file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_congr | [
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Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.op_norm_neg | [
{
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Mathlib/Computability/Primrec.lean | Primrec.ulower_down | [] | [
1261,
21
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Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.mem_frange_iff | [
{
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] | [
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.map_iSup | [] | [
1517,
26
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Mathlib/LinearAlgebra/Matrix/ToLin.lean | LinearMap.toMatrixAlgEquiv'_apply | [
{
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.sigmaUncurry_add | [] | [
1567,
28
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Std/Data/List/Lemmas.lean | List.pairwise_reverse | [
{
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Mathlib/RepresentationTheory/Action.lean | CategoryTheory.MonoidalFunctor.mapAction_μ_inv_hom | [
{
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1024,
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Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | deriv_exp | [] | [
246,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Std/Data/Int/Lemmas.lean | Int.ofNat_add_negSucc | [] | [
52,
90
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Hom.range_eq_map | [
{
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.hasFiniteIntegral_congr | [] | [
171,
46
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169,
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Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.autCongr_refl | [
{
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698,
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696,
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Mathlib/Data/Set/Prod.lean | Set.prod_preimage_right | [] | [
211,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
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Mathlib/Order/BoundedOrder.lean | bot_ne_top | [] | [
893,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
893,
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Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.Measure.LebesgueDecomposition.sup_mem_measurableLE | [
{
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64
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Mathlib/GroupTheory/Subsemigroup/Centralizer.lean | Set.inv_mem_centralizer₀ | [
{
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... | [
103,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
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Mathlib/RingTheory/Int/Basic.lean | Int.gcd_eq_one_of_gcd_mul_right_eq_one_left | [] | [
219,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
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Mathlib/Order/Closure.lean | LowerAdjoint.closure_top | [] | [
430,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
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Mathlib/Analysis/Analytic/Linear.lean | ContinuousLinearMap.fpowerSeries_radius | [] | [
49,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Multiset/Basic.lean | Multiset.countp_eq_countp_filter_add | [
{
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Mathlib/Topology/Bases.lean | TopologicalSpace.isTopologicalBasis_of_open_of_nhds | [
{
"state_after": "case refine'_1\nα : Type u\nt : TopologicalSpace α\ns : Set (Set α)\nh_open : ∀ (u : Set α), u ∈ s → IsOpen u\nh_nhds : ∀ (a : α) (u : Set α), a ∈ u → IsOpen u → ∃ v, v ∈ s ∧ a ∈ v ∧ v ⊆ u\n⊢ ⋃₀ s = univ\n\ncase refine'_2\nα : Type u\nt : TopologicalSpace α\ns : Set (Set α)\nh_open : ∀ (u : Se... | [
141,
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Mathlib/Analysis/Calculus/FDeriv/Star.lean | Differentiable.star | [] | [
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22
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.abs_im_div_norm_le_one | [
{
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"tactic": "rw [abs_div, abs_norm]"
},
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
756,
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Mathlib/Algebra/Associated.lean | irreducible_isUnit_mul | [] | [
263,
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261,
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Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.GroupSmul.linearMap_apply | [] | [
987,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/MeanInequalitiesPow.lean | ENNReal.rpow_arith_mean_le_arith_mean_rpow | [
{
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"state_before": "ι : T... | [
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Mathlib/Order/Monotone/Monovary.lean | AntivaryOn.dual_left | [] | [
236,
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src/lean/Init/Core.lean | PUnit.subsingleton | [
