file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Data/Vector.lean | Vector.cons_head_tail | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nφ : Type w\nn : ℕ\nh : List.length [] = succ n\n⊢ cons (head { val := [], property := h }) (tail { val := [], property := h }) = { val := [], property := h }",
"tactic": "contradiction"
}
] | [
84,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Data/Num/Lemmas.lean | PosNum.cast_sub' | [
{
"state_after": "α : Type u_1\ninst✝ : AddGroupWithOne α\na : PosNum\n⊢ ↑(↑a - 1) = ↑a - ↑1",
"state_before": "α : Type u_1\ninst✝ : AddGroupWithOne α\na : PosNum\n⊢ ↑(sub' a 1) = ↑a - ↑1",
"tactic": "rw [sub'_one, Num.cast_toZNum, ← Num.cast_to_nat, pred'_to_nat, ← Nat.sub_one]"
},
{
"state_af... | [
1213,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1188,
1
] |
Mathlib/Algebra/Group/Defs.lean | inv_mul_cancel_right | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝ : Group G\na✝ b✝ c a b : G\n⊢ a * b⁻¹ * b = a",
"tactic": "rw [mul_assoc, mul_left_inv, mul_one]"
}
] | [
1125,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1124,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infiniteNeg_mul_infiniteNeg | [] | [
869,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
867,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean | HomogeneousLocalization.NumDenSameDeg.deg_zero | [] | [
147,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion_ite | [] | [
633,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
631,
1
] |
Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.IsRefl.ker_eq_bot_iff_ker_flip_eq_bot | [
{
"state_after": "R : Type u_1\nR₁ : Type u_2\nR₂ : Type ?u.124036\nR₃ : Type ?u.124039\nM : Type ?u.124042\nM₁ : Type u_3\nM₂ : Type ?u.124048\nMₗ₁ : Type ?u.124051\nMₗ₁' : Type ?u.124054\nMₗ₂ : Type ?u.124057\nMₗ₂' : Type ?u.124060\nK : Type ?u.124063\nK₁ : Type ?u.124066\nK₂ : Type ?u.124069\nV : Type ?u.124... | [
205,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.head_zip | [] | [
213,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Order/Lattice.lean | right_eq_sup | [] | [
195,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Data/Nat/Choose/Central.lean | Nat.succ_mul_centralBinom_succ | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ choose (2 * n + 2) (n + 1) * (n + 1) = choose (2 * n + 1) n * (2 * n + 2)",
"tactic": "rw [choose_succ_right_eq, choose_mul_succ_eq]"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ choose (2 * n + 1) n * (2 * n + 2) = 2 * (cho... | [
83,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | image_smul_setₛₗ | [
{
"state_after": "case h₁\nR : Type u_2\nR₁ : Type ?u.144905\nR₂ : Type ?u.144908\nR₃ : Type ?u.144911\nk : Type ?u.144914\nS : Type u_3\nS₃ : Type ?u.144920\nT : Type ?u.144923\nM : Type u_4\nM₁ : Type ?u.144929\nM₂ : Type ?u.144932\nM₃ : Type u_5\nN₁ : Type ?u.144938\nN₂ : Type ?u.144941\nN₃ : Type ?u.144944\... | [
367,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.piecewise_mem_Icc | [] | [
2585,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2583,
1
] |
Mathlib/Data/Nat/Cast/Basic.lean | toDual_natCast | [] | [
354,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/Tactic/NormNum/GCD.lean | Tactic.NormNum.nat_gcd_helper_dvd_left | [] | [
31,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
1
] |
Mathlib/Analysis/Complex/CauchyIntegral.lean | Complex.two_pi_I_inv_smul_circleIntegral_sub_inv_smul_of_differentiable_on_off_countable | [
{
"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\nhc : ContinuousOn f (closedBall c R)\nhd : ∀ (x : ℂ), x ∈ ball c R \\ s → DifferentiableAt ℂ f x\nhR : 0 < R\n⊢ ((2 * ↑π ... | [
