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/Int/Log.lean | Int.log_one_right | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹ : LinearOrderedSemifield R\ninst✝ : FloorSemiring R\nb : ℕ\n⊢ log b 1 = 0",
"tactic": "rw [log_of_one_le_right _ le_rfl, Nat.floor_one, Nat.log_one_right, Int.ofNat_zero]"
}
] | [
131,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Algebra/Hom/Equiv/Units/Basic.lean | Units.mulLeft_bijective | [] | [
82,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | TendstoUniformly.tendstoUniformlyOnFilter | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝ : UniformSpace β\nF : ι → α → β\nf : α → β\ns s' : Set α\nx : α\np : Filter ι\np' : Filter α\ng : ι → α\nh : TendstoUniformly F f p\n⊢ TendstoUniformlyOnFilter F f p ⊤",
"tactic": "rwa [← tendstoUniformly... | [
150,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidHom.cancel_right | [] | [
1177,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1174,
1
] |
Mathlib/Data/Pi/Algebra.lean | Pi.mulSingle_eq_of_ne' | [] | [
256,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/Tactic/CategoryTheory/BicategoryCoherence.lean | Mathlib.Tactic.BicategoryCoherence.bicategoricalComp_refl | [
{
"state_after": "B : Type u\ninst✝ : Bicategory B\na b c d e : B\nf g h : a ⟶ b\nη : f ⟶ g\nθ : g ⟶ h\n⊢ η ≫ 𝟙 g ≫ θ = η ≫ θ",
"state_before": "B : Type u\ninst✝ : Bicategory B\na b c d e : B\nf g h : a ⟶ b\nη : f ⟶ g\nθ : g ⟶ h\n⊢ η ⊗≫ θ = η ≫ θ",
"tactic": "dsimp [bicategoricalComp]"
},
{
"s... | [
243,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.toAddSubgroup_injective | [] | [
270,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Logic/IsEmpty.lean | IsEmpty.prop_iff | [] | [
113,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
11
] |
Mathlib/Algebra/GroupWithZero/Semiconj.lean | SemiconjBy.div_right | [
{
"state_after": "α : Type ?u.2687\nM₀ : Type ?u.2690\nG₀ : Type u_1\nM₀' : Type ?u.2696\nG₀' : Type ?u.2699\nF : Type ?u.2702\nF' : Type ?u.2705\ninst✝ : GroupWithZero G₀\na x y x' y' : G₀\nh : SemiconjBy a x y\nh' : SemiconjBy a x' y'\n⊢ SemiconjBy a (x * x'⁻¹) (y * y'⁻¹)",
"state_before": "α : Type ?u.26... | [
67,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Data/List/Sigma.lean | List.dlookup_kinsert_ne | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : α → Type v\nl✝ l₁ l₂ : List (Sigma β)\ninst✝ : DecidableEq α\na a' : α\nb' : β a'\nl : List (Sigma β)\nh : a ≠ a'\n⊢ dlookup a (kinsert a' b' l) = dlookup a l",
"tactic": "simp [h]"
}
] | [
594,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
] |
Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | BilinForm.toMatrix'_symm | [] | [
195,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.smul_C | [] | [
516,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.countable_meas_level_set_pos | [] | [
3631,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3625,
1
] |
Mathlib/Topology/Algebra/GroupCompletion.lean | UniformSpace.Completion.coe_zero | [] | [
61,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.not_bddAbove_setOf_prime | [
{
"state_after": "⊢ ∀ (x : ℕ), ∃ y, y ∈ {p | Prime p} ∧ x < y",
"state_before": "⊢ ¬BddAbove {p | Prime p}",
"tactic": "rw [not_bddAbove_iff]"
},
{
"state_after": "n : ℕ\n⊢ ∃ y, y ∈ {p | Prime p} ∧ n < y",
"state_before": "⊢ ∀ (x : ℕ), ∃ y, y ∈ {p | Prime p} ∧ x < y",
"tactic": "intro n"... | [
492,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.natDegree_of_zero | [] | [
444,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
1
] |
Mathlib/Topology/UrysohnsLemma.lean | Urysohns.CU.lim_le_one | [] | [
250,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.minFac_eq | [] | [
279,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.blockDiagonal_sub | [] | [
453,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
1
] |
Std/Data/Nat/Gcd.lean | Nat.coprime.symm | [] | [
244,
73
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
244,
1
] |
Mathlib/Topology/Filter.lean | Filter.tendsto_nhds_atBot_iff | [] | [
203,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
11
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | HasFDerivAt.smul_const | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝¹² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nF : Type u_4\ninst✝⁹ : NormedAddCommGroup F\ninst✝⁸ : NormedSpace 𝕜 F\nG : Type ?u.594580\ninst✝⁷ : NormedAddCommGroup G\ninst✝⁶ : Nor... | [
241,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_sub' | [] | [
895,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
893,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | Module.End.natCast_def | [] | [
