file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurableSet_Ico | [] | [
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44
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521,
1
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Mathlib/ModelTheory/Satisfiability.lean | FirstOrder.Language.Formula.imp_semanticallyEquivalent_not_sup | [] | [
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56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/List/Perm.lean | List.Perm.refl | [] | [
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37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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11
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.prod_comp | [] | [
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31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1146,
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.op_norm_le_of_unit_norm | [
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Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.range_le | [] | [
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Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.adj_symm | [] | [
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Mathlib/Topology/Bases.lean | DenseRange.separableSpace | [] | [
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Mathlib/AlgebraicGeometry/PrimeSpectrum/Noetherian.lean | PrimeSpectrum.exists_primeSpectrum_prod_le_and_ne_bot_of_domain | [
{
"state_after": "R : Type u\ninst✝⁴ : CommRing R\ninst✝³ : IsNoetherianRing R\nA : Type u\ninst✝² : CommRing A\ninst✝¹ : IsDomain A\ninst✝ : IsNoetherianRing A\nh_fA : ¬IsField A\nI : Ideal A\n⊢ I ≠ ⊥ → ∃ Z, Multiset.prod (Multiset.map asIdeal Z) ≤ I ∧ Multiset.prod (Multiset.map asIdeal Z) ≠ ⊥",
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102,
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Mathlib/Algebra/Order/Sub/Defs.lean | eq_tsub_of_add_eq | [] | [
350,
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Mathlib/Data/Matrix/Block.lean | Matrix.toBlock_diagonal_disjoint | [
{
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Mathlib/Computability/Primrec.lean | Primrec.pair | [
{
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371,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Basic.lean | mem_closure_iff_frequently | [
{
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Mathlib/MeasureTheory/Function/Floor.lean | Nat.measurable_floor | [
{
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Mathlib/LinearAlgebra/Eigenspace/Basic.lean | Module.End.eigenspaces_independent | [
{
"state_after": "K R : Type v\nV M : Type w\ninst✝⁵ : CommRing R\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\ninst✝² : Field K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nf : End K V\nS : (Π₀ (μ : K), { x // x ∈ eigenspace f μ }) →ₗ[K] V := ↑(Dfinsupp.lsum ℕ) fun μ => Submodule.subtype (eigenspace f μ)\n⊢ ... | [
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Mathlib/Tactic/NormNum/Core.lean | Mathlib.Meta.NormNum.IsNat.to_eq | [] | [
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Mathlib/RingTheory/Subring/Basic.lean | RingHom.eq_of_eqOn_set_top | [] | [
1241,
26
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Mathlib/Data/PFun.lean | PFun.mem_dom | [
{
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}
] | [
83,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Nat/Bits.lean | Nat.div2_bits_eq_tail | [
{
"state_after": "case z\nn : ℕ\n⊢ bits (div2 0) = List.tail (bits 0)\n\ncase f\nn✝ : ℕ\nb : Bool\nn : ℕ\nh : n = 0 → b = true\na✝ : bits (div2 n) = List.tail (bits n)\n⊢ bits (div2 (bit b n)) = List.tail (bits (bit b n))",
"state_before": "n✝ n : ℕ\n⊢ bits (div2 n) = List.tail (bits n)",
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249,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
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Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.IsFundamentalSequence.monotone | [
{
"state_after": "case inl\nα : Type ?u.69712\nr : α → α → Prop\na o : Ordinal\nf : (b : Ordinal) → b < o → Ordinal\nhf : IsFundamentalSequence a o f\ni j : Ordinal\nhi : i < o\nhj : j < o\nhij✝ : i ≤ j\nhij : i < j\n⊢ f i hi ≤ f j hj\n\ncase inr\nα : Type ?u.69712\nr : α → α → Prop\na o : Ordinal\nf : (b : Ord... | [
