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/Data/Nat/Factorization/Basic.lean | Nat.factorization_mul | [
{
"state_after": "case h\na b : ℕ\nha : a ≠ 0\nhb : b ≠ 0\np : ℕ\n⊢ ↑(factorization (a * b)) p = ↑(factorization a + factorization b) p",
"state_before": "a b : ℕ\nha : a ≠ 0\nhb : b ≠ 0\n⊢ factorization (a * b) = factorization a + factorization b",
"tactic": "ext p"
},
{
"state_after": "no goal... | [
226,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Algebra/Group/Basic.lean | div_eq_of_eq_mul'' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.59035\nβ : Type ?u.59038\nG : Type u_1\ninst✝ : Group G\na b c d : G\nh : a = c * b\n⊢ a / b = c",
"tactic": "simp [h]"
}
] | [
775,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
775,
1
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Mathlib/Data/List/Basic.lean | List.insertNth_succ_cons | [] | [
1607,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1605,
1
] |
Mathlib/Algebra/Order/Nonneg/Ring.lean | Nonneg.mk_eq_one | [] | [
207,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Independent.lean | affineIndependent_of_subsingleton | [] | [
71,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.forall₃_congr | [] | [
901,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
898,
11
] |
Mathlib/Topology/MetricSpace/Basic.lean | dist_nonneg | [] | [
274,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Data/List/Permutation.lean | List.map_map_permutationsAux2 | [] | [
130,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Analysis/Convex/StrictConvexSpace.lean | openSegment_subset_ball_of_ne | [] | [
170,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | CompleteLatticeHom.comp_id | [] | [
762,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
761,
1
] |
Mathlib/Data/Fintype/Basic.lean | Finset.subset_univ | [] | [
127,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Data/List/Sublists.lean | List.mem_sublists | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns t : List α\n⊢ s ∈ sublists t ↔ s <+ t",
"tactic": "rw [← reverse_sublist, ← mem_sublists', sublists'_reverse,\n mem_map_of_injective reverse_injective]"
}
] | [
206,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
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Mathlib/Analysis/Normed/Group/Basic.lean | mem_closedBall_iff_norm''' | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type ?u.95628\n𝕜 : Type ?u.95631\nα : Type ?u.95634\nι : Type ?u.95637\nκ : Type ?u.95640\nE : Type u_1\nF : Type ?u.95646\nG : Type ?u.95649\ninst✝² : SeminormedGroup E\ninst✝¹ : SeminormedGroup F\ninst✝ : SeminormedGroup G\ns : Set E\na a₁ a₂ b b₁ b₂ : E... | [
646,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
645,
1
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_subtype_le_of_subset | [] | [
1975,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1973,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | BilinForm.toQuadraticForm_add | [] | [
670,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
668,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_eq_zero_iff_of_nonneg | [] | [
1236,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1234,
1
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Mathlib/Data/Part.lean | Part.induction_on | [] | [
371,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
11
] |
Mathlib/Algebra/Module/Basic.lean | map_inv_nat_cast_smul | [
{
"state_after": "case pos\nα : Type ?u.178772\nR✝ : Type ?u.178775\nk : Type ?u.178778\nS✝ : Type ?u.178781\nM : Type u_1\nM₂ : Type u_2\nM₃ : Type ?u.178790\nι : Type ?u.178793\ninst✝⁶ : AddCommMonoid M\ninst✝⁵ : AddCommMonoid M₂\nF : Type u_3\ninst✝⁴ : AddMonoidHomClass F M M₂\nf : F\nR : Type u_4\nS : Type ... | [
481,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
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] |
