file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/Order/Heyting/Hom.lean | CoheytingHom.comp_id | [] | [
475,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
1
] |
Mathlib/Data/Nat/Interval.lean | Finset.range_add_eq_union | [
{
"state_after": "a b c : ℕ\n⊢ Ico 0 (a + b) = Ico 0 a ∪ image (↑(addLeftEmbedding a)) (Ico 0 b)",
"state_before": "a b c : ℕ\n⊢ range (a + b) = range a ∪ map (addLeftEmbedding a) (range b)",
"tactic": "rw [Finset.range_eq_Ico, map_eq_image]"
},
{
"state_after": "case h.e'_3.h.e'_4\na b c : ℕ\n⊢... | [
339,
33
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336,
1
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Mathlib/CategoryTheory/CommSq.lean | CategoryTheory.CommSq.op | [
{
"state_after": "no goals",
"state_before": "C : Type u_1\ninst✝ : Category C\nW X Y Z : C\nf : W ⟶ X\ng : W ⟶ Y\nh : X ⟶ Z\ni : Y ⟶ Z\np : CommSq f g h i\n⊢ i.op ≫ g.op = h.op ≫ f.op",
"tactic": "simp only [← op_comp, p.w]"
}
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Mathlib/Data/Nat/Squarefree.lean | Nat.minSqFacAux_has_prop | [
{
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Mathlib/Algebra/BigOperators/Finprod.lean | finprod_eq_prod_of_fintype | [] | [
437,
91
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436,
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.mulSingle_mem_pi | [
{
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1883,
26
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Mathlib/Data/Set/Lattice.lean | Set.iUnion_dite | [] | [
628,
18
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626,
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Mathlib/Analysis/InnerProductSpace/Orientation.lean | Orientation.volumeForm_zero_pos | [
{
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"tacti... | [
199,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Logic/Equiv/Defs.lean | Equiv.symm_comp_self | [] | [
289,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
9
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Mathlib/Data/Set/Lattice.lean | Set.iInf_eq_iInter | [] | [
135,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
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Mathlib/Order/Disjointed.lean | disjointed_unique | [
{
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"state_before": "α : Type u_1\nβ : Type ?u.7993\ninst✝ : GeneralizedBooleanAlgebra α\nf d : ℕ →... | [
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69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Polynomial/Expand.lean | Polynomial.expand_aeval | [
{
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200,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/AffineSpace/Independent.lean | AffineIndependent.exists_mem_inter_of_exists_mem_inter_affineSpan | [
{
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431,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
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Mathlib/Algebra/Associated.lean | Associates.dvd_of_mk_le_mk | [
{
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936,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
925,
1
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Mathlib/Data/List/Chain.lean | List.relationReflTransGen_of_exists_chain | [] | [
442,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
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Mathlib/Analysis/NormedSpace/Pointwise.lean | closedBall_sub_closedBall | [
{
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"state_before": "𝕜 : Type ?u.1613309\nE : Type u_1\ninst✝⁴ : NormedField 𝕜\ninst✝³ : SeminormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedSpace ℝ E\nx y z : E\nδ ε : ℝ\ninst✝ : ProperSpace E\nhε : 0 ≤ ε\nhδ : 0 ≤ δ\na b : E\n⊢ Metric.closedBall a ε - Metric.clos... | [
386,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
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Mathlib/Analysis/Calculus/ContDiff.lean | ContinuousLinearMap.iteratedFDerivWithin_comp_right | [] | [
410,
15
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404,
1
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.map_add | [] | [
495,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurableSet_Iic | [] | [
443,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.smul_X_eq_monomial | [
{
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"tactic": "rw [X_pow_eq_monomial, smul_monomial, smul_eq_mul, mul_one]"
}
] | [
899,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
