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/Topology/MetricSpace/PiNat.lean | PiNat.mem_cylinder_firstDiff | [] | [
167,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | WithBot.sInf_eq | [] | [
76,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Data/Int/ConditionallyCompleteOrder.lean | Int.csSup_eq_greatest_of_bdd | [
{
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70,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Lie/Submodule.lean | LieModuleHom.comp_ker_incl | [
{
"state_after": "case h.mk\nR : Type u\nL : Type v\nM : Type w\nN : Type w₁\ninst✝¹⁰ : CommRing R\ninst✝⁹ : LieRing L\ninst✝⁸ : LieAlgebra R L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³ : AddCommGroup N\ninst✝² : Module R N\ninst✝¹ : LieRingModul... | [
1195,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1195,
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Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | ENNReal.continuous_rpow_const | [
{
"state_after": "y : ℝ\nx : ℝ≥0∞\n⊢ ContinuousAt (fun a => a ^ y) x",
"state_before": "y : ℝ\n⊢ Continuous fun a => a ^ y",
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},
{
"state_after": "case inl\ny : ℝ\nx : ℝ≥0∞\nhy : 0 < y\n⊢ ContinuousAt (fun a => a ^ y) x\n\ncase inr.inl\... | [
525,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
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Mathlib/Order/Monotone/Monovary.lean | MonotoneOn.antivaryOn | [] | [
342,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
11
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Mathlib/Algebra/GCDMonoid/Basic.lean | lcm_eq_left_iff | [] | [
841,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
838,
1
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Mathlib/Data/Set/Basic.lean | Set.not_nontrivial_empty | [] | [
2536,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2536,
1
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Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean | MeasureTheory.Measure.add_haar_ball_mul | [
{
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433,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/NumberTheory/Padics/Hensel.lean | soln_dist_to_a_lt_deriv | [
{
"state_after": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nF : Polynomial ℤ_[p]\na : ℤ_[p]\nhnorm : ‖Polynomial.eval a F‖ < ‖Polynomial.eval a (↑Polynomial.derivative F)‖ ^ 2\nhnsol : Polynomial.eval a F ≠ 0\n⊢ ‖Polynomial.eval a F‖ <\n ‖Polynomial.eval a (↑Polynomial.derivative F)‖ * ‖Polynomial.eval a (↑Polynomi... | [
420,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
9
] |
Mathlib/Data/Nat/ModEq.lean | Nat.ModEq.mul_left_cancel' | [
{
"state_after": "no goals",
"state_before": "m✝ n a✝ b✝ c✝ d a b c m : ℕ\nhc : c ≠ 0\n⊢ c * a ≡ c * b [MOD c * m] → a ≡ b [MOD m]",
"tactic": "simp [modEq_iff_dvd, ← mul_sub, mul_dvd_mul_iff_left (by simp [hc] : (c : ℤ) ≠ 0)]"
},
{
"state_after": "no goals",
"state_before": "m✝ n a✝ b✝ c✝ d... | [
181,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
11
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.C_pow | [] | [
531,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
530,
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.memℒp_top_of_bound | [
{
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562,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
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Mathlib/Data/List/Count.lean | List.countp_mono_left | [
{
"state_after": "case nil\nα : Type u_1\nl : List α\np q : α → Bool\nh✝ : ∀ (x : α), x ∈ l → p x = true → q x = true\nh : ∀ (x : α), x ∈ [] → p x = true → q x = true\n⊢ countp p [] ≤ countp q []\n\ncase cons\nα : Type u_1\nl✝ : List α\np q : α → Bool\nh✝ : ∀ (x : α), x ∈ l✝ → p x = true → q x = true\na : α\nl ... | [
156,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
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Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.nat_cast_snd | [] | [
311,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
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Mathlib/Data/Stream/Init.lean | Stream'.nth_tails | [
{
"state_after": "α : Type u\nβ : Type v\nδ : Type w\nn : ℕ\n⊢ ∀ (s : Stream' α), nth (tails s) n = drop n (tail s)",
"state_before": "α : Type u\nβ : Type v\nδ : Type w\n⊢ ∀ (n : ℕ) (s : Stream' α), nth (tails s) n = drop n (tail s)",
"tactic": "intro n"
},
{
"state_after": "case zero\nα : Type... | [
678,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
673,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.support_update | [
{
"state_after": "no goals",
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"tactic": "classical\n cases p\n simp only [support... | [
1116,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1111,
1
] |
Mathlib/CategoryTheory/Opposites.lean | CategoryTheory.NatTrans.unop_id | [] | [
340,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | SemiconjBy.cast_int_mul_left | [] | [
1070,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1069,
1
] |
Mathlib/CategoryTheory/Limits/IsLimit.lean | CategoryTheory.Limits.IsColimit.OfNatIso.cocone_fac | [
{
