file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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|---|---|---|---|---|---|---|
Mathlib/Algebra/DirectSum/Finsupp.lean | finsuppLEquivDirectSum_symm_lof | [] | [
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Mathlib/Topology/Bases.lean | TopologicalSpace.IsTopologicalBasis.quotient | [] | [
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44
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866,
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Mathlib/Data/Set/Function.lean | Set.piecewise_eq_of_not_mem | [] | [
1390,
12
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1389,
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Std/Data/RBMap/Alter.lean | Std.RBNode.Ordered.alter | [
{
"state_after": "α : Type u_1\ncut : α → Ordering\nf : Option α → Option α\ncmp : α → α → Ordering\nt : RBNode α\nH :\n ∀ {x : α} {t' : RBNode α} {p : Path α},\n RBNode.zoom cut t Path.root = (t', p) → f (root? t') = some x → Path.RootOrdered cmp p x ∧ OnRoot (cmpEq cmp x) t'\nh : Ordered cmp t\n⊢ Ordered ... | [
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343,
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Mathlib/Data/MvPolynomial/Counit.lean | MvPolynomial.counitNat_X | [] | [
113,
16
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112,
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Mathlib/FieldTheory/RatFunc.lean | RatFunc.ofFractionRing_mk' | [
{
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"state_before": "K : Type u\ninst✝¹ : CommRing K\ninst✝ : IsDomain K\nx : K[X]\ny : { x // x ∈ K[X]⁰ }\n⊢ { toFractionRing := IsLocalization.mk' (FractionRing K[X]) x y } = IsLocalization.mk' (RatFunc K) x y",
"tactic": "rw [IsFractionRing.mk'_eq_div, IsFractionRing.mk'_eq_d... | [
1039,
87
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1035,
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Mathlib/Data/Set/Intervals/OrdConnected.lean | Set.ordConnected_of_uIcc_subset_left | [
{
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}
] | [
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272,
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Mathlib/Algebra/Category/ModuleCat/Basic.lean | ModuleCat.forget₂_map | [] | [
171,
6
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169,
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Mathlib/Analysis/Normed/Group/Pointwise.lean | IsCompact.closedBall_one_div | [
{
"state_after": "no goals",
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"tactic": "simp [div_eq_mul_inv, mul_comm, hs.inv.mul_closedBall_one hδ]"
}
] | [
279,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
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Mathlib/LinearAlgebra/Matrix/Block.lean | Matrix.BlockTriangular.sub | [
{
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100,
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Mathlib/Algebra/FreeAlgebra.lean | FreeAlgebra.algebraMap_leftInverse | [
{
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}
] | [
417,
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415,
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Mathlib/Data/Finsupp/WellFounded.lean | Finsupp.Lex.wellFounded_of_finite | [] | [
67,
77
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Mathlib/Order/Chain.lean | IsChain.image | [] | [
107,
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104,
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Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.frontier_cthickening_subset | [] | [
1385,
61
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1383,
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Mathlib/Order/Filter/Prod.lean | Filter.tendsto_prod_swap | [] | [
154,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
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Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.mul_div_self_cancel_iff | [
{
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1187,
89
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src/lean/Init/Data/Nat/Basic.lean | Nat.lt.step | [] | [
286,
60
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
286,
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Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.HomotopicWith.refl | [] | [
563,
27
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562,
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Std/Data/Array/Lemmas.lean | Array.swap_def | [
{
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},
{
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"state_before": "α : Type u_1\na : Array α\ni j : Fin (size a)\n⊢ swap a i j = set (set a i (get a j))... | [
117,
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115,
