file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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|---|---|---|---|---|---|---|
Mathlib/Order/Compare.lean | cmp_ofDual | [] | [
209,
6
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207,
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Mathlib/Data/Matrix/Basic.lean | Matrix.smul_dotProduct | [
{
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885,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.blsub_type | [
{
"state_after": "α✝ : Type ?u.358821\nβ : Type ?u.358824\nγ : Type ?u.358827\nr✝ : α✝ → α✝ → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nα : Type u\nr : α → α → Prop\ninst✝ : IsWellOrder α r\nf : (a : Ordinal) → a < type r → Ordinal\no : Ordinal\n⊢ (∀ (i : Ordinal) (h : i < type r), f i h < o) ↔ ∀ (i : α), f (ty... | [
1902,
94
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1897,
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Mathlib/Algebra/Hom/Ring.lean | RingHom.coe_addMonoidHom_injective | [] | [
550,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
549,
1
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Mathlib/Algebra/ContinuedFractions/Translations.lean | GeneralizedContinuedFraction.zeroth_denominator_eq_one | [] | [
143,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
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Std/Data/List/Basic.lean | List.eraseP_eq_erasePTR | [
{
"state_after": "case h.h.h\nα : Type u_1\np : α → Bool\nl : List α\n⊢ eraseP p l = erasePTR p l",
"state_before": "⊢ @eraseP = @erasePTR",
"tactic": "funext α p l"
},
{
"state_after": "case h.h.h\nα : Type u_1\np : α → Bool\nl : List α\n⊢ eraseP p l = erasePTR.go p l l #[]",
"state_before"... | [
951,
28
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943,
10
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Mathlib/GroupTheory/Exponent.lean | Monoid.exponent_eq_zero_of_order_zero | [] | [
98,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
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Mathlib/Order/Closure.lean | ClosureOperator.closure_le_closed_iff_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nι : Sort ?u.5784\nκ : ι → Sort ?u.5789\ninst✝¹ inst✝ : PartialOrder α\nc : ClosureOperator α\nx y : α\nhy : closed c y\n⊢ ↑c.toOrderHom x ≤ y ↔ x ≤ y",
"tactic": "rw [← c.closure_eq_self_of_mem_closed hy, ← le_closure_iff]"
}
] | [
205,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
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Mathlib/Analysis/Calculus/TangentCone.lean | UniqueDiffOn.prod | [] | [
372,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
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Mathlib/Analysis/Normed/Group/AddTorsor.lean | Filter.Tendsto.vsub | [] | [
279,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
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Mathlib/Data/Complex/Exponential.lean | Complex.cosh_conj | [
{
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"tactic": "rw [cosh, ← RingHom.map_neg, exp_conj, exp_conj, ← RingHom.map_add, cosh, map_d... | [
671,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
668,
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Mathlib/Data/Set/Intervals/Pi.lean | Set.pi_univ_Ioo_subset | [] | [
76,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
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Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.coeFn_zero | [] | [
226,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
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Mathlib/LinearAlgebra/Matrix/Block.lean | Matrix.BlockTriangular.add | [
{
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96,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Std/Data/Nat/Lemmas.lean | Nat.lt_succ | [] | [
398,
33
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
397,
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Mathlib/Topology/Algebra/Group/Basic.lean | continuousInv_inf | [
{
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403,
25
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399,
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Mathlib/Topology/MetricSpace/Contracting.lean | ContractingWith.edist_efixedPoint_lt_top | [] | [
153,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
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Mathlib/CategoryTheory/Abelian/LeftDerived.lean | CategoryTheory.Abelian.Functor.leftDerived_zero_to_self_natural | [
{
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181,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
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Mathlib/Data/Prod/PProd.lean | PProd.forall | [] | [