Mathlib/Data/Multiset/Basic.lean | Multiset.card_cons | [] | [
744,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
743,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.const_mul_right | [] | [
1533,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1531,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | ContDiff.cosh | [] | [
1102,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1101,
1
] |
Mathlib/GroupTheory/Commutator.lean | Subgroup.commutator_pi_pi_of_finite | [
{
"state_after": "G : Type ?u.102458\nG' : Type ?u.102461\nF : Type ?u.102464\ninst✝⁴ : Group G\ninst✝³ : Group G'\ninst✝² : MonoidHomClass F G G'\nf : F\ng₁ g₂ g₃ g : G\nH₁ H₂ H₃ K₁ K₂ : Subgroup G\nη : Type u_1\ninst✝¹ : Finite η\nGs : η → Type u_2\ninst✝ : (i : η) → Group (Gs i)\nH K : (i : η) → Subgroup (Gs... | [
241,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/CategoryTheory/Limits/Opposites.lean | CategoryTheory.Limits.pushoutIsoUnopPullback_inr_hom | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝³ : Category C\nJ : Type u₂\ninst✝² : Category J\nX✝ : Type v₂\nX Y Z : C\nf : X ⟶ Z\ng : X ⟶ Y\ninst✝¹ : HasPushout f g\ninst✝ : HasPullback f.op g.op\n⊢ (PullbackCone.unop (limit.cone (cospan f.op g.op))).ι.app WalkingSpan.right = pullback.sn... | [
690,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
686,
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] |
Mathlib/Analysis/Convex/Basic.lean | convex_halfspace_ge | [] | [
264,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/Analysis/LocallyConvex/ContinuousOfBounded.lean | LinearMap.clmOfExistsBoundedImage_apply | [] | [
88,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.eq_or_lt_of_not_lt | [] | [
372,
44
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
371,
11
] |
Std/Data/Int/Lemmas.lean | Int.neg_mul_eq_mul_neg | [
{
"state_after": "no goals",
"state_before": "a b : Int\n⊢ a * b + a * -b = 0",
"tactic": "rw [← Int.mul_add, Int.add_right_neg, Int.mul_zero]"
}
] | [
465,
86
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
464,
11
] |
Mathlib/GroupTheory/GroupAction/Option.lean | Option.smul_none | [] | [
48,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.floor_int | [] | [
614,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
613,
1
] |
Mathlib/Data/Prod/Basic.lean | Prod.snd_swap | [] | [
173,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Computability/EpsilonNFA.lean | εNFA.subset_εClosure | [] | [
59,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Data/Fintype/Card.lean | Tactic.card_univ_pos | [] | [
1224,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1222,
9
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_Iic_atBot | [
{
"state_after": "ι : Type ?u.336964\nι' : Type ?u.336967\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.336976\ninst✝ : SemilatticeInf α\na : α\nf : β → ↑(Iic a)\nl : Filter β\n⊢ Tendsto (Subtype.val ∘ f) l atBot ↔ Tendsto (fun x => ↑(f x)) l atBot",
"state_before": "ι : Type ?u.336964\nι' : Type ?u.336967\nα : ... | [
1612,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1610,
1
] |
Mathlib/Topology/Algebra/StarSubalgebra.lean | StarSubalgebra.closedEmbedding_inclusion | [
{
"state_after": "case h.e'_2.h.e'_4\nR : Type u_1\nA : Type u_2\nB : Type ?u.20732\ninst✝⁶ : CommSemiring R\ninst✝⁵ : StarRing R\ninst✝⁴ : TopologicalSpace A\ninst✝³ : Semiring A\ninst✝² : Algebra R A\ninst✝¹ : StarRing A\ninst✝ : StarModule R A\nS₁ S₂ : StarSubalgebra R A\nh : S₁ ≤ S₂\nhS₁ : IsClosed ↑S₁\nsrc... | [
64,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
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] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | HasDerivAt.ccosh | [] | [
243,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Order/UpperLower/Basic.lean | upperBounds_lowerClosure | [] | [
