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/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.ofLEMk_comp | [
{
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Mathlib/Analysis/Convex/Function.lean | StrictConcaveOn.sub_convexOn | [] | [
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src/lean/Init/Data/Nat/Basic.lean | Nat.mul_zero | [] | [
160,
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] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
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Mathlib/Order/WithBot.lean | WithTop.coe_le_iff | [] | [
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Mathlib/Algebra/Star/StarAlgHom.lean | StarAlgHom.comp_apply | [] | [
454,
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Mathlib/Order/JordanHolder.lean | CompositionSeries.injective | [] | [
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Mathlib/Algebra/BigOperators/Basic.lean | Int.cast_multiset_sum | [] | [
2238,
36
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Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.nat_cast_imI | [] | [
415,
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Std/Logic.lean | imp_iff_not | [] | [
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90
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Mathlib/CategoryTheory/Subobject/Limits.lean | CategoryTheory.Limits.factorThruKernelSubobject_comp_arrow | [
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Mathlib/Data/Real/CauSeq.lean | CauSeq.lt_inf | [
{
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Mathlib/LinearAlgebra/Matrix/GeneralLinearGroup.lean | Matrix.GeneralLinearGroup.coe_toLinear | [] | [
139,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
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Mathlib/Algebra/Order/Field/Basic.lean | exists_add_lt_and_pos_of_lt | [] | [
975,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/IndicatorFunction.lean | Set.indicator_const_smul | [] | [
511,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/LiminfLimsup.lean | Filter.le_limsSup_of_le | [] | [
455,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/BigOperators/Intervals.lean | Finset.prod_Ico_add | [
{
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Mathlib/Analysis/Calculus/Deriv/Star.lean | derivWithin.star | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Sign.lean | Left.sign_neg | [
{
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445,
9
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Mathlib/Data/List/Duplicate.lean | List.Duplicate.mem_cons_self | [
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"tactic": "cases' h with _ h _ _ h"
},
{
"state_after":... | [
59,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Seminorm.lean | Seminorm.convex_closedBall | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Order/Floor.lean | Int.fract_add | [
{
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Mathlib/Topology/Category/Compactum.lean | Compactum.cl_eq_closure | [
{
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{
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384,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Calculus/MeanValue.lean | hasStrictFDerivAt_of_hasFDerivAt_of_continuousAt | [
{
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1348,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Seq/Seq.lean | Stream'.Seq.cons_append | [
{
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660,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
657,
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Mathlib/RingTheory/Ideal/LocalRing.lean | LocalRing.isLocalRingHom_residue | [
{
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"state_before": "R : Type u\nS : Type v\nT : ... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Bitvec/Lemmas.lean | Bitvec.bitsToNat_toList | [] | [