598,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Num/Lemmas.lean | Num.cmp_swap | [
{
"state_after": "case pos.pos\nα : Type ?u.468320\na✝¹ a✝ : PosNum\n⊢ Ordering.swap (cmp (pos a✝¹) (pos a✝)) = cmp (pos a✝) (pos a✝¹)",
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"tactic": "cases m <;> cases n <;> try { unfold cmp } <;> try { rfl }"
},
{
... | [
855,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
854,
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Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.coe_toAddSubgroup | [] | [
527,
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526,
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Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.ext | [
{
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76,
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70,
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Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.eq_of_coeff_monomial_ne_zero | [] | [
173,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
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Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPullback.of_isBilimit | [
{
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"tactic": "convert IsPullb... | [
562,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
560,
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src/lean/Init/Data/Nat/Div.lean | Nat.mod_zero | [] | [
109,
27
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
105,
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_subtype_map_embedding | [
{
"state_after": "ι : Type ?u.382203\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf✝ g✝ : α → β\ninst✝ : CommMonoid β\np : α → Prop\ns : Finset { x // p x }\nf : { x // p x } → β\ng : α → β\nh : ∀ (x : { x // p x }), x ∈ s → g ↑x = f x\n⊢ ∏ x in s, g (↑(Function.Embedding.subtype fun x => p ... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
891,
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Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_sin_mul_cos₁ | [
{
"state_after": "no goals",
"state_before": "a b : ℝ\nn : ℕ\n⊢ (∫ (x : ℝ) in a..b, sin x * cos x) = (sin b ^ 2 - sin a ^ 2) / 2",
"tactic": "simpa using integral_sin_pow_mul_cos_pow_odd 1 0"
}
] | [
769,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
768,
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Mathlib/Data/List/Cycle.lean | Cycle.nil_toFinset | [] | [
815,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
814,
1
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Std/Tactic/Ext.lean | Unit.ext | [] | [
206,
55
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
206,
11
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Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.prod_eq_inf | [
{
"state_after": "case a\nC : Type u₁\ninst✝³ : Category C\nX Y Z : C\nD : Type u₂\ninst✝² : Category D\ninst✝¹ : HasPullbacks C\nA : C\nf₁ f₂ : Subobject A\ninst✝ : HasBinaryProduct f₁ f₂\n⊢ (f₁ ⨯ f₂) ≤ f₁ ⊓ f₂\n\ncase a\nC : Type u₁\ninst✝³ : Category C\nX Y Z : C\nD : Type u₂\ninst✝² : Category D\ninst✝¹ : H... | [
480,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
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Mathlib/Data/Real/CauSeq.lean | CauSeq.cauchy₃ | [] | [
179,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
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Mathlib/Logic/Equiv/Set.lean | Equiv.prod_assoc_symm_preimage | [
{
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"state_before": "α✝ : Sort u\nβ✝ : Sort v\nγ✝ : Sort w\nα : Type u_1\nβ : Type u_2... | [
150,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
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Mathlib/Algebra/Regular/SMul.lean | IsSMulRegular.mul_iff | [
{
"state_after": "R : Type u_1\nS : Type ?u.29294\nM : Type u_2\na b : R\ns : S\ninst✝² : CommSemigroup R\ninst✝¹ : SMul R M\ninst✝ : IsScalarTower R R M\n⊢ IsSMulRegular M (a * b) ↔ IsSMulRegular M (a * b) ∧ IsSMulRegular M (b * a)",
"state_before": "R : Type u_1\nS : Type ?u.29294\nM : Type u_2\na b : R\n... | [
226,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
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Mathlib/RingTheory/FinitePresentation.lean | Algebra.FinitePresentation.mvPolynomial | [
