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/Finsupp/Interval.lean | Finsupp.card_Iic | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : Type u_2\ninst✝¹ : CanonicallyOrderedAddMonoid α\ninst✝ : LocallyFiniteOrder α\nf : ι →₀ α\n⊢ card (Iic f) = ∏ i in f.support, card (Iic (↑f i))",
"tactic": "classical simp_rw [Iic_eq_Icc, card_Icc, Finsupp.bot_eq_zero, support_zero, empty_... | [
139,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Order/Disjoint.lean | disjoint_sup_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : DistribLattice α\ninst✝ : OrderBot α\na b c : α\n⊢ Disjoint a (b ⊔ c) ↔ Disjoint a b ∧ Disjoint a c",
"tactic": "simp only [disjoint_iff, inf_sup_left, sup_eq_bot_iff]"
}
] | [
193,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Algebra/GroupPower/Basic.lean | ite_pow | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.4429\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝¹ : Pow M ℕ\nP : Prop\ninst✝ : Decidable P\na b : M\nc : ℕ\n⊢ (if P then a else b) ^ c = if P then a ^ c else b ^ c",
"tactic": "split_if... | [
61,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Algebra/Lie/Free.lean | FreeLieAlgebra.liftAux_spec | [
{
"state_after": "case lie_self\nR : Type u\nX : Type v\ninst✝² : CommRing R\nL : Type w\ninst✝¹ : LieRing L\ninst✝ : LieAlgebra R L\nf : X → L\na b a✝ : lib R X\n⊢ ↑(liftAux R f) (a✝ * a✝) = ↑(liftAux R f) 0\n\ncase leibniz_lie\nR : Type u\nX : Type v\ninst✝² : CommRing R\nL : Type w\ninst✝¹ : LieRing L\ninst✝... | [
214,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Data/List/Sublists.lean | List.sublistsLen_sublist_sublists' | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u\nβ : Type v\nγ : Type w\nα : Type u_1\nl : List α\n⊢ sublistsLen 0 l <+ sublists' l",
"tactic": "simp"
},
{
"state_after": "α✝ : Type u\nβ : Type v\nγ : Type w\nα : Type u_1\nn : ℕ\na : α\nl : List α\n⊢ sublistsLen (n + 1) l ++ map (cons ... | [
295,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | zero_eq_nndist | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.552184\nι : Type ?u.552187\ninst✝¹ : PseudoMetricSpace α\nγ : Type w\ninst✝ : MetricSpace γ\nx y : γ\n⊢ 0 = nndist x y ↔ x = y",
"tactic": "simp only [← NNReal.eq_iff, ← dist_nndist, imp_self, NNReal.coe_zero, zero_eq_dist... | [
2890,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2889,
1
] |
Mathlib/Topology/Order/Basic.lean | Dense.exists_lt | [] | [
757,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
755,
11
] |
Mathlib/Data/Real/NNReal.lean | NNReal.coe_indicator | [] | [
297,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/Order/WithBot.lean | WithBot.coe_mono | [] | [
334,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Midpoint.lean | Equiv.pointReflection_midpoint_right | [
{
"state_after": "no goals",
"state_before": "R : Type u_3\nV : Type u_2\nV' : Type ?u.28779\nP : Type u_1\nP' : Type ?u.28785\ninst✝⁷ : Ring R\ninst✝⁶ : Invertible 2\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module R V\ninst✝³ : AddTorsor V P\ninst✝² : AddCommGroup V'\ninst✝¹ : Module R V'\ninst✝ : AddTorsor V' P... | [
89,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidWithZeroHom.id_comp | [] | [
712,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
712,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.equiv_congr_left | [] | [
879,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
878,
1
] |
Mathlib/Topology/UnitInterval.lean | unitInterval.le_one | [] | [
149,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | AEMeasurable.smul_const | [] | [
642,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
640,
1
] |
Mathlib/Data/List/Sigma.lean | List.lookupAll_nodup | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : α → Type v\nl✝ l₁ l₂ : List (Sigma β)\ninst✝ : DecidableEq α\na : α\nl : List (Sigma β)\nh : NodupKeys l\n⊢ Nodup (lookupAll a l)",
"tactic": "(rw [lookupAll_eq_dlookup a h]; apply Option.toList_nodup)"
},
{
"state_after": "α : Type u... | [
329,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/Order/FixedPoints.lean | OrderHom.isFixedPt_gfp | [] | [
123,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Data/List/Zip.lean | List.zip_cons_cons | [] | [
43,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/Logic/Encodable/Basic.lean | Quotient.rep_spec | [] | [
