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/Factorial/Basic.lean | Nat.ascFactorial_succ | [] | [
247,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
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Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.ringHom_ext' | [] | [
789,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
784,
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] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.toRingHom_eq_coe | [] | [
685,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
684,
1
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Mathlib/Analysis/Calculus/BumpFunctionInner.lean | expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul | [
{
"state_after": "case inl\np : ℝ[X]\nx : ℝ\nhx : x < 0\n⊢ HasDerivAt (fun x => Polynomial.eval x⁻¹ p * expNegInvGlue x)\n (Polynomial.eval x⁻¹ (X ^ 2 * (p - ↑derivative p)) * expNegInvGlue x) x\n\ncase inr.inl\np : ℝ[X]\n⊢ HasDerivAt (fun x => Polynomial.eval x⁻¹ p * expNegInvGlue x)\n (Polynomial.eval 0... | [
138,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Init/Data/Nat/Lemmas.lean | Nat.one_le_bit0 | [] | [
206,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/InnerProductSpace/Calculus.lean | ContDiffOn.dist | [] | [
211,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
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Mathlib/FieldTheory/IsAlgClosed/Basic.lean | IsAlgClosed.exists_pow_nat_eq | [
{
"state_after": "k : Type u\ninst✝¹ : Field k\ninst✝ : IsAlgClosed k\nx : k\nn : ℕ\nhn : 0 < n\nthis : degree (X ^ n - ↑C x) ≠ 0\n⊢ ∃ z, z ^ n = x",
"state_before": "k : Type u\ninst✝¹ : Field k\ninst✝ : IsAlgClosed k\nx : k\nn : ℕ\nhn : 0 < n\n⊢ ∃ z, z ^ n = x",
"tactic": "have : degree (X ^ n - C x) ... | [
92,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Hom/GroupAction.lean | DistribMulActionHom.toMulActionHom_injective | [
{
"state_after": "case a\nM' : Type ?u.113752\nX : Type ?u.113755\ninst✝²³ : SMul M' X\nY : Type ?u.113762\ninst✝²² : SMul M' Y\nZ : Type ?u.113769\ninst✝²¹ : SMul M' Z\nM : Type u_1\ninst✝²⁰ : Monoid M\nA : Type u_2\ninst✝¹⁹ : AddMonoid A\ninst✝¹⁸ : DistribMulAction M A\nA' : Type ?u.113810\ninst✝¹⁷ : AddGroup... | [
296,
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Mathlib/Order/SuccPred/IntervalSucc.lean | Antitone.pairwise_disjoint_on_Ioo_pred | [] | [
142,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
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Mathlib/Data/Real/Basic.lean | Real.exists_isLUB | [
{
"state_after": "case intro.intro\nx y : ℝ\nS : Set ℝ\nL : ℝ\nhL : L ∈ S\nU : ℝ\nhU : U ∈ upperBounds S\n⊢ ∃ x, IsLUB S x",
"state_before": "x y : ℝ\nS : Set ℝ\nhne : Set.Nonempty S\nhbdd : BddAbove S\n⊢ ∃ x, IsLUB S x",
"tactic": "rcases hne, hbdd with ⟨⟨L, hL⟩, ⟨U, hU⟩⟩"
},
{
"state_after": "... | [
730,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
682,
1
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.toGerm_injective | [
{
"state_after": "no goals",
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"ta... | [
387,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/Dynamics/Ergodic/Ergodic.lean | Ergodic.ae_empty_or_univ_of_ae_le_preimage' | [
{
"state_after": "case h_fin\nα : Type u_1\nm : MeasurableSpace α\nf : α → α\ns : Set α\nμ : MeasureTheory.Measure α\nhf : Ergodic f\nhs : MeasurableSet s\nhs' : s ≤ᶠ[ae μ] f ⁻¹' s\nh_fin : ↑↑μ s ≠ ⊤\n⊢ ↑↑μ (f ⁻¹' s) ≠ ⊤\n\nα : Type u_1\nm : MeasurableSpace α\nf : α → α\ns : Set α\nμ : MeasureTheory.Measure α\n... | [
151,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Data/Matrix/Basic.lean | Matrix.smul_mulVec_assoc | [
{
"state_after": "case h\nl : Type ?u.851375\nm : Type u_3\nn : Type u_1\no : Type ?u.851384\nm' : o → Type ?u.851389\nn' : o → Type ?u.851394\nR : Type u_2\nS : Type ?u.851400\nα : Type v\nβ : Type w\nγ : Type ?u.851407\ninst✝⁴ : NonUnitalNonAssocSemiring α\ninst✝³ : Fintype n\ninst✝² : Monoid R\ninst✝¹ : Dist... | [
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Mathlib/Order/BoundedOrder.lean | subsingleton_of_bot_eq_top | [] | [
683,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
682,
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Mathlib/Data/Finset/Pointwise.lean | Finset.subset_vsub | [] | [