{
"state_after": "case intro\nR : Type w₁\nA : Type w₂\nB : Type w₃\ninst✝⁵ : CommRing R\ninst✝⁴ : CommRing A\ninst✝³ : Algebra R A\ninst✝² : CommRing B\ninst✝¹ : Algebra R B\nι : Type u_2\ninst✝ : Finite ι\nval✝ : Fintype ι\n⊢ FinitePresentation R (MvPolynomial ι R)",
"state_before": "R : Type w₁\nA : Type... | [
112,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
11
] |
Mathlib/Data/Prod/TProd.lean | List.TProd.fst_mk | [] | [
71,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
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Std/Data/Nat/Gcd.lean | Nat.coprime.gcd_mul | [] | [
409,
39
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
404,
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Mathlib/Algebra/Order/Interval.lean | NonemptyInterval.snd_pow | [] | [
267,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.comp_continuousAt_iff' | [
{
"state_after": "no goals",
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"tactic": "simp"
}
] | [
426,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
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Mathlib/Order/Ideal.lean | Order.Ideal.sup_mem | [] | [
348,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
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Mathlib/LinearAlgebra/AffineSpace/Basis.lean | AffineBasis.coord_apply_centroid | [
{
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317,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
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Mathlib/Data/Polynomial/Module.lean | PolynomialModule.smul_single_apply | [
{
"state_after": "case h_add\nR : Type u_1\nM : Type u_2\ninst✝⁶ : CommRing R\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\nI : Ideal R\nS : Type ?u.264988\ninst✝³ : CommSemiring S\ninst✝² : Algebra S R\ninst✝¹ : Module S M\ninst✝ : IsScalarTower S R M\ni : ℕ\nm : M\nn : ℕ\np q : R[X]\nhp : ↑(p • ↑(single R i)... | [
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165,
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Mathlib/Topology/UniformSpace/Completion.lean | UniformSpace.Completion.continuous_map | [] | [
593,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
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Mathlib/Analysis/Calculus/ExtendDeriv.lean | has_deriv_at_interval_left_endpoint_of_tendsto_deriv | [
{
"state_after": "case intro.intro\nE : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type ?u.104384\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\ns : Set ℝ\ne : E\na : ℝ\nf : ℝ → E\nf_diff : DifferentiableOn ℝ f s\nf_lim : ContinuousWithinAt f s a\nhs : s ∈ 𝓝[Ioi a] a\nf_li... | [
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114,
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Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.toLin_finTwoProd | [] | [
826,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
822,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.sin_eq_real_sin_iff_eq_or_add_eq_pi | [
{
"state_after": "case h\nψ x✝ : ℝ\n⊢ sin ↑x✝ = Real.sin ψ ↔ ↑x✝ = ↑ψ ∨ ↑x✝ + ↑ψ = ↑π",
"state_before": "θ : Angle\nψ : ℝ\n⊢ sin θ = Real.sin ψ ↔ θ = ↑ψ ∨ θ + ↑ψ = ↑π",
"tactic": "induction θ using Real.Angle.induction_on"
},
{
"state_after": "no goals",
"state_before": "case h\nψ x✝ : ℝ\n⊢ ... | [
349,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/Data/Set/Basic.lean | Set.eq_empty_of_forall_not_mem | [] | [
585,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
584,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | LinearMap.comp_id | [] | [
554,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
1
] |
Mathlib/CategoryTheory/Generator.lean | CategoryTheory.isCodetecting_iff_isCoseparating | [] | [
198,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Topology/Connected.lean | isPreconnected_iff_preconnectedSpace | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Type ?u.72105\nπ : ι → Type ?u.72110\ninst✝ : TopologicalSpace α\ns✝ t u v s : Set α\nh : PreconnectedSpace ↑s\n⊢ IsPreconnected s",
"tactic": "simpa using isPreconnected_univ.image ((↑) : s → α) continuous_subtype_val.continuousO... | [
873,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
871,
1
] |
Mathlib/Topology/Order/Basic.lean | IsGLB.isGLB_of_tendsto | [] | [