494,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | DifferentiableOn.hasFDerivAt | [] | [
526,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
524,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Submodule.smul_assoc | [] | [
221,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
11
] |
Mathlib/Data/Complex/Basic.lean | Complex.AbsTheory.mul_self_abs | [] | [
908,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
907,
9
] |
Mathlib/Order/MinMax.lean | max_eq_right_iff | [] | [
152,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.intervalIntegral_eq_integral_uIoc | [
{
"state_after": "case inl\nι : Type ?u.10052960\n𝕜 : Type ?u.10052963\nE : Type u_1\nF : Type ?u.10052969\nA : Type ?u.10052972\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\na✝ b✝ : ℝ\nf✝ g : ℝ → E\nμ✝ : MeasureTheory.Measure ℝ\nf : ℝ → E\na b : ℝ\nμ : MeasureTheory.Measur... | [
488,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.mem_mk | [] | [
441,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
Mathlib/Data/PFun.lean | PFun.comp_apply | [] | [
583,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
582,
1
] |
Mathlib/Analysis/InnerProductSpace/Positive.lean | ContinuousLinearMap.IsPositive.adjoint_conj | [
{
"state_after": "case h.e'_7.h.e'_24.h.e'_24\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁶ : IsROrC 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : InnerProductSpace 𝕜 F\ninst✝¹ : CompleteSpace E\ninst✝ : CompleteSpace F\nT : E →L[𝕜] E\nhT : Is... | [
104,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Order/Hom/Lattice.lean | SupBotHom.symm_dual_id | [] | [
1463,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1462,
1
] |
Mathlib/GroupTheory/Submonoid/Basic.lean | Submonoid.closure_union | [] | [
530,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | lcm_dvd_lcm_mul_right | [] | [
853,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
852,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.card_functions_sum | [
{
"state_after": "no goals",
"state_before": "L : Language\nL' : Language\ni : ℕ\n⊢ (#Functions (Language.sum L L') i) = lift (#Functions L i) + lift (#Functions L' i)",
"tactic": "simp [Language.sum]"
}
] | [
256,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.prod_mono_left | [] | [
1066,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1065,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.stronglyMeasurable_const | [] | [
162,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | InitialSeg.ordinal_type_le | [] | [
367,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPolynomial.coe_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\nφ ψ : MvPolynomial σ R\n⊢ ↑φ = 0 ↔ φ = 0",
"tactic": "rw [← coe_zero, coe_inj]"
}
] | [
1150,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1150,
1
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.eq_symm_apply | [] | [
411,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
] |
Mathlib/Order/Hom/Basic.lean | codisjoint_map_orderIso_iff | [] | [
1233,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1230,
1
] |
Mathlib/Algebra/Order/UpperLower.lean | IsUpperSet.mul_right | [
{
"state_after": "α : Type u_1\ninst✝ : OrderedCommGroup α\ns t : Set α\na : α\nhs : IsUpperSet s\n⊢ IsUpperSet (t * s)",
"state_before": "α : Type u_1\ninst✝ : OrderedCommGroup α\ns t : Set α\na : α\nhs : IsUpperSet s\n⊢ IsUpperSet (s * t)",
"tactic": "rw [mul_comm]"
},
{
"state_after": "no goa... | [
77,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.lt_of_lt_pred | [] | [
258,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Order/Antichain.lean | IsAntichain.insert | [] | [
110,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
11
