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 |
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Mathlib/Data/Int/Cast/Lemmas.lean | Int.cast_one_le_of_pos | [
{
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}
] | [
177,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/SymplecticGroup.lean | Matrix.J_det_mul_J_det | [
{
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Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.right_not_mem_Ioo | [] | [
150,
27
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149,
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Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.IsThreeCycle.card_support | [
{
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"tactic": "rw [← sum_cycleType, h.cycleType, Multiset.sum_singleton]"
}
] | [
572,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
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Mathlib/Algebra/Order/Sub/Canonical.lean | tsub_lt_tsub_iff_left_of_le | [] | [
487,
94
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Mathlib/Data/ZMod/Basic.lean | ZMod.neg_one_ne_one | [] | [
824,
34
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Mathlib/Order/CompleteLattice.lean | ofDual_sSup | [] | [
435,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/MetricSpace/Basic.lean | dist_le_Ico_sum_of_dist_le | [] | [
254,
86
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250,
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Mathlib/Topology/ContinuousOn.lean | Filter.EventuallyEq.congr_continuousWithinAt | [
{
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957,
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Mathlib/LinearAlgebra/Matrix/Trace.lean | Matrix.trace_sub | [] | [
122,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
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Mathlib/CategoryTheory/Sites/Sheaf.lean | CategoryTheory.Presheaf.IsSheaf.amalgamate_map | [
{
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236,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Homology/Homotopy.lean | Homotopy.prevD_chainComplex | [
{
"state_after": "ι : Type ?u.294299\nV : Type u\ninst✝¹ : Category V\ninst✝ : Preadditive V\nc : ComplexShape ι\nC D E : HomologicalComplex V c\nf✝ g : C ⟶ D\nh k : D ⟶ E\ni : ι\nP Q : ChainComplex V ℕ\nf : (i j : ℕ) → X P i ⟶ X Q j\nj : ℕ\n⊢ f j (ComplexShape.prev (ComplexShape.down ℕ) j) ≫ d Q (ComplexShape.... | [
466,
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_mono_of_nonneg | [
{
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Mathlib/Data/Nat/Multiplicity.lean | Nat.Prime.multiplicity_one | [] | [
81,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Order/Basic.lean | IsGLB.mem_closure | [] | [
1989,
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1988,
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Mathlib/Data/Finset/LocallyFinite.lean | Finset.left_not_mem_Ioc | [] | [
144,
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Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.coe_commutes | [] | [
591,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Multiset/Nodup.lean | Multiset.Nodup.of_cons | [] | [
58,
21
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Mathlib/Algebra/Group/Ext.lean | CommMonoid.ext | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/Basic.lean | Set.not_mem_of_mem_diff | [] | [
1811,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1810,
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Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.lineMap_injective | [] | [
594,
48
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Mathlib/Data/ENat/Lattice.lean | ENat.coe_iSup | [] | [
36,
23
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Mathlib/Algebra/Algebra/Subalgebra/Tower.lean | Subalgebra.coe_restrictScalars | [] | [
101,
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100,
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Std/Logic.lean | if_true | [] | [
685,
92
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685,
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Mathlib/Analysis/BoxIntegral/Partition/Split.lean | BoxIntegral.Prepartition.not_disjoint_imp_le_of_subset_of_mem_splitMany | [
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"state_before": "ι : Type u_1\nM : Type ?u.47705\nn : ℕ\nI✝ J... | [