26,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Bounded.lean | Set.unbounded_le_inter_lt | [
{
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"state_before": "α : Type u_1\nr : α → α → Prop\ns t : Set α\ninst✝ : LinearOrder α\na : α\n⊢ Unbounded (fun x x_1 => x ≤ x_1) (s ∩ {b | a < b}) ↔ Unboun... | [
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Differentiable.sinh | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.closedBall_eq_bInter_ball | [
{
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Mathlib/Algebra/Order/Monoid/Lemmas.lean | lt_mul_of_one_lt_of_lt | [] | [
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40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
911,
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Mathlib/Topology/Order/Basic.lean | exists_seq_tendsto_sInf | [] | [
2202,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Adjunction/Basic.lean | CategoryTheory.Adjunction.he' | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nF : C ⥤ D\nG : D ⥤ C\nF_obj : C → D\ne : (X : C) → (Y : D) → (F_obj X ⟶ Y) ≃ (X ⟶ G.obj Y)\nhe : ∀ (X : C) (Y Y' : D) (g : Y ⟶ Y') (h : F_obj X ⟶ Y), ↑(e X Y') (h ≫ g) = ↑(e X Y) h ≫ G.map g\nX : C\nY Y' : D\nf : X ⟶ G.obj Y\ng... | [
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Mathlib/Data/Set/Ncard.lean | Set.ncard_lt_ncard | [
{
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"state_before": "α : Type u_1\nβ : Type ?u.71247\ns t : Set α\na b x y : α\nf : α →... | [
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41
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342,
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Mathlib/Data/Sum/Interval.lean | Sum.Icc_inl_inr | [] | [
159,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
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Mathlib/Algebra/Order/UpperLower.lean | IsLowerSet.mul_right | [] | [
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22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Module/LocalizedModule.lean | IsLocalizedModule.mk'_eq_zero' | [
{
"state_after": "no goals",
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1032,
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Mathlib/Tactic/CancelDenoms.lean | CancelDenoms.cancel_factors_lt | [
{
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Mathlib/Algebra/GroupWithZero/Units/Basic.lean | isUnit_zero_iff | [
{
"state_after": "no goals",
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"tactic": "rwa [zero_mul] at a0... | [
73,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/SetTheory/ZFC/Basic.lean | PSet.Equiv.exists_right | [] | [
167,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
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Mathlib/Algebra/Order/Module.lean | smul_le_smul_of_nonpos | [
{
"state_after": "k : Type u_2\nM : Type u_1\nN : Type ?u.12824\ninst✝³ : OrderedRing k\ninst✝² : OrderedAddCommGroup M\ninst✝¹ : Module k M\ninst✝ : OrderedSMul k M\na b : M\nc : k\nh : a ≤ b\nhc : c ≤ 0\n⊢ -c • a ≤ -c • b",
"state_before": "k : Type u_2\nM : Type u_1\nN : Type ?u.12824\ninst✝³ : OrderedRi... | [
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Mathlib/Data/Set/Lattice.lean | Set.biUnion_range | [] | [
1678,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1677,
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Mathlib/Order/Bounds/Basic.lean | IsLUB.exists_between' | [] | [
1129,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1127,
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] |
Mathlib/Algebra/Order/Group/Defs.lean | Left.one_le_inv_iff | [
{
"state_after": "α : Type u\ninst✝² : Group α\ninst✝¹ : LE α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b c d : α\n⊢ a * 1 ≤ a * a⁻¹ ↔ a ≤ 1",
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111,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