2059,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2056,
1
] |
Mathlib/Analysis/NormedSpace/Basic.lean | norm_algebraMap' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.480957\nβ : Type ?u.480960\nγ : Type ?u.480963\nι : Type ?u.480966\n𝕜 : Type u_2\n𝕜' : Type u_1\ninst✝³ : NormedField 𝕜\ninst✝² : SeminormedRing 𝕜'\ninst✝¹ : NormedAlgebra 𝕜 𝕜'\ninst✝ : NormOneClass 𝕜'\nx : 𝕜\n⊢ ‖↑(algebraMap 𝕜 𝕜') x‖ = ‖x‖... | [
512,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
511,
1
] |
Mathlib/Data/Rel.lean | Rel.dom_mono | [] | [
74,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Data/Nat/GCD/Basic.lean | Nat.gcd_add_self_right | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\n⊢ gcd m (n + m) = gcd m (n + 1 * m)",
"tactic": "rw [one_mul]"
}
] | [
77,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Data/Nat/Choose/Basic.lean | Nat.choose_zero_right | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ choose n 0 = 1",
"tactic": "cases n <;> rfl"
}
] | [
56,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Order/Basic.lean | PUnit.le | [] | [
1376,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1375,
11
] |
Mathlib/Topology/MetricSpace/Contracting.lean | ContractingWith.apriori_edist_iterate_efixedPoint_le | [] | [
141,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/LinearAlgebra/Dfinsupp.lean | Submodule.mem_iSup_iff_exists_dfinsupp' | [
{
"state_after": "ι : Type u_3\nR : Type u_1\nS : Type ?u.436512\nM : ι → Type ?u.436517\nN : Type u_2\ndec_ι : DecidableEq ι\ninst✝³ : Semiring R\ninst✝² : AddCommMonoid N\ninst✝¹ : Module R N\np : ι → Submodule R N\ninst✝ : (i : ι) → (x : { x // x ∈ p i }) → Decidable (x ≠ 0)\nx : N\n⊢ (∃ f, ↑(↑(lsum ℕ) fun i... | [
366,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisCoinsertion.u_sup_l | [] | [
805,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
803,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.disjoint_or_nonempty_inter | [
{
"state_after": "α : Type u_1\nβ : Type ?u.203129\nγ : Type ?u.203132\ninst✝ : DecidableEq α\ns✝ s₁ s₂ t✝ t₁ t₂ u v : Finset α\na b : α\ns t : Finset α\n⊢ _root_.Disjoint s t ∨ ¬_root_.Disjoint s t",
"state_before": "α : Type u_1\nβ : Type ?u.203129\nγ : Type ?u.203132\ninst✝ : DecidableEq α\ns✝ s₁ s₂ t✝ t... | [
1835,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1833,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.bfamilyOfFamily'_typein | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.271133\nγ : Type ?u.271136\nr✝ : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nι : Type u_1\nr : ι → ι → Prop\ninst✝ : IsWellOrder ι r\nf : ι → α\ni : ι\n⊢ bfamilyOfFamily' r f (typein r i) (_ : typein r i < type r) = f i",
"tac... | [
1144,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1142,
1
] |
Mathlib/Data/Nat/Fib.lean | Nat.fib_dvd | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\nh : m ∣ n\n⊢ fib m ∣ fib n",
"tactic": "rwa [gcd_eq_left_iff_dvd, ← fib_gcd, gcd_eq_left_iff_dvd.mp]"
}
] | [
289,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.diam_insert | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.293762\ninst✝ : PseudoEMetricSpace α\nx y z : α\nε ε₁ ε₂ : ℝ≥0∞\ns t : Set α\nd : ℝ≥0∞\n⊢ diam (insert x s) ≤ d ↔ max (⨆ (y : α) (_ : y ∈ s), edist x y) (diam s) ≤ d",
"tactic": "simp only [diam_le_iff, ball_insert_iff, ed... | [
926,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
923,
1
] |
Mathlib/Algebra/ContinuedFractions/ConvergentsEquiv.lean | GeneralizedContinuedFraction.squashSeq_succ_n_tail_eq_squashSeq_tail_n | [
{
"state_after": "case none\nK : Type u_1\nn : ℕ\ng : GeneralizedContinuedFraction K\ns : Stream'.Seq (Pair K)\ninst✝ : DivisionRing K\ns_succ_succ_nth_eq : Stream'.Seq.get? s (n + 2) = none\n⊢ Stream'.Seq.tail (squashSeq s (n + 1)) = squashSeq (Stream'.Seq.tail s) n\n\ncase some\nK : Type u_1\nn : ℕ\ng : Gener... | [
155,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | exists_hasDerivAt_eq_slope | [
{
"state_after": "case intro.intro\nE : Type ?u.317721\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type ?u.317817\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf f' : ℝ → ℝ\na b : ℝ\nhab : a < b\nhfc : ContinuousOn f (Icc a b)\nhff' : ∀ (x : ℝ), x ∈ Ioo a b → HasDerivAt f (f' x) x\n... | [
