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/Finmap.lean | Finmap.union_comm_of_disjoint | [
{
"state_after": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\ns₁✝ s₂✝ : Finmap β\ns₁ s₂ : AList β\nh : Disjoint ⟦s₁⟧ ⟦s₂⟧\n⊢ ⟦s₁⟧ ∪ ⟦s₂⟧ = ⟦s₂⟧ ∪ ⟦s₁⟧",
"state_before": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\ns₁✝ s₂✝ : Finmap β\ns₁ s₂ : AList β\n⊢ Disjoint ⟦s₁⟧ ⟦s₂⟧ → ⟦s₁⟧ ∪ ⟦s₂⟧ = ⟦s₂⟧ ∪... | [
685,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
682,
1
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Mathlib/Data/Sym/Sym2.lean | Sym2.relBool_spec | [
{
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"state_before": "α : Type u_1\nβ : Type ?u.59102\nγ : Type ?u.59105\ninst✝ : DecidableEq α\nx y : α × α\n⊢ relBool x y = true ↔ Rel α x... | [
647,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
645,
1
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Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | extChartAt_preimage_mem_nhdsWithin | [] | [
1215,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1213,
1
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.HasFiniteIntegral.mono | [
{
"state_after": "α : Type u_1\nβ : Type u_3\nγ : Type u_2\nδ : Type ?u.704421\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝² : MeasurableSpace δ\ninst✝¹ : NormedAddCommGroup β\ninst✝ : NormedAddCommGroup γ\nf : α → β\ng : α → γ\nh : ∀ᵐ (a : α) ∂μ, ‖f a‖ ≤ ‖g a‖\nhg : (∫⁻ (a : α), ENNReal.ofReal ‖g a‖ ∂μ) < ⊤\... | [
146,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
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Mathlib/Analysis/Calculus/MeanValue.lean | strictConcaveOn_of_deriv2_neg' | [] | [
1247,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1245,
1
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Mathlib/Tactic/Abel.lean | Mathlib.Tactic.Abel.unfold_smul | [] | [
255,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
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Mathlib/Logic/Equiv/Fin.lean | finSuccEquiv'_at | [
{
"state_after": "no goals",
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"tactic": "simp [finSuccEquiv']"
}
] | [
142,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Topology/Perfect.lean | exists_countable_union_perfect_of_isClosed | [
{
"state_after": "case intro.intro.intro\nα : Type u_1\ninst✝¹ : TopologicalSpace α\nC : Set α\ninst✝ : SecondCountableTopology α\nhclosed : IsClosed C\nb : Set (Set α)\nbct : Set.Countable b\nleft✝ : ¬∅ ∈ b\nbbasis : IsTopologicalBasis b\n⊢ ∃ V D, Set.Countable V ∧ Perfect D ∧ C = V ∪ D",
"state_before": "... | [
202,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Algebra/Group/OrderSynonym.lean | ofLex_pow | [] | [
290,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/Order/BoundedOrder.lean | OrderDual.toDual_bot | [] | [
305,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/NumberTheory/Multiplicity.lean | multiplicity.pow_prime_sub_pow_prime | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nn : ℕ\ninst✝² : CommRing R\na b x y : R\np : ℕ\ninst✝¹ : IsDomain R\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\nhp : Prime ↑p\nhp1 : Odd p\nhxy : ↑p ∣ x - y\nhx : ¬↑p ∣ x\n⊢ multiplicity (↑p) (x ^ p - y ^ p) = multiplicity (↑p) (x - y) + 1",
"t... | [
184,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | borel_eq_generateFrom_Ioi | [
{
"state_after": "no goals",
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157,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.Memℒp.of_nnnorm_le_mul | [] | [
1320,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1316,
1
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Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | MeasureTheory.LocallyIntegrable.locallyIntegrableOn | [] | [
133,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
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Mathlib/Data/List/Cycle.lean | Cycle.mk_eq_coe | [] | [
473,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
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Mathlib/Analysis/Calculus/MeanValue.lean | Convex.monotoneOn_of_deriv_nonneg | [
{
"state_after": "no goals",