1240,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1238,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.coeToSubmodule_eq_bot | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝² : CommRing R\nS : Submonoid R\nP : Type u_2\ninst✝¹ : CommRing P\ninst✝ : Algebra R P\nloc : IsLocalization S P\nI : FractionalIdeal S P\nh : ↑I = ⊥\n⊢ (fun I => ↑I) I = (fun I => ↑I) 0",
"tactic": "simp [h]"
},
{
"state_after": ... | [
333,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
Mathlib/GroupTheory/Abelianization.lean | Abelianization.mk_eq_of | [] | [
120,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Order/Heyting/Basic.lean | sup_le_of_le_sdiff_left | [] | [
588,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
587,
1
] |
Mathlib/Order/Filter/Extr.lean | IsMinOn.comp_antitone | [] | [
358,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/Topology/Bornology/Hom.lean | LocallyBoundedMap.coe_ofMapBounded | [] | [
129,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Data/Set/Intervals/Disjoint.lean | Set.eq_of_Ico_disjoint | [
{
"state_after": "ι : Sort u\nα : Type v\nβ : Type w\ninst✝ : LinearOrder α\na₁ a₂ b₁ b₂ x₁ x₂ y₁ y₂ : α\nh : x₂ ≤ x₁ ∨ x₂ ≤ y₁\nhx : x₁ < x₂\nh2 : x₂ ∈ Ico y₁ y₂\n⊢ y₁ = x₂",
"state_before": "ι : Sort u\nα : Type v\nβ : Type w\ninst✝ : LinearOrder α\na₁ a₂ b₁ b₂ x₁ x₂ y₁ y₂ : α\nh : Disjoint (Ico x₁ x₂) (I... | [
150,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.coe_restrictScalars | [] | [
441,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
Mathlib/Topology/Category/Compactum.lean | Compactum.join_distrib | [
{
"state_after": "X : Compactum\nuux : Ultrafilter (Ultrafilter X.A)\n⊢ ((Monad.μ β).app X.A ≫ X.a) uux = str X (Ultrafilter.map (str X) uux)",
"state_before": "X : Compactum\nuux : Ultrafilter (Ultrafilter X.A)\n⊢ str X (join X uux) = str X (Ultrafilter.map (str X) uux)",
"tactic": "change ((β ).μ.app ... | [
165,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/ModelTheory/Encoding.lean | FirstOrder.Language.Term.card_le | [] | [
124,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Analysis/Calculus/Series.lean | fderiv_tsum_apply | [] | [
182,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.xor_assoc | [
{
"state_after": "no goals",
"state_before": "⊢ ∀ (a b c : Bool), xor (xor a b) c = xor a (xor b c)",
"tactic": "decide"
}
] | [
267,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Algebra/EuclideanDomain/Basic.lean | EuclideanDomain.mul_div_mul_cancel | [
{
"state_after": "case pos\nR : Type u\ninst✝ : EuclideanDomain R\na b c : R\nha : a ≠ 0\nhcb : c ∣ b\nhc : c = 0\n⊢ a * b / (a * c) = b / c\n\ncase neg\nR : Type u\ninst✝ : EuclideanDomain R\na b c : R\nha : a ≠ 0\nhcb : c ∣ b\nhc : ¬c = 0\n⊢ a * b / (a * c) = b / c",
"state_before": "R : Type u\ninst✝ : E... | [
347,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.refl_source | [] | [
609,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
608,
1
] |
Mathlib/Topology/Order/Basic.lean | Monotone.map_csSup_of_continuousAt | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝⁶ : ConditionallyCompleteLinearOrder α\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : OrderTopology α\ninst✝³ : ConditionallyCompleteLinearOrder β\ninst✝² : TopologicalSpace β\ninst✝¹ : OrderClosedTopology β\ninst✝ : Nonempty γ\nf : α → β\ns : Set α\nCf : Conti... | [
2799,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2795,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSpace.gc_comap_map | [] | [
132,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Data/Int/Parity.lean | Int.two_mul_ediv_two_of_even | [] | [
253,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Order/Minimal.lean | minimals_subset | [] | [
49,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/GroupTheory/Perm/List.lean | List.formPerm_mem_iff_mem | [] | [
124,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.equivMapDomain_trans' | [
{
"state_after": "case h.h\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nι : Type ?u.142684\nM : Type u_4\nM' : Type ?u.142690\nN : Type ?u.142693\nP : Type ?u.142696\nG : Type ?u.142699\nH : Type ?u.142702\nR : Type ?u.142705\nS : Type ?u.142708\ninst✝ : Zero M\nf : α ≃ β\ng : β ≃ γ\nx : α →₀ M\na✝ : γ\n⊢ ↑(equiv... | [
341,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/Data/PNat/Factors.lean | PNat.factorMultiset_le_iff | [
{
"state_after": "case mp\nm n : ℕ+\n⊢ factorMultiset m ≤ factorMultiset n → m ∣ n\n\ncase mpr\nm n : ℕ+\n⊢ m ∣ n → factorMultiset m ≤ factorMultiset n",
"state_before": "m n : ℕ+\n⊢ factorMultiset m ≤ factorMultiset n ↔ m ∣ n",
"tactic": "constructor"
},
{
"state_after": "case mp\nm n : ℕ+\nh :... | [
337,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/Data/MvPolynomial/Division.lean | MvPolynomial.X_dvd_monomial | [
{