1560,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1558,
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Mathlib/Topology/Order/Basic.lean | Ioo_mem_nhdsWithin_Ioi' | [] | [
403,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
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Mathlib/Topology/Order/Basic.lean | Continuous.if_le | [] | [
663,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
660,
1
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Mathlib/Algebra/Ring/Regular.lean | isRegular_iff_ne_zero' | [
{
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"state_before": "α : Type u_1\ninst✝² : Nontrivial α\ninst✝¹ : NonUnitalNonAssocRing α\ninst✝ : NoZeroDivisors α\nk : α\nh : IsRegular k\n⊢ k ≠ 0",
"tactic": "rin... | [
49,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
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Mathlib/Data/Sym/Sym2.lean | Sym2.isDiag_iff_mem_range_diag | [] | [
461,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
460,
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Mathlib/Algebra/BigOperators/Order.lean | Finset.prod_mono_set' | [] | [
414,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
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Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Hom.comp_codRestrict | [] | [
813,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Data/Real/ENNReal.lean | ENNReal.sub_top | [] | [
1108,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1108,
1
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Mathlib/CategoryTheory/Adjunction/Basic.lean | CategoryTheory.Adjunction.homEquiv_apply_eq | [
{
"state_after": "case refl\nC : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nF : C ⥤ D\nG : D ⥤ C\nadj : F ⊣ G\nX' X : C\nY Y' : D\nA : C\nB : D\nf : F.obj A ⟶ B\n⊢ f = ↑(homEquiv adj A B).symm (↑(homEquiv adj A B) f)",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝... | [
223,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
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Mathlib/Logic/Embedding/Basic.lean | Function.Embedding.coe_quotientOut | [] | [
246,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
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Mathlib/Data/PNat/Xgcd.lean | PNat.XgcdType.reduce_isReduced' | [] | [
374,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/LinearAlgebra/Span.lean | LinearMap.toSpanSingleton_one | [] | [
927,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
926,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | BoundedContinuousFunction.coeFn_toLp | [] | [
1656,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1654,
1
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Mathlib/Data/Real/NNReal.lean | NNReal.iSup_div | [
{
"state_after": "no goals",
"state_before": "ι : Sort u_1\nf✝ f : ι → ℝ≥0\na : ℝ≥0\n⊢ (⨆ (i : ι), f i) / a = ⨆ (i : ι), f i / a",
"tactic": "simp only [div_eq_mul_inv, iSup_mul]"
}
] | [
973,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
972,
1
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Mathlib/GroupTheory/Submonoid/Basic.lean | Submonoid.closure_mono | [] | [
430,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
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Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.ratio_le_opNorm | [] | [
278,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/RingTheory/ReesAlgebra.lean | adjoin_monomial_eq_reesAlgebra | [
{
"state_after": "case a\nR M : Type u\ninst✝² : CommRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nI : Ideal R\n⊢ Algebra.adjoin R ↑(Submodule.map (monomial 1) I) ≤ reesAlgebra I\n\ncase a\nR M : Type u\ninst✝² : CommRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nI : Ideal R\n⊢ reesAlgebra I ≤ Alge... | [
111,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
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Mathlib/RingTheory/WittVector/Defs.lean | WittVector.constantCoeff_wittMul | [
{
"state_after": "p : ℕ\nR : Type ?u.121832\nhp : Fact (Nat.Prime p)\ninst✝ : CommRing R\nn : ℕ\n⊢ ↑constantCoeff (X 0 * X 1) = 0",