686,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.neighborSet_singletonSubgraph | [] | [
872,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
871,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.ToPartrec.Code.zero_eval | [
{
"state_after": "no goals",
"state_before": "v : List ℕ\n⊢ eval zero v = pure [0]",
"tactic": "simp [zero]"
}
] | [
204,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | MonoidHom.range_top_iff_surjective | [
{
"state_after": "no goals",
"state_before": "G : Type u_2\nG' : Type ?u.475486\ninst✝⁵ : Group G\ninst✝⁴ : Group G'\nA : Type ?u.475495\ninst✝³ : AddGroup A\nN✝ : Type ?u.475501\nP : Type ?u.475504\ninst✝² : Group N✝\ninst✝¹ : Group P\nK : Subgroup G\nN : Type u_1\ninst✝ : Group N\nf : G →* N\n⊢ ↑(range f)... | [
2658,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2656,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.lf_congr | [] | [
814,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
813,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.Nontrivial.einfsep_exists_of_finite | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.36701\ninst✝¹ : EDist α\nx y : α\ns t : Set α\ninst✝ : Finite ↑s\nhs : Set.Nontrivial s\n⊢ ∃ x x_1 y x_2 _hxy, einfsep s = edist x y",
"tactic": "classical\n cases nonempty_fintype s\n simp_rw [einfsep_of_fintype]\n rcases@Finset... | [
202,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Topology/Algebra/Nonarchimedean/Bases.lean | RingSubgroupsBasis.of_comm | [
{
"state_after": "A✝ : Type ?u.910\nι✝ : Type ?u.913\ninst✝¹ : Ring A✝\nA : Type u_1\nι : Type u_2\ninst✝ : CommRing A\nB : ι → AddSubgroup A\ninter : ∀ (i j : ι), ∃ k, B k ≤ B i ⊓ B j\nmul : ∀ (i : ι), ∃ j, ↑(B j) * ↑(B j) ⊆ ↑(B i)\nleftMul : ∀ (x : A) (i : ι), ∃ j, ↑(B j) ⊆ (fun y => x * y) ⁻¹' ↑(B i)\nx : A\... | [
69,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.Iso.cancel_iso_inv_right | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX✝ Y✝ Z✝ X Y Z : C\nf f' : X ⟶ Y\ng : Z ≅ Y\n⊢ f ≫ g.inv = f' ≫ g.inv ↔ f = f'",
"tactic": "simp only [cancel_mono]"
}
] | [
556,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infiniteNeg_mul_of_infinitePos_not_infinitesimal_neg | [
{
"state_after": "x y : ℝ*\n⊢ InfinitePos x → ¬Infinitesimal (-y) → 0 < -y → InfinitePos (x * -y)",
"state_before": "x y : ℝ*\n⊢ InfinitePos x → ¬Infinitesimal y → y < 0 → InfiniteNeg (x * y)",
"tactic": "rw [← infinitePos_neg, ← neg_pos, neg_mul_eq_mul_neg, ← infinitesimal_neg]"
},
{
"state_aft... | [
843,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
840,
1
] |
Mathlib/Data/Matrix/Basic.lean | LinearMap.mapMatrix_id | [] | [
1473,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1472,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.iSupLift_mk | [
{
"state_after": "R : Type u\nA : Type v\nB : Type w\ninst✝⁵ : CommSemiring R\ninst✝⁴ : Semiring A\ninst✝³ : Algebra R A\ninst✝² : Semiring B\ninst✝¹ : Algebra R B\nS : Subalgebra R A\nι : Type u_1\ninst✝ : Nonempty ι\nK : ι → Subalgebra R A\ndir : Directed (fun x x_1 => x ≤ x_1) K\nf : (i : ι) → { x // x ∈ K i... | [
1226,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1223,
1
] |
Mathlib/Order/SymmDiff.lean | symmDiff_left_inj | [] | [
537,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
536,
1
] |
Mathlib/CategoryTheory/Category/Basic.lean | CategoryTheory.epi_of_epi_fac | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\nX✝ Y✝ Z✝ X Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\ninst✝ : Epi (f ≫ g)\n⊢ Epi g",
"state_before": "C : Type u\ninst✝¹ : Category C\nX✝ Y✝ Z✝ X Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\nh : X ⟶ Z\ninst✝ : Epi h\nw : f ≫ g = h\n⊢ Epi g",
"tactic": "subst h"
},
{
"sta... | [
347,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.inv_image_trans_target | [] | [
739,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
738,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.coe_comp' | [] | [
788,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
787,
1
] |
Mathlib/Algebra/Algebra/Basic.lean | Algebra.commutes | [] | [
368,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | le_one_of_mul_le_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.17091\ninst✝² : MulOneClass α\ninst✝¹ : LE α\ninst✝ : ContravariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b : α\nh : a * b ≤ b\n⊢ a * ?m.17465 h ≤ 1 * ?m.17465 h",