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285,
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Mathlib/Analysis/Convex/SpecificFunctions/Deriv.lean | int_prod_range_pos | [
{
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"tactic": "refine' (int_prod_range_nonneg m n hn).lt_of_ne fun h => hm _"
}... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Group/Basic.lean | mul_div_cancel'' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.57451\nβ : Type ?u.57454\nG : Type u_1\ninst✝ : Group G\na✝ b✝ c d a b : G\n⊢ a * b / b = a",
"tactic": "rw [div_eq_mul_inv, mul_inv_cancel_right a b]"
}
] | [
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Mathlib/Algebra/Parity.lean | Odd.pow | [
{
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"state_before": "F : Type ?u.91525\nα : Type u_1\nβ : Type ?u.91531\nR : Type ?u.91534\ninst✝¹ : Semiring α\ninst✝ : Semiring β\nm n : α\nhm : Odd ... | [
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Mathlib/RingTheory/MatrixAlgebra.lean | MatrixEquivTensor.invFun_add | [
{
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"tactic": "simp [invFun, add_tmu... | [
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasurableEmbedding.exists_stronglyMeasurable_extend | [] | [
863,
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Mathlib/Data/Finset/Lattice.lean | Finset.inf_map | [] | [
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Mathlib/Data/Set/Image.lean | Set.preimage_const | [
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Mathlib/LinearAlgebra/Span.lean | Submodule.mem_iSup_of_directed | [
{
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Mathlib/Data/Fin/Basic.lean | Fin.succ_inj | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/SymmDiff.lean | bihimp_eq_inf_himp_inf | [
{
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"state_before": "ι : Type ?u.40596\nα : Type u_1\nβ : Type ?u.40602\nπ : ι → Type ?u.40607\ninst✝ : GeneralizedHeytingAlgebra α\na b c d : α\n⊢ a ⇔ b = a ⊔ b ⇨ a ⊓ b",
"tactic": "simp [himp_inf_distrib, bihimp]"
}
] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Group/Arithmetic.lean | Measurable.div' | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/GroupTheory/Submonoid/Pointwise.lean | AddSubmonoid.natCast_mem_one | [] | [
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Mathlib/RingTheory/Multiplicity.lean | multiplicity.pos_of_dvd | [
{
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Mathlib/Data/Complex/Exponential.lean | Complex.tan_ofReal_re | [] | [
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Mathlib/Data/Finset/Prod.lean | Finset.Nonempty.snd | [] | [
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Mathlib/Computability/Halting.lean | Nat.Partrec'.rfindOpt | [
{
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Mathlib/CategoryTheory/ConcreteCategory/Basic.lean | CategoryTheory.coe_id | [] | [
132,
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131,
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Mathlib/Order/Filter/Pi.lean | Filter.Tendsto.pi_map_coprodᵢ | [] | [
270,
47
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268,
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Mathlib/Data/Real/Sqrt.lean | Real.sqrt_eq_one | [
{
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"state_before": "x y : ℝ\n⊢ 1 * 1 = x ↔ x = 1",
"tactic": "rw [eq_comm, mul_one]"
}
] | [
231,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
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Mathlib/Data/Int/Log.lean | Int.zpow_lt_iff_lt_clog | [] | [
299,
80
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297,
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Mathlib/Data/Finset/Basic.lean | Finset.dedup_eq_self | [] | [
168,
12
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167,
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Mathlib/Topology/LocalExtr.lean | IsLocalMaxOn.comp_antitone | [] | [
268,
22
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266,
8
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Mathlib/Analysis/Convex/Cone/Basic.lean | ConvexCone.smul_mem_iff | [] | [
248,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