898,
1
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Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesOnBall.hasFPowerSeriesAt | [] | [
416,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
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Mathlib/Analysis/Calculus/Darboux.lean | exists_hasDerivWithinAt_eq_of_lt_of_gt | [] | [
77,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
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Mathlib/Data/List/Rotate.lean | List.nodup_rotate | [] | [
198,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
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Mathlib/Data/Real/ENNReal.lean | ENNReal.iInf_add_iInf | [
{
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"tactic": "simp_rw [iInf_add, add_iInf]"
}
] | [
2427,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2421,
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.mul_apply | [] | [
852,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
851,
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Mathlib/Analysis/InnerProductSpace/Orientation.lean | Orientation.volumeForm_zero_neg | [
{
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Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.SimpleFunc.integrable_pair | [
{
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Mathlib/Algebra/Order/Monoid/Canonical/Defs.lean | le_iff_forall_one_lt_lt_mul' | [] | [
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69
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Mathlib/Algebra/AddTorsor.lean | Equiv.pointReflection_involutive | [
{
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}
] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Order/Floor.lean | Int.preimage_Ioi | [
{
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"state_before": "F : Type ?u.245095\nα : Type u_1\nβ : Type ?u.245101\ninst✝¹ : LinearOrderedRing α\ninst✝ : Flo... | [
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1294,
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Mathlib/Logic/Equiv/Basic.lean | Equiv.sumArrowEquivProdArrow_symm_apply_inl | [] | [
892,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
890,
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Std/Data/List/Lemmas.lean | List.exists_or_eq_self_of_eraseP | [] | [
962,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
955,
1
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Mathlib/Order/Closure.lean | LowerAdjoint.closure_sup_closure_left | [] | [
447,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
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Mathlib/RingTheory/HahnSeries.lean | HahnSeries.embDomain_notin_range | [] | [
312,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
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Mathlib/Analysis/InnerProductSpace/Projection.lean | orthogonalProjection_isSymmetric | [] | [
1076,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1074,
1
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Mathlib/Analysis/Convex/StrictConvexSpace.lean | abs_lt_norm_sub_of_not_sameRay | [
{
"state_after": "𝕜 : Type ?u.64814\nE : Type u_1\ninst✝⁴ : NormedLinearOrderedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : StrictConvexSpace ℝ E\nx y z : E\na b r : ℝ\nh : ¬SameRay ℝ x y\n⊢ ‖y‖ - ‖x‖ < ‖x - y‖",
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.prod_eq_one | [] | [
1809,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1807,
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Mathlib/Algebra/CubicDiscriminant.lean | Cubic.of_a_eq_zero | [
{
"state_after": "no goals",
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"tactic": "rw [toPoly, ha, C_0, MulZeroClass.zero_mul, zer... | [
141,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
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Std/Data/Nat/Gcd.lean | Nat.gcd_dvd_right | [] | [
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Mathlib/Algebra/Tropical/Basic.lean | Tropical.tropEquiv_coe_fn | [] | [
127,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
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Mathlib/Algebra/MonoidAlgebra/Degree.lean | AddMonoidAlgebra.le_inf_support_finset_prod | [
{
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171,
94
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Mathlib/Analysis/NormedSpace/lpSpace.lean | memℓp_gen' | [
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122,