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918,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
914,
1
] |
Mathlib/Topology/Separation.lean | minimal_nonempty_open_subsingleton | [
{
"state_after": "α : Type u\ninst✝¹ : TopologicalSpace α\ninst✝ : T0Space α\ns : Set α\nhs : IsOpen s\nhmin : ∀ (t : Set α), t ⊆ s → Set.Nonempty t → IsOpen t → t = s\n⊢ Set.Subsingleton s",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : TopologicalSpace α\ninst✝ : T0Space α\ns : Set α\nhs : IsOpen s\nh... | [
292,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
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Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.C_inv | [] | [
2192,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2191,
1
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Mathlib/Logic/Function/Basic.lean | Function.surjInv_eq | [] | [
491,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Homeomorph.isLittleO_congr | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\nE : Type u_3\ninst✝¹ : Norm E\nF : Type u_4\ninst✝ : Norm F\ne : α ≃ₜ β\nb : β\nf : β → E\ng : β → F\n⊢ (∀ ⦃c : ℝ⦄, 0 < c → IsBigOWith c (𝓝 b) f g) ↔\n ∀ ⦃c : ℝ⦄, 0 < c → IsBigOWith c (𝓝 (↑(Homeomorph.sy... | [
2237,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2234,
1
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Mathlib/Order/Monotone/Basic.lean | monotoneOn_id | [] | [
514,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
514,
1
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Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.mul_inv_rev | [
{
"state_after": "l : Type ?u.349525\nm : Type u\nn : Type u'\nα : Type v\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommRing α\nA✝ B✝ A B : Matrix n n α\n⊢ Ring.inverse (det (A ⬝ B)) • adjugate (A ⬝ B) =\n (Ring.inverse (det B) • adjugate B) ⬝ (Ring.inverse (det A) • adjugate A)",
"state_befor... | [
591,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Memℒp.toLp_sub | [] | [
150,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.find_mono | [] | [
854,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
852,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesOnBall.eventually_eq_zero | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.469661\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✝ : NormedS... | [
509,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
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Mathlib/LinearAlgebra/FiniteDimensional.lean | Submodule.finiteDimensional_of_le | [] | [
709,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
704,
1
] |
Mathlib/Data/Fintype/Basic.lean | Set.toFinset_nonempty | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.81654\nγ : Type ?u.81657\ns✝ t s : Set α\ninst✝ : Fintype ↑s\n⊢ Finset.Nonempty (toFinset s) ↔ Set.Nonempty s",
"tactic": "rw [← Finset.coe_nonempty, coe_toFinset]"
}
] | [
643,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
642,
1
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Mathlib/Order/Minimal.lean | maximals_of_symm | [] | [
111,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.adjoin_eq_range_algebraMap_adjoin | [] | [
303,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
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Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.measure_lt_top_of_isCompact_of_isMulLeftInvariant' | [] | [
603,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
600,
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Mathlib/Data/Finset/Basic.lean | Finset.erase_val | [] | [
1855,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1854,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | GaloisConnection.u_csInf' | [] | [
1305,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1303,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieModuleHom.coe_smul | [] | [
938,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
937,
1
] |
Mathlib/Order/PFilter.lean | Order.PFilter.directed | [] | [
93,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Data/Sum/Order.lean | Sum.not_inr_lt_inl | [] | [
168,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