"state_after": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\ni : σ\nj : σ →₀ ℕ\nr : R\n⊢ (r = 0 ∨ Finsupp.single i 1 ≤ j) ∧ 1 ∣ r ↔ r = 0 ∨ ↑j i ≠ 0",
"state_before": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\ni : σ\nj : σ →₀ ℕ\nr : R\n⊢ X i ∣ ↑(monomial j) r ↔ r = 0 ∨ ↑j i ≠ 0",
"tac... | [
266,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_eq_sum | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q r : R[X]\nx : R\n⊢ (sum p fun e a => ↑(RingHom.id R) a * x ^ e) = sum p fun e a => a * x ^ e",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝ : Semiring R\np ... | [
318,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_const_mul | [
{
"state_after": "case e_f\nα : Type u_1\nβ : Type ?u.933531\nγ : Type ?u.933534\nδ : Type ?u.933537\nm : MeasurableSpace α\nμ ν : Measure α\nr : ℝ≥0∞\nf : α → ℝ≥0∞\nhf : Measurable f\n⊢ (fun a => r * f a) = fun a => ⨆ (n : ℕ), ↑(const α r * eapprox f n) a",
"state_before": "α : Type u_1\nβ : Type ?u.933531... | [
696,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
679,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.integrable_of_summable_norm_restrict | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_3\nE : Type u_2\nF : Type ?u.312326\ninst✝⁶ : MeasurableSpace α\nμ : Measure α\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : Countable β\ninst✝³ : TopologicalSpace α\ninst✝² : BorelSpace α\ninst✝¹ : MetrizableSpace α\ninst✝ : IsLocallyFiniteM... | [
826,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
823,
1
] |
Mathlib/Analysis/Convex/Gauge.lean | gauge_def | [] | [
64,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.coe_one | [] | [
259,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.le_congr_imp | [] | [
798,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
797,
1
] |
Mathlib/Algebra/Ring/Defs.lean | one_add_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nR : Type x\ninst✝² : Add α\ninst✝¹ : MulOneClass α\ninst✝ : RightDistribClass α\na b : α\n⊢ (1 + a) * b = b + a * b",
"tactic": "rw [add_mul, one_mul]"
}
] | [
166,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Std/Data/Int/Lemmas.lean | Int.le_add_one | [] | [
854,
40
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
853,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.AEEqFun.integrable_zero | [] | [
1224,
66
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1223,
1
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Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.mk_inf_mk | [] | [
172,
6
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170,
1
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Mathlib/Analysis/Convex/Extreme.lean | IsExtreme.antisymm | [] | [
91,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
11
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Mathlib/Algebra/BigOperators/Basic.lean | Multiset.toFinset_prod_dvd_prod | [
{
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2171,
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.source_inter_preimage_target_inter | [] | [
307,
54
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305,
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Mathlib/RingTheory/Ideal/Operations.lean | Ideal.comap_bot_le_of_injective | [
{
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1627,
47
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1624,
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Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingIso.symm_bijective | [] | [
510,
36
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508,
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Mathlib/RingTheory/WittVector/IsPoly.lean | WittVector.addIsPoly₂ | [
{
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542,
55
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539,
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Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.restrict_smul | [
{
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802,
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793,
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Std/Data/PairingHeap.lean | Std.PairingHeapImp.Heap.WF.merge_node | [
{
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237,
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232,
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Mathlib/Topology/Bases.lean | TopologicalSpace.IsTopologicalBasis.quotientMap | [
{
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851,
64
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839,
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Mathlib/Order/Lattice.lean | inf_inf_inf_comm | [] | [
532,
34
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531,