"tactic": "simpa only [one_mul]"
}
] | [
394,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
1
] |
Mathlib/Data/QPF/Multivariate/Constructions/Fix.lean | MvQPF.recF_eq | [
{
"state_after": "n : ℕ\nF : TypeVec (n + 1) → Type u\ninst✝ : MvFunctor F\nq : MvQPF F\nα : TypeVec n\nβ : Type u\ng : F (α ::: β) → β\na : (P F).A\nf' : MvPFunctor.B (MvPFunctor.drop (P F)) a ⟹ α\nf : PFunctor.B (MvPFunctor.last (P F)) a → MvPFunctor.W (P F) α\n⊢ g\n (abs\n { fst := a,\n ... | [
70,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.adjoin_finset_isCompactElement | [
{
"state_after": "F : Type u_2\ninst✝² : Field F\nE : Type u_1\ninst✝¹ : Field E\ninst✝ : Algebra F E\nS✝ : Set E\nα : E\nS : Finset E\nkey : adjoin F ↑S = ⨆ (x : E) (_ : x ∈ S), F⟮x⟯\n⊢ IsCompactElement (adjoin F ↑S)",
"state_before": "F : Type u_2\ninst✝² : Field F\nE : Type u_1\ninst✝¹ : Field E\ninst✝ :... | [
621,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
613,
1
] |
Mathlib/MeasureTheory/Decomposition/Jordan.lean | MeasureTheory.SignedMeasure.toJordanDecomposition_zero | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.74138\ninst✝ : MeasurableSpace α\n⊢ toSignedMeasure (toJordanDecomposition 0) = toSignedMeasure 0",
"state_before": "α : Type u_1\nβ : Type ?u.74138\ninst✝ : MeasurableSpace α\n⊢ toJordanDecomposition 0 = 0",
"tactic": "apply toSignedMeasure_injective"... | [
457,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Comp.lean | DifferentiableOn.iterate | [] | [
212,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
11
] |
Mathlib/Analysis/SpecificLimits/Normed.lean | NormedAddCommGroup.cauchy_series_of_le_geometric'' | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1175572\nι : Type ?u.1175575\ninst✝ : SeminormedAddCommGroup α\nr✝ C✝ : ℝ\nf : ℕ → α\nC : ℝ\nu : ℕ → α\nN : ℕ\nr : ℝ\nhr₀ : 0 < r\nhr₁ : r < 1\nh : ∀ (n : ℕ), n ≥ N → ‖u n‖ ≤ C * r ^ n\nv : ℕ → α := fun n => if n < N then 0 else u n\n⊢ CauchySeq fun n => ∑ k in Finset... | [
448,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.map_eq_of_subset | [] | [
279,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Deriv.lean | Real.hasStrictDerivAt_log | [
{
"state_after": "case inl\nx : ℝ\nhx✝ : x ≠ 0\nhx : x < 0\n⊢ HasStrictDerivAt log x⁻¹ x\n\ncase inr\nx : ℝ\nhx✝ : x ≠ 0\nhx : 0 < x\n⊢ HasStrictDerivAt log x⁻¹ x",
"state_before": "x : ℝ\nhx : x ≠ 0\n⊢ HasStrictDerivAt log x⁻¹ x",
"tactic": "cases' hx.lt_or_lt with hx hx"
},
{
"state_after": "c... | [
50,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.uniformContinuous_equiv | [] | [
452,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
1
] |
Mathlib/Algebra/Invertible.lean | mul_invOf_self' | [] | [
112,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.toWithTop_zero | [] | [
565,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
1
] |
src/lean/Init/SimpLemmas.lean | Bool.and_false | [
{
"state_after": "no goals",
"state_before": "b : Bool\n⊢ (b && false) = false",
"tactic": "cases b <;> rfl"
}
] | [
110,
87
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
110,
9
] |
Mathlib/Algebra/DirectSum/Ring.lean | DirectSum.one_mul | [
{
"state_after": "ι : Type u_1\ninst✝³ : DecidableEq ι\nA : ι → Type u_2\ninst✝² : (i : ι) → AddCommMonoid (A i)\ninst✝¹ : AddMonoid ι\ninst✝ : GSemiring A\nx : ⨁ (i : ι), A i\n⊢ ↑(mulHom A) One.one = AddMonoidHom.id (⨁ (i : ι), A i)",
"state_before": "ι : Type u_1\ninst✝³ : DecidableEq ι\nA : ι → Type u_2\... | [
234,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
16
] |
Mathlib/Combinatorics/Quiver/Cast.lean | Quiver.Path.cast_nil | [
{
"state_after": "U : Type u_1\ninst✝ : Quiver U\nu' : U\n⊢ cast (_ : u' = u') (_ : u' = u') nil = nil",
"state_before": "U : Type u_1\ninst✝ : Quiver U\nu u' : U\nhu : u = u'\n⊢ cast hu hu nil = nil",
"tactic": "subst_vars"
},
{
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112,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
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Mathlib/Data/W/Basic.lean | WType.ofSigma_toSigma | [] | [
65,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
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Mathlib/Data/Finset/Lattice.lean | Finset.min_erase_ne_self | [