"state_before": "p : ℕ\nR : Type ?u.121832\nhp : Fact (Nat.Prime p)\ninst✝ : CommRing R\nn : ℕ\n⊢ ↑constantCoeff (wittMul p n) = 0",
"tactic": "apply constantCoeff_wittStru... | [
308,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.integral_add_compl | [] | [
167,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Order/CompleteLattice.lean | sup_sInf_le_iInf_sup | [] | [
1922,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1921,
1
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src/lean/Init/Control/StateCps.lean | StateCpsT.runK_set | [] | [
55,
139
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
55,
9
] |
Mathlib/RingTheory/Subring/Pointwise.lean | Subring.smul_mem_pointwise_smul_iff | [] | [
114,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.norm_of_nonneg | [] | [
692,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.Equiv.refl | [] | [
608,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
607,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Products.lean | CategoryTheory.Limits.fan_mk_proj | [] | [
91,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Data/Nat/Size.lean | Nat.shiftl'_ne_zero_left | [
{
"state_after": "no goals",
"state_before": "b : Bool\nm : ℕ\nh : m ≠ 0\nn : ℕ\n⊢ shiftl' b m n ≠ 0",
"tactic": "induction n <;> simp [bit_ne_zero, shiftl', *]"
}
] | [
63,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
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Mathlib/LinearAlgebra/LinearPMap.lean | Submodule.existsUnique_from_graph | [
{
"state_after": "case refine'_1\nR : Type u_1\ninst✝⁶ : Ring R\nE : Type u_3\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module R E\nF : Type u_2\ninst✝³ : AddCommGroup F\ninst✝² : Module R F\nG : Type ?u.618707\ninst✝¹ : AddCommGroup G\ninst✝ : Module R G\ng : Submodule R (E × F)\nhg : ∀ {x : E × F}, x ∈ g → x.fst = 0... | [
936,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
926,
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | HasFDerivAt.lim | [
{
"state_after": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.219286\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.219381\... | [
469,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biproduct.matrix_π | [
{
"state_after": "case w\nJ : Type\ninst✝⁴ : Fintype J\nK : Type\ninst✝³ : Fintype K\nC : Type u\ninst✝² : Category C\ninst✝¹ : HasZeroMorphisms C\ninst✝ : HasFiniteBiproducts C\nf : J → C\ng : K → C\nm : (j : J) → (k : K) → f j ⟶ g k\nk : K\nj✝ : J\n⊢ ι (fun j => f j) j✝ ≫ matrix m ≫ π g k = ι (fun j => f j) j... | [
833,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
830,
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Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.StableUnderComposition.diagonal | [
{
"state_after": "C : Type u\ninst✝² : Category C\nD : Type ?u.77182\ninst✝¹ : Category D\ninst✝ : HasPullbacks C\nP : MorphismProperty C\nhP : StableUnderComposition P\nhP' : RespectsIso P\nhP'' : StableUnderBaseChange P\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\nh₁ : MorphismProperty.diagonal P f\nh₂ : MorphismPropert... | [
546,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
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] |
Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingHom.cancel_right | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.48360\nα : Type u_3\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.48372\ninst✝⁷ : NonAssocSemiring α\ninst✝⁶ : Preorder α\ninst✝⁵ : NonAssocSemiring β\ninst✝⁴ : Preorder β\ninst✝³ : NonAssocSemiring γ\ninst✝² : Preorder γ\ninst✝¹ : NonAssocSemiring δ\nins... | [
334,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
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Mathlib/Data/Real/Irrational.lean | irrational_nat_sub_iff | [] | [
573,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
572,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_multiset_count_of_subset | [
{
"state_after": "ι : Type ?u.595257\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf g : α → β\ninst✝² : CommMonoid β\ninst✝¹ : DecidableEq α\ninst✝ : CommMonoid α\nm : Multiset α\ns : Finset α\n⊢ Multiset.toFinset m ⊆ s → Multiset.prod m = ∏ i in s, i ^ Multiset.count i m",
"state_before... | [