31,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
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Mathlib/Data/Num/Lemmas.lean | PosNum.succ'_pred' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.327087\nn : PosNum\n⊢ ↑(succ' (pred' n)) = ↑n",
"tactic": "rw [succ'_to_nat, pred'_to_nat, Nat.add_one, Nat.succ_pred_eq_of_pos (to_nat_pos _)]"
}
] | [
556,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
1
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Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.coe_ringEquiv_injective | [] | [
204,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
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Mathlib/Data/Nat/Prime.lean | Nat.prime_def_minFac | [] | [
370,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.map_pure_prod | [
{
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"state_before": "α : Type u_3\nβ : Type u_1\nγ : Type u_2\nδ... | [
412,
29
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410,
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Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.destruct_congr | [] | [
528,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
526,
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Mathlib/Data/Complex/Exponential.lean | Real.sinh_eq | [
{
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}
] | [
1342,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1341,
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Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_const_sub_Icc | [
{
"state_after": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\nthis : ∀ (a_1 : Set α), ((fun x => a + x) ∘ fun x => -x) '' a_1 = (fun x => a + x) '' ((fun x => -x) '' a_1)\n⊢ (fun x => a - x) '' Icc b c = Icc (a - c) (a - b)",
"state_before": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : ... | [
347,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
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Mathlib/Algebra/Field/Defs.lean | Semifield.toIsField | [] | [
201,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
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Mathlib/Data/Polynomial/DenomsClearable.lean | denomsClearable_of_natDegree_le | [] | [
74,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
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Mathlib/Logic/Equiv/Defs.lean | Equiv.Perm.subsingleton_eq_refl | [] | [
231,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
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Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.toLin'_mul_apply | [
{
"state_after": "no goals",
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.tendsto_iff | [
{
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875,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
873,
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Mathlib/Computability/Halting.lean | Nat.Partrec'.part_iff₁ | [
{
"state_after": "no goals",
"state_before": "f : ℕ →. ℕ\nh : _root_.Partrec fun v => f (Vector.head v)\nv : ℕ\n⊢ f (Vector.head (ofFn fun i => id v)) = f v",
"tactic": "simp only [id.def, head_ofFn]"
}
] | [
424,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
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Mathlib/Data/Sum/Basic.lean | Sum.map_map | [] | [
230,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
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] |
Mathlib/Analysis/Calculus/Deriv/Pow.lean | deriv_pow'' | [] | [
123,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/CategoryTheory/Monoidal/Opposite.lean | CategoryTheory.mop_id | [] | [
130,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
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Mathlib/Topology/LocallyFinite.lean | LocallyFinite.exists_forall_eventually_atTop_eventuallyEq | [] | [
193,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Types.lean | CategoryTheory.Limits.Types.coequalizerIso_quot_comp_inv | [] | [
521,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
1
] |
Mathlib/Data/List/Rdrop.lean | List.rtakeWhile_eq_self_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\np : α → Bool\nl : List α\nn : ℕ\n⊢ rtakeWhile p l = l ↔ ∀ (x : α), x ∈ l → p x = true",
"tactic": "simp [rtakeWhile, reverse_eq_iff]"
}
] | [
225,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
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Mathlib/Data/List/Basic.lean | List.All₂.imp | [
{
"state_after": "ι : Type ?u.480589\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\np q : α → Prop\nl✝ : List α\nh : ∀ (x : α), p x → q x\nx : α\nl : List α\n⊢ p x → All₂ p l → q x ∧ All₂ q l",
"state_before": "ι : Type ?u.480589\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : Lis... | [