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Mathlib/Order/ModularLattice.lean | sup_lt_sup_of_lt_of_inf_le_inf | [] | [
251,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
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Mathlib/Data/Polynomial/Derivative.lean | Polynomial.derivative_C_mul_X_sq | [
{
"state_after": "no goals",
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"tactic": "rw [derivative_C_mul_X_pow, Nat.cast_two, pow_one]"
}
] | [
109,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
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Mathlib/Algebra/Order/Monoid/Lemmas.lean | Right.one_le_mul | [] | [
936,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/Basis.lean | Submodule.exists_le_ker_of_lt_top | [
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1629,
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Mathlib/Data/Set/Basic.lean | Set.inter_eq_right_iff_subset | [] | [
973,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
972,
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Mathlib/Algebra/Order/Floor.lean | Nat.preimage_ceil_zero | [] | [
369,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
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Mathlib/MeasureTheory/Decomposition/Jordan.lean | MeasureTheory.JordanDecomposition.zero_negPart | [] | [
109,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
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Mathlib/Data/Real/CauSeqCompletion.lean | CauSeq.lim_eq_of_equiv_const | [] | [
355,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
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Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.BoundedFormula.IsQF.toPrenexImp | [] | [
841,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
833,
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Mathlib/Analysis/Calculus/FDeriv/Mul.lean | HasFDerivAt.const_mul | [] | [
475,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
473,
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Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.map_le_map_iff_of_injective | [] | [
598,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
597,
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Mathlib/Data/PEquiv.lean | PEquiv.single_trans_single | [] | [
383,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/GroupPower/Lemmas.lean | Int.toAdd_pow | [] | [
1218,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1217,
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Mathlib/Data/List/Forall2.lean | List.forall₂_refl | [] | [
65,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/VectorBundle/Basic.lean | VectorBundleCore.trivializationAt_symmL | [] | [
823,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Bounded.lean | Set.unbounded_gt_inter_not_gt | [] | [
435,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
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Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.one_toProd | [] | [
238,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
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Mathlib/FieldTheory/PerfectClosure.lean | MonoidHom.map_pthRoot | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝⁶ : CommSemiring R\nS : Type v\ninst✝⁵ : CommSemiring S\nf : R →* S\ng : R →+* S\np : ℕ\ninst✝⁴ : Fact (Nat.Prime p)\ninst✝³ : CharP R p\ninst✝² : PerfectRing R p\ninst✝¹ : CharP S p\ninst✝ : PerfectRing S p\nx : R\n⊢ ↑(frobenius ((fun x => S) (... | [
106,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
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Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.sin_arg | [
{
"state_after": "x : ℂ\n⊢ Real.sin\n (if 0 ≤ x.re then arcsin (x.im / ↑abs x)\n else if 0 ≤ x.im then arcsin ((-x).im / ↑abs x) + π else arcsin ((-x).im / ↑abs x) - π) =\n x.im / ↑abs x",
"state_before": "x : ℂ\n⊢ Real.sin (arg x) = x.im / ↑abs x",
"tactic": "unfold arg"
},
{
"stat... | [
43,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/List/BigOperators/Basic.lean | List.prod_take_succ | [
{
"state_after": "no goals",
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183,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
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Mathlib/Data/Set/Prod.lean | Set.disjoint_diagonal_offDiag | [] | [
593,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
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Mathlib/RingTheory/IsTensorProduct.lean | Algebra.lift_algHom_comp_left | [] | [
500,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
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Mathlib/Algebra/DirectSum/Ring.lean | DirectSum.ringHom_ext' | [] | [