1339,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1334,
1
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Mathlib/MeasureTheory/Measure/Haar/NormedSpace.lean | MeasureTheory.Integrable.comp_mul_right' | [] | [
178,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
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Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.trailingDegree_zero | [] | [
88,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Topology/MetricSpace/ThickenedIndicator.lean | thickenedIndicatorAux_one | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : PseudoEMetricSpace α\nδ : ℝ\nE : Set α\nx : α\nx_in_E : x ∈ E\n⊢ thickenedIndicatorAux δ E x = 1",
"tactic": "simp [thickenedIndicatorAux, infEdist_zero_of_mem x_in_E, tsub_zero]"
}
] | [
89,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
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Mathlib/Analysis/Calculus/Deriv/Add.lean | differentiable_neg | [] | [
281,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.inv_def | [] | [
414,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Order/JordanHolder.lean | CompositionSeries.length_eq_zero_of_bot_eq_bot_of_top_eq_top_of_length_eq_zero | [
{
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"state_before": "X : Type u\ninst✝¹ : Lattice X\ninst✝ : JordanHolderLattice X\ns₁ s₂ : Com... | [
723,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
716,
1
] |
Mathlib/Topology/Order/Basic.lean | IsGLB.mem_of_isClosed | [] | [
2096,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2094,
1
] |
Mathlib/Data/Set/Intervals/Disjoint.lean | Set.iUnion_Ico_right | [
{
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"tactic": "simp only [← Ici_inter_Iio, ← inter_iUnion, iUnion_Iio, inter_univ]"
}
] | [
108,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
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Mathlib/Algebra/Order/Group/MinMax.lean | min_inv_inv' | [] | [
42,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
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Mathlib/Analysis/InnerProductSpace/Adjoint.lean | ContinuousLinearMap.adjointAux_apply | [] | [
81,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.mul_smul | [
{
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979,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
976,
1
] |
Mathlib/Data/List/OfFn.lean | List.ofFn_get | [
{
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"state_before": "α : Type u\na : α\nl : List α\n⊢ ofFn (get (a :: l)) = a :: l",
"tactic": "rw [ofFn_succ]"
},
{
"state_after": "case e_tail\nα : Type u\na : α\nl : List α\n⊢... | [
193,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Data/Set/Finite.lean | Set.iUnion_univ_pi_of_monotone | [] | [
1562,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1559,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.mul_apply | [] | [
198,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Dynamics/OmegaLimit.lean | mapsTo_omegaLimit | [] | [
112,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | tendstoLocallyUniformly_iff_filter | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝¹ : UniformSpace β\nF : ι → α → β\nf : α → β\ns s' : Set α\nx : α\np : Filter ι\np' : Filter α\ng : ι → α\ninst✝ : TopologicalSpace α\n⊢ TendstoLocallyUniformly F f p ↔ ∀ (x : α), TendstoUniformlyOnFilter F f ... | [
771,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
768,
1
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Mathlib/MeasureTheory/Integral/SetIntegral.lean | ContinuousLinearMap.integral_comp_L1_comm | [] | [
1123,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1121,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | lt_mul_of_one_lt_of_lt' | [] | [
925,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
922,
1
] |
Mathlib/Data/FunLike/Basic.lean | FunLike.congr_arg | [] | [
221,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
11
] |
Mathlib/Algebra/Algebra/Subalgebra/Pointwise.lean | Subalgebra.pointwise_smul_toSubsemiring | [] | [
96,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Data/Set/NAry.lean | Set.image2_subset | [
{