4277,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4275,
1
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Ici_diff_Ioi_same | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.45184\ninst✝ : PartialOrder α\na b c : α\n⊢ Ici a \\ Ioi a = {a}",
"tactic": "rw [← Ici_diff_left, diff_diff_cancel_left (singleton_subset_iff.2 left_mem_Ici)]"
}
] | [
837,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Complex.differentiableAt_sinh | [] | [
127,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
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Mathlib/Analysis/Seminorm.lean | Seminorm.ball_zero_eq | [] | [
669,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
668,
1
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Mathlib/MeasureTheory/Integral/IntegrableOn.lean | integrableOn_Ioc_iff_integrableOn_Ioo | [
{
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"state_before": "α : ... | [
694,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
692,
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Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.coeff_monomial_same | [] | [
1359,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1358,
1
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Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.neBot_iff | [] | [
393,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
11
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Mathlib/Algebra/Order/ToIntervalMod.lean | AddCommGroup.modEq_iff_toIcoMod_ne_toIocMod | [] | [
651,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
650,
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.comap_comap | [] | [
1382,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1380,
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.reverse_append | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v w : V\np : Walk G u v\nq : Walk G v w\n⊢ reverse (append p q) = append (reverse q) (reverse p)",
"tactic": "simp [reverse]"
}
] | [
369,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
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Mathlib/CategoryTheory/Preadditive/Basic.lean | CategoryTheory.Preadditive.mono_of_cancel_zero | [] | [
236,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
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Mathlib/Order/Closure.lean | ClosureOperator.mem_closed_iff_closure_le | [] | [
178,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
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Mathlib/Topology/Constructions.lean | IsOpen.prod | [] | [
507,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
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Mathlib/Analysis/Complex/UnitDisc/Basic.lean | Complex.UnitDisc.coe_smul_closedBall | [] | [
176,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
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Mathlib/Init/Data/Nat/Bitwise.lean | Nat.testBit_ldiff' | [] | [
515,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
514,
1
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Mathlib/Data/Fintype/BigOperators.lean | Equiv.prod_comp | [] | [
217,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
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] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | HasStrictFDerivAt.cos | [] | [
925,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
923,
1
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Mathlib/Control/Traversable/Equiv.lean | Equiv.id_traverse | [
{
"state_after": "no goals",
"state_before": "t t' : Type u → Type u\neqv : (α : Type u) → t α ≃ t' α\ninst✝⁵ : Traversable t\ninst✝⁴ : IsLawfulTraversable t\nF G : Type u → Type u\ninst✝³ : Applicative F\ninst✝² : Applicative G\ninst✝¹ : LawfulApplicative F\ninst✝ : LawfulApplicative G\nη : ApplicativeTran... | [
139,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
11
] |
Mathlib/Algebra/Tropical/Basic.lean | Tropical.trop_injective | [] | [
79,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/CategoryTheory/Preadditive/AdditiveFunctor.lean | CategoryTheory.Functor.map_add | [] | [
59,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/AlgebraicTopology/DoldKan/Projections.lean | AlgebraicTopology.DoldKan.Q_f_naturality | [
{
"state_after": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX✝ : SimplicialObject C\nq n : ℕ\nX Y : SimplicialObject C\nf : X ⟶ Y\n⊢ f.app [n].op ≫ 𝟙 (HomologicalComplex.X K[Y] n) = 𝟙 (HomologicalComplex.X K[X] n) ≫ f.app [n].op",
"state_before": "C : Type u_2\ninst✝¹ : Category C\ninst✝ :... | [
211,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Std/Data/Range/Lemmas.lean | Std.Range.numElems_step_1 | [
{
"state_after": "no goals",