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Mathlib/Topology/Instances/Matrix.lean | Summable.matrix_conjTranspose | [] | [
325,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
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Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Embedding.subtype_comp_codRestrict | [] | [
944,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
942,
1
] |
Mathlib/Data/Matrix/Notation.lean | Matrix.tail_val' | [
{
"state_after": "case h\nα : Type u\no n m : ℕ\nm' : Type uₘ\nn' : Type uₙ\no' : Type uₒ\na b : ℕ\nB : Fin (Nat.succ m) → n' → α\nj : n'\nx✝ : Fin m\n⊢ vecTail (fun i => B i j) x✝ = vecTail B x✝ j",
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Computability/EpsilonNFA.lean | εNFA.accept_one | [] | [
260,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Data/Analysis/Topology.lean | Ctop.Realizer.ofEquiv_F | [
{
"state_after": "α : Type u_1\nβ : Type ?u.24148\nσ : Type ?u.24151\nτ : Type u_3\ninst✝ : TopologicalSpace α\nF : Realizer α\nE : F.σ ≃ τ\ns : τ\n⊢ f { σ := τ, F := Ctop.ofEquiv E F.F, eq := (_ : toTopsp (Ctop.ofEquiv E F.F) = inst✝) }.F s = f F.F (↑E.symm s)",
"state_before": "α : Type u_1\nβ : Type ?u.2... | [
208,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | norm_eq_sqrt_real_inner | [] | [
1005,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1004,
1
] |
Mathlib/RingTheory/WittVector/Defs.lean | WittVector.ext | [
{
"state_after": "case mk'\np : ℕ\nR : Type u_1\ny : 𝕎 R\ncoeff✝ : ℕ → R\nh : ∀ (n : ℕ), coeff { coeff := coeff✝ } n = coeff y n\n⊢ { coeff := coeff✝ } = y",
"state_before": "p : ℕ\nR : Type u_1\nx y : 𝕎 R\nh : ∀ (n : ℕ), coeff x n = coeff y n\n⊢ x = y",
"tactic": "cases x"
},
{
"state_after":... | [
87,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Analysis/Complex/ReImTopology.lean | Complex.interior_setOf_le_im | [
{
"state_after": "no goals",
"state_before": "a : ℝ\n⊢ interior {z | a ≤ z.im} = {z | a < z.im}",
"tactic": "simpa only [interior_Ici] using interior_preimage_im (Ici a)"
}
] | [
113,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Std/Data/Int/Lemmas.lean | Int.mul_pos | [
{
"state_after": "a b : Int\nha : 0 < a\nhb : 0 < b\nn : Nat\nhn : a = ↑(succ n)\n⊢ 0 < a * b",
"state_before": "a b : Int\nha : 0 < a\nhb : 0 < b\n⊢ 0 < a * b",
"tactic": "let ⟨n, hn⟩ := eq_succ_of_zero_lt ha"
},
{
"state_after": "a b : Int\nha : 0 < a\nhb : 0 < b\nn : Nat\nhn : a = ↑(succ n)\n... | [
652,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
649,
11
] |
Mathlib/Analysis/Complex/UnitDisc/Basic.lean | Complex.UnitDisc.conj_mul | [] | [
248,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.isUnit_to_basicOpen_self | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : CommRing R\nf : R\n⊢ ↑(toOpen R (PrimeSpectrum.basicOpen f)) f *\n const R 1 f (PrimeSpectrum.basicOpen f)\n (_ : ∀ (x : ↑(PrimeSpectrum.Top R)), x ∈ PrimeSpectrum.basicOpen f → x ∈ PrimeSpectrum.basicOpen f) =\n 1",
"tacti... | [
467,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.pow_zero | [
{
"state_after": "no goals",
"state_before": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na : R\n⊢ a ^ 0 = Nat.rawCast 1 + 0",
"tactic": "simp"
}
] | [
796,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | PosMulMono.toPosMulReflectLT | [] | [
312,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | EuclideanGeometry.angle_eq_angle_of_angle_eq_pi_of_angle_eq_pi | [
{
"state_after": "no goals",
"state_before": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\np1 p2 p3 p4 p5 : P\nhapc : ∠ p1 p5 p3 = π\nhbpd : ∠ p2 p5 p4 = π\n⊢ ∠ p1 p5 p2 = ∠ p3 p5 p4",
"tactic": "linarith ... | [
204,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Ring.lean | summable_mul_left_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\nκ : Type ?u.13116\nR : Type ?u.13119\nα : Type u_1\ninst✝² : DivisionSemiring α\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSemiring α\nf g : ι → α\na a₁ a₂ : α\nh : a ≠ 0\nH : Summable fun i => a * f i\n⊢ Summable f",