{
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1564,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1559,
1
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Mathlib/RingTheory/Ideal/Over.lean | Ideal.Quotient.mk_smul_mk_quotient_map_quotient | [] | [
176,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
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Mathlib/Analysis/SpecialFunctions/Polynomials.lean | Polynomial.div_tendsto_atTop_of_degree_gt | [] | [
195,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
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Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.roots_X_sub_C | [
{
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"state_before": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np q : R[X]\nr... | [
650,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
648,
1
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Mathlib/Data/ZMod/Basic.lean | ZMod.ringHom_surjective | [] | [
1176,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1175,
1
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Mathlib/Data/List/Basic.lean | List.length_modifyNthTail | [] | [
1549,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1545,
1
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Mathlib/Computability/TMToPartrec.lean | Turing.ToPartrec.Code.id_eval | [
{
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"state_before": "v : List ℕ\n⊢ eval id v = pure v",
"tactic": "simp [id]"
}
] | [
186,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
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Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.neg_snd | [] | [
277,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
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Mathlib/Data/Bool/Count.lean | List.Chain'.count_true_le_count_false_add_one | [] | [
100,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
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Mathlib/Algebra/Associated.lean | prime_pow_succ_dvd_mul | [
{
"state_after": "α✝ : Type ?u.61415\nβ : Type ?u.61418\nγ : Type ?u.61421\nδ : Type ?u.61424\nα : Type u_1\ninst✝ : CancelCommMonoidWithZero α\np x y : α\nh : Prime p\ni : ℕ\nhxy : p ^ (i + 1) ∣ x * y\n⊢ ¬p ∣ y → p ^ (i + 1) ∣ x",
"state_before": "α✝ : Type ?u.61415\nβ : Type ?u.61418\nγ : Type ?u.61421\nδ... | [
158,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
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Mathlib/Algebra/CharP/MixedCharZero.lean | isEmpty_algebraRat_iff_mixedCharZero | [
{
"state_after": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : CharZero R\n⊢ ¬IsEmpty (Algebra ℚ R) ↔ ¬∃ p, p > 0 ∧ MixedCharZero R p",
"state_before": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : CharZero R\n⊢ IsEmpty (Algebra ℚ R) ↔ ∃ p, p > 0 ∧ MixedCharZero R p",
"tactic": "rw [← not_iff_not]"
},
{... | [
310,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
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Mathlib/Data/Finset/Lattice.lean | Finset.iSup_biUnion | [
{
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1988,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1987,
1
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Mathlib/CategoryTheory/Simple.lean | CategoryTheory.simple_of_isSimpleOrder_subobject | [
{
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"state_before": "C : Type u\ninst✝³ : Category C\ninst✝² : HasZeroMorp... | [
252,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
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Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.closure_eq_image_prod | [
{
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"state_before": "M : Type u_1\nA : Type ?u.78612\nB : Type ?u.78615\ninst✝ : Monoid M\ns : Set M\n⊢ ↑(closure s) = L... | [
366,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
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Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | hasSum_subtype_iff_of_support_subset | [
{
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"tactic": "simpa... | [
154,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