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Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.symm_apply | [] | [
602,
13
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600,
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Mathlib/Data/Int/Lemmas.lean | Int.injOn_natAbs_Ici | [] | [
98,
28
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Mathlib/Order/WellFounded.lean | WellFounded.eq_strictMono_iff_eq_range | [
{
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"state_before": "α : Type ?u.4618\nβ : Type u_1\ninst... | [
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158,
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Mathlib/RingTheory/PowerBasis.lean | PowerBasis.constr_pow_aeval | [
{
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251,
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.preimage_eventuallyEq_target_inter_preimage_inter | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type ?u.35170\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\ne✝ : LocalHomeomorph α β\ne' : LocalHomeomorph β γ\ne : LocalHomeomorph α β\ns : Set α\nt : Set γ\nx : α\nf : α → γ\nh... | [
436,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/AlgebraicTopology/DoldKan/SplitSimplicialObject.lean | SimplicialObject.Splitting.σ_comp_πSummand_id_eq_zero | [
{
"state_after": "case h\nC : Type u_2\ninst✝² : Category C\ninst✝¹ : HasFiniteCoproducts C\nX : SimplicialObject C\ns : Splitting X\ninst✝ : Preadditive C\nn : ℕ\ni : Fin (n + 1)\n⊢ ∀ (A : IndexSet [n].op),\n ιSummand s A ≫ SimplicialObject.σ X i ≫ πSummand s (IndexSet.id [n + 1].op) = ιSummand s A ≫ 0",
... | [
90,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | MulEquiv.map_finprod_mem | [] | [
720,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
718,
1
] |
Mathlib/RingTheory/PrincipalIdealDomain.lean | IsPrincipalIdealRing.of_prime | [
{
"state_after": "R : Type u\nM : Type v\ninst✝ : CommRing R\nH : ∀ (P : Ideal R), IsPrime P → IsPrincipal P\n⊢ ∀ (x : Ideal R), ¬x ∈ nonPrincipals R",
"state_before": "R : Type u\nM : Type v\ninst✝ : CommRing R\nH : ∀ (P : Ideal R), IsPrime P → IsPrincipal P\n⊢ IsPrincipalIdealRing R",
"tactic": "rw [←... | [
548,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.denom_mul_dvd | [
{
"state_after": "K : Type u\ninst✝ : Field K\nx y : RatFunc K\n⊢ ∃ p, x * y = ↑(algebraMap K[X] (RatFunc K)) p / ↑(algebraMap K[X] (RatFunc K)) (denom x * denom y)",
"state_before": "K : Type u\ninst✝ : Field K\nx y : RatFunc K\n⊢ denom (x * y) ∣ denom x * denom y",
"tactic": "rw [denom_dvd (mul_ne_zer... | [
1328,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1325,
1
] |
Mathlib/Order/Hom/Bounded.lean | BotHom.cancel_right | [] | [
478,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
1
] |
Mathlib/Data/PNat/Factors.lean | PNat.factorMultiset_lcm | [
{
"state_after": "case a\nm n : ℕ+\n⊢ factorMultiset (lcm m n) ≤ factorMultiset m ⊔ factorMultiset n\n\ncase a\nm n : ℕ+\n⊢ factorMultiset m ⊔ factorMultiset n ≤ factorMultiset (lcm m n)",
"state_before": "m n : ℕ+\n⊢ factorMultiset (lcm m n) = factorMultiset m ⊔ factorMultiset n",
"tactic": "apply le_a... | [
390,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | dist_div_div_le | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type ?u.646954\n𝕜 : Type ?u.646957\nα : Type ?u.646960\nι : Type ?u.646963\nκ : Type ?u.646966\nE : Type u_1\nF : Type ?u.646972\nG : Type ?u.646975\ninst✝¹ : SeminormedCommGroup E\ninst✝ : SeminormedCommGroup F\na a₁✝ a₂✝ b b₁✝ b₂✝ : E\nr r₁ r₂ : ℝ\na₁ a₂... | [
1442,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1441,
1
] |
Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.eval_basisDivisor_left_of_ne | [
{
"state_after": "F : Type u_1\ninst✝ : Field F\nx y : F\nhxy : x ≠ y\n⊢ (x - y)⁻¹ * (x - y) = 1",
"state_before": "F : Type u_1\ninst✝ : Field F\nx y : F\nhxy : x ≠ y\n⊢ eval x (basisDivisor x y) = 1",
"tactic": "simp only [basisDivisor, eval_mul, eval_C, eval_sub, eval_X]"
},
{
"state_after": ... | [
176,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Std/Data/List/Lemmas.lean | List.subset_append_of_subset_left | [] | [
254,
50
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
253,
1
] |
Mathlib/Analysis/Complex/ReImTopology.lean | Complex.isOpenMap_re | [] | [
57,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
src/lean/Init/Prelude.lean | of_decide_eq_true | [] | [