"state_after": "J : Type u₁\ninst✝² : Category J\nK : Type u₂\ninst✝¹ : Category K\nC : Type u₃\ninst✝ : Category C\nF : J ⥤ C\nt : Cocone F\nX : C\nh : coyoneda.obj X.op ⋙ uliftFunctor ≅ Functor.cocones F\ns : Cocone F\n⊢ Cocone.extend (colimitCocone h) (homOfCocone h (coconeOfHom h (homOfCocone h s))) = coc... | [
1040,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1037,
1
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Mathlib/GroupTheory/Submonoid/Basic.lean | Submonoid.mem_iSup | [
{
"state_after": "M : Type u_2\nN : Type ?u.29131\nA : Type ?u.29134\ninst✝¹ : MulOneClass M\ns : Set M\ninst✝ : AddZeroClass A\nt : Set A\nS : Submonoid M\nι : Sort u_1\np : ι → Submonoid M\nm : M\n⊢ (∀ (b : Submonoid M), (∀ (i : ι), p i ≤ b) → closure {m} ≤ b) ↔ ∀ (N : Submonoid M), (∀ (i : ι), p i ≤ N) → m ∈... | [
551,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mul_eq_left_iff | [
{
"state_after": "a b : Cardinal\n⊢ a * b = a ↔ (ℵ₀ ≤ a ∧ b ≤ a) ∧ b ≠ 0 ∨ b = 1 ∨ a = 0",
"state_before": "a b : Cardinal\n⊢ a * b = a ↔ max ℵ₀ b ≤ a ∧ b ≠ 0 ∨ b = 1 ∨ a = 0",
"tactic": "rw [max_le_iff]"
},
{
"state_after": "case refine'_1\na b : Cardinal\nh : a * b = a\n⊢ (ℵ₀ ≤ a ∧ b ≤ a) ∧ b ... | [
711,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
669,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | BilinForm.toQuadraticForm_neg | [] | [
731,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
730,
1
] |
Mathlib/Algebra/Star/Basic.lean | star_natCast | [] | [
336,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.Memℒp.of_measure_le_smul | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.2303726\nG : Type ?u.2303729\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nμ' : Measure α\nc : ℝ≥0∞\nhc : c ≠ ⊤\nhμ'_le : μ' ≤ c • μ\nf : α → E\nhf... | [
654,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
646,
1
] |
Mathlib/Topology/Instances/Real.lean | Real.mem_closure_iff | [
{
"state_after": "no goals",
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"tactic": "simp [mem_closure_iff_nhds_basis nhds_basis_ball, Real.dist_eq]"
}
] | [
95,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | IsPreconnected.intermediate_value | [] | [
129,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Order/Antisymmetrization.lean | OrderHom.antisymmetrization_apply | [] | [
232,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | ContinuousLinearMap.norm_compLpL_le | [] | [
1061,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1060,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.closure_union | [] | [
395,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.const_min | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝ : PseudoEMetricSpace α\nf g : α → ℝ\nKf Kg : ℝ≥0\nhf : LipschitzWith Kf f\na : ℝ\n⊢ LipschitzWith Kf fun x => min a (f x)",
"tactic": "simpa only [min_comm] using hf.min_const a"
}
] | [
464,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.piCongr_symm_apply | [] | [
1792,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1790,
1
] |
Mathlib/LinearAlgebra/Eigenspace/Basic.lean | Module.End.eigenvectors_linearIndependent | [] | [
248,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Std/Logic.lean | and_congr_left' | [] | [
167,
72
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
167,
1
] |
Mathlib/Algebra/Lie/CartanSubalgebra.lean | LieSubalgebra.normalizer_eq_self_of_isCartanSubalgebra | [
{
"state_after": "no goals",
"state_before": "R : Type u\nL : Type v\ninst✝³ : CommRing R\ninst✝² : LieRing L\ninst✝¹ : LieAlgebra R L\nH✝ H : LieSubalgebra R L\ninst✝ : IsCartanSubalgebra H\n⊢ LieSubmodule.normalizer (toLieSubmodule H) = toLieSubmodule H",
"tactic": "rw [← LieSubmodule.coe_toSubmodule_... | [
63,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Data/PNat/Prime.lean | PNat.Coprime.gcd_mul | [
{
"state_after": "k m n : ℕ+\nh : coprime ↑m ↑n\n⊢ gcd k (m * n) = gcd k m * gcd k n",
"state_before": "k m n : ℕ+\nh : Coprime m n\n⊢ gcd k (m * n) = gcd k m * gcd k n",
"tactic": "rw [← coprime_coe] at h"
},
{
"state_after": "case a\nk m n : ℕ+\nh : coprime ↑m ↑n\n⊢ ↑(gcd k (m * n)) = ↑(gcd k ... | [
290,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.aevalTower_C | [] | [
1602,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1601,
1
] |
Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.coe_comap | [] | [
377,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion_empty | [] | [
697,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
696,
1
] |
Mathlib/Topology/UniformSpace/Equiv.lean | UniformEquiv.bijective | [] | [
183,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
11
] |
Mathlib/Data/List/Count.lean | List.countp_le_length | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : List α\np q : α → Bool\n⊢ countp p l ≤ length l",
"tactic": "simpa only [countp_eq_length_filter] using length_filter_le _ _"
}
] | [
88,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Std/Data/String/Lemmas.lean | String.append_nil | [] | [
487,
89
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
487,
9
] |
Mathlib/AlgebraicTopology/SimplicialObject.lean | CategoryTheory.CosimplicialObject.eqToIso_refl | [
{