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Mathlib/CategoryTheory/Limits/Preserves/Shapes/Biproducts.lean | CategoryTheory.Functor.mapBiproduct_hom | [] | [
307,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
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Mathlib/CategoryTheory/Abelian/NonPreadditive.lean | CategoryTheory.NonPreadditiveAbelian.sub_self | [
{
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"tactic": "rw [sub_def, ← Category.comp_id a, ← prod.comp_lift, Category.assoc, diag_σ, comp_zero]"
}
] | [
363,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/Data/PFunctor/Univariate/M.lean | PFunctor.M.casesOn_mk' | [] | [
461,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
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Mathlib/Analysis/NormedSpace/MStructure.lean | IsLprojection.coe_bot | [] | [
253,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.map_one | [] | [
724,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
723,
11
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Std/Data/List/Init/Lemmas.lean | List.foldl_reverse | [
{
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"state_before": "α : Type u_1\nβ : Type u_2\nl : List α\nf : β → α → β\nb : β\n⊢ foldl f b (reverse l) = foldr (fun x y => f y x) b l",
"tactic": "simp [foldl_eq_foldlM, foldr_eq_foldrM]"
}
] | [
186,
101
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
185,
9
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Std/Data/Nat/Lemmas.lean | Nat.mul_mod_mul_left | [
{
"state_after": "no goals",
"state_before": "z x y : Nat\ny0 : y = 0\n⊢ z * x % (z * y) = z * (x % y)",
"tactic": "rw [y0, Nat.mul_zero, mod_zero, mod_zero]"
},
{
"state_after": "no goals",
"state_before": "z x y : Nat\ny0 : ¬y = 0\nz0 : z = 0\n⊢ z * x % (z * y) = z * (x % y)",
"tactic"... | [
525,
58
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
510,
1
] |
Mathlib/Data/Fintype/Basic.lean | Fintype.univ_ofSubsingleton | [] | [
584,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
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Mathlib/Topology/OmegaCompletePartialOrder.lean | Scott.isOpen_univ | [] | [
57,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Module.map_eval_injective | [
{
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"state_before": "K : Type u₁\nV : Type u₂\ninst✝² : Field K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\n⊢ Function.Injective (Submodule.map (eval K V))",
... | [
551,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
1
] |
Mathlib/Algebra/Star/Unitary.lean | unitary.star_eq_inv | [] | [
125,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Analysis/Convex/Between.lean | Sbtw.not_swap_left | [] | [
404,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.image₂_empty_right | [
{
"state_after": "no goals",
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145,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Analysis/Calculus/Deriv/Comp.lean | fderivWithin.comp_derivWithin | [] | [
271,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/Computability/Reduce.lean | equivalence_of_manyOneEquiv | [] | [
180,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Std/Data/String/Lemmas.lean | Substring.ValidFor.next_stop | [
{
"state_after": "no goals",
"state_before": "l m r : List Char\n⊢ Substring.next\n { str := { data := l ++ m ++ r }, startPos := { byteIdx := utf8Len l },\n stopPos := { byteIdx := utf8Len l + utf8Len m } }\n { byteIdx := utf8Len m } =\n { byteIdx := utf8Len m }",
"tactic": "simp [S... | [
841,
50
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
840,
1
] |
Mathlib/Algebra/Associated.lean | Associates.isUnit_iff_eq_bot | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.294633\nγ : Type ?u.294636\nδ : Type ?u.294639\ninst✝ : CommMonoid α\na : Associates α\n⊢ IsUnit a ↔ a = ⊥",
"tactic": "rw [Associates.isUnit_iff_eq_one, bot_eq_one]"
}
] | [
890,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
889,
1
] |
Mathlib/LinearAlgebra/FreeModule/Finite/Rank.lean | FiniteDimensional.Submodule.finrank_map_subtype_eq | [] | [
48,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/InformationTheory/Hamming.lean | hammingDist_nonneg | [] | [
56,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.subset_adjoin | [] | [