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Mathlib/LinearAlgebra/Matrix/DotProduct.lean | Matrix.dotProduct_self_eq_zero | [
{
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}
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85,
31
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1
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Mathlib/Topology/OmegaCompletePartialOrder.lean | continuous_of_scottContinuous | [
{
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36
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151,
1
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Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.bot_coe | [] | [
370,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
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Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ico_union_Ico_eq_Ico | [
{
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758,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
756,
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Mathlib/Algebra/GroupPower/Order.lean | sq_lt_sq | [
{
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693,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
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Mathlib/Data/List/Rotate.lean | List.IsRotated.symm | [
{
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},
{
"state_after": "case intro.nil\nα : Type u\nn : ℕ\n⊢ rotate [] n ~r []\n\ncase intro.cons\nα : Type u\nn : ℕ... | [
451,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
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Mathlib/Topology/Algebra/Group/Basic.lean | Homeomorph.shearMulRight_coe | [] | [
662,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
660,
1
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Mathlib/Topology/Algebra/GroupWithZero.lean | ContinuousAt.zpow₀ | [] | [
338,
15
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336,
8
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | aemeasurable_coe_nnreal_ennreal_iff | [] | [
1911,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1909,
1
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Mathlib/Algebra/EuclideanDomain/Basic.lean | EuclideanDomain.dvd_gcd | [
{
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},
{
"state_after": "R : Type u\ninst✝¹ : EuclideanDomain R\ninst✝ : DecidableEq R... | [
176,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
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Std/Classes/Order.lean | Std.OrientedCmp.cmp_eq_gt | [
{
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32,
45
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31,
1
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Mathlib/Topology/Inseparable.lean | specializes_pi | [
{
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217,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
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Mathlib/LinearAlgebra/FreeModule/Finite/Rank.lean | FiniteDimensional.nonempty_linearEquiv_of_finrank_eq | [
{
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144,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
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Mathlib/Analysis/Convex/Basic.lean | Convex.affinity | [
{
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433,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.card_image_le | [
{
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}
] | [
220,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Std/Data/Int/DivMod.lean | Int.dvd_antisymm | [
{
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"state_before": "a b : Int\nH1 : 0 ≤ a\nH2 : 0 ≤ b\n⊢ a ∣ b → b ∣ a → a = b",
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},
{
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670,
25
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
667,
1
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Mathlib/Algebra/Order/Hom/Basic.lean | map_div_rev | [
{
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"tactic": "rw [← inv_div, map_... | [
253,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/AlgebraicTopology/DoldKan/PInfty.lean | AlgebraicTopology.DoldKan.Q_is_eventually_constant | [
{
"state_after": "no goals",
"state_before": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX : SimplicialObject C\nq n : ℕ\nhqn : n ≤ q\n⊢ HomologicalComplex.Hom.f (Q (q + 1)) n = HomologicalComplex.Hom.f (Q q) n",
"tactic": "simp only [Q, HomologicalComplex.sub_f_apply, P_is_eventually_con... | [
50,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Data/Polynomial/Expand.lean | Polynomial.expand_char | [
{