"state_before": "start stop : Nat\n⊢ numElems { start := start, stop := stop, step := 1 } = stop - start",
"tactic": "simp [numElems]"
}
] | [
21,
18
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
20,
1
] |
Mathlib/AlgebraicGeometry/Stalks.lean | AlgebraicGeometry.PresheafedSpace.stalkMap.congr_hom | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : HasColimits C\nX Y : PresheafedSpace C\nα β : X ⟶ Y\nh : α = β\nx : ↑↑X\n⊢ stalk Y ((CategoryTheory.forget TopCat).map α.base x) = stalk Y ((CategoryTheory.forget TopCat).map β.base x)",
"tactic": "rw [h]"
},
{
... | [
176,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | NonarchAddGroupSeminorm.coe_sup | [] | [
589,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biproduct.map_π | [] | [
527,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
525,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEStronglyMeasurable.mono_set | [] | [
1242,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1240,
1
] |
Mathlib/LinearAlgebra/Charpoly/Basic.lean | LinearMap.aeval_self_charpoly | [
{
"state_after": "R : Type u\nM : Type v\ninst✝⁵ : CommRing R\ninst✝⁴ : Nontrivial R\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : Module.Free R M\ninst✝ : Module.Finite R M\nf : M →ₗ[R] M\n⊢ ↑(AlgEquiv.toLinearEquiv (algEquivMatrix (chooseBasis R M))) (↑(aeval f) (charpoly f)) = 0",
"state_before... | [
75,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Data/MvPolynomial/Expand.lean | MvPolynomial.expand_C | [] | [
42,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | HasFDerivAt.mul_const' | [] | [
413,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.sups_subset | [] | [
89,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Arctan.lean | Real.tan_two_mul | [
{
"state_after": "x : ℝ\nthis : Complex.tan (2 * ↑x) = 2 * Complex.tan ↑x / (1 - Complex.tan ↑x ^ 2)\n⊢ tan (2 * x) = ↑2 * tan x / (↑1 - tan x ^ 2)",
"state_before": "x : ℝ\n⊢ tan (2 * x) = ↑2 * tan x / (↑1 - tan x ^ 2)",
"tactic": "have := @Complex.tan_two_mul x"
},
{
"state_after": "no goals",... | [
48,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiff.add | [] | [
1210,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1208,
1
] |
Mathlib/Topology/Order/Basic.lean | Dense.exists_le | [] | [
767,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
765,
11
] |
Mathlib/Combinatorics/SimpleGraph/Density.lean | Rel.edgeDensity_empty_left | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.20604\nι : Type ?u.20607\nκ : Type ?u.20610\nα : Type u_2\nβ : Type u_1\ninst✝¹ : LinearOrderedField 𝕜\nr : α → β → Prop\ninst✝ : (a : α) → DecidablePred (r a)\ns s₁ s₂ : Finset α\nt✝ t₁ t₂ : Finset β\na : α\nb : β\nδ : 𝕜\nt : Finset β\n⊢ edgeDens... | [
154,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Probability/Integration.lean | ProbabilityTheory.lintegral_mul_eq_lintegral_mul_lintegral_of_independent_measurableSpace | [
{
"state_after": "Ω : Type u_1\nmΩ✝ : MeasurableSpace Ω\nμ✝ : MeasureTheory.Measure Ω\nf : Ω → ℝ≥0∞\nX Y : Ω → ℝ\nMf Mg mΩ : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\nhMf : Mf ≤ mΩ\nhMg : Mg ≤ mΩ\nh_ind : Indep Mf Mg\nh_meas_f : Measurable f\n⊢ ∀ {g : Ω → ℝ≥0∞}, Measurable g → (∫⁻ (ω : Ω), f ω * g ω ∂μ) =... | [
106,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Data/List/Perm.lean | List.singleton_perm | [] | [
215,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Analysis/Convex/Segment.lean | openSegment_eq_image_lineMap | [
{
"state_after": "case h.e'_3.h\n𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.93217\nG : Type ?u.93220\nι : Type ?u.93223\nπ : ι → Type ?u.93228\ninst✝⁵ : OrderedRing 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : AddCommGroup F\ninst✝² : AddCommGroup G\ninst✝¹ : Module 𝕜 E\ninst✝ : Module 𝕜 F\nx y : E\na✝¹ : 𝕜\na✝ : a✝¹... | [
233,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | MonoidHom.restrict_apply | [] | [
1112,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1110,
1
] |
Mathlib/Analysis/Convex/Between.lean | sbtw_of_sbtw_of_sbtw_of_mem_affineSpan_pair | [
{
"state_after": "R : Type u_1\nV : Type u_2\nV' : Type ?u.373168\nP : Type u_3\nP' : Type ?u.373174\ninst✝⁴ : LinearOrderedRing R\ninst✝³ : AddCommGroup V\ninst✝² : Module R V\ninst✝¹ : AddTorsor V P\ninst✝ : NoZeroSMulDivisors R V\nt : Affine.Triangle R P\ni₁ i₂ i₃ : Fin 3\nh₁₂ : i₁ ≠ i₂\np₁ p₂ p : P\nh₁ : Sb... | [
666,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
] |
Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.det_eq_of_forall_row_eq_smul_add_const | [] | [
513,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.natCast_inj | [] | [
116,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Order/UpperLower/Basic.lean | subset_lowerClosure | [] | [