"state_after": "case intro.intro.intro.intro\nα : Type u_1\nα' : Type ?u.1411\nβ : Type u_2\nβ' : Type ?u.1417\nγ : Type u_3\nγ' : Type ?u.1423\nδ : Type ?u.1426\nδ' : Type ?u.1429\nε : Type ?u.1432\nε' : Type ?u.1435\nζ : Type ?u.1438\nζ' : Type ?u.1441\nν : Type ?u.1444\nf f' : α → β → γ\ng g' : α → β → γ →... | [
61,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/CategoryTheory/Preadditive/Biproducts.lean | CategoryTheory.Limits.biproduct.map_matrix | [
{
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270,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
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Mathlib/Data/Finset/Lattice.lean | Finset.ofDual_sup | [] | [
497,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
495,
1
] |
Mathlib/Data/Set/Intervals/Group.lean | Set.sub_mem_Ico_iff_left | [] | [
108,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.rescale_rescale | [
{
"state_after": "case h\nR : Type u_1\ninst✝ : CommSemiring R\nf : PowerSeries R\na b : R\nn : ℕ\n⊢ ↑(coeff R n) (↑(rescale b) (↑(rescale a) f)) = ↑(coeff R n) (↑(rescale (a * b)) f)",
"state_before": "R : Type u_1\ninst✝ : CommSemiring R\nf : PowerSeries R\na b : R\n⊢ ↑(rescale b) (↑(rescale a) f) = ↑(res... | [
1794,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1790,
1
] |
Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.toNatOrdinal_symm_eq | [] | [
155,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Data/Int/ModEq.lean | Int.modEq_and_modEq_iff_modEq_mul | [
{
"state_after": "m✝ n✝ a✝ b✝ c d a b m n : ℤ\nhmn : Nat.coprime (natAbs m) (natAbs n)\nh : m ∣ b - a ∧ n ∣ b - a\n⊢ a ≡ b [ZMOD m * n]",
"state_before": "m✝ n✝ a✝ b✝ c d a b m n : ℤ\nhmn : Nat.coprime (natAbs m) (natAbs n)\nh : a ≡ b [ZMOD m] ∧ a ≡ b [ZMOD n]\n⊢ a ≡ b [ZMOD m * n]",
"tactic": "rw [modE... | [
277,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/Init/Logic.lean | Implies.trans | [] | [
28,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
27,
15
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.lt_lift_iff | [] | [
831,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
826,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_finset_product | [
{
"state_after": "ι : Type ?u.317398\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf✝ g : α → β\ninst✝ : CommMonoid β\nr : Finset (γ × α)\ns : Finset γ\nt : γ → Finset α\nh : ∀ (p : γ × α), p ∈ r ↔ p.fst ∈ s ∧ p.snd ∈ t p.fst\nf : γ × α → β\n⊢ ∏ p in r, f p = ∏ x in Finset.sigma s t, f (x.fst... | [
606,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
599,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | powCoprime_inv | [] | [
993,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
991,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.comap_lift_eq2 | [] | [
125,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/RingTheory/PrincipalIdealDomain.lean | IsPrincipalIdealRing.of_surjective | [] | [
345,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/GroupTheory/Subsemigroup/Basic.lean | Subsemigroup.not_mem_bot | [] | [
193,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | lcm_mul_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : NormalizedGCDMonoid α\na b c : α\n⊢ lcm (b * a) (c * a) = lcm b c * ↑normalize a",
"tactic": "simp only [mul_comm, lcm_mul_left]"
}
] | [
835,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
834,
1
] |
Mathlib/Analysis/Convex/Integral.lean | Convex.average_mem | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.245931\nm0 : MeasurableSpace α\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : CompleteSpace E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace ℝ F\ninst✝¹ : CompleteSpace F\nμ : MeasureTheory.Measure α\ns : Set E\nt : Set α\nf : α... | [
94,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Std/Data/List/Lemmas.lean | List.infix_of_mem_join | [] | [
1707,
78
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1702,
1
] |
Mathlib/Order/CompleteBooleanAlgebra.lean | PUnit.sInf_eq | [] | [
406,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
1
] |
Mathlib/Algebra/Order/CompleteField.lean | LinearOrderedField.inducedMap_nonneg | [] | [
215,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Data/List/Forall2.lean | List.forall₂_cons | [
{