"state_after": "case refine'_1\nR : Type u\ninst✝² : CommSemiring R\nS : Type v\ninst✝¹ : CommSemiring S\np q : ℕ\ninst✝ : CharP R p\nhp : Fact (Nat.Prime p)\nf a b : R[X]\nha : map (frobenius R p) (↑(expand R p) a) = a ^ p\nhb : map (frobenius R p) (↑(expand R p) b) = b ^ p\n⊢ map (frobenius R p) (↑(expand R... | [
253,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.top_prod | [
{
"state_after": "no goals",
"state_before": "M : Type u_2\nN : Type u_1\nP : Type ?u.51321\nσ : Type ?u.51324\ninst✝² : Mul M\ninst✝¹ : Mul N\ninst✝ : Mul P\nS : Subsemigroup M\ns : Subsemigroup N\nx : M × N\n⊢ x ∈ prod ⊤ s ↔ x ∈ comap (MulHom.snd M N) s",
"tactic": "simp [mem_prod, MulHom.coe_snd]"
... | [
674,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
673,
1
] |
Mathlib/Data/List/Rotate.lean | List.isRotated_nil_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nl l' : List α\nx✝ : l ~r []\nn : ℕ\nhn : rotate l n = []\n⊢ l = []",
"tactic": "simpa using hn"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nl l' : List α\nh : l = []\n⊢ l ~r l",
"tactic": "rfl"
}
] | [
492,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
491,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.congr_fun | [] | [
162,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
11
] |
Mathlib/ModelTheory/Definability.lean | Set.Definable.image_comp_embedding | [
{
"state_after": "no goals",
"state_before": "M : Type w\nA : Set M\nL : Language\ninst✝¹ : Structure L M\nα : Type u₁\nβ : Type u_1\nB : Set M\ns✝ : Set (α → M)\ns : Set (β → M)\nh : Definable A L s\nf : α ↪ β\ninst✝ : Finite β\n⊢ Definable A L ((fun g => g ∘ ↑f) '' s)",
"tactic": "classical\n cases n... | [
203,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.decide_and | [
{
"state_after": "no goals",
"state_before": "p q : Prop\ninst✝¹ : Decidable p\ninst✝ : Decidable q\n⊢ decide (p ∧ q) = (decide p && decide q)",
"tactic": "by_cases p <;> by_cases q <;> simp [*]"
}
] | [
69,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.mem_pair | [
{
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"tactic": "simp"
}
] | [
938,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
937,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.IsTrail.of_append_left | [
{
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"state_before": "V : Type u\nV' : Type v\nV'' ... | [
946,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
943,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.card_lt_of_lt | [] | [
774,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
773,
1
] |
Mathlib/Init/CcLemmas.lean | eq_false_of_or_eq_false_right | [] | [
108,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.continuous | [] | [
274,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
11
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffAt.sum | [
{
"state_after": "𝕜 : Type u_2\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝⁹ : NormedAddCommGroup D\ninst✝⁸ : NormedSpace 𝕜 D\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : Normed... | [
1357,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1354,
1
] |
Mathlib/Order/Circular.lean | btw_rfl_left_right | [] | [
299,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Monad.lean | Pmf.bindOnSupport_comm | [
{
"state_after": "case h\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\np✝ : Pmf α\nf✝ : (a : α) → a ∈ support p✝ → Pmf β\np : Pmf α\nq : Pmf β\nf : (a : α) → a ∈ support p → (b : β) → b ∈ support q → Pmf γ\n⊢ ∀ (x : γ),\n ↑(bindOnSupport p fun a ha => bindOnSupport q (f a ha)) x =\n ↑(bindOnSupport q fun b... | [
304,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/Order/Monotone/Monovary.lean | antivaryOn_const_right | [] | [
144,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.setToL1_add_left' | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type u_3\nF' : Type ?u.1092386\nG : Type ?u.1092389\n𝕜 : Type ?u.1092392\np : ℝ≥0∞\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace ℝ E\ninst✝⁸ : NormedAddCommGroup F\ninst✝⁷ : NormedSpace ℝ F\ninst✝⁶ : NormedAddCommGroup F'\ninst✝⁵ : NormedSpace ℝ F'\nins... | [
1108,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1097,
1
] |
Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean | SimpleGraph.ComponentCompl.infinite_iff_in_all_ranges | [
{
"state_after": "case mp\nV : Type u\nG : SimpleGraph V\nK✝ L L' M : Set V\nK : Finset V\nC : ComponentCompl G ↑K\n⊢ Set.Infinite (supp C) → ∀ (L : Finset V) (h : K ⊆ L), ∃ D, hom h D = C\n\ncase mpr\nV : Type u\nG : SimpleGraph V\nK✝ L L' M : Set V\nK : Finset V\nC : ComponentCompl G ↑K\n⊢ (∀ (L : Finset V) (... | [
245,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
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