{
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{
"state_after": "case unit.unit\na b c d : Prop\n⊢ unit = unit",
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Mathlib/Data/Fin/VecNotation.lean | Matrix.head_fin_const | [] | [
124,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
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Mathlib/Topology/UniformSpace/Cauchy.lean | le_nhds_of_cauchy_adhp_aux | [
{
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"state_before": "α : Type u\nβ : Type v\ninst✝ : UniformSpace α\nf : Filter α\nx : α\nadhs : ∀ ... | [
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111,
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Mathlib/Analysis/Calculus/FDeriv/Add.lean | DifferentiableWithinAt.neg | [] | [
419,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
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Mathlib/ModelTheory/Types.lean | FirstOrder.Language.Theory.CompleteType.setOf_mem_eq_univ_iff | [
{
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"tac... | [
134,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
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Mathlib/Analysis/Calculus/MeanValue.lean | mul_sub_lt_image_sub_of_lt_deriv | [] | [
812,
50
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809,
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Mathlib/Computability/Ackermann.lean | ack_le_iff_left | [] | [
239,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
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Mathlib/Topology/Sheaves/SheafCondition/UniqueGluing.lean | TopCat.Presheaf.compatible_iff_leftRes_eq_rightRes | [
{
"state_after": "case mp\nC : Type u\ninst✝¹ : Category C\ninst✝ : ConcreteCategory C\nX : TopCat\nF : Presheaf (Type v) X\nι : Type v\nU : ι → Opens ↑X\nsf : piOpens F U\nh : IsCompatible F U ((piOpensIsoSectionsFamily F U).hom sf)\n⊢ leftRes F U sf = rightRes F U sf\n\ncase mpr\nC : Type u\ninst✝¹ : Category... | [
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110,
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Mathlib/Data/Real/EReal.lean | EReal.top_mul_coe_of_neg | [] | [
919,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.integrableOn_const | [
{
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68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.Poly.denote_reverseAux | [
{
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},
{
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314,
61
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.finite_neighborSet_toSubgraph | [
{
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"tactic": "induction p with\n| nil =>\n rw [Walk.toSubgraph, neighbo... | [
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2280,
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Mathlib/RingTheory/MvPolynomial/Homogeneous.lean | MvPolynomial.homogeneousComponent_isHomogeneous | [
{
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45
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267,
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Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isInt_le_true | [] | [
696,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
694,
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Std/Data/Nat/Gcd.lean | Nat.gcd_eq_right | [
{
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"tactic": "rw [gcd_comm, gcd_eq_left H]"
}
] | [
147,
31
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
146,
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Mathlib/Order/SuccPred/Basic.lean | Order.pred_mono | [] | [
649,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Std/Logic.lean | true_eq_false_of_false | [] | [
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70
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Mathlib/Data/Fin/Basic.lean | Fin.succAbove_left_inj | [] | [
2202,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2201,
1
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Mathlib/Analysis/Complex/CauchyIntegral.lean | Complex.circleIntegral_sub_inv_smul_of_differentiable_on_off_countable_aux | [
{
"state_after": "E : Type u\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nR : ℝ\nc w : ℂ\nf : ℂ → E\ns : Set ℂ\nhs : Set.Countable s\nhw : w ∈ ball c R \\ s\nhc : ContinuousOn f (closedBall c R)\nhd : ∀ (x : ℂ), x ∈ ball c R \\ s → DifferentiableAt ℂ f x\nhR : 0 < R\n⊢ (∮ (... | [
456,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | Subgroup.pointwise_smul_le_pointwise_smul_iff | [] | [
354,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycleOn.of_zpow | [] | [
934,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
932,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.inductionOn | [] | [
313,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.compl_adj | [] | [
280,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Topology/Category/TopCat/Opens.lean | TopologicalSpace.Opens.map_comp_map | [] | [