758,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
753,
1
] |
Mathlib/Algebra/Order/Monoid/MinMax.lean | mul_lt_mul_iff_of_le_of_le | [
{
"state_after": "α : Type u_1\nβ : Type ?u.6644\ninst✝⁵ : LinearOrder α\ninst✝⁴ : Mul α\ninst✝³ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\ninst✝² : CovariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\ninst✝¹ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x < x_1... | [
127,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Algebra/Algebra/Bilinear.lean | NonUnitalAlgHom.coe_lmul_eq_mul | [] | [
135,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | MeasureTheory.IntegrableOn.continuousOn_mul_of_subset | [
{
"state_after": "case intro\nX : Type u_1\nY : Type ?u.2480793\nE : Type ?u.2480796\nR : Type u_2\ninst✝⁷ : MeasurableSpace X\ninst✝⁶ : TopologicalSpace X\ninst✝⁵ : MeasurableSpace Y\ninst✝⁴ : TopologicalSpace Y\ninst✝³ : NormedAddCommGroup E\nf : X → E\nμ : Measure X\ns : Set X\ninst✝² : OpensMeasurableSpace ... | [
414,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.aevalTower_X | [] | [
398,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.digits_zero_zero | [] | [
95,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.flip_add | [] | [
815,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
814,
1
] |
Mathlib/Data/Real/Pointwise.lean | Real.iSup_mul_of_nonneg | [
{
"state_after": "no goals",
"state_before": "ι : Sort u_1\nα : Type ?u.16214\ninst✝ : LinearOrderedField α\nr : ℝ\nha : 0 ≤ r\nf : ι → ℝ\n⊢ (⨆ (i : ι), f i) * r = ⨆ (i : ι), f i * r",
"tactic": "simp only [Real.mul_iSup_of_nonneg ha, mul_comm]"
}
] | [
139,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Topology/SubsetProperties.lean | finite_cover_nhds_interior | [] | [
806,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
802,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.sInter_prod_sInter_subset | [] | [
1825,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1823,
1
] |
Mathlib/Analysis/Convex/Exposed.lean | IsExposed.eq_inter_halfspace' | [
{
"state_after": "case intro\n𝕜 : Type u_2\nE : Type u_1\ninst✝⁴ : TopologicalSpace 𝕜\ninst✝³ : OrderedRing 𝕜\ninst✝² : AddCommMonoid E\ninst✝¹ : TopologicalSpace E\ninst✝ : Module 𝕜 E\nl✝ : E →L[𝕜] 𝕜\nA✝ B C : Set E\nX : Finset E\nx : E\nA : Set E\nl : E →L[𝕜] 𝕜\nhAB : IsExposed 𝕜 A {x | x ∈ A ∧ ∀ (y ... | [
124,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.closedBall_zero_eq_preimage_closedBall | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.1026847\nR' : Type ?u.1026850\n𝕜 : Type u_2\n𝕜₂ : Type ?u.1026856\n𝕜₃ : Type ?u.1026859\n𝕝 : Type ?u.1026862\nE : Type u_1\nE₂ : Type ?u.1026868\nE₃ : Type ?u.1026871\nF : Type ?u.1026874\nG : Type ?u.1026877\nι : Type ?u.1026880\ninst✝⁶ : Semino... | [
824,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
822,
1
] |
Mathlib/Data/Nat/Squarefree.lean | Nat.squarefree_and_prime_pow_iff_prime | [
{
"state_after": "n : ℕ\n⊢ Squarefree n ∧ IsPrimePow n → Prime n",
"state_before": "n : ℕ\n⊢ Squarefree n ∧ IsPrimePow n ↔ Prime n",
"tactic": "refine' ⟨_, fun hn => ⟨hn.squarefree, hn.isPrimePow⟩⟩"
},
{
"state_after": "n : ℕ\n⊢ (Squarefree n ∧ ∃ p k, Prime p ∧ 0 < k ∧ p ^ k = n) → Prime n",
... | [
103,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Topology/Sheaves/Stalks.lean | TopCat.Presheaf.isIso_of_stalkFunctor_map_iso | [
{
"state_after": "C : Type u\ninst✝⁷ : Category C\ninst✝⁶ : HasColimits C\nX Y Z : TopCat\ninst✝⁵ : ConcreteCategory C\ninst✝⁴ : PreservesFilteredColimits (forget C)\ninst✝³ : HasLimits C\ninst✝² : PreservesLimits (forget C)\ninst✝¹ : ReflectsIsomorphisms (forget C)\nF G : Sheaf C X\nf : F ⟶ G\ninst✝ : ∀ (x : ↑... | [
625,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
616,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | eq_orthogonalProjection_of_mem_of_inner_eq_zero | [] | [
498,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
1
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.default_eq | [] | [
43,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | Padic.coe_mul | [] | [
551,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
550,
1
] |
Mathlib/Order/Bounds/Basic.lean | IsGLB.inter_Iic_of_mem | [] | [