595,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
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Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.hasBasis_nhdsSet_thickening | [] | [
1288,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1285,
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Mathlib/Algebra/Category/ModuleCat/Colimits.lean | ModuleCat.Colimits.quot_smul | [] | [
226,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
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Mathlib/Topology/QuasiSeparated.lean | isQuasiSeparated_iff_quasiSeparatedSpace | [
{
"state_after": "α : Type u_1\nβ : Type ?u.15502\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α → β\ns : Set α\nhs : IsOpen s\n⊢ IsQuasiSeparated s ↔ IsQuasiSeparated Set.univ",
"state_before": "α : Type u_1\nβ : Type ?u.15502\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α... | [
108,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_eq_comp | [] | [
2888,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2886,
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Mathlib/Analysis/Calculus/ContDiffDef.lean | contDiffOn_iff_forall_nat_le | [] | [
686,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
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src/lean/Init/Data/List/Basic.lean | List.mem_append_of_mem_left | [
{
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{
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380,
39
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376,
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Mathlib/Data/PNat/Defs.lean | Nat.toPNat'_coe | [
{
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"tactic": "rw [if_pos (succ_pos m)]"
},
{
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"state_before": "m : ℕ\n⊢ ↑(toPNat' (m + 1)) = m + 1",
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}
] | [
111,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
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Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.bind₁_X_left | [
{
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168,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
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Mathlib/Analysis/Normed/Field/Basic.lean | List.nnnorm_prod | [] | [
561,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
560,
11
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Mathlib/GroupTheory/Subsemigroup/Centralizer.lean | Set.inv_mem_centralizer | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\nS T : Set M\na b : M\ninst✝ : Group M\nha : a ∈ centralizer S\ng : M\nhg : g ∈ S\n⊢ g * a⁻¹ = a⁻¹ * g",
"tactic": "rw [mul_inv_eq_iff_eq_mul, mul_assoc, eq_inv_mul_iff_mul_eq, ha g hg]"
}
] | [
82,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Topology/Sets/Order.lean | ClopenUpperSet.coe_sup | [] | [
91,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
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Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ico_filter_le_of_right_le | [] | [
339,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
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Mathlib/Order/Filter/Basic.lean | Function.Commute.filter_map | [] | [
2123,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2121,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.isComplete_ker | [] | [
985,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
982,
1
] |
Mathlib/Combinatorics/SetFamily/LYM.lean | Finset.IsAntichain.disjoint_slice_shadow_falling | [
{
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180,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
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Mathlib/Tactic/Sat/FromLRAT.lean | Sat.Clause.reify_one | [] | [
207,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
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Mathlib/Data/Option/Basic.lean | Option.pmap_eq_map | [
{
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"tactic": "cases x <;> si... | [
197,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
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Mathlib/Order/CompleteLattice.lean | le_iInf_iff | [] | [
909,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
908,
1
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Mathlib/RingTheory/Subring/Basic.lean | Subring.coe_iSup_of_directed | [
{
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"tactic": "simp [mem_iS... | [
1156,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1154,
1
] |
Mathlib/RingTheory/Nakayama.lean | Submodule.eq_smul_of_le_smul_of_le_jacobson | [
{
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"state_before": "R : Type u_1\nM : Type u_2\ninst✝² : CommRing R\ninst✝¹ : AddCommGroup M\ninst✝... | [