321,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
] |
Mathlib/Topology/Algebra/OpenSubgroup.lean | OpenSubgroup.coe_comap | [] | [
279,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.signBijAux_mem | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝ : DecidableEq α\nn : ℕ\nf : Perm (Fin n)\nx✝ : (_ : Fin n) × Fin n\na₁ a₂ : Fin n\nha : { fst := a₁, snd := a₂ } ∈ finPairsLT n\n⊢ (if x : ↑f { fst := a₁, snd := a₂ }.snd < ↑f { fst := a₁, snd := a₂ }.fst then\n { fst := ↑f { fst := a₁, snd := a₂ }.fst, snd :... | [
369,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.ofLe_injective | [] | [
633,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
632,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.eq_zero_or_eq_zero_of_mul_eq_zero | [
{
"state_after": "R : Type u_1\ninst✝¹ : Ring R\ninst✝ : NoZeroDivisors R\nφ ψ : PowerSeries R\nh : φ * ψ = 0\n⊢ ¬φ = 0 → ψ = 0",
"state_before": "R : Type u_1\ninst✝¹ : Ring R\ninst✝ : NoZeroDivisors R\nφ ψ : PowerSeries R\nh : φ * ψ = 0\n⊢ φ = 0 ∨ ψ = 0",
"tactic": "rw [or_iff_not_imp_left]"
},
{
... | [
2021,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1985,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | PosMulReflectLT.toPosMulMonoRev | [] | [
1006,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1003,
1
] |
Mathlib/Data/Quot.lean | Quotient.out_eq' | [] | [
792,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
791,
1
] |
Mathlib/Data/PNat/Basic.lean | PNat.natPred_inj | [] | [
72,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.pointReflection_symm | [] | [
567,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
566,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.sum_left | [] | [
429,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/GroupTheory/CommutingProbability.lean | commProb_def' | [
{
"state_after": "M : Type ?u.17813\ninst✝³ : Mul M\ninst✝² : Finite M\nG : Type u_1\ninst✝¹ : Group G\ninst✝ : Finite G\n⊢ ↑(Nat.card (ConjClasses G)) * ↑(Nat.card G) / (↑(Nat.card G) * ↑(Nat.card G)) =\n ↑(Nat.card (ConjClasses G)) / ↑(Nat.card G)",
"state_before": "M : Type ?u.17813\ninst✝³ : Mul M\ni... | [
92,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.bit1_im | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nE : Type ?u.1882781\ninst✝ : IsROrC K\nz : K\n⊢ ↑im (bit1 z) = bit0 (↑im z)",
"tactic": "simp only [bit1, map_add, bit0_im, one_im, add_zero]"
}
] | [
196,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | iSup_eq_of_forall_le_of_tendsto | [] | [
430,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/CategoryTheory/Limits/Constructions/FiniteProductsOfBinaryProducts.lean | CategoryTheory.hasProduct_fin | [
{
"state_after": "J : Type v\ninst✝⁴ : SmallCategory J\nC : Type u\ninst✝³ : Category C\nD : Type u'\ninst✝² : Category D\ninst✝¹ : HasBinaryProducts C\ninst✝ : HasTerminal C\nf : Fin 0 → C\nthis : HasLimitsOfShape (Discrete (Fin 0)) C :=\n hasLimitsOfShape_of_equivalence (Discrete.equivalence finZeroEquiv'.sy... | [
108,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
9
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | hasDerivWithinAt_Iio_iff_Iic | [
{
"state_after": "no goals",
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339,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/CategoryTheory/Monoidal/Mon_.lean | Mon_.one_rightUnitor | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\ninst✝ : MonoidalCategory C\nM : Mon_ C\n⊢ (λ_ (𝟙_ C)).inv ≫ (λ_ (𝟙_ C)).hom ≫ M.one = M.one",
"state_before": "C : Type u₁\ninst✝¹ : Category C\ninst✝ : MonoidalCategory C\nM : Mon_ C\n⊢ ((λ_ (𝟙_ C)).inv ≫ (M.one ⊗ 𝟙 (𝟙_ C))) ≫ (ρ_ M.X).hom = M.one",
... | [
405,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
1
] |
Mathlib/RingTheory/PowerBasis.lean | PowerBasis.equivOfRoot_symm | [] | [
388,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/Data/Fintype/Sum.lean | Fintype.card_subtype_or | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.13939\np q : α → Prop\ninst✝² : Fintype { x // p x }\ninst✝¹ : Fintype { x // q x }\ninst✝ : Fintype { x // p x ∨ q x }\n⊢ card { x // p x ∨ q x } ≤ card { x // p x } + card { x // q x }",
"tactic": "classical\n convert Fintype.car... | [
126,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
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