1477,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1476,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.limsInf_bot | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.84212\nγ : Type ?u.84215\nι : Type ?u.84218\ninst✝ : CompleteLattice α\n⊢ ⊤ ∈ {a | ∀ᶠ (n : α) in ⊥, a ≤ n}",
"tactic": "simp"
}
] | [
623,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
622,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.toDual_sup | [] | [
485,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/Data/Set/Image.lean | Set.nonempty_image_iff | [] | [
461,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
460,
1
] |
Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.le_prod_of_submultiplicative_on_pred | [
{
"state_after": "ι : Type ?u.138424\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.138433\ninst✝¹ : CommMonoid α\ninst✝ : OrderedCommMonoid β\nf : α → β\np : α → Prop\nh_one : f 1 = 1\nhp_one : p 1\nh_mul : ∀ (a b : α), p a → p b → f (a * b) ≤ f a * f b\nhp_mul : ∀ (a b : α), p a → p b → p (a * b)\n⊢ ∀ (s : Multiset... | [
474,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
] |
Mathlib/Data/Set/Basic.lean | Set.diff_eq_empty | [] | [
1902,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1901,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.map_sub | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹³ : Ring R\nR₂ : Type u_2\ninst✝¹² : Ring R₂\nR₃ : Type ?u.721138\ninst✝¹¹ : Ring R₃\nM : Type u_3\ninst✝¹⁰ : TopologicalSpace M\ninst✝⁹ : AddCommGroup M\nM₂ : Type u_4\ninst✝⁸ : TopologicalSpace M₂\ninst✝⁷ : AddCommGroup M₂\nM₃ : Type ?u.721... | [
1303,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1302,
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] |
Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.comp | [
{
"state_after": "ι : Type u'\nι' : Type u_3\nR : Type u_1\nK : Type ?u.86731\nM : Type u_2\nM' : Type ?u.86737\nM'' : Type ?u.86740\nV : Type u\nV' : Type ?u.86745\nv : ι → M\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : AddCommMonoid M'\ninst✝³ : AddCommMonoid M''\ninst✝² : Module R M\ninst✝¹ : Mod... | [
202,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Topology/Algebra/Order/LeftRightLim.lean | Antitone.tendsto_leftLim_within | [] | [
342,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
Mathlib/LinearAlgebra/Prod.lean | LinearEquiv.skewProd_symm_apply | [] | [
825,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
823,
1
] |
Mathlib/Algebra/Order/Nonneg/Field.lean | Nonneg.mk_div_mk | [] | [
66,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Tactic/Sat/FromLRAT.lean | Sat.Literal.reify_pos | [] | [
210,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
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Mathlib/Analysis/Calculus/Inverse.lean | ApproximatesLinearOn.mono_set | [] | [
146,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.sUnion_prod_const | [
{
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1798,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1796,
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] |
Mathlib/RingTheory/Subsemiring/Basic.lean | RingHom.eq_of_eqOn_stop | [] | [
1207,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1206,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.coe_toOrderIso | [] | [
236,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.tendsto_sin_neg_pi_div_two | [
{
"state_after": "case h.e'_5.h.e'_3\n\n⊢ -1 = sin (-(π / 2))",
"state_before": "⊢ Tendsto sin (𝓝[Ioi (-(π / 2))] (-(π / 2))) (𝓝 (-1))",
"tactic": "convert continuous_sin.continuousWithinAt.tendsto using 2"
},
{
"state_after": "no goals",
"state_before": "case h.e'_5.h.e'_3\n\n⊢ -1 = sin (... | [
1079,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1077,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | monotone_mul_right_of_nonneg | [] | [
