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/Order/BooleanAlgebra.lean | compl_sdiff_compl | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.59519\nw x y z : α\ninst✝ : BooleanAlgebra α\n⊢ xᶜ \\ yᶜ = y \\ x",
"tactic": "rw [sdiff_compl, sdiff_eq, inf_comm]"
}
] | [
726,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
726,
1
] |
Mathlib/Algebra/Module/Opposites.lean | MulOpposite.coe_opLinearEquiv_toLinearMap | [] | [
51,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/Data/Set/Sups.lean | Set.sups_inter_subset_left | [] | [
169,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Analysis/Normed/Group/Pointwise.lean | Metric.Bounded.mul | [
{
"state_after": "case intro\nE : Type u_1\ninst✝ : SeminormedGroup E\nε δ : ℝ\ns t : Set E\nx y : E\nhs : Bounded s\nht : Bounded t\nRs : ℝ\nhRs : ∀ (x : E), x ∈ s → ‖x‖ ≤ Rs\n⊢ Bounded (s * t)",
"state_before": "E : Type u_1\ninst✝ : SeminormedGroup E\nε δ : ℝ\ns t : Set E\nx y : E\nhs : Bounded s\nht : B... | [
36,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
31,
1
] |
Mathlib/Order/Interval.lean | Interval.dual_pure | [] | [
395,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.hasSum_single | [
{
"state_after": "α : Type u_1\nE : α → Type u_2\np q : ℝ≥0∞\ninst✝⁵ : (i : α) → NormedAddCommGroup (E i)\n𝕜 : Type ?u.961936\ninst✝⁴ : NormedRing 𝕜\ninst✝³ : (i : α) → Module 𝕜 (E i)\ninst✝² : ∀ (i : α), BoundedSMul 𝕜 (E i)\ninst✝¹ : DecidableEq α\ninst✝ : Fact (1 ≤ p)\nhp : p ≠ ⊤\nf : { x // x ∈ lp E p }\... | [
1102,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1082,
11
] |
Mathlib/Algebra/Order/Group/MinMax.lean | abs_max_sub_max_le_max | [
{
"state_after": "case refine'_1\nα : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\na✝ b✝ c✝ a b c d : α\n⊢ max a b - max c d ≤ max (abs (a - c)) (abs (b - d))\n\ncase refine'_2\nα : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\na✝ b✝ c✝ a b c d : α\n⊢ max c d - max a b ≤ max (abs (a - c)) (abs (b - d))",
... | [
98,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.IsIso.inv_id | [
{
"state_after": "case hom_inv_id\nC : Type u\ninst✝ : Category C\nX Y Z : C\nf g : X ⟶ Y\nh : Y ⟶ Z\n⊢ 𝟙 X ≫ 𝟙 X = 𝟙 X",
"state_before": "C : Type u\ninst✝ : Category C\nX Y Z : C\nf g : X ⟶ Y\nh : Y ⟶ Z\n⊢ inv (𝟙 X) = 𝟙 X",
"tactic": "apply inv_eq_of_hom_inv_id"
},
{
"state_after": "no go... | [
395,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | linearIndependent_le_span_aux' | [
{
"state_after": "case f\nK : Type u\nV V₁ V₂ V₃ : Type v\nV' V'₁ : Type v'\nV'' : Type v''\nι✝ : Type w\nι' : Type w'\nη : Type u₁'\nφ : η → Type ?u.336435\nR : Type u\ninst✝⁵ : Ring R\ninst✝⁴ : StrongRankCondition R\nM : Type v\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\nι : Type u_1\ninst✝¹ : Fintype ι\nv... | [
673,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
659,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.reachable_is_equivalence | [] | [
1921,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1920,
1
] |
Mathlib/Analysis/Convex/Function.lean | convexOn_id | [
{
"state_after": "𝕜 : Type u_2\nE : Type ?u.13974\nF : Type ?u.13977\nα : Type ?u.13980\nβ : Type u_1\nι : Type ?u.13986\ninst✝⁷ : OrderedSemiring 𝕜\ninst✝⁶ : AddCommMonoid E\ninst✝⁵ : AddCommMonoid F\ninst✝⁴ : OrderedAddCommMonoid α\ninst✝³ : OrderedAddCommMonoid β\ninst✝² : SMul 𝕜 E\ninst✝¹ : SMul 𝕜 α\nin... | [