480,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.IsPath.dropUntil | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\ninst✝ : DecidableEq V\nu v w : V\np : Walk G v w\nhc : IsPath p\nh : u ∈ support p\n⊢ IsPath (append (?m.256082 hc h) (dropUntil p u h))",
"tactic": "rwa [←... | [
1199,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1197,
11
] |
Mathlib/Order/Filter/ENNReal.lean | ENNReal.limsup_add_le | [] | [
87,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Algebra/GroupWithZero/Basic.lean | div_self_mul_self' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.26175\nM₀ : Type ?u.26178\nG₀ : Type u_1\nM₀' : Type ?u.26184\nG₀' : Type ?u.26187\nF : Type ?u.26190\nF' : Type ?u.26193\ninst✝ : GroupWithZero G₀\na✝ b c a : G₀\n⊢ a / (a * a) = a⁻¹⁻¹ * a⁻¹ * a⁻¹",
"tactic": "simp [mul_inv_rev]"
}
] | [
390,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Algebra/Group/Basic.lean | mul_eq_of_eq_inv_mul | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.52331\nβ : Type ?u.52334\nG : Type u_1\ninst✝ : Group G\na b c d : G\nh : b = a⁻¹ * c\n⊢ a * b = c",
"tactic": "rw [h, mul_inv_cancel_left]"
}
] | [
658,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
658,
1
] |
Mathlib/MeasureTheory/Measure/Content.lean | MeasureTheory.Content.outerMeasure_preimage | [
{
"state_after": "G : Type w\ninst✝¹ : TopologicalSpace G\nμ : Content G\ninst✝ : T2Space G\nf : G ≃ₜ G\nh : ∀ ⦃K : Compacts G⦄, (fun s => ↑(toFun μ s)) (Compacts.map ↑f (_ : Continuous ↑f) K) = (fun s => ↑(toFun μ s)) K\nA : Set G\n⊢ ∀ (s : Set G) (hs : IsOpen s),\n innerContent μ { carrier := ↑f.toEquiv ⁻¹... | [
308,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.iSup_join | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.103075\nι✝ : Sort x\nf✝ g : Filter α\ns t : Set α\nι : Sort w\nf : ι → Filter (Filter α)\nx : Set α\n⊢ (x ∈ ⨆ (x : ι), join (f x)) ↔ x ∈ join (⨆ (x : ι), f x)",
"tactic": "simp only [mem_iSup, mem_join]"
}
] | [
865,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
864,
1
] |
Mathlib/RingTheory/NonZeroDivisors.lean | mem_nonZeroDivisors_of_ne_zero | [] | [
123,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Order/CompleteBooleanAlgebra.lean | biInf_sup_biInf | [] | [
225,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Algebra/Opposites.lean | MulOpposite.unop_comp_op | [] | [
118,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.TaggedPrepartition.isPartition_single_iff | [] | [
310,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.compl_Ici | [] | [
1066,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1065,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Series.lean | Complex.hasSum_sin | [
{
"state_after": "case h.e'_5\nz : ℂ\n⊢ (fun n => (-1) ^ n * z ^ (2 * n + 1) / ↑(2 * n + 1)!) = fun n => (z * I) ^ (2 * n + 1) / ↑(2 * n + 1)! / I",
"state_before": "z : ℂ\n⊢ HasSum (fun n => (-1) ^ n * z ^ (2 * n + 1) / ↑(2 * n + 1)!) (sin z)",
"tactic": "convert Complex.hasSum_sin' z using 1"
},
{... | [
81,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Std/Data/Nat/Gcd.lean | Nat.dvd_gcd | [
{
"state_after": "no goals",
"state_before": "k m n : Nat\n⊢ k ∣ m → k ∣ n → k ∣ gcd m n",
"tactic": "induction m, n using gcd.induction with intro km kn\n| H0 n => rw [gcd_zero_left]; exact kn\n| H1 n m _ IH => rw [gcd_rec]; exact IH ((dvd_mod_iff km).2 kn) km"
},
{
"state_after": "case H0\nk n... | [
52,
69
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
49,
1
] |
Mathlib/GroupTheory/GroupAction/Prod.lean | Prod.smul_mk | [] | [
61,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_sin_pow_three | [
{
"state_after": "a b : ℝ\nn : ℕ\nthis : (∫ (x : ℝ) in a..b, sin x ^ (2 * 1 + 1) * cos x ^ 0) = ∫ (u : ℝ) in cos b..cos a, u ^ 0 * (1 - u ^ 2) ^ 1\n⊢ (∫ (x : ℝ) in a..b, sin x ^ 3) = cos a - cos b - (cos a ^ 3 - cos b ^ 3) / 3",
"state_before": "a b : ℝ\nn : ℕ\n⊢ (∫ (x : ℝ) in a..b, sin x ^ 3) = cos a - cos... | [
822,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
819,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.smul_iUnion₂ | [] | [
264,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/CategoryTheory/Action.lean | CategoryTheory.ActionCategory.coe_back | [] | [
88,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | EuclideanGeometry.angle_lt_pi_of_not_collinear | [] | [
477,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
1
] |
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