64,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
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Mathlib/RingTheory/Subring/Basic.lean | Subring.smul_def | [] | [
1435,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1434,
1
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Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.of'_eq_of | [] | [
1605,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1604,
1
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Mathlib/Data/List/Sigma.lean | List.lookupAll_eq_nil | [
{
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"tactic": "simp"
},
{
"state_after": "case pos\nα : Type u\nβ : α → Type v\nl✝ l₁ l₂ : List (Sigma... | [
281,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.HasFiniteIntegral.smul_measure | [
{
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220,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
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Mathlib/Topology/CompactOpen.lean | ContinuousMap.continuous_comp' | [
{
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149,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
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Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.mem_ball_self | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.188592\ninst✝ : PseudoEMetricSpace α\nx y z : α\nε ε₁ ε₂ : ℝ≥0∞\ns t : Set α\nh : 0 < ε\n⊢ x ∈ ball x ε",
"tactic": "rwa [mem_ball, edist_self]"
}
] | [
561,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
560,
1
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Mathlib/Data/List/Perm.lean | List.Perm.subset | [] | [
99,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.coe_fn_injective | [
{
"state_after": "case mk\nα : Type u_1\nβ : Type ?u.23243\nR : Type ?u.23246\nR' : Type ?u.23249\nms : Set (OuterMeasure α)\nm μ₂ : OuterMeasure α\nmeasureOf✝ : Set α → ℝ≥0∞\nempty✝ : measureOf✝ ∅ = 0\nmono✝ : ∀ {s₁ s₂ : Set α}, s₁ ⊆ s₂ → measureOf✝ s₁ ≤ measureOf✝ s₂\niUnion_nat✝ : ∀ (s : ℕ → Set α), measureO... | [
240,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Algebra/Order/Interval.lean | Interval.coe_one | [] | [
135,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Data/Option/NAry.lean | Option.map₂_left_comm | [
{
"state_after": "no goals",
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137,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.mk_eq_one_iff | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nG' : Type ?u.147239\ninst✝² : Group G\ninst✝¹ : Group G'\nA : Type ?u.147248\ninst✝ : AddGroup A\nH K : Subgroup G\ng : G\nh : g ∈ H\n⊢ { val := g, property := h } = { val := 1, property := (_ : 1 ∈ H) } ↔ g = 1",
"tactic": "simp"
}
] | [
747,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
746,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiff.hasStrictFDerivAt | [] | [
1981,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1979,
1
] |
Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.IsOrtho.map | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace 𝕜 F\nf : E →ₗᵢ[𝕜] F\nU V : Submodule 𝕜 E\nh : ∀ (u : E), u ∈ U → ∀ (v : E), v ∈ V → inner u v = 0\n⊢ ∀ (u :... | [
389,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/Topology/Algebra/Polynomial.lean | Polynomial.continuousOn | [] | [
72,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
11
] |
Mathlib/Topology/Algebra/Polynomial.lean | Polynomial.continuous_aeval | [] | [
84,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
11
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.card_support_prod_list_of_pairwise_disjoint | [
{
"state_after": "case nil\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\nl : List (Perm α)\nh✝ : List.Pairwise Disjoint l\nh : List.Pairwise Disjoint []\n⊢ card (support (List.prod [])) = List.sum (List.map (card ∘ support) [])\n\ncase cons\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ ... | [
655,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
649,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.eq_comp_symm | [] | [
590,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
589,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.row_smul | [
{
"state_after": "case a.h\nl : Type ?u.1213482\nm : Type u_2\nn : Type ?u.1213488\no : Type ?u.1213491\nm' : o → Type ?u.1213496\nn' : o → Type ?u.1213501\nR : Type u_1\nS : Type ?u.1213507\nα : Type v\nβ : Type w\nγ : Type ?u.1213514\ninst✝ : SMul R α\nx : R\nv : m → α\ni✝ : Unit\nx✝ : m\n⊢ row (x • v) i✝ x✝ ... | [
2675,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2673,
1
] |
Mathlib/Data/Pi/Algebra.lean | Pi.mulSingle_op | [] | [
309,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.alephIdx_lt | [] | [