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.mk'_eq_iff_eq_mul | [] | [
291,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/Order/Monotone/Union.lean | StrictAntiOn.union | [] | [
69,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
11
] |
Mathlib/Data/Sign.lean | SignType.coe_one | [] | [
265,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/Algebra/CharP/Basic.lean | ringChar.of_eq | [] | [
226,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.quotientMap | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.58426\nδ : Type ?u.58429\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nh : α ≃ₜ β\n⊢ QuotientMap (↑h ∘ ↑(Homeomorph.symm h))",
"tactic": "simp only ... | [
238,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
11
] |
Mathlib/Order/Hom/Lattice.lean | LatticeHom.ext | [] | [
1059,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1058,
1
] |
Mathlib/Order/RelIso/Basic.lean | RelEmbedding.isStrictTotalOrder | [] | [
388,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
11
] |
Mathlib/Order/Heyting/Basic.lean | inf_himp | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.28319\nα : Type u_1\nβ : Type ?u.28325\ninst✝ : GeneralizedHeytingAlgebra α\na✝ b✝ c d a b : α\n⊢ a ⊓ (a ⇨ b) ≤ b",
"tactic": "rw [inf_comm, ← le_himp_iff]"
}
] | [
356,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Mathlib/Algebra/Polynomial/GroupRingAction.lean | prodXSubSmul.coeff | [
{
"state_after": "no goals",
"state_before": "M : Type ?u.109284\ninst✝⁴ : Monoid M\nG : Type u_2\ninst✝³ : Group G\ninst✝² : Fintype G\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : MulSemiringAction G R\nx : R\ng : G\nn : ℕ\n⊢ g • Polynomial.coeff (prodXSubSmul G R x) n = Polynomial.coeff (prodXSubSmul G R x... | [
123,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.snd_sum | [] | [
304,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/LinearAlgebra/Finrank.lean | FiniteDimensional.finrank_self | [
{
"state_after": "no goals",
"state_before": "K : Type u\nV : Type v\ninst✝⁵ : Ring K\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module K V\nV₂ : Type v'\ninst✝² : AddCommGroup V₂\ninst✝¹ : Module K V₂\ninst✝ : StrongRankCondition K\n⊢ Module.rank K K = ↑1",
"tactic": "simp"
}
] | [
144,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.mem_sups | [] | [
63,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/GroupTheory/PGroup.lean | IsPGroup.orderOf_coprime | [] | [
103,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/GroupTheory/Subsemigroup/Basic.lean | Subsemigroup.mk_le_mk | [] | [
132,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Algebra/Regular/SMul.lean | IsSMulRegular.smul | [] | [
72,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Algebra/Order/Rearrangement.lean | MonovaryOn.sum_smul_comp_perm_lt_sum_smul_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝³ : LinearOrderedRing α\ninst✝² : LinearOrderedAddCommGroup β\ninst✝¹ : Module α β\ninst✝ : OrderedSMul α β\ns : Finset ι\nσ : Perm ι\nf : ι → α\ng : ι → β\nhfg : MonovaryOn f g ↑s\nhσ : {x | ↑σ x ≠ x} ⊆ ↑s\n⊢ ∑ i i... | [
149,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.dual_node3R | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : Ordnode α\nx : α\nm : Ordnode α\ny : α\nr : Ordnode α\n⊢ dual (node3R l x m y r) = node3L (dual r) y (dual m) x (dual l)",
"tactic": "simp [node3L, node3R, dual_node', add_comm]"
}
] | [
322,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Std/Data/String/Lemmas.lean | String.Iterator.Valid.prev | [] | [
644,
35
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
640,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Pretrivialization.coe_coe | [] | [