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Mathlib/RingTheory/Ideal/Basic.lean | coe_subset_nonunits | [] | [
851,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
850,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.toReal_mem_Ioc | [] | [
575,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
574,
1
] |
Mathlib/Computability/PartrecCode.lean | Nat.Partrec.Code.encode_lt_pair | [
{
"state_after": "cf cg : Code\n⊢ encodeCode cf < 2 * (2 * Nat.pair (encodeCode cf) (encodeCode cg)) + 4 ∧\n encodeCode cg < 2 * (2 * Nat.pair (encodeCode cf) (encodeCode cg)) + 4",
"state_before": "cf cg : Code\n⊢ encode cf < encode (pair cf cg) ∧ encode cg < encode (pair cf cg)",
"tactic": "simp [e... | [
211,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
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Mathlib/Data/Set/Finite.lean | Set.Infinite.nonempty | [
{
"state_after": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\nh : Set.Infinite ∅\n⊢ False",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ns : Set α\nh : Set.Infinite s\n⊢ s ≠ ∅",
"tactic": "rintro rfl"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Ty... | [
833,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
830,
11
] |
Mathlib/Topology/Instances/AddCircle.lean | AddCircle.coe_eq_coe_iff_of_mem_Ico | [
{
"state_after": "𝕜 : Type u_1\nB : Type ?u.79444\ninst✝³ : LinearOrderedAddCommGroup 𝕜\ninst✝² : TopologicalSpace 𝕜\ninst✝¹ : OrderTopology 𝕜\np : 𝕜\nhp : Fact (0 < p)\na : 𝕜\ninst✝ : Archimedean 𝕜\nx y : 𝕜\nhx : x ∈ Ico a (a + p)\nhy : y ∈ Ico a (a + p)\nh : ↑x = ↑y\n⊢ x = y",
"state_before": "𝕜 ... | [
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10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
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Std/Data/List/Lemmas.lean | List.length_pos_iff_exists_mem | [] | [
45,
64
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
44,
1
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Mathlib/Order/Chain.lean | IsMaxChain.not_superChain | [] | [
146,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.coeFn_smul | [] | [
386,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/Algebra/ContinuedFractions/Translations.lean | GeneralizedContinuedFraction.terminatedAt_iff_s_none | [
{
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"tactic": "rfl"
}
] | [
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81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.preimage_comap_zeroLocus | [] | [
621,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
620,
1
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Std/Data/Nat/Lemmas.lean | Nat.sub_add_min_cancel | [
{
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"tactic": "rw [sub_eq_sub_min, Nat.sub_add_cancel (Nat.min_le_left n m)]"
}
] | [
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64
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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19
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Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | Collinear.mem_affineSpan_of_mem_of_ne | [
{
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525,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Over.lean | CategoryTheory.Over.map_map_left | [] | [
186,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
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Mathlib/Analysis/NormedSpace/FiniteDimension.lean | ContinuousLinearMap.exists_right_inverse_of_surjective | [] | [
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89
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Mathlib/RingTheory/FiniteType.lean | MonoidAlgebra.mvPolynomial_aeval_of_surjective_of_closure | [
{
"state_after": "R : Type u_1\nM : Type u_2\ninst✝¹ : CommMonoid M\ninst✝ : CommSemiring R\nS : Set M\nhS : closure S = ⊤\nf : MonoidAlgebra R M\n⊢ ∃ a, ↑(MvPolynomial.aeval fun s => ↑(of R M) ↑s) a = f",
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41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
580,
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Mathlib/Analysis/Complex/PhragmenLindelof.lean | PhragmenLindelof.quadrant_II | [
{