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Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | eq_add_of_hasSum_ite | [
{
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445,
1
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Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.natCoe_nat | [] | [
157,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
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Mathlib/Analysis/Calculus/Deriv/Add.lean | HasDerivWithinAt.const_sub | [] | [
357,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
8
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Mathlib/Analysis/Normed/Field/UnitBall.lean | coe_inv_unitSphere | [] | [
129,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | hasDerivWithinAt_const | [] | [
687,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
686,
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Mathlib/Algebra/Tropical/Basic.lean | Tropical.tropOrderIso_symm_coe_fn | [] | [
215,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
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] |
Mathlib/RingTheory/FiniteType.lean | RingHom.Finite.finiteType | [] | [
205,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/RingTheory/Int/Basic.lean | Int.nonneg_iff_normalize_eq_self | [] | [
128,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
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] |
Mathlib/Topology/FiberBundle/Basic.lean | FiberBundleCore.mem_localTriv_target | [] | [
722,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
720,
1
] |
Mathlib/Topology/GDelta.lean | isGδ_biInter_of_open | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.1242\nγ : Type ?u.1245\nι : Type u_1\ninst✝ : TopologicalSpace α\nI : Set ι\nhI : Set.Countable I\nf : ι → Set α\nhf : ∀ (i : ι), i ∈ I → IsOpen (f i)\n⊢ ∀ (t : Set α), t ∈ f '' I → IsOpen t",
"tactic": "rwa [ball_image_iff]"
},
... | [
73,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.sum_def | [] | [
939,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
937,
1
] |
Mathlib/Data/Set/Prod.lean | Set.univ_prod | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.7346\nδ : Type ?u.7349\ns s₁ s₂ : Set α\nt✝ t₁ t₂ : Set β\na : α\nb : β\nt : Set β\n⊢ univ ×ˢ t = Prod.snd ⁻¹' t",
"tactic": "simp [prod_eq]"
}
] | [
128,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/MeasureTheory/Decomposition/Jordan.lean | MeasureTheory.JordanDecomposition.eq_of_posPart_eq_posPart | [
{
"state_after": "case posPart\nα : Type u_1\nβ : Type ?u.69483\ninst✝ : MeasurableSpace α\nj₁ j₂ : JordanDecomposition α\nhj : j₁.posPart = j₂.posPart\nhj' : toSignedMeasure j₁ = toSignedMeasure j₂\n⊢ j₁.posPart = j₂.posPart\n\ncase negPart\nα : Type u_1\nβ : Type ?u.69483\ninst✝ : MeasurableSpace α\nj₁ j₂ : J... | [
374,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
9
] |
Mathlib/Topology/Support.lean | not_mem_mulTSupport_iff_eventuallyEq | [
{
"state_after": "no goals",
"state_before": "X : Type ?u.5462\nα : Type u_1\nα' : Type ?u.5468\nβ : Type u_2\nγ : Type ?u.5474\nδ : Type ?u.5477\nM : Type ?u.5480\nE : Type ?u.5483\nR : Type ?u.5486\ninst✝⁴ : TopologicalSpace α\ninst✝³ : TopologicalSpace α'\ninst✝² : One β\ninst✝¹ : One γ\ninst✝ : One δ\ng... | [
118,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Data/List/Basic.lean | List.indexOf_cons | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.78601\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\ninst✝ : DecidableEq α\na b : α\nl : List α\n⊢ indexOf a (b :: l) = if a = b then 0 else succ (indexOf a l)",
"tactic": "simp only [indexOf, findIdx_cons, Bool.cond_eq_ite, beq... | [
1180,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1178,
1
] |
Std/Data/Rat/Basic.lean | Rat.add.aux | [
{
"state_after": "a b : Rat\ng ad bd : Nat\nhg : g = Nat.gcd a.den b.den\nhad : ad = a.den / g\nhbd : bd = b.den / g\nden : Nat := ad * b.den\nnum : Int := a.num * ↑bd + b.num * ↑ad\n⊢ Nat.gcd (Int.natAbs num) g = Nat.gcd (Int.natAbs num) den",
"state_before": "a b : Rat\ng ad bd : Nat\nhg : g = Nat.gcd a.d... | [
207,
70
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
181,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.infDist_zero_of_mem | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.58987\nα : Type u\nβ : Type v\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\ns t u : Set α\nx y : α\nΦ : α → β\nh : x ∈ s\n⊢ infDist x s = 0",
"tactic": "simp [infEdist_zero_of_mem h, infDist]"
}
] | [
500,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