113,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Combinatorics/Young/YoungDiagram.lean | YoungDiagram.coe_bot | [
{
"state_after": "case refine'_1\n\n⊢ ↑⊥.cells ⊆ ∅\n\ncase refine'_2\n\n⊢ ∅ ⊆ ↑⊥.cells",
"state_before": "⊢ ↑⊥.cells = ∅",
"tactic": "refine' Set.eq_of_subset_of_subset _ _"
},
{
"state_after": "case refine'_1\nx : ℕ × ℕ\nh : x ∈ ↑⊥.cells\n⊢ x ∈ ∅\n\ncase refine'_2\n\n⊢ ∅ ⊆ ↑⊥.cells",
"state... | [
182,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pullbackAssoc_inv_fst_snd | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝⁷ : Category C\nD : Type u₂\ninst✝⁶ : Category D\nW X Y Z X₁ X₂ X₃ Y₁ Y₂ : C\nf₁ : X₁ ⟶ Y₁\nf₂ : X₂ ⟶ Y₁\nf₃ : X₂ ⟶ Y₂\nf₄ : X₃ ⟶ Y₂\ninst✝⁵ : HasPullback f₁ f₂\ninst✝⁴ : HasPullback f₃ f₄\ninst✝³ : HasPullback (pullback.snd ≫ sorryAx (sorryAx C... | [
2441,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2438,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn' | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.1014853\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf g : E → F\np pf pg... | [
864,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
855,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | one_le_div_iff | [
{
"state_after": "case inl\nι : Type ?u.164600\nα : Type u_1\nβ : Type ?u.164606\ninst✝ : LinearOrderedField α\na b c d : α\nn : ℤ\nhb : b < 0\n⊢ 1 ≤ a / b ↔ 0 < b ∧ b ≤ a ∨ b < 0 ∧ a ≤ b\n\ncase inr.inl\nι : Type ?u.164600\nα : Type u_1\nβ : Type ?u.164606\ninst✝ : LinearOrderedField α\na c d : α\nn : ℤ\n⊢ 1 ≤... | [
846,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
842,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.ofReal_neg | [] | [
226,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Data/Nat/Pow.lean | Nat.pow_lt_pow_of_lt_left | [] | [
31,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.comap_inf | [] | [
2184,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2184,
9
] |
Mathlib/Data/Set/Intervals/Disjoint.lean | IsGLB.biUnion_Ici_eq_Ioi | [
{
"state_after": "case refine'_1\nι : Sort u\nα : Type v\nβ : Type w\ninst✝ : LinearOrder α\ns : Set α\na : α\nf : ι → α\na_glb : IsGLB s a\na_not_mem : ¬a ∈ s\nx : α\nhx : x ∈ s\n⊢ Ici x ⊆ Ioi a\n\ncase refine'_2\nι : Sort u\nα : Type v\nβ : Type w\ninst✝ : LinearOrder α\ns : Set α\na : α\nf : ι → α\na_glb : I... | [
210,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.eta | [] | [
56,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Std/Data/List/Lemmas.lean | List.mem_of_find?_eq_some | [
{
"state_after": "case pos\nα✝ : Type u_1\np : α✝ → Bool\na b : α✝\nl : List α✝\nh : p b = true\nH : b = a\n⊢ a ∈ b :: l\n\ncase neg\nα✝ : Type u_1\np : α✝ → Bool\na b : α✝\nl : List α✝\nh : ¬p b = true\nH : find? p l = some a\n⊢ a ∈ b :: l",
"state_before": "α✝ : Type u_1\np : α✝ → Bool\na b : α✝\nl : List... | [
1272,
45
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1268,
9
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | gcd_greatest_associated | [] | [
676,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
672,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.familyOfBFamily'_enum | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.271765\nβ : Type ?u.271768\nγ : Type ?u.271771\nr✝ : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nι : Type u\nr : ι → ι → Prop\ninst✝ : IsWellOrder ι r\no : Ordinal\nho : type r = o\nf : (a : Ordinal) → a < o → α\ni : Ordinal\nhi : i < o\n⊢ i < ... | [
1157,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1154,
1
] |
Mathlib/Data/List/Chain.lean | List.chain_iff_forall₂ | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nR r : α → α → Prop\nl l₁ l₂ : List α\na✝ b a : α\n⊢ Chain R a [] ↔ [] = [] ∨ Forall₂ R (a :: dropLast []) []",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nR r : α → α → Prop\nl... | [