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488,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
] |
Mathlib/RingTheory/Valuation/Quotient.lean | AddValuation.comap_supp | [] | [
117,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.zero_re | [] | [
141,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/RingTheory/Localization/InvSubmonoid.lean | IsLocalization.surj'' | [
{
"state_after": "case intro.mk\nR : Type u_1\ninst✝⁴ : CommRing R\nM : Submonoid R\nS : Type u_2\ninst✝³ : CommRing S\ninst✝² : Algebra R S\nP : Type ?u.160993\ninst✝¹ : CommRing P\ninst✝ : IsLocalization M S\nz : S\nr : R\nm : { x // x ∈ M }\ne : z * ↑(algebraMap R S) ↑(r, m).snd = ↑(algebraMap R S) r\n⊢ ∃ r ... | [
97,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.span_X_isPrime | [
{
"state_after": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\n⊢ Ideal.span {X} = RingHom.ker (constantCoeff R)",
"state_before": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\n⊢ Ideal.IsPrime (Ideal.span {X})",
"tactic": "suffices Ideal.span ({X} : Set (PowerSeries R)) = RingHom.ker ... | [
2044,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2038,
1
] |
Std/Logic.lean | Decidable.iff_iff_not_or_and_or_not | [
{
"state_after": "a b : Prop\ninst✝¹ : Decidable a\ninst✝ : Decidable b\n⊢ (a → b) ∧ (b → a) ↔ (¬a ∨ b) ∧ (a ∨ ¬b)",
"state_before": "a b : Prop\ninst✝¹ : Decidable a\ninst✝ : Decidable b\n⊢ (a ↔ b) ↔ (¬a ∨ b) ∧ (a ∨ ¬b)",
"tactic": "rw [iff_iff_implies_and_implies a b]"
},
{
"state_after": "no ... | [
594,
76
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
592,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.mapsTo_sInter | [] | [
1450,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1449,
1
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Mathlib/Data/Finset/Pointwise.lean | Finset.smul_mem_smul_finset_iff₀ | [] | [
2036,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2035,
1
] |
Mathlib/Data/MvPolynomial/PDeriv.lean | MvPolynomial.pderiv_monomial_single | [
{
"state_after": "no goals",
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"tactic": "simp"
}
] | [
117,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Algebra/GroupPower/Basic.lean | mul_zpow | [] | [
387,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/Topology/Algebra/GroupCompletion.lean | AddMonoidHom.continuous_extension | [] | [
265,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infinitePos_add_infinitePos | [] | [
564,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.valid_nil | [] | [
1064,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1063,
1
] |
Mathlib/Order/ModularLattice.lean | inf_covby_of_covby_sup_of_covby_sup_right | [
{
"state_after": "α : Type u_1\ninst✝¹ : Lattice α\ninst✝ : IsWeakLowerModularLattice α\na b : α\n⊢ a ⋖ b ⊔ a → b ⋖ b ⊔ a → b ⊓ a ⋖ b",
"state_before": "α : Type u_1\ninst✝¹ : Lattice α\ninst✝ : IsWeakLowerModularLattice α\na b : α\n⊢ a ⋖ a ⊔ b → b ⋖ a ⊔ b → a ⊓ b ⋖ b",
"tactic": "rw [sup_comm, inf_comm... | [
131,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Data/PFun.lean | PFun.fix_fwd_eq | [
{
"state_after": "case H\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.29936\nδ : Type ?u.29939\nε : Type ?u.29942\nι : Type ?u.29945\nf : α →. β ⊕ α\na a' : α\nha' : Sum.inr a' ∈ f a\nb : β\n⊢ b ∈ fix f a ↔ b ∈ fix f a'",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.29936\nδ : Type ?u.29939\nε : Typ... | [
322,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/LinearAlgebra/StdBasis.lean | LinearMap.ker_stdBasis | [] | [
86,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEStronglyMeasurable.mul | [] | [
1290,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1287,
11
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.le_add_sub | [] | [
542,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_def_of_neg | [
{
"state_after": "x : ℝ\nhx : x < 0\ny : ℝ\n⊢ (Complex.exp (Complex.log ↑x * ↑y)).re = exp (log x * y) * cos (y * π)\n\ncase hnc\nx : ℝ\nhx : x < 0\ny : ℝ\n⊢ ¬↑x = 0",
"state_before": "x : ℝ\nhx : x < 0\ny : ℝ\n⊢ x ^ y = exp (log x * y) * cos (y * π)",
"tactic": "rw [rpow_def, Complex.cpow_def, if_neg]"... | [