274,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.image_closure | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.66092\nδ : Type ?u.66095\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nh : α ≃ₜ β\ns : Set α\n⊢ ↑h '' closure s = closure (↑h '' s)",
"tactic": "rw ... | [
348,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
1
] |
Mathlib/Data/PFunctor/Multivariate/W.lean | MvPFunctor.wPathDestLeft_wPathCasesOn | [] | [
102,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | inv_lt_inv_of_lt | [] | [
282,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/Data/Finsupp/ToDfinsupp.lean | sigmaFinsuppEquivDfinsupp_support | [
{
"state_after": "case a\nι : Type u_1\nR : Type ?u.69432\nM : Type ?u.69435\nη : ι → Type u_3\nN : Type u_2\ninst✝³ : Semiring R\ninst✝² : DecidableEq ι\ninst✝¹ : Zero N\ninst✝ : (i : ι) → (x : η i →₀ N) → Decidable (x ≠ 0)\nf : (i : ι) × η i →₀ N\na✝ : ι\n⊢ a✝ ∈ Dfinsupp.support (↑sigmaFinsuppEquivDfinsupp f)... | [
322,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.exists_antitone_basis | [] | [
1100,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1097,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.coe_one | [] | [
208,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/CategoryTheory/Sites/Grothendieck.lean | CategoryTheory.GrothendieckTopology.Cover.Relation.base_snd | [] | [
585,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
] |
Mathlib/AlgebraicTopology/SplitSimplicialObject.lean | SimplicialObject.Split.congr_f | [
{
"state_after": "no goals",
"state_before": "C : Type u_1\ninst✝¹ : Category C\ninst✝ : HasFiniteCoproducts C\nS₁ S₂ : Split C\nΦ₁ Φ₂ : S₁ ⟶ S₂\nh : Φ₁ = Φ₂\nn : ℕ\n⊢ Hom.f Φ₁ n = Hom.f Φ₂ n",
"tactic": "rw [h]"
}
] | [
433,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/Topology/Sheaves/SheafCondition/UniqueGluing.lean | TopCat.Presheaf.isSheaf_of_isSheafUniqueGluing_types | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\ninst✝ : ConcreteCategory C\nX : TopCat\nF : Presheaf (Type v) X\nι : Type v\nU : ι → Opens ↑X\nFsh : IsSheafUniqueGluing F\n⊢ IsSheafEqualizerProducts F",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : ConcreteCategory C\nX : TopCat\nF : Presheaf... | [
171,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/RepresentationTheory/Action.lean | Action.functorCategoryMonoidalEquivalence.unit_app_hom | [] | [
690,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
688,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.comap_iSup_map_of_injective | [] | [
979,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
977,
1
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidWithZeroHom.mul_apply | [] | [
744,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
743,
1
] |
Mathlib/Analysis/NormedSpace/Complemented.lean | ContinuousLinearMap.equivProdOfSurjectiveOfIsCompl_apply | [] | [
78,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Data/Finite/Card.lean | Finite.card_le_of_embedding' | [] | [
136,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/NumberTheory/Multiplicity.lean | multiplicity.Int.pow_sub_pow | [
{
"state_after": "case zero\nR : Type ?u.833926\nn : ℕ\ninst✝ : CommRing R\na b x✝ y✝ : R\np : ℕ\nhp : Nat.Prime p\nhp1 : Odd p\nx y : ℤ\nhxy : ↑p ∣ x - y\nhx : ¬↑p ∣ x\n⊢ multiplicity (↑p) (x ^ Nat.zero - y ^ Nat.zero) = multiplicity (↑p) (x - y) + multiplicity p Nat.zero\n\ncase succ\nR : Type ?u.833926\nn✝ :... | [
220,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/RingTheory/Ideal/Quotient.lean | Ideal.Quotient.isDomain_iff_prime | [
{
"state_after": "case refine'_1\nR : Type u\ninst✝ : CommRing R\nI✝ : Ideal R\na b : R\nS : Type v\nx y : R\nI : Ideal R\nH : IsDomain (R ⧸ I)\n⊢ 0 ≠ 1\n\ncase refine'_2\nR : Type u\ninst✝ : CommRing R\nI✝ : Ideal R\na b : R\nS : Type v\nx✝ y✝ : R\nI : Ideal R\nH : IsDomain (R ⧸ I)\nx y : R\nh : x * y ∈ I\n⊢ x... | [