78,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Tactic/PushNeg.lean | Mathlib.Tactic.PushNeg.not_ge_eq | [] | [
31,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
31,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.mem_support_onFinset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.175978\nγ : Type ?u.175981\nι : Type ?u.175984\nM : Type u_2\nM' : Type ?u.175990\nN : Type ?u.175993\nP : Type ?u.175996\nG : Type ?u.175999\nH : Type ?u.176002\nR : Type ?u.176005\nS : Type ?u.176008\ninst✝ : Zero M\ns : Finset α\nf :... | [
713,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
711,
1
] |
Mathlib/Algebra/AddTorsor.lean | Prod.mk_vsub_mk | [] | [
332,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/Algebra/GeomSum.lean | geom_sum₂_self | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u\nα : Type u_1\ninst✝ : CommRing α\nx : α\nn : ℕ\n⊢ ∑ i in range n, x ^ i * x ^ (n - 1 - i) = ∑ i in range n, x ^ (i + (n - 1 - i))",
"tactic": "simp_rw [← pow_add]"
},
{
"state_after": "no goals",
"state_before": "α✝ : Type u\nα : Typ... | [
156,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.sdiff_eq_self_iff_disjoint | [] | [
2360,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2359,
1
] |
Mathlib/Order/Atoms.lean | isCoatomic_dual_iff_isAtomic | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.11708\ninst✝¹ : PartialOrder α\ninst✝ : OrderBot α\nh : IsCoatomic αᵒᵈ\nb : α\n⊢ b = ⊥ ∨ ∃ a, IsAtom a ∧ a ≤ b",
"tactic": "apply h.eq_top_or_exists_le_coatom"
},
{
"state_after": "no goals",
"state_before": "α : Type u_... | [
257,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/Algebra/Ring/Prod.lean | false_of_nontrivial_of_product_domain | [
{
"state_after": "α : Type ?u.54070\nβ : Type ?u.54073\nR✝ : Type ?u.54076\nR' : Type ?u.54079\nS✝ : Type ?u.54082\nS' : Type ?u.54085\nT : Type ?u.54088\nT' : Type ?u.54091\nR : Type u_1\nS : Type u_2\ninst✝⁴ : Ring R\ninst✝³ : Ring S\ninst✝² : IsDomain (R × S)\ninst✝¹ : Nontrivial R\ninst✝ : Nontrivial S\nthi... | [
344,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/Data/Set/Intervals/Group.lean | Set.sub_mem_Ico_iff_right | [] | [
127,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Order/Bounds/Basic.lean | mem_lowerBounds | [] | [
91,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Topology/Algebra/ConstMulAction.lean | Continuous.const_smul | [] | [
112,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Data/Quot.lean | Quotient.out_inj | [] | [
406,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.semiconj₂_conj | [
{
"state_after": "no goals",
"state_before": "α₁ : Type u_1\nβ₁ : Type u_2\ne : α₁ ≃ β₁\nf : α₁ → α₁ → α₁\nx y : α₁\n⊢ ↑e (f x y) = ↑(arrowCongr e (conj e)) f (↑e x) (↑e y)",
"tactic": "simp [arrowCongr]"
}
] | [
1849,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1849,
1
] |
Mathlib/Deprecated/Subgroup.lean | Group.mclosure_inv_subset | [] | [
623,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
621,
1
] |
Mathlib/LinearAlgebra/Quotient.lean | Submodule.Quotient.eq' | [] | [
82,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
11
] |
Mathlib/Algebra/Lie/Basic.lean | lie_self | [] | [
151,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/FieldTheory/Laurent.lean | RatFunc.laurent_X | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : CommRing R\nhdomain : IsDomain R\nr s : R\np q : R[X]\nf : RatFunc R\n⊢ ↑(laurent r) X = X + ↑C r",
"tactic": "rw [← algebraMap_X, laurent_algebraMap, taylor_X, _root_.map_add, algebraMap_C]"
}
] | [
101,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Order/SymmDiff.lean | symmDiff_symmDiff_right' | [