1296,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1296,
1
] |
Mathlib/LinearAlgebra/Finrank.lean | FiniteDimensional.finrank_lt_of_rank_lt | [
{
"state_after": "case hc\nK : Type u\nV : Type v\ninst✝⁴ : Ring K\ninst✝³ : AddCommGroup V\ninst✝² : Module K V\nV₂ : Type v'\ninst✝¹ : AddCommGroup V₂\ninst✝ : Module K V₂\nn : ℕ\nh : Module.rank K V < ↑n\n⊢ Module.rank K V < ℵ₀\n\ncase hd\nK : Type u\nV : Type v\ninst✝⁴ : Ring K\ninst✝³ : AddCommGroup V\nins... | [
80,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Order/Antichain.lean | IsAntichain.mono_on | [] | [
59,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Logic/Equiv/Set.lean | Equiv.ofPreimageEquiv_map | [] | [
693,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
] |
Mathlib/Order/Filter/Pi.lean | Filter.coprodᵢ_mono | [] | [
254,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/NumberTheory/Liouville/LiouvilleWith.lean | LiouvilleWith.nat_mul | [
{
"state_after": "p q x y : ℝ\nr : ℚ\nm : ℤ\nn : ℕ\nh : LiouvilleWith p x\nhn : n ≠ 0\n⊢ LiouvilleWith p (x * ↑n)",
"state_before": "p q x y : ℝ\nr : ℚ\nm : ℤ\nn : ℕ\nh : LiouvilleWith p x\nhn : n ≠ 0\n⊢ LiouvilleWith p (↑n * x)",
"tactic": "rw [mul_comm]"
},
{
"state_after": "no goals",
"st... | [
181,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.lt_iff_cmp | [] | [
881,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
880,
1
] |
Mathlib/Data/Rat/Lemmas.lean | Rat.inv_coe_nat_den | [
{
"state_after": "no goals",
"state_before": "a : ℕ\n⊢ (↑a)⁻¹.den = if a = 0 then 1 else a",
"tactic": "simpa [-inv_coe_int_den, ofInt_eq_cast] using inv_coe_int_den a"
}
] | [
303,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/Data/Rat/NNRat.lean | Rat.coe_toNNRat | [] | [
104,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.t3Space | [] | [
298,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
11
] |
src/lean/Init/Control/StateCps.lean | StateCpsT.run_eq | [] | [
75,
116
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
75,
9
] |
Mathlib/Algebra/Order/Rearrangement.lean | AntivaryOn.sum_mul_le_sum_comp_perm_mul | [] | [
430,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/Data/Finset/Sum.lean | Finset.val_disjSum | [] | [
39,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
Mathlib/Topology/ContinuousFunction/Basic.lean | ContinuousMap.const_apply | [] | [
231,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/Algebra/GeomSum.lean | op_geom_sum₂ | [
{
"state_after": "α : Type u\ninst✝ : Semiring α\nx y : α\nn : ℕ\n⊢ ∑ i in range n, op y ^ (n - 1 - i) * op x ^ i = ∑ i in range n, op y ^ i * op x ^ (n - 1 - i)",
"state_before": "α : Type u\ninst✝ : Semiring α\nx y : α\nn : ℕ\n⊢ ∑ i in range n, op y ^ (n - 1 - i) * op x ^ i = ∑ i in range n, op y ^ i * op... | [
98,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/RingTheory/Coprime/Basic.lean | IsCoprime.add_mul_right_left_iff | [] | [
328,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | DifferentiableOn.smul | [] | [
209,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Analysis/Convex/Extrema.lean | IsMinOn.of_isLocalMinOn_of_convexOn | [
{
"state_after": "E : Type u_1\nβ : Type u_2\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : TopologicalSpace E\ninst✝⁵ : Module ℝ E\ninst✝⁴ : TopologicalAddGroup E\ninst✝³ : ContinuousSMul ℝ E\ninst✝² : OrderedAddCommGroup β\ninst✝¹ : Module ℝ β\ninst✝ : OrderedSMul ℝ β\ns : Set E\nf : E → β\na : E\na_in_s : a ∈ s\nh_local... | [
71,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Algebra/Ring/Defs.lean | mul_ite | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u\nβ : Type v\nγ : Type w\nR : Type x\nα : Type u_1\ninst✝¹ : Mul α\nP : Prop\ninst✝ : Decidable P\na b c : α\n⊢ (a * if P then b else c) = if P then a * b else a * c",
"tactic": "split_ifs <;> rfl"
}
] | [
199,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieHom.idealRange_eq_top_of_surjective | [
{
"state_after": "R : Type u\nL : Type v\nL' : Type w₂\nM : Type w\nM' : Type w₁\ninst✝¹² : CommRing R\ninst✝¹¹ : LieRing L\ninst✝¹⁰ : LieAlgebra R L\ninst✝⁹ : LieRing L'\ninst✝⁸ : LieAlgebra R L'\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³ : AddCo... | [
1001,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
995,
1
] |
Mathlib/Algebra/DirectSum/Internal.lean | DirectSum.coe_of_mul_apply_of_not_le | [
{
"state_after": "ι : Type u_3\nσ : Type u_2\nS : Type ?u.273217\nR : Type u_1\ninst✝⁵ : DecidableEq ι\ninst✝⁴ : Semiring R\ninst✝³ : SetLike σ R\ninst✝² : AddSubmonoidClass σ R\nA : ι → σ\ninst✝¹ : CanonicallyOrderedAddMonoid ι\ninst✝ : SetLike.GradedMonoid A\ni : ι\nr : { x // x ∈ A i }\nr' : ⨁ (i : ι), { x /... | [
239,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
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