"state_after": "case w\nC : Type u\ninst✝ : Category C\nX : CosimplicialObject C\nn : ℕ\nh : n = n\n⊢ (eqToIso X h).hom = (Iso.refl (X.obj [n])).hom",
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"tactic": "ext"
}... | [
477,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
1
] |
Mathlib/Data/Real/ConjugateExponents.lean | Real.IsConjugateExponent.pos | [] | [
50,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/Data/Finsupp/Indicator.lean | Finsupp.indicator_of_not_mem | [] | [
52,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Data/Set/Function.lean | Set.restrict_ite | [] | [
99,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.sup_ker_aeval_le_ker_aeval_mul | [
{
"state_after": "R : Type u\nS : Type ?u.718761\nσ : Type v\nM : Type w\ninst✝³ : CommRing R\ninst✝² : CommRing S\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nf : M →ₗ[R] M\np q : R[X]\nv : M\nhv : v ∈ LinearMap.ker (↑(aeval f) p) ⊔ LinearMap.ker (↑(aeval f) q)\n⊢ v ∈ LinearMap.ker (↑(aeval f) (p * q))",
... | [
1028,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1020,
1
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.sup_vanishingIdeal_le | [
{
"state_after": "R : Type u_2\nA : Type u_1\ninst✝³ : CommSemiring R\ninst✝² : CommRing A\ninst✝¹ : Algebra R A\n𝒜 : ℕ → Submodule R A\ninst✝ : GradedAlgebra 𝒜\nt t' : Set (ProjectiveSpectrum 𝒜)\nr : A\n⊢ r ∈ vanishingIdeal t ⊔ vanishingIdeal t' → r ∈ vanishingIdeal (t ∩ t')",
"state_before": "R : Type ... | [
318,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/RingTheory/Artinian.lean | IsArtinian.monotone_stabilizes | [] | [
210,
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Mathlib/Data/List/Func.lean | List.Func.mem_get_of_ne_zero | [
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Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffWithinAt.exists_lipschitzOnWith | [
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_singleton | [
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Mathlib/Data/Nat/Choose/Basic.lean | Nat.choose_symm_half | [
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Mathlib/Algebra/Group/Pi.lean | OneHom.single_apply | [] | [
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Mathlib/CategoryTheory/Sites/Sheafification.lean | CategoryTheory.GrothendieckTopology.sheafifyMap_id | [
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Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.map.comp | [
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_mul | [] | [
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50
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Mathlib/GroupTheory/FreeProduct.lean | FreeGroup.injective_lift_of_ping_pong | [
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Mathlib/Algebra/CharZero/Lemmas.lean | Nat.cast_pow_eq_one | [
{
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Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.cramerMap_is_linear | [] | [
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Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.linear_eq_zero_iff_exists_const | [
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Mathlib/Topology/Algebra/Group/Basic.lean | IsOpen.rightCoset | [] | [
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Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.vanishingIdeal_anti_mono_iff | [
{
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Mathlib/Data/Bitvec/Lemmas.lean | Bitvec.toNat_lt | [
{
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{
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112,
19
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Mathlib/Data/Set/Lattice.lean | Set.biUnion_range_preimage_singleton | [
{
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Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.roots_prod | [
{
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Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.surjective | [] | [
647,
17
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646,
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Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.StableUnderCobaseChange.inr | [] | [
274,
42
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271,
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Mathlib/Topology/Connected.lean | isClopen_connectedComponent | [] | [
1165,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Std/Data/Nat/Gcd.lean | Nat.gcd_comm | [] | [
61,
53
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58,
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Mathlib/GroupTheory/GroupAction/SubMulAction.lean | SubMulAction.smul_mem_iff' | [] | [
267,
82
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265,
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Mathlib/Order/Max.lean | Prod.isBot_iff | [] | [
448,
57
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447,
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Mathlib/MeasureTheory/Group/Integration.lean | MeasureTheory.integral_eq_zero_of_mul_left_eq_neg | [
{
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Mathlib/FieldTheory/Adjoin.lean | IntermediateField.AlgEquiv.fieldRange_eq_top | [] | [
292,
44