{
"state_after": "case e_a\nι : Type ?u.91463\nα : Type u_1\nβ : Type ?u.91469\nπ : ι → Type ?u.91474\ninst✝ : BooleanAlgebra α\na b c d : α\n⊢ a ⊓ b ⊓ c ⊔ a ⊓ bᶜ ⊓ cᶜ ⊔ b ⊓ cᶜ ⊓ aᶜ = a ⊓ b ⊓ c ⊔ a ⊓ bᶜ ⊓ cᶜ ⊔ aᶜ ⊓ b ⊓ cᶜ\n\ncase e_a\nι : Type ?u.91463\nα : Type u_1\nβ : Type ?u.91469\nπ : ι → Type ?u.91474\nin... | [
789,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
778,
1
] |
Mathlib/Topology/ContinuousFunction/Basic.lean | ContinuousMap.continuousAt | [] | [
149,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
11
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | tendstoLocallyUniformlyOn_iff_filter | [
{
"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\n⊢ TendstoLocallyUniformlyOn F f p s ↔\n ∀ (x : α),\n x ∈ s →\n ∀ (u : Set (β × β)),\n ... | [
765,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
756,
1
] |
Mathlib/Algebra/Order/UpperLower.lean | UpperSet.coe_one | [] | [
149,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_const_mul_Ici | [] | [
617,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
616,
1
] |
Mathlib/Topology/Instances/EReal.lean | EReal.mem_nhds_bot_iff | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.16219\ninst✝ : TopologicalSpace α\ns : Set EReal\n⊢ (∃ i, True ∧ Iio ↑i ⊆ s) ↔ ∃ y, Iio ↑y ⊆ s",
"tactic": "simp only [true_and]"
}
] | [
168,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.nat_sub | [] | [
316,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/Data/Set/Basic.lean | Set.inter_assoc | [] | [
930,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
929,
1
] |
Mathlib/Computability/EpsilonNFA.lean | NFA.toεNFA_correct | [
{
"state_after": "α : Type u\nσ σ' : Type v\nM✝ : εNFA α σ\nS : Set σ\nx : List α\ns : σ\na : α\nM : NFA α σ\n⊢ {x | ∃ S, S ∈ (toεNFA M).accept ∧ S ∈ evalFrom M (toεNFA M).start x} = accepts M",
"state_before": "α : Type u\nσ σ' : Type v\nM✝ : εNFA α σ\nS : Set σ\nx : List α\ns : σ\na : α\nM : NFA α σ\n⊢ εN... | [
212,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Data/PFun.lean | PFun.preimage_union | [] | [
451,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.map_map_zero_lt | [] | [
487,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.mex_lt_ord_succ_mk | [
{
"state_after": "α : Type ?u.378408\nβ : Type ?u.378411\nγ : Type ?u.378414\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nι : Type u\nf : ι → Ordinal\nh : ord (succ (#ι)) ≤ mex f\n⊢ False",
"state_before": "α : Type ?u.378408\nβ : Type ?u.378411\nγ : Type ?u.378414\nr : α → α → Prop\ns : β → β → P... | [
2059,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2046,
1
] |
Mathlib/Topology/GDelta.lean | isGδ_singleton | [
{
"state_after": "case intro.intro\nα : Type u_1\nβ : Type ?u.12419\nγ : Type ?u.12422\nι : Type ?u.12425\ninst✝² : TopologicalSpace α\ninst✝¹ : T1Space α\ninst✝ : FirstCountableTopology α\na : α\nU : ℕ → Set α\nhU : ∀ (i : ℕ), a ∈ U i ∧ IsOpen (U i)\nh_basis : HasAntitoneBasis (𝓝 a) fun i => U i\n⊢ IsGδ {a}",... | [
166,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.sup_eq_of_range_eq | [] | [
1333,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1331,
1
] |
Mathlib/Topology/ContinuousOn.lean | ContinuousWithinAt.mono | [] | [
698,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
696,
1
] |
Mathlib/Data/Set/Intervals/Monoid.lean | Set.image_const_add_Ico | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\ninst✝¹ : OrderedCancelAddCommMonoid M\ninst✝ : ExistsAddOfLE M\na b c d : M\n⊢ (fun x => a + x) '' Ico b c = Ico (a + b) (a + c)",
"tactic": "simp only [add_comm a, image_add_const_Ico]"
}
] | [
132,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.