206,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Order/Hom/Lattice.lean | BoundedLatticeHom.coe_comp_inf_hom | [] | [
1333,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1331,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.liftNC_smul | [
{
"state_after": "k : Type u₁\nG : Type u₂\nR✝ : Type ?u.528207\ninst✝² : Semiring k\ninst✝¹ : MulOneClass G\nR : Type u_1\ninst✝ : Semiring R\nf : k →+* R\ng : G →* R\nc : k\nφ : MonoidAlgebra k G\nthis :\n AddMonoidHom.comp (liftNC ↑f ↑g) (↑(smulAddHom k (MonoidAlgebra k G)) c) =\n AddMonoidHom.comp (AddM... | [
616,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
605,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | fderivWithin_mul_const | [] | [
450,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidHom.coe_mul | [] | [
518,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.le_mk_diff_add_mk | [] | [
2126,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2125,
1
] |
Mathlib/Data/Num/Lemmas.lean | ZNum.cast_bit1 | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : AddGroupWithOne α\n⊢ ↑(ZNum.bit1 0) = _root_.bit1 ↑0",
"tactic": "simp [ZNum.bit1, _root_.bit1, _root_.bit0]"
},
{
"state_after": "α : Type u_1\ninst✝ : AddGroupWithOne α\np : PosNum\n⊢ ↑(PosNum.bit1 p) = _root_.bit1 ↑p",
"s... | [
1151,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1137,
1
] |
Mathlib/Data/Finset/Finsupp.lean | Finset.mem_finsupp_iff_of_support_subset | [
{
"state_after": "case refine'_1\nι : Type u_1\nα : Type u_2\ninst✝ : Zero α\ns : Finset ι\nf : ι →₀ α\nt : ι →₀ Finset α\nht : t.support ⊆ s\ni : ι\nh : (i ∈ f.support → i ∈ s) ∧ (i ∈ s → ↑f i ∈ ↑t i)\n⊢ ↑f i ∈ ↑t i\n\ncase refine'_2\nι : Type u_1\nα : Type u_2\ninst✝ : Zero α\ns : Finset ι\nf : ι →₀ α\nt : ι ... | [
76,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Real.contDiff_sinh | [] | [
640,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
639,
1
] |
Mathlib/Topology/Algebra/WithZeroTopology.lean | WithZeroTopology.hasBasis_nhds_zero | [
{
"state_after": "α : Type ?u.3501\nΓ₀ : Type u_1\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nγ γ₁ γ₂ : Γ₀\nl : Filter α\nf : α → Γ₀\n⊢ HasBasis (⨅ (γ : Γ₀) (_ : γ ≠ 0), 𝓟 (Iio γ)) (fun γ => γ ≠ 0) Iio",
"state_before": "α : Type ?u.3501\nΓ₀ : Type u_1\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nγ γ₁ γ₂ : ... | [
68,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | Commute.cast_int_mul_self | [] | [
1193,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1192,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.Tendsto.atBot_mul_const | [] | [
1215,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1213,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Basis.toDual_eq_repr | [] | [
346,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/Algebra/Homology/ShortExact/Preadditive.lean | CategoryTheory.Splitting.iso_hom_fst | [] | [
243,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Algebra/Hom/Group.lean | MulHom.comp_apply | [] | [
1119,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1118,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.norm_ofNormedAddCommGroup_le | [] | [
890,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
888,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | TendstoLocallyUniformlyOn.union | [
{
"state_after": "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\ns₁ s₂ : Set α\nhs₁ : IsOpen s₁\nhs₂ : IsOpen s₂\nh₁ : TendstoLocallyUniformlyOn F f p s₁\nh₂ : TendstoLoca... | [
679,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
675,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.piecewise_piecewise_of_subset_left | [] | [
2511,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2508,
1
] |
Mathlib/CategoryTheory/Types.lean | Equiv.toIso_hom | [] | [
325,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | coe_finsetBasisOfLinearIndependentOfCardEqFinrank | [
{
"state_after": "K : Type u\nV : Type v\ninst✝² : DivisionRing K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\ns : Finset V\nhs : Finset.Nonempty s\nlin_ind : LinearIndependent K Subtype.val\ncard_eq : Finset.card s = finrank K V\n⊢ ↑(basisOfLinearIndependentOfCardEqFinrank lin_ind (_ : Fintype.card { x // x ∈... | [
1217,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1212,
1
] |
Std/Logic.lean | not_nonempty_pempty | [] | [
730,
76
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
730,
9
] |
Mathlib/Analysis/Convex/Extreme.lean | extremePoints_empty | [] | [
157,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.take_take | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nδ : Type w\ns : Stream' α\nn : ℕ\n⊢ List.take 0 (take n s) = take (min n 0) s",
"tactic": "rw [min_zero, List.take_zero, take_zero]"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nδ : Type w\ns : ... | [
596,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
] |