858,
70
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
855,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_inv_two | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.218569\nβ : Type ?u.218572\na b c d : ℝ≥0∞\nr p q : ℝ≥0\n⊢ ↑2⁻¹ = 2⁻¹",
"tactic": "rw [coe_inv _root_.two_ne_zero, coe_two]"
}
] | [
1355,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1355,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | HomogeneousIdeal.toIdeal_top | [] | [
365,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
] |
Mathlib/Topology/Partial.lean | open_dom_of_pcontinuous | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α →. β\nh : PContinuous f\n⊢ IsOpen (PFun.preimage f Set.univ)",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α →. β\nh : PContinuous f\n⊢ I... | [
61,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | ContDiffWithinAt.csinh | [] | [
570,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
1
] |
Mathlib/Topology/Sheaves/Stalks.lean | TopCat.Presheaf.stalkFunctor_map_germ | [] | [
130,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Analysis/NormedSpace/Banach.lean | ContinuousLinearMap.coe_ofSeqClosedGraph | [
{
"state_after": "case h\n𝕜 : Type u_3\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_2\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nf : E →L[𝕜] F\ninst✝¹ : CompleteSpace F\ninst✝ : CompleteSpace E\ng : E →ₗ[𝕜] F\nhg : ∀ ... | [
523,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.coe_one | [] | [
372,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.not_mem_Ico_of_ge | [] | [
743,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
743,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.Subsingleton.infsep_zero | [
{
"state_after": "α : Type u_1\nβ : Type ?u.55704\ninst✝ : EDist α\nx y : α\ns : Set α\nhs : Set.Subsingleton s\n⊢ Set.einfsep s = 0 ∨ Set.einfsep s = ⊤",
"state_before": "α : Type u_1\nβ : Type ?u.55704\ninst✝ : EDist α\nx y : α\ns : Set α\nhs : Set.Subsingleton s\n⊢ infsep s = 0",
"tactic": "rw [infse... | [
356,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.RespectsIso.monomorphisms | [
{
"state_after": "case right\nC : Type u\ninst✝¹ : Category C\nD : Type ?u.60407\ninst✝ : Category D\nX Y Z : C\ne : Y ≅ Z\nf : X ⟶ Y\n⊢ MorphismProperty.monomorphisms C f → MorphismProperty.monomorphisms C (f ≫ e.hom)",
"state_before": "case right\nC : Type u\ninst✝¹ : Category C\nD : Type ?u.60407\ninst✝ ... | [
434,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.natAbs_valMinAbs_neg | [
{
"state_after": "case pos\nn : ℕ\na : ZMod n\nh2a : 2 * val a = n\n⊢ Int.natAbs (valMinAbs (-a)) = Int.natAbs (valMinAbs a)\n\ncase neg\nn : ℕ\na : ZMod n\nh2a : ¬2 * val a = n\n⊢ Int.natAbs (valMinAbs (-a)) = Int.natAbs (valMinAbs a)",
"state_before": "n : ℕ\na : ZMod n\n⊢ Int.natAbs (valMinAbs (-a)) = In... | [
1032,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1029,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.num_mul_denom_add_denom_mul_num_ne_zero | [
{
"state_after": "K : Type u\ninst✝ : Field K\nx y : RatFunc K\nhxy : x + y ≠ 0\nh_zero : num x * denom y + denom x * num y = 0\n⊢ False",
"state_before": "K : Type u\ninst✝ : Field K\nx y : RatFunc K\nhxy : x + y ≠ 0\n⊢ num x * denom y + denom x * num y ≠ 0",
"tactic": "intro h_zero"
},
{
"stat... | [
1374,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1369,
1
] |
Mathlib/Data/PNat/Find.lean | PNat.find_eq_iff | [
{
"state_after": "case mp\np q : ℕ+ → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred q\nh : ∃ n, p n\nn m : ℕ+\n⊢ PNat.find h = m → p m ∧ ∀ (n : ℕ+), n < m → ¬p n\n\ncase mpr\np q : ℕ+ → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred q\nh : ∃ n, p n\nn m : ℕ+\n⊢ (p m ∧ ∀ (n : ℕ+), n < m → ¬p n) → ... | [
81,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/LinearAlgebra/Prod.lean | LinearMap.prod_ext_iff | [] | [
294,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Topology/FiberBundle/Basic.lean | FiberBundle.totalSpaceMk_embedding | [] | [
278,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.lift_comp_map | [] | [
762,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
760,
1
] |
Mathlib/Algebra/Module/Projective.lean | Module.projective_lifting_property | [
{