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290,
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.mem_support_iff | [
{
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurable_coe_nnreal_real | [] | [
1764,
35
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Mathlib/Analysis/NormedSpace/CompactOperator.lean | ContinuousLinearMap.mkOfIsCompactOperator_mem_compactOperator | [] | [
395,
5
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392,
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Mathlib/Data/Matrix/Notation.lean | Matrix.vecMul_empty | [] | [
272,
13
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Mathlib/Topology/Constructions.lean | isOpen_pi_iff' | [
{
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Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.kernel.ι_of_zero | [] | [
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24
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533,
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Mathlib/Data/Rat/NNRat.lean | NNRat.natAbs_num_coe | [] | [
464,
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463,
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Mathlib/LinearAlgebra/Basic.lean | LinearMap.id_pow | [] | [
364,
12
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Mathlib/Analysis/Convex/Function.lean | ConvexOn.sub_strictConcaveOn | [] | [
907,
59
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Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.lieSpan_le | [
{
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Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.Measure.LebesgueDecomposition.iSup_monotone' | [] | [
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87
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530,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.measure_subtype_coe_eq_zero_of_comap_eq_zero | [] | [
1424,
68
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1422,
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Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.natTransOfLe_comm | [] | [
776,
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Mathlib/Data/Set/Basic.lean | Set.subsingleton_of_subsingleton | [] | [
2389,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.subgroupOf_sup | [
{
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3601,
82
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Mathlib/Algebra/Group/Units.lean | isUnit_of_mul_isUnit_right | [
{
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702,
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Mathlib/Algebra/Order/LatticeGroup.lean | LatticeOrderedCommGroup.abs_inv_comm | [
{
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{
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... | [
579,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
577,
1
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Mathlib/CategoryTheory/Over.lean | CategoryTheory.Under.epi_of_epi_right | [] | [
483,
31
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482,
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Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | UniformOnFun.comap_eq | [
{
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753,
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Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.exists_le | [] | [
374,
21
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372,
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Mathlib/FieldTheory/PerfectClosure.lean | PerfectClosure.mk_zero | [
{
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... | [
322,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
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Mathlib/Algebra/Group/Basic.lean | mul_one_eq_id | [] | [
86,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Algebra/Associated.lean | Associated.refl | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.144651\nγ : Type ?u.144654\nδ : Type ?u.144657\ninst✝ : Monoid α\nx : α\n⊢ x * ↑1 = x",
"tactic": "simp"
}
] | [
387,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
11
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.toWithTop_some | [] | [
574,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
573,
1
] |
Mathlib/Data/Finset/Prod.lean | Finset.inter_product | [
{
"state_after": "case a.mk\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.74538\ns s' : Finset α\nt t' : Finset β\na : α\nb : β\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\nx : α\ny : β\n⊢ (x, y) ∈ (s ∩ s') ×ˢ t ↔ (x, y) ∈ s ×ˢ t ∩ s' ×ˢ t",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.74538\ns s'... | [
248,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.sup_apply | [
{
"state_after": "α : Type u_1\nβ : Type ?u.69435\nR : Type ?u.69438\nR' : Type ?u.69441\nms : Set (OuterMeasure α)\nm m₁ m₂ : OuterMeasure α\ns : Set α\nthis : ↑(⨆ (i : Bool), bif i then m₁ else m₂) s = ⨆ (i : Bool), ↑(bif i then m₁ else m₂) s\n⊢ ↑(m₁ ⊔ m₂) s = ↑m₁ s ⊔ ↑m₂ s",
"state_before": "α : Type u_1... | [
429,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
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