"state_after": "no goals",
"state_before":... | [
358,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.coeFn_neg | [] | [
232,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
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