"tactic": "simpa onl... | [
105,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.mk_bit1 | [
{
"state_after": "case h\nn✝ m✝ m n : ℕ\ninst✝ : NeZero n\nh : bit1 m < n\n⊢ ↑{ val := bit1 m, isLt := h } = ↑(bit1 { val := m, isLt := (_ : m < n) })",
"state_before": "n✝ m✝ m n : ℕ\ninst✝ : NeZero n\nh : bit1 m < n\n⊢ { val := bit1 m, isLt := h } = bit1 { val := m, isLt := (_ : m < n) }",
"tactic": "... | [
777,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
772,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.op_norm_le_of_ball | [
{
"state_after": "case intro\n𝕜 : Type u_1\n𝕜₂ : Type u_2\n𝕜₃ : Type ?u.354772\nE : Type u_3\nEₗ : Type ?u.354778\nF : Type u_4\nFₗ : Type ?u.354784\nG : Type ?u.354787\nGₗ : Type ?u.354790\n𝓕 : Type ?u.354793\ninst✝¹⁷ : SeminormedAddCommGroup E\ninst✝¹⁶ : SeminormedAddCommGroup Eₗ\ninst✝¹⁵ : SeminormedAddC... | [
240,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Data/List/Basic.lean | List.bind_append | [] | [
538,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
536,
1
] |
Mathlib/Topology/FiberBundle/Basic.lean | FiberPrebundle.inducing_totalSpaceMk_of_inducing_comp | [
{
"state_after": "ι : Type ?u.63469\nB : Type u_2\nF : Type u_3\nX : Type ?u.63478\ninst✝³ : TopologicalSpace X\nE : B → Type u_1\ninst✝² : TopologicalSpace B\ninst✝¹ : TopologicalSpace F\ninst✝ : (x : B) → TopologicalSpace (E x)\na : FiberPrebundle F E\ne : Pretrivialization F TotalSpace.proj\nb : B\nh : Induc... | [
886,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
877,
1
] |
Mathlib/Topology/Separation.lean | IsCompact.finite_compact_cover | [
{
"state_after": "case empty\nα : Type u\nβ : Type v\ninst✝³ : TopologicalSpace α\nγ : Type ?u.134916\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : T2Space α\ns✝ : Set α\nhs✝ : IsCompact s✝\nι : Type u_1\nt : Finset ι\nU✝ : ι → Set α\nhU✝ : ∀ (i : ι), i ∈ t → IsOpen (U✝ i)\nhsC✝ : s✝ ⊆ ⋃ (i... | [
1373,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1352,
1
] |
Mathlib/Order/Basic.lean | le_trans' | [] | [
75,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Algebra/Group/Basic.lean | leftInverse_mul_left_div | [] | [
861,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
860,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.bounded_iff_isBounded | [
{
"state_after": "α : Type u\nβ : Type v\nX : Type ?u.467547\nι : Type ?u.467550\ninst✝ : PseudoMetricSpace α\nx : α\ns✝ t : Set α\nr : ℝ\ns : Set α\n⊢ Bounded s ↔ sᶜ ∈ (cobounded α).sets",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.467547\nι : Type ?u.467550\ninst✝ : PseudoMetricSpace α\nx : α\ns... | [
2300,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2298,
1
] |
Mathlib/Analysis/Calculus/TangentCone.lean | UniqueDiffOn.inter | [] | [
327,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | IntervalIntegrable.norm | [] | [
178,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.mk_eq_mk | [] | [
192,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Data/PFunctor/Multivariate/M.lean | MvPFunctor.M.bisim₀ | [
{
"state_after": "n : ℕ\nP : MvPFunctor (n + 1)\nα : TypeVec n\nR : M P α → M P α → Prop\nh₀ : Equivalence R\nh : ∀ (x y : M P α), R x y → (TypeVec.id ::: Quot.mk R) <$$> dest P x = (TypeVec.id ::: Quot.mk R) <$$> dest P y\nx y : M P α\nr : R x y\n⊢ ∀ (x y : M P α),\n R x y →\n ∃ a f f₁ f₂,\n des... | [
347,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.tail_def | [] | [
66,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Data/PFun.lean | PFun.image_inter | [] | [
417,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.snorm'_lim_le_liminf_snorm' | [
{