] |
Mathlib/Data/List/Sort.lean | List.sorted_insertionSort | [] | [
287,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/Algebra/Hom/Units.lean | Units.mul_liftRight_inv | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.30089\nM : Type u\nN : Type v\nP : Type w\ninst✝² : Monoid M\ninst✝¹ : Monoid N\ninst✝ : Monoid P\nf : M →* N\ng : M → Nˣ\nh : ∀ (x : M), ↑(g x) = ↑f x\nx : M\n⊢ ↑f x * ↑(↑(liftRight f g h) x)⁻¹ = 1",
"tactic": "rw [Units.mul_inv_eq_iff_eq_mul, o... | [
177,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Topology/ContinuousFunction/Ordered.lean | ContinuousMap.sup'_coe | [
{
"state_after": "case h\nα : Type ?u.63285\nβ : Type u_2\nγ : Type u_3\ninst✝⁴ : TopologicalSpace α\ninst✝³ : TopologicalSpace β\ninst✝² : TopologicalSpace γ\ninst✝¹ : LinearOrder γ\ninst✝ : OrderClosedTopology γ\nι : Type u_1\ns : Finset ι\nH : Finset.Nonempty s\nf : ι → C(β, γ)\nx✝ : β\n⊢ ↑(Finset.sup' s H f... | [
130,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | zpow_le_zpow | [] | [
349,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.IsOrtho.mono_right | [] | [
295,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.comp_smul | [
{
"state_after": "case h\nR : Type u_4\nR₂ : Type ?u.1028649\nR₃ : Type ?u.1028652\nS : Type u_3\nS₃ : Type ?u.1028658\ninst✝³³ : Semiring R\ninst✝³² : Semiring R₂\ninst✝³¹ : Semiring R₃\ninst✝³⁰ : Monoid S\ninst✝²⁹ : Monoid S₃\nM : Type u_5\ninst✝²⁸ : TopologicalSpace M\ninst✝²⁷ : AddCommMonoid M\ninst✝²⁶ : Mo... | [
1521,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1518,
1
] |
Mathlib/Order/SuccPred/Basic.lean | WithBot.pred_coe | [] | [
1337,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1336,
1
] |
Mathlib/Analysis/Convex/Combination.lean | Finset.mem_convexHull | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nE : Type u_1\nF : Type ?u.232358\nι : Type ?u.232361\nι' : Type ?u.232364\nα : Type ?u.232367\ninst✝⁷ : LinearOrderedField R\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : AddCommGroup F\ninst✝⁴ : LinearOrderedAddCommGroup α\ninst✝³ : Module R E\ninst✝² : Modu... | [
350,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/Data/Set/Basic.lean | Set.union_inter_cancel_left | [] | [
1023,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1022,
1
] |
Mathlib/Topology/Algebra/Module/StrongTopology.lean | ContinuousLinearMap.strongTopology.t2Space | [
{
"state_after": "𝕜₁ : Type u_3\n𝕜₂ : Type u_4\ninst✝¹⁴ : NormedField 𝕜₁\ninst✝¹³ : NormedField 𝕜₂\nσ : 𝕜₁ →+* 𝕜₂\nE : Type u_2\nE' : Type ?u.49322\nF : Type u_1\nF' : Type ?u.49328\ninst✝¹² : AddCommGroup E\ninst✝¹¹ : Module 𝕜₁ E\ninst✝¹⁰ : AddCommGroup E'\ninst✝⁹ : Module ℝ E'\ninst✝⁸ : AddCommGroup F\... | [
137,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.sdiff_eq_self_of_disjoint | [] | [
2364,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2363,
1
] |
Mathlib/RepresentationTheory/Action.lean | Action.tensorUnit_rho | [] | [
488,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
487,
1
] |
Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.iIndep.iIndepSets | [] | [
326,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/Data/Nat/Interval.lean | Nat.card_Iio | [
{
"state_after": "no goals",
"state_before": "a b c : ℕ\n⊢ card (Iio b) = b",
"tactic": "rw [Iio_eq_Ico, card_Ico, bot_eq_zero, tsub_zero]"
}
] | [
121,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.empty_sups | [] | [
136,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Data/Set/Finite.lean | Set.infinite_image2 | [
{
"state_after": "case refine'_1\nα : Type u\nβ : Type v\nι : Sort w\nγ : Type x\nf : α → β → γ\ns : Set α\nt : Set β\na : α\nb : β\nhfs : ∀ (b : β), b ∈ t → InjOn (fun a => f a b) s\nhft : ∀ (a : α), a ∈ s → InjOn (f a) t\nh : Set.Infinite (image2 f s t)\n⊢ Set.Infinite (s ×ˢ t)\n\ncase refine'_2\nα : Type u\n... | [
1356,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1349,
1
] |
Mathlib/Algebra/Hom/Units.lean | Units.liftRight_inv_mul | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.32564\nM : Type u\nN : Type v\nP : Type w\ninst✝² : Monoid M\ninst✝¹ : Monoid N\ninst✝ : Monoid P\nf : M →* N\ng : M → Nˣ\nh : ∀ (x : M), ↑(g x) = ↑f x\nx : M\n⊢ ↑(↑(liftRight f g h) x)⁻¹ * ↑f x = 1",
"tactic": "rw [Units.inv_mul_eq_iff_eq_mul, m... | [
184,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.AbsolutelyContinuous.ennrealToMeasure | [
{