106,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidHom.mul_apply | [] | [
1503,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1502,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.nnnorm_eq_ciSup | [
{
"state_after": "case a\np : ℝ≥0∞\n𝕜 : Type ?u.236805\n𝕜' : Type ?u.236808\nι : Type u_2\nα : ι → Type ?u.236816\nβ✝ : ι → Type ?u.236821\ninst✝² : Fintype ι\ninst✝¹ : Fact (1 ≤ p)\nβ : ι → Type u_1\ninst✝ : (i : ι) → SeminormedAddCommGroup (β i)\nf : PiLp ⊤ β\n⊢ ↑‖f‖₊ = ↑(⨆ (i : ι), ‖f i‖₊)",
"state_bef... | [
570,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
567,
1
] |
Mathlib/CategoryTheory/Closed/Monoidal.lean | CategoryTheory.MonoidalClosed.uncurry_natural_right | [] | [
192,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.summable_mul | [] | [
548,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
11
] |
Mathlib/AlgebraicGeometry/LocallyRingedSpace.lean | AlgebraicGeometry.LocallyRingedSpace.Γ_obj_op | [] | [
283,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infinitePos_iff_infinite_and_pos | [] | [
499,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/Data/List/Indexes.lean | List.indexesValues_eq_filter_enum | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\np : α → Prop\ninst✝ : DecidablePred p\nas : List α\n⊢ indexesValues (fun b => decide (p b)) as = filter ((fun b => decide (p b)) ∘ Prod.snd) (enum as)",
"tactic": "simp [indexesValues, foldrIdx_eq_foldr_enum, uncurry, filter_eq_foldr]... | [
243,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Data/Nat/Factorial/BigOperators.lean | Nat.prod_factorial_dvd_factorial_sum | [
{
"state_after": "case empty\nα : Type u_1\ns : Finset α\nf : α → ℕ\n⊢ ∏ i in ∅, (f i)! ∣ (∑ i in ∅, f i)!\n\ncase insert\nα : Type u_1\ns : Finset α\nf : α → ℕ\na' : α\ns' : Finset α\nhas : ¬a' ∈ s'\nih : ∏ i in s', (f i)! ∣ (∑ i in s', f i)!\n⊢ ∏ i in insert a' s', (f i)! ∣ (∑ i in insert a' s', f i)!",
"... | [
42,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.span_union | [] | [
676,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
675,
1
] |
Mathlib/Topology/Algebra/Module/LinearPMap.lean | LinearPMap.isClosable_iff_exists_closed_extension | [] | [
158,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.multiplicity_ne_zero | [] | [
210,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.coe_toMulHom | [] | [
219,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Analysis/NormedSpace/CompactOperator.lean | IsCompactOperator.continuous | [
{
"state_after": "𝕜₁ : Type u_1\n𝕜₂ : Type u_2\ninst✝¹² : NontriviallyNormedField 𝕜₁\ninst✝¹¹ : NontriviallyNormedField 𝕜₂\nσ₁₂ : 𝕜₁ →+* 𝕜₂\ninst✝¹⁰ : RingHomIsometric σ₁₂\nM₁ : Type u_3\nM₂ : Type u_4\ninst✝⁹ : TopologicalSpace M₁\ninst✝⁸ : AddCommGroup M₁\ninst✝⁷ : TopologicalSpace M₂\ninst✝⁶ : AddCommG... | [
370,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
Mathlib/Data/List/Basic.lean | List.indexOf_get? | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.93582\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\ninst✝ : DecidableEq α\na : α\nl : List α\nh : a ∈ l\n⊢ get? l (indexOf a l) = some a",
"tactic": "rw [nthLe_get?, indexOf_nthLe (indexOf_lt_length.2 h)]"
}
] | [
1416,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1415,
1
] |
Mathlib/Order/RelIso/Basic.lean | RelIso.map_rel_iff | [] | [
674,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
673,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | MonoidHom.isOfFinOrder | [
{
"state_after": "case intro.intro\nG : Type u\nA : Type v\nx✝ y : G\na b : A\nn✝ m : ℕ\ninst✝² : Monoid G\ninst✝¹ : AddMonoid A\nH : Type v\ninst✝ : Monoid H\nf : G →* H\nx : G\nh : IsOfFinOrder x\nn : ℕ\nnpos : 0 < n\nhn : x ^ n = 1\n⊢ ∃ n, 0 < n ∧ ↑f x ^ n = 1",
"state_before": "G : Type u\nA : Type v\nx... | [
108,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Data/Set/Image.lean | Set.image_preimage_eq_inter_range | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.73849\nι : Sort ?u.73852\nι' : Sort ?u.73855\nf✝ : ι → α\ns t✝ : Set α\nf : α → β\nt : Set β\nx : β\nx✝ : x ∈ t ∩ range f\nhx : x ∈ t\ny : α\nh_eq : f y = x\n⊢ x ∈ t",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.73849\nι : Sort ?u.73852\... | [
783,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
780,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | mem_ball_symmetry | [
{
"state_after": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.55006\ninst✝ : UniformSpace α\nV : Set (β × β)\nhV : Prod.swap ⁻¹' V = V\nx y : β\n⊢ (x, y) ∈ Prod.swap ⁻¹' V ↔ (x, y) ∈ V",
"state_before": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.55006\ninst✝ : Unifo... | [
654,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
650,
1
] |
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