"state_after": "α : Type u_2\nE✝ : Type ?u.8107923\nF : Type ?u.8107926\nG : Type ?u.8107929\nm m0 : MeasurableSpace α\np✝ : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝³ : NormedAddCommGroup E✝\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedAddCommGroup G\nE : Type u_1\ninst✝ : NormedAddCommGroup E\nf : ℕ → α → E\np ... | [
1192,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1178,
1
] |
Std/Data/List/Lemmas.lean | List.get_append_right_aux | [
{
"state_after": "α : Type u_1\nl₁ l₂ : List α\nn : Nat\nh₁ : length l₁ ≤ n\nh₂ : n < length l₁ + length l₂\n⊢ n - length l₁ < length l₂",
"state_before": "α : Type u_1\nl₁ l₂ : List α\nn : Nat\nh₁ : length l₁ ≤ n\nh₂ : n < length (l₁ ++ l₂)\n⊢ n - length l₁ < length l₂",
"tactic": "rw [length_append] a... | [
603,
40
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
600,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.power_le_power_left | [
{
"state_after": "case mk.mk.mk.intro\nα✝ β✝ : Type u\na✝ : Cardinal\nα : Type u_1\nb✝ : Cardinal\nβ : Type u_1\nc✝ : Cardinal\nγ : Type u_1\nhα : Quot.mk Setoid.r α ≠ 0\ne : β ↪ γ\n⊢ Quot.mk Setoid.r α ^ Quot.mk Setoid.r β ≤ Quot.mk Setoid.r α ^ Quot.mk Setoid.r γ",
"state_before": "α β : Type u\n⊢ ∀ {a b ... | [
721,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
718,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | edist_le_coe | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.20756\nι : Type ?u.20759\ninst✝ : PseudoMetricSpace α\nx y : α\nc : ℝ≥0\n⊢ edist x y ≤ ↑c ↔ nndist x y ≤ c",
"tactic": "rw [edist_nndist, ENNReal.coe_le_coe]"
}
] | [
338,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/Analysis/InnerProductSpace/EuclideanDist.lean | Euclidean.closedBall_eq_preimage | [] | [
70,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Order/Monotone/Basic.lean | Int.rel_of_forall_rel_succ_of_le | [] | [
1052,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1050,
1
] |
Mathlib/Logic/Function/Iterate.lean | Function.Commute.iterate_self | [] | [
155,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.add_comp | [
{
"state_after": "case h\nR₁ : Type u_5\nR₂ : Type u_2\nR₃ : Type u_3\ninst✝¹⁸ : Semiring R₁\ninst✝¹⁷ : Semiring R₂\ninst✝¹⁶ : Semiring R₃\nσ₁₂ : R₁ →+* R₂\nσ₂₃ : R₂ →+* R₃\nσ₁₃ : R₁ →+* R₃\nM₁ : Type u_6\ninst✝¹⁵ : TopologicalSpace M₁\ninst✝¹⁴ : AddCommMonoid M₁\nM'₁ : Type ?u.524611\ninst✝¹³ : TopologicalSpac... | [
828,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
825,
1
] |
Mathlib/Analysis/SpecificLimits/Basic.lean | dist_le_of_le_geometric_two_of_tendsto | [
{
"state_after": "case h.e'_4\nα : Type u_1\nβ : Type ?u.457947\nι : Type ?u.457950\ninst✝ : PseudoMetricSpace α\nr C : ℝ\nhr : r < 1\nf : ℕ → α\nhu : ∀ (n : ℕ), dist (f n) (f (n + 1)) ≤ C * r ^ n\nhu₂ : ∀ (n : ℕ), dist (f n) (f (n + 1)) ≤ C / 2 / 2 ^ n\na : α\nha : Tendsto f atTop (𝓝 a)\nn : ℕ\n⊢ C / 2 ^ n = ... | [
427,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/Analysis/MeanInequalitiesPow.lean | ENNReal.rpow_arith_mean_le_arith_mean2_rpow | [
{
"state_after": "case refine_2\nι : Type u\ns : Finset ι\nw₁ w₂ z₁ z₂ : ℝ≥0∞\nhw' : w₁ + w₂ = 1\np : ℝ\nhp : 1 ≤ p\nh :\n (∑ i : Fin (Nat.succ (Nat.succ 0)), Matrix.vecCons w₁ ![w₂] i * Matrix.vecCons z₁ ![z₂] i) ^ p ≤\n ∑ i : Fin (Nat.succ (Nat.succ 0)), Matrix.vecCons w₁ ![w₂] i * Matrix.vecCons z₁ ![z₂]... | [
291,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_strictMono | [] | [
94,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Computability/Reduce.lean | ManyOneEquiv.of_equiv | [] | [
240,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroObjects.lean | CategoryTheory.Limits.IsZero.to_eq | [] | [
68,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.ball_eq_emptyset | [
{
"state_after": "case h\nR : Type ?u.1149982\nR' : Type ?u.1149985\n𝕜 : Type u_1\n𝕜₂ : Type ?u.1149991\n𝕜₃ : Type ?u.1149994\n𝕝 : Type ?u.1149997\nE : Type u_2\nE₂ : Type ?u.1150003\nE₃ : Type ?u.1150006\nF : Type ?u.1150009\nG : Type ?u.1150012\nι : Type ?u.1150015\ninst✝⁶ : SeminormedRing 𝕜\ninst✝⁵ : Ad... | [