97,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.indepFun_iff_measure_inter_preimage_eq_mul | [
{
"state_after": "case mp\nΩ : Type u_3\nι : Type ?u.3034448\nβ : Type u_1\nβ' : Type u_2\nγ : Type ?u.3034457\nγ' : Type ?u.3034460\nmΩ : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\nf : Ω → β\ng : Ω → β'\nmβ : MeasurableSpace β\nmβ' : MeasurableSpace β'\nh : IndepFun f g\n⊢ ∀ (s : Set β) (t : Set β'),\n ... | [
663,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
656,
1
] |
Mathlib/MeasureTheory/Measure/AEMeasurable.lean | aemeasurable_uIoc_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.3149429\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.3149438\nδ : Type ?u.3149441\nR : Type ?u.3149444\nm0 : MeasurableSpace α\ninst✝³ : MeasurableSpace β\ninst✝² : MeasurableSpace γ\ninst✝¹ : MeasurableSpace δ\nf✝ g : α → β\nμ ν : MeasureTheory.Measure ... | [
255,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/IsOpenComapC.lean | AlgebraicGeometry.Polynomial.comap_C_mem_imageOfDf | [] | [
52,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Data/PNat/Find.lean | PNat.lt_find_iff | [
{
"state_after": "no goals",
"state_before": "p q : ℕ+ → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred q\nh : ∃ n, p n\nn✝ m n : ℕ+\n⊢ n < PNat.find h ↔ ∀ (m : ℕ+), m ≤ n → ¬p m",
"tactic": "simp only [← add_one_le_iff, le_find_iff, add_le_add_iff_right]"
}
] | [
102,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Tactic/Abel.lean | Mathlib.Tactic.Abel.zero_termg | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : AddCommGroup α\nx a : α\n⊢ termg 0 x a = a",
"tactic": "simp [termg, zero_zsmul]"
}
] | [
156,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | sInfHom.dual_id | [] | [
843,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
842,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.le_comap_map | [] | [
880,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
879,
1
] |
Mathlib/Topology/Order/Hom/Basic.lean | ContinuousOrderHom.ext | [] | [
119,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.limsSup_le_limsSup_of_le | [] | [
533,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/Analysis/InnerProductSpace/Orientation.lean | Orientation.abs_volumeForm_apply_of_pairwise_orthogonal | [
{
"state_after": "case zero\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : InnerProductSpace ℝ E\n_i : Fact (finrank ℝ E = Nat.zero)\no : Orientation ℝ E (Fin Nat.zero)\nv : Fin Nat.zero → E\nhv : Pairwise fun i j => inner (v i) (v j) = 0\n⊢ abs (↑(volumeForm o) v) = ∏ i : Fin Nat.zero, ‖v i‖\n\ncase suc... | [
311,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.mk_of_lt | [
{
"state_after": "M : Type u_1\nN : Type ?u.1556454\nG : Type ?u.1556457\nR : Type ?u.1556460\nS : Type ?u.1556463\nF : Type ?u.1556466\ninst✝² : CommMonoid M\ninst✝¹ : CommMonoid N\ninst✝ : DivisionCommMonoid G\nk l✝ : ℕ\nζ : M\nhk : 0 < k\nh1 : ζ ^ k = 1\nh : ∀ (l : ℕ), 0 < l → l < k → ζ ^ l ≠ 1\nl : ℕ\nhl : ... | [