Mathlib/Data/List/Chain.lean | List.Chain'.prefix | [] | [
319,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.IsSwap.sign_eq | [] | [
589,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
587,
1
] |
Mathlib/Algebra/Algebra/Hom.lean | AlgHom.coe_coe | [] | [
125,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
11
] |
Mathlib/Data/Set/Intervals/Monotone.lean | MonotoneOn.Ico | [] | [
131,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
11
] |
Mathlib/Analysis/InnerProductSpace/Calculus.lean | DifferentiableOn.inner | [] | [
139,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Topology/Homotopy/Contractible.lean | ContinuousMap.nullhomotopic_of_constant | [
{
"state_after": "no goals",
"state_before": "X : Type u_1\nY : Type u_2\nZ : Type ?u.173\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : TopologicalSpace Z\ny : Y\n⊢ Homotopic (const X y) (const X y)",
"tactic": "rfl"
}
] | [
33,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
] |
Mathlib/Order/Lattice.lean | sup_left_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : SemilatticeSup α\na✝ b✝ c✝ d a b c : α\n⊢ a ⊔ (b ⊔ c) = b ⊔ (a ⊔ c)",
"tactic": "rw [← sup_assoc, ← sup_assoc, @sup_comm α _ a]"
}
] | [
274,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.autToPow_spec | [
{
"state_after": "M : Type ?u.3884431\nN : Type ?u.3884434\nG : Type ?u.3884437\nR : Type u_1\nS : Type u_2\nF : Type ?u.3884446\ninst✝⁶ : CommMonoid M\ninst✝⁵ : CommMonoid N\ninst✝⁴ : DivisionCommMonoid G\nk l : ℕ\ninst✝³ : CommRing S\ninst✝² : IsDomain S\nμ : S\nn : ℕ+\nhμ : IsPrimitiveRoot μ ↑n\ninst✝¹ : Com... | [
998,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
989,
1
] |
Mathlib/Order/CompleteLattice.lean | biSup_sup | [
{
"state_after": "α : Type u_2\nβ : Type ?u.102985\nβ₂ : Type ?u.102988\nγ : Type ?u.102991\nι : Sort u_1\nι' : Sort ?u.102997\nκ : ι → Sort ?u.103002\nκ' : ι' → Sort ?u.103007\ninst✝ : CompleteLattice α\nf✝ g s t : ι → α\na✝ b : α\np : ι → Prop\nf : (i : ι) → p i → α\na : α\nh : ∃ i, p i\nthis : Nonempty { i /... | [
1270,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1265,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.cos_sub_pi_div_two | [
{
"state_after": "no goals",
"state_before": "x : ℂ\n⊢ cos (x - ↑π / 2) = sin x",
"tactic": "simp [sub_eq_add_neg, cos_add]"
}
] | [
1291,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1291,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.mk_coe_nat | [] | [
399,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.mem_map_of_mem | [] | [
88,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Order/Heyting/Basic.lean | le_himp | [] | [
331,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.coe_toLinearEquiv | [] | [
1799,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1798,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | compact_open_separated_mul_left | [
{
"state_after": "case intro.intro\nα : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝² : TopologicalSpace G\ninst✝¹ : MulOneClass G\ninst✝ : ContinuousMul G\nK U : Set G\nhK : IsCompact K\nhU : IsOpen U\nhKU : K ⊆ U\nV : Set Gᵐᵒᵖ\nhV : V ∈ 𝓝 (op 1)\nhV' : op '' K * V ⊆ op '' U\n⊢ ∃ V, V ∈ 𝓝 1 ∧ V * K ⊆ U"... | [
1570,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1563,
1
] |
Mathlib/Analysis/InnerProductSpace/GramSchmidtOrtho.lean | span_gramSchmidt_Iio | [] | [
173,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Topology/UniformSpace/Completion.lean | CauchyFilter.uniformEmbedding_pureCauchy | [] | [
175,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Analysis/InnerProductSpace/Adjoint.lean | ContinuousLinearMap.isSelfAdjoint_iff_isSymmetric | [] | [
311,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/Data/List/Card.lean | List.card_union_disjoint | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Sort ?u.54436\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\nas bs : List α\nh : Disjoint as bs\n⊢ card (List.union as bs) = card as + card bs",
"tactic": "rw [card_eq_of_equiv (union_equiv_append as bs), card_append_disjoint h]"
}
] | [
190,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Std/Data/String/Lemmas.lean | String.endPos_eq_zero | [] | [
163,
67
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
162,
1
] |
Mathlib/Data/Set/Image.lean | Set.preimage_union | [] | [
95,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Data/List/Lattice.lean | List.subset_inter | [] | [
178,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Data/Matrix/Hadamard.lean | Matrix.diagonal_hadamard_diagonal | [] | [
140,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Topology/Instances/AddCircle.lean | continuousAt_toIcoMod | [] | [
111,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/WideEqualizers.lean | CategoryTheory.Limits.hasWideEqualizers_of_hasLimit_parallelFamily | [] | [
797,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
794,
1
] |
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