"state_after": "case mp\nα : Type u_1\nβ : Type ?u.644845\nm : MeasurableSpace α\nL : Type ?u.644851\nM : Type u_2\nN : Type ?u.644857\ninst✝⁵ : AddCommMonoid L\ninst✝⁴ : TopologicalSpace L\ninst✝³ : AddCommMonoid M\ninst✝² : TopologicalSpace M\ninst✝¹ : AddCommMonoid N\ninst✝ : TopologicalSpace N\nv : Vector... | [
1164,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1155,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.lt_add_of_limit | [
{
"state_after": "a b c : Ordinal\nh : IsLimit c\nthis : (bsup c fun x x_1 => (fun x x_2 => x + x_2) b x) = (fun x x_1 => x + x_1) b c\n⊢ a < b + c ↔ ∃ c', c' < c ∧ a < b + c'",
"state_before": "a b c : Ordinal\nh : IsLimit c\n⊢ a < b + c ↔ ∃ c', c' < c ∧ a < b + c'",
"tactic": "have := IsNormal.bsup_eq... | [
2401,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2395,
1
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | strictAnti_iff_map_neg | [] | [
269,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.prod.map_id_comp | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝³ : Category C\nX✝ Y✝ X Y Z W : C\nf : X ⟶ Y\ng : Y ⟶ Z\ninst✝² : HasBinaryProduct W X\ninst✝¹ : HasBinaryProduct W Y\ninst✝ : HasBinaryProduct W Z\n⊢ map (𝟙 W) (f ≫ g) = map (𝟙 W) f ≫ map (𝟙 W) g",
"tactic": "simp"
}
] | [
775,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
773,
1
] |
Mathlib/Order/Monotone/Monovary.lean | Antivary.dual_left | [] | [
212,
5
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Data/List/Basic.lean | List.attach_map_val | [] | [
3127,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3126,
1
] |
Mathlib/Data/List/Duplicate.lean | List.Duplicate.not_nodup | [] | [
142,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.real_lt_real | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ ↑x < ↑y ↔ x < y",
"tactic": "simp [lt_def, ofReal']"
}
] | [
1161,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1161,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | Measurable.sumMap | [] | [
1017,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1015,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.set_integral_mono_ae | [] | [
690,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
689,
1
] |
Std/Data/Array/Lemmas.lean | Array.toArray_data | [] | [
38,
33
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
37,
9
] |
Mathlib/Analysis/SpecificLimits/Basic.lean | tsum_geometric_two' | [] | [
258,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_fst | [] | [
644,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
642,
1
] |
Std/Data/Int/Lemmas.lean | Int.ofNat_zero | [] | [
19,
58
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
19,
9
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | AEMeasurable.ae_eq_mk | [] | [
698,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
697,
1
] |
Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.indepSets_of_indepSets_of_le_right | [] | [
189,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Order/RelIso/Basic.lean | RelEmbedding.injective | [] | [
268,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Topology/Basic.lean | continuousAt_const | [] | [
1682,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1681,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.image_mul_left' | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.622921\nα : Type u_1\nβ : Type ?u.622927\nγ : Type ?u.622930\ninst✝⁴ : DecidableEq α\ninst✝³ : DecidableEq β\ninst✝² : Group α\ninst✝¹ : DivisionMonoid β\ninst✝ : MonoidHomClass F α β\nf : F\ns t : Finset α\na b : α\n⊢ image (fun b => a⁻¹ * b) t =\n ... | [
1169,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1167,
1
] |
Mathlib/Data/Polynomial/Splits.lean | Polynomial.splits_pow | [
{
"state_after": "F : Type u\nK : Type v\nL : Type w\ninst✝² : CommRing K\ninst✝¹ : Field L\ninst✝ : Field F\ni : K →+* L\nf : K[X]\nhf : Splits i f\nn : ℕ\n⊢ Splits i (∏ _x in Finset.range n, f)",
"state_before": "F : Type u\nK : Type v\nL : Type w\ninst✝² : CommRing K\ninst✝¹ : Field L\ninst✝ : Field F\ni... | [
163,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Order/RelClasses.lean | WellFoundedRelation.asymmetric | [] | [
294,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.monotone_arcsin | [] | [
87,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | LinearMap.mul_eq_one_comm | [] | [
944,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
943,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Basis.mem_ideal_iff | [] | [
1975,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1973,
1
] |
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