87,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/GroupTheory/Nilpotent.lean | is_ascending_rev_series_of_is_descending | [
{
"state_after": "case intro\nG : Type u_1\ninst✝¹ : Group G\nH✝ : Subgroup G\ninst✝ : Normal H✝\nH : ℕ → Subgroup G\nn : ℕ\nhn : H n = ⊥\nh0 : H 0 = ⊤\nhH : ∀ (x : G) (n : ℕ), x ∈ H n → ∀ (g : G), x * g * x⁻¹ * g⁻¹ ∈ H (n + 1)\n⊢ IsAscendingCentralSeries fun m => H (n - m)",
"state_before": "G : Type u_1\n... | [
260,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_zero' | [] | [
852,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
851,
1
] |
Mathlib/Analysis/Convex/Between.lean | sbtw_const_vsub_iff | [
{
"state_after": "no goals",
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228,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Order/Bounds/Basic.lean | union_lowerBounds_subset_lowerBounds_inter | [] | [
379,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Order/Monotone/Basic.lean | StrictAnti.prod_map | [
{
"state_after": "ι : Type ?u.48700\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type u_1\nπ : ι → Type ?u.48714\nr : α → α → Prop\ninst✝³ : PartialOrder α\ninst✝² : PartialOrder β\ninst✝¹ : Preorder γ\ninst✝ : Preorder δ\nf : α → γ\ng : β → δ\nhf : StrictAnti f\nhg : StrictAnti g\na b : α × β\n⊢ a.fst < b.fst ∧ a.... | [
1179,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1176,
1
] |
Mathlib/AlgebraicTopology/SimplicialObject.lean | CategoryTheory.SimplicialObject.augment_hom_zero | [
{
"state_after": "C : Type u\ninst✝ : Category C\nX✝ X : SimplicialObject C\nX₀ : C\nf : X.obj [0].op ⟶ X₀\nw : ∀ (i : SimplexCategory) (g₁ g₂ : [0] ⟶ i), X.map g₁.op ≫ f = X.map g₂.op ≫ f\n⊢ X.map (SimplexCategory.const [0] 0).op ≫ f = f",
"state_before": "C : Type u\ninst✝ : Category C\nX✝ X : SimplicialO... | [
406,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
Mathlib/Data/Finset/Sigma.lean | Finset.sigma_eq_biUnion | [
{
"state_after": "case a.mk\nι : Type u_2\nα : ι → Type u_1\nβ : Type ?u.9726\ns✝ s₁ s₂ : Finset ι\nt✝ t₁ t₂ : (i : ι) → Finset (α i)\ninst✝ : DecidableEq ((i : ι) × α i)\ns : Finset ι\nt : (i : ι) → Finset (α i)\nx : ι\ny : α x\n⊢ { fst := x, snd := y } ∈ Finset.sigma s t ↔\n { fst := x, snd := y } ∈ Finset... | [
97,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Analysis/Convex/Basic.lean | Convex.starConvex_iff | [] | [
167,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.EqOnSource.symm' | [] | [
947,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
946,
1
] |
Mathlib/Order/Max.lean | not_isBot | [] | [
216,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Data/Set/Pairwise/Lattice.lean | Pairwise.subset_of_biUnion_subset_biUnion | [] | [
128,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Init/Algebra/Classes.lean | irrefl | [] | [
258,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | GroupSeminorm.zero_apply | [] | [
264,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_finset_prod | [] | [
637,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
635,
1
] |
src/lean/Init/SimpLemmas.lean | ite_false | [] | [
78,
74
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
78,
9
] |
Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.coe_iSup_of_directed | [
{
"state_after": "no goals",
"state_before": "M : Type u_2\nA : Type ?u.34491\nB : Type ?u.34494\ninst✝¹ : MulOneClass M\nι : Sort u_1\ninst✝ : Nonempty ι\nS : ι → Submonoid M\nhS : Directed (fun x x_1 => x ≤ x_1) S\nx : M\n⊢ x ∈ ↑(⨆ (i : ι), S i) ↔ x ∈ ⋃ (i : ι), ↑(S i)",
"tactic": "simp [mem_iSup_of_d... | [
217,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | IsPreconnected.Icc_subset | [
{
"state_after": "no goals",
"state_before": "X : Type u\nα : Type v\ninst✝³ : TopologicalSpace X\ninst✝² : LinearOrder α\ninst✝¹ : TopologicalSpace α\ninst✝ : OrderClosedTopology α\ns : Set α\nhs : IsPreconnected s\na b : α\nha : a ∈ s\nhb : b ∈ s\n⊢ Icc a b ⊆ s",
"tactic": "simpa only [image_id] using... | [
219,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/NumberTheory/FermatPsp.lean | FermatPsp.probablePrime_iff_modEq | [
{
"state_after": "n b : ℕ\nh : 1 ≤ b\nthis : 1 ≤ b ^ (n - 1)\n⊢ ProbablePrime n b ↔ b ^ (n - 1) ≡ 1 [MOD n]",