199,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Data/Set/Basic.lean | Set.eq_empty_of_ssubset_singleton | [] | [
1511,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1510,
1
] |
Mathlib/Algebra/Group/Conj.lean | IsConj.refl | [] | [
37,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
] |
Mathlib/Analysis/NormedSpace/MazurUlam.lean | IsometryEquiv.midpoint_fixed | [
{
"state_after": "E : Type u_2\nPE : Type u_1\nF : Type ?u.569\nPF : Type ?u.572\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : MetricSpace PE\ninst✝⁴ : NormedAddTorsor E PE\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace ℝ F\ninst✝¹ : MetricSpace PF\ninst✝ : NormedAddTorsor F PF\nx y :... | [
88,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Data/Finset/Slice.lean | Set.sized_iUnion | [
{
"state_after": "α : Type u_1\nι : Sort u_2\nκ : ι → Sort ?u.406\nA B : Set (Finset α)\nr : ℕ\nf : ι → Set (Finset α)\n⊢ (∀ ⦃x : Finset α⦄ (x_1 : ι), x ∈ f x_1 → card x = r) ↔ ∀ (i : ι) ⦃x : Finset α⦄, x ∈ f i → card x = r",
"state_before": "α : Type u_1\nι : Sort u_2\nκ : ι → Sort ?u.406\nA B : Set (Finse... | [
68,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Data/Polynomial/Div.lean | Polynomial.map_divByMonic | [] | [
379,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.logb_lt_logb_iff_of_base_lt_one | [
{
"state_after": "b x y : ℝ\nb_pos : 0 < b\nb_lt_one : b < 1\nhx : 0 < x\nhy : 0 < y\n⊢ log y < log x ↔ y < x",
"state_before": "b x y : ℝ\nb_pos : 0 < b\nb_lt_one : b < 1\nhx : 0 < x\nhy : 0 < y\n⊢ logb b x < logb b y ↔ y < x",
"tactic": "rw [logb, logb, div_lt_div_right_of_neg (log_neg b_pos b_lt_one)... | [
269,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Data/Finset/Sort.lean | Finset.max'_eq_sorted_last | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.23141\nβ : Type ?u.23144\ninst✝ : LinearOrder α\ns : Finset α\nh : Finset.Nonempty s\n⊢ List.length (sort (fun x x_1 => x ≤ x_1) s) - 1 < List.length (sort (fun x x_1 => x ≤ x_1) s)",
"tactic": "simpa using Nat.sub_lt (card_pos.mpr h) zero_lt_one... | [
142,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | ciInf_mono | [] | [
808,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
807,
1
] |
Mathlib/Algebra/IsPrimePow.lean | IsPrimePow.pow | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : CommMonoidWithZero R\nn✝ p✝ : R\nk✝ : ℕ\nn : R\nhn✝ : IsPrimePow n\nk : ℕ\nhk : k ≠ 0\np : R\nk' : ℕ\nhp : Prime p\nhk' : 0 < k'\nhn : p ^ k' = n\n⊢ p ^ (k * k') = n ^ k",
"tactic": "rw [pow_mul', hn]"
}
] | [
66,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.head?_toList | [] | [
236,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.ball_comp | [
{
"state_after": "case h\nR : Type ?u.894129\nR' : Type ?u.894132\n𝕜 : Type u_3\n𝕜₂ : Type u_1\n𝕜₃ : Type ?u.894141\n𝕝 : Type ?u.894144\nE : Type u_4\nE₂ : Type u_2\nE₃ : Type ?u.894153\nF : Type ?u.894156\nG : Type ?u.894159\nι : Type ?u.894162\ninst✝⁶ : SeminormedRing 𝕜\ninst✝⁵ : AddCommGroup E\ninst✝⁴ :... | [
796,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
793,
1
] |
Mathlib/GroupTheory/Coset.lean | leftCoset_assoc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Semigroup α\ns : Set α\na b : α\n⊢ a *l (b *l s) = a * b *l s",
"tactic": "simp [leftCoset, rightCoset, (image_comp _ _ _).symm, Function.comp, mul_assoc]"
}
] | [
128,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.piecewise_compl | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.35722\nδ : Type ?u.35725\ninst✝ : MeasurableSpace α\ns : Set α\nhs : MeasurableSet (sᶜ)\nf g : α →ₛ β\n⊢ Set.piecewise (sᶜ) ↑f ↑g = Set.piecewise s ↑g ↑f",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.35722\nδ : Type ?u.35725\ninst✝ : Mea... | [
257,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.Tendsto.basis_right | [] | [