"state_after": "R : Type u_1\ninst✝⁶ : Semiring R\nP : Type u_2\ninst✝⁵ : AddCommMonoid P\ninst✝⁴ : Module R P\nM : Type u_3\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\nN : Type u_4\ninst✝¹ : AddCommMonoid N\ninst✝ : Module R N\nh : Projective R P\nf : M →ₗ[R] N\ng : P →ₗ[R] N\nhf : Function.Surjective ↑f... | [
118,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.FiniteAtFilter.inf_of_left | [] | [
4106,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4105,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.filter_lt_eq_Ioi | [
{
"state_after": "case a\nι : Type ?u.61874\nα : Type u_1\ninst✝³ : Preorder α\ninst✝² : LocallyFiniteOrderTop α\na : α\ninst✝¹ : Fintype α\ninst✝ : DecidablePred ((fun x x_1 => x < x_1) a)\na✝ : α\n⊢ a✝ ∈ filter ((fun x x_1 => x < x_1) a) univ ↔ a✝ ∈ Ioi a",
"state_before": "ι : Type ?u.61874\nα : Type u_1... | [
475,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
473,
1
] |
Mathlib/Order/Heyting/Regular.lean | Heyting.Regular.toRegular_coe | [] | [
205,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | nhds_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝² : TopologicalSpace G\ninst✝¹ : Group G\ninst✝ : TopologicalGroup G\nx y : G\n⊢ 𝓝 (x * y) = map ((fun x x_1 => x * x_1) x) (map (fun a => a * y) (𝓝 1 * 𝓝 1))",
"tactic": "simp"
},
{
"state_afte... | [
1686,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1679,
1
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | IsUnit.measurable_const_smul_iff | [] | [
744,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
741,
8
] |
Mathlib/FieldTheory/Finiteness.lean | IsNoetherian.iff_fg | [
{
"state_after": "case mp\nK : Type u\nV : Type v\ninst✝² : DivisionRing K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\n⊢ IsNoetherian K V → Module.Finite K V\n\ncase mpr\nK : Type u\nV : Type v\ninst✝² : DivisionRing K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\n⊢ Module.Finite K V → IsNoetherian K V",
... | [
121,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.mem_span | [] | [
141,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.symm_image_target_eq_source | [] | [
315,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.inter_erase | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.261085\nγ : Type ?u.261088\ninst✝ : DecidableEq α\ns✝ t✝ u v : Finset α\na✝ b a : α\ns t : Finset α\n⊢ s ∩ erase t a = erase (s ∩ t) a",
"tactic": "simp only [erase_eq, inter_sdiff]"
}
] | [
2245,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2244,
1
] |
Mathlib/Data/Set/Intervals/OrdConnected.lean | Set.ordConnected_univ | [] | [
188,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Algebra/Group/Basic.lean | bit1_zero | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.11341\nβ : Type ?u.11344\nG : Type ?u.11347\nM : Type u\ninst✝¹ : AddMonoid M\na b c : M\ninst✝ : One M\n⊢ bit1 0 = 1",
"tactic": "rw [bit1, bit0_zero, zero_add]"
}
] | [
158,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Logic/Relation.lean | Relation.symmetric_join | [] | [
626,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
626,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mul_eq_right | [
{
"state_after": "no goals",
"state_before": "a b : Cardinal\nhb : ℵ₀ ≤ b\nha : a ≤ b\nha' : a ≠ 0\n⊢ a * b = b",
"tactic": "rw [mul_comm, mul_eq_left hb ha ha']"
}
] | [
656,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | MonoidHom.comap_bot' | [] | [
1190,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1189,
1
] |
Std/Logic.lean | Decidable.imp_or' | [
{
"state_after": "no goals",
"state_before": "b : Prop\na : Sort u_1\nc : Prop\ninst✝ : Decidable b\nh : b\n⊢ a → b ∨ c ↔ (a → b) ∨ (a → c)",
"tactic": "simp [h]"
},
{
"state_after": "b : Prop\na : Sort u_1\nc : Prop\ninst✝ : Decidable b\nh : ¬b\n⊢ a → c ↔ (a → False) ∨ (a → c)",
"state_befo... | [
566,
88
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
564,
1
] |
Mathlib/Algebra/Order/Sub/Defs.lean | le_add_tsub_swap | [] | [
229,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.apply_lt_nfpFamily_iff | [] | [
102,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Hom.eq_of_eqOn_top | [] | [
889,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
888,
1
] |
Mathlib/Order/Heyting/Basic.lean | ofDual_hnot | [] | [
957,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
956,
1
] |
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