911,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
908,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | InnerProductSpace.Core.inner_self_ofReal_re | [
{
"state_after": "𝕜 : Type u_1\nE : Type ?u.547403\nF : Type u_2\ninst✝² : IsROrC 𝕜\ninst✝¹ : AddCommGroup F\ninst✝ : Module 𝕜 F\nc : Core 𝕜 F\nx : F\n⊢ ↑re ↑(↑re (inner x x)) = ↑re (inner x x) ∧ ↑im ↑(↑re (inner x x)) = 0",
"state_before": "𝕜 : Type u_1\nE : Type ?u.547403\nF : Type u_2\ninst✝² : IsRO... | [
276,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infiniteNeg_mul_of_not_infinitesimal_pos_infiniteNeg | [
{
"state_after": "x y : ℝ*\nhx : ¬Infinitesimal x\nhp : 0 < x\nhy : InfiniteNeg y\n⊢ InfiniteNeg (y * x)",
"state_before": "x y : ℝ*\nhx : ¬Infinitesimal x\nhp : 0 < x\nhy : InfiniteNeg y\n⊢ InfiniteNeg (x * y)",
"tactic": "rw [mul_comm]"
},
{
"state_after": "no goals",
"state_before": "x y ... | [
859,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
857,
1
] |
Mathlib/Topology/SubsetProperties.lean | isCompact_iff_isCompact_univ | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Type ?u.94686\nπ : ι → Type ?u.94691\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns✝ t s : Set α\n⊢ IsCompact s ↔ IsCompact univ",
"tactic": "rw [isCompact_iff_isCompact_in_subtype, image_univ, Subtype.range_coe]"
}... | [
915,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
914,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | LinearMap.lTensor_zero | [] | [
1048,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1047,
1
] |
Mathlib/Data/Vector.lean | Vector.map_nil | [] | [
136,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Data/Set/Finite.lean | Set.exists_upper_bound_image | [] | [
1467,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1465,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffAt.restrict_scalars | [] | [
2228,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2227,
1
] |
Mathlib/Data/List/Perm.lean | List.Perm.inter_append | [
{
"state_after": "case nil\nα : Type uu\nβ : Type vv\nl₁ l₂ : List α\ninst✝ : DecidableEq α\nt₁ t₂ : List α\nh : Disjoint t₁ t₂\n⊢ [] ∩ (t₁ ++ t₂) ~ [] ∩ t₁ ++ [] ∩ t₂\n\ncase cons\nα : Type uu\nβ : Type vv\nl₁ l₂ : List α\ninst✝ : DecidableEq α\nt₁ t₂ : List α\nh : Disjoint t₁ t₂\nhead✝ : α\ntail✝ : List α\nta... | [
1036,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1021,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesOnBall.tendstoUniformlyOn' | [
{
"state_after": "case h.e'_6\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.994563\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf g : E ... | [
849,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
843,
1
] |
Mathlib/Combinatorics/SimpleGraph/Matching.lean | SimpleGraph.Subgraph.isPerfectMatching_iff_forall_degree | [
{
"state_after": "no goals",
"state_before": "V : Type u\nG : SimpleGraph V\nM✝ M : Subgraph G\ninst✝ : (v : V) → Fintype ↑(neighborSet M v)\n⊢ IsPerfectMatching M ↔ ∀ (v : V), degree M v = 1",
"tactic": "simp [degree_eq_one_iff_unique_adj, isPerfectMatching_iff]"
}
] | [
127,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.pred_strictMono | [] | [
722,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
722,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.reindex_apply | [
{
"state_after": "no goals",
"state_before": "ι : Type u_4\nι' : Type u_2\nR : Type u_3\nR₂ : Type ?u.344299\nK : Type ?u.344302\nM : Type u_1\nM' : Type ?u.344308\nM'' : Type ?u.344311\nV : Type u\nV' : Type ?u.344316\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\ninst✝¹ : AddCommMono... | [
423,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_iff_le_map | [] | [
205,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Std/Data/String/Lemmas.lean | String.revPosOf_eq | [] | [
319,
69
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
319,
1
] |
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