886,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
884,
1
] |
Mathlib/Analysis/BoxIntegral/DivergenceTheorem.lean | BoxIntegral.norm_volume_sub_integral_face_upper_sub_lower_smul_le | [
{
"state_after": "E : Type u\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\nn : ℕ\ninst✝ : CompleteSpace E\nI : Box (Fin (n + 1))\ni : Fin (n + 1)\nf : (Fin (n + 1) → ℝ) → E\nf' : (Fin (n + 1) → ℝ) →L[ℝ] E\nhfc : ContinuousOn f (↑Box.Icc I)\nx : Fin (n + 1) → ℝ\nhxI : x ∈ ↑Box.Icc I\na : E\nε : ℝ\nh0... | [
142,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | HomogeneousIdeal.eq_top_iff | [] | [
419,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometry.map_sub | [] | [
219,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
11
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.card_le_card_mul_left | [] | [
1900,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1899,
1
] |
Mathlib/Algebra/Module/Basic.lean | AddMonoid.End.int_cast_def | [] | [
247,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Topology/ContinuousFunction/Basic.lean | ContinuousMap.map_specializes | [] | [
172,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieModuleEquiv.trans_apply | [] | [
1092,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1091,
1
] |
Mathlib/Analysis/Calculus/BumpFunctionInner.lean | ContDiffBump.support_normed_eq | [
{
"state_after": "E : Type u_1\nX : Type ?u.1976566\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace ℝ E\ninst✝⁷ : NormedAddCommGroup X\ninst✝⁶ : NormedSpace ℝ X\ninst✝⁵ : HasContDiffBump E\nc : E\nf : ContDiffBump c\nx : E\nn : ℕ∞\ninst✝⁴ : MeasurableSpace E\nμ : MeasureTheory.Measure E\ninst✝³ : BorelSpac... | [
537,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.norm_re_le_norm | [] | [
725,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
724,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.filter_curry | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.549060\nι : Type ?u.549063\nM : Type u_3\nM' : Type ?u.549069\nN : Type ?u.549072\nP : Type ?u.549075\nG : Type ?u.549078\nH : Type ?u.549081\nR : Type ?u.549084\nS : Type ?u.549087\ninst✝¹ : AddCommMonoid M\ninst✝ : AddCommMonoid N\nf : α × β →₀ M\np : ... | [
1279,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1269,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.mem_toSubmonoid | [] | [
523,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
522,
1
] |
Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.aeval_algHom_eq_zero | [
{
"state_after": "R : Type u\nS : Type v\nK : Type w\ninst✝² : CommRing R\nf : R[X]\ninst✝¹ : CommRing S\ni : R →+* S\na : S\nh✝ : eval₂ i a f = 0\ninst✝ : Algebra R S\nϕ : AdjoinRoot f →ₐ[R] S\nh : RingHom.comp (↑ϕ) (of f) = algebraMap R S\n⊢ ↑(aeval (↑ϕ (root f))) f = 0",
"state_before": "R : Type u\nS : ... | [
321,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Mathlib/Data/List/Basic.lean | List.cons_injective | [] | [
60,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
9
] |
Mathlib/Data/Finset/Basic.lean | Finset.insert_union_distrib | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.150533\nγ : Type ?u.150536\ninst✝ : DecidableEq α\ns✝ s₁ s₂ t✝ t₁ t₂ u v : Finset α\na✝ b a : α\ns t : Finset α\n⊢ insert a (s ∪ t) = insert a s ∪ insert a t",
"tactic": "simp only [insert_union, union_insert, insert_idem]"
}
] | [
1461,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1459,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.coe_piCongr_symm | [] | [
1787,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1785,
1
] |
Mathlib/Logic/Equiv/Functor.lean | Bifunctor.mapEquiv_symm_apply | [] | [
89,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.mk_mul_mk | [] | [
349,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
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