"state_after": "case cons\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.620\nδ : Type ?u.623\nR S : α → β → Prop\nP : γ → δ → Prop\nRₐ : α → α → Prop\na : α\nb : β\nl₁ : List α\nl₂ : List β\na✝¹ : R a b\na✝ : Forall₂ R l₁ l₂\n⊢ R a b ∧ Forall₂ R l₁ l₂",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.... | [
39,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.snd_pow_of_smul_comm | [
{
"state_after": "R : Type u\nM : Type v\ninst✝⁴ : Monoid R\ninst✝³ : AddMonoid M\ninst✝² : DistribMulAction R M\ninst✝¹ : DistribMulAction Rᵐᵒᵖ M\ninst✝ : SMulCommClass R Rᵐᵒᵖ M\nx : tsze R M\nn : ℕ\nh : op (fst x) • snd x = fst x • snd x\nthis : ∀ (n : ℕ), op (fst x ^ n) • snd x = fst x ^ n • snd x\n⊢ List.su... | [
628,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
609,
1
] |
Mathlib/Algebra/Module/Zlattice.lean | Zspan.fract_apply | [] | [
117,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.Tape.mk'_nth_nat | [
{
"state_after": "no goals",
"state_before": "Γ : Type u_1\ninst✝ : Inhabited Γ\nL R : ListBlank Γ\nn : ℕ\n⊢ nth (mk' L R) ↑n = ListBlank.nth R n",
"tactic": "rw [← Tape.right₀_nth, Tape.mk'_right₀]"
}
] | [
629,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
627,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.le_comap_map | [] | [
1662,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1661,
1
] |
Mathlib/LinearAlgebra/FreeModule/PID.lean | eq_bot_of_generator_maximal_map_eq_zero | [
{
"state_after": "R : Type u\nM : Type v\ninst✝³ : Ring R\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\nι : Type u_1\nb✝ b : Basis ι R M\nN : Submodule R M\nϕ : M →ₗ[R] R\nhϕ : ∀ (ψ : M →ₗ[R] R), ¬map ϕ N < map ψ N\ninst✝ : IsPrincipal (map ϕ N)\nhgen : generator (map ϕ N) = 0\n⊢ ∀ (x : M), x ∈ N → x = 0",
... | [
77,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.sign_pi_add | [
{
"state_after": "no goals",
"state_before": "θ : Angle\n⊢ sign (↑π + θ) = -sign θ",
"tactic": "rw [add_comm, sign_add_pi]"
}
] | [
880,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
880,
1
] |
Mathlib/Algebra/Lie/Abelian.lean | LieModule.coe_maxTrivEquiv_apply | [] | [
199,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Data/Multiset/Lattice.lean | Multiset.inf_ndinsert | [
{
"state_after": "α : Type u_1\ninst✝² : SemilatticeInf α\ninst✝¹ : OrderTop α\ninst✝ : DecidableEq α\na : α\ns : Multiset α\n⊢ ∀ (a_1 : α), a_1 ∈ ndinsert a s ↔ a_1 ∈ a ::ₘ s",
"state_before": "α : Type u_1\ninst✝² : SemilatticeInf α\ninst✝¹ : OrderTop α\ninst✝ : DecidableEq α\na : α\ns : Multiset α\n⊢ inf... | [
177,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Deprecated/Submonoid.lean | Multiplicative.isSubmonoid_iff | [] | [
81,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Combinatorics/SimpleGraph/Triangle/Basic.lean | SimpleGraph.farFromTriangleFree.mono | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\n𝕜 : Type u_2\ninst✝¹ : Fintype α\ninst✝ : LinearOrderedField 𝕜\nG H : SimpleGraph α\nε δ : 𝕜\nn : ℕ\ns : Finset α\nhε : FarFromTriangleFree G ε\nh : δ ≤ ε\n⊢ δ * ↑(Fintype.card α ^ 2) ≤ ε * ↑(Fintype.card α ^ 2)",
"tactic": "gcongr"
}
] | [
58,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/GroupTheory/FreeAbelianGroup.lean | FreeAbelianGroup.sub_bind | [] | [
262,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Algebra/Module/Basic.lean | Units.neg_smul | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.106759\nR : Type u_1\nk : Type ?u.106765\nS : Type ?u.106768\nM : Type u_2\nM₂ : Type ?u.106774\nM₃ : Type ?u.106777\nι : Type ?u.106780\ninst✝² : Ring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nr s : R\nx✝ y : M\nu : Rˣ\nx : M\n⊢ -u • x = -(u •... | [
312,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/Algebra/Algebra/Bilinear.lean | LinearMap.commute_mulLeft_right | [
{
"state_after": "case h\nR : Type u_2\nA : Type u_1\ninst✝⁴ : CommSemiring R\ninst✝³ : NonUnitalSemiring A\ninst✝² : Module R A\ninst✝¹ : SMulCommClass R A A\ninst✝ : IsScalarTower R A A\na b c : A\n⊢ ↑(mulLeft R a * mulRight R b) c = ↑(mulRight R b * mulLeft R a) c",
"state_before": "R : Type u_2\nA : Typ... | [
140,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
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