"state_before": "n b : ℕ\nh : 1 ≤ b\n⊢ ProbablePrime n b ↔ b ^ (n - 1) ≡ 1 [MOD n]",
"tactic": "have : 1 ≤ b ^ (n - 1) := one_le_pow_of_one_le h (n - 1)"
},
{
"state_after": "n b : ℕ\nh ... | [
117,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.add_vecMul | [
{
"state_after": "case h\nl : Type ?u.857786\nm : Type u_1\nn : Type u_2\no : Type ?u.857795\nm' : o → Type ?u.857800\nn' : o → Type ?u.857805\nR : Type ?u.857808\nS : Type ?u.857811\nα : Type v\nβ : Type w\nγ : Type ?u.857818\ninst✝¹ : NonUnitalNonAssocSemiring α\ninst✝ : Fintype m\nA : Matrix m n α\nx y : m →... | [
1769,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1766,
1
] |
Mathlib/LinearAlgebra/Prod.lean | LinearMap.coprod_zero_right | [] | [
243,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.disjoint_comm | [] | [
57,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Order/Circular.lean | sbtw_of_btw_not_btw | [] | [
211,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Algebra/Category/GroupCat/EpiMono.lean | GroupCat.SurjectiveOfEpiAuxs.fromCoset_ne_of_nin_range | [
{
"state_after": "A B : GroupCat\nf : A ⟶ B\nb : ↑B\nhb : ¬b ∈ MonoidHom.range f\nr :\n fromCoset\n { val := b *l (MonoidHom.range f).toSubmonoid.toSubsemigroup.carrier,\n property :=\n (_ :\n ∃ y,\n Function.swap leftCoset (MonoidHom.range f).toSubmonoid.toSubsemig... | [
170,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Data/List/Pairwise.lean | List.pairwise_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.7483\nR✝ S T : α → α → Prop\na✝ : α\nl : List α\nR : α → α → Prop\na : α\n⊢ Pairwise R [a]",
"tactic": "simp [Pairwise.nil]"
}
] | [
156,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/LinearAlgebra/Prod.lean | LinearMap.inr_map_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nM₅ : Type ?u.152136\nM₆ : Type ?u.152139\nS : Type ?u.152142\ninst✝¹⁷ : Semiring R\ninst✝¹⁶ : Semiring S\ninst✝¹⁵ : AddCommMonoid M\n... | [
409,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
] |
Mathlib/Combinatorics/Additive/SalemSpencer.lean | MulSalemSpencer.image | [
{
"state_after": "case intro.intro.intro.intro.intro.intro\nF : Type u_1\nα : Type u_2\nβ : Type u_3\n𝕜 : Type ?u.12908\nE : Type ?u.12911\ninst✝² : CommMonoid α\ninst✝¹ : CommMonoid β\ns : Set α\na✝ : α\ninst✝ : MulHomClass F α β\nf : F\nhf : InjOn (↑f) (s * s)\nh : MulSalemSpencer s\na : α\nha : a ∈ s\nb : α... | [
137,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.apply_mem_support | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\nx : α\n⊢ ↑f x ∈ support f ↔ x ∈ support f",
"tactic": "rw [mem_support, mem_support, Ne.def, Ne.def, apply_eq_iff_eq]"
}
] | [
360,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/Data/Multiset/FinsetOps.lean | Multiset.ndinsert_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns✝ : Multiset α\na : α\ns t : Multiset α\nx✝ : s ≤ t ∧ a ∈ t\nl : s ≤ t\nm : a ∈ t\nh : a ∈ s\n⊢ ndinsert a s ≤ t",
"tactic": "simp [h, l]"
},
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\ns✝ : Multiset α... | [
100,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Data/Int/Associated.lean | Int.natAbs_eq_iff_associated | [
{
"state_after": "a b : ℤ\n⊢ a = b ∨ a = -b ↔ Associated a b",
"state_before": "a b : ℤ\n⊢ natAbs a = natAbs b ↔ Associated a b",
"tactic": "refine' Int.natAbs_eq_natAbs_iff.trans _"
},
{
"state_after": "case mp\na b : ℤ\n⊢ a = b ∨ a = -b → Associated a b\n\ncase mpr\na b : ℤ\n⊢ Associated a b →... | [
34,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
25,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Measurable.ennreal_ofReal | [] | [
1799,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1797,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.reindexFinsetRange_self | [
{
"state_after": "ι : Type u_2\nι' : Type ?u.421677\nR : Type u_3\nR₂ : Type ?u.421683\nK : Type ?u.421686\nM : Type u_1\nM' : Type ?u.421692\nM'' : Type ?u.421695\nV : Type u\nV' : Type ?u.421700\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\ninst✝³ : AddCommMonoid M'\ninst✝² : Module R M... | [
529,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
526,
1
] |
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