350,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/Order/Filter/ZeroAndBoundedAtFilter.lean | Filter.BoundedAtFilter.add | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\ninst✝ : NormedAddCommGroup β\nl : Filter α\nf g : α → β\nhf : BoundedAtFilter l f\nhg : BoundedAtFilter l g\n⊢ BoundedAtFilter l (f + g)",
"tactic": "simpa using hf.add hg"
}
] | [
96,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
8
] |
Mathlib/LinearAlgebra/AdicCompletion.lean | IsAdicComplete.le_jacobson_bot | [
{
"state_after": "R : Type u_1\ninst✝⁵ : CommRing R\nI : Ideal R\nM : Type ?u.289904\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\nN : Type ?u.290446\ninst✝² : AddCommGroup N\ninst✝¹ : Module R N\ninst✝ : IsAdicComplete I R\nx : R\nhx : x ∈ I\n⊢ x ∈ Ideal.jacobson ⊥",
"state_before": "R : Type u_1\ninst✝⁵ ... | [
321,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/NumberTheory/ADEInequality.lean | ADEInequality.admissible_E'4 | [] | [
143,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | ChainComplex.next_nat_zero | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.6212\nV : Type u\ninst✝¹ : Category V\ninst✝ : HasZeroMorphisms V\n⊢ ComplexShape.next (ComplexShape.down ℕ) 0 = 0",
"tactic": "classical\n refine' dif_neg _\n push_neg\n intro\n apply Nat.noConfusion"
},
{
"state_after": "ι : Type ?u... | [
133,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.conj_trans | [
{
"state_after": "case h.h\nR : Type u_1\nR₁ : Type ?u.2210347\nR₂ : Type ?u.2210350\nR₃ : Type ?u.2210353\nR₄ : Type ?u.2210356\nS : Type ?u.2210359\nK : Type ?u.2210362\nK₂ : Type ?u.2210365\nM : Type u_2\nM' : Type ?u.2210371\nM₁ : Type ?u.2210374\nM₂ : Type u_3\nM₃ : Type u_4\nM₄ : Type ?u.2210383\nN : Type... | [
2391,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2388,
1
] |
Std/Data/Int/DivMod.lean | Int.ediv_sign | [
{
"state_after": "no goals",
"state_before": "x✝ : Int\nn✝ : Nat\n⊢ x✝ / sign ↑(succ n✝) = x✝ * sign ↑(succ n✝)",
"tactic": "simp [sign, Int.mul_one]"
},
{
"state_after": "no goals",
"state_before": "x✝ : Int\n⊢ x✝ / sign 0 = x✝ * sign 0",
"tactic": "simp [sign, Int.mul_zero]"
},
{
... | [
832,
58
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
829,
1
] |
Mathlib/Order/Concept.lean | Concept.sSup_fst | [] | [
353,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.leadingCoeff_neg | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Ring R\np : R[X]\n⊢ leadingCoeff (-p) = -leadingCoeff p",
"tactic": "rw [leadingCoeff, leadingCoeff, natDegree_neg, coeff_neg]"
}
] | [
551,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
550,
1
] |
src/lean/Init/Data/Nat/Power2.lean | Nat.pos_of_isPowerOfTwo | [
{
"state_after": "n : Nat\nh✝ : isPowerOfTwo n\nk : Nat\nh : n = 2 ^ k\n⊢ n > 0",
"state_before": "n : Nat\nh : isPowerOfTwo n\n⊢ n > 0",
"tactic": "have ⟨k, h⟩ := h"
},
{
"state_after": "n : Nat\nh✝ : isPowerOfTwo n\nk : Nat\nh : n = 2 ^ k\n⊢ 2 ^ k > 0",
"state_before": "n : Nat\nh✝ : isPow... | [
40,
9
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
36,
1
] |
Mathlib/Topology/PathConnected.lean | Path.truncate_one_one | [
{
"state_after": "no goals",
"state_before": "X✝ : Type ?u.477521\nY : Type ?u.477524\ninst✝² : TopologicalSpace X✝\ninst✝¹ : TopologicalSpace Y\nx y z : X✝\nι : Type ?u.477539\nγ✝ : Path x y\nX : Type ?u.477588\ninst✝ : TopologicalSpace X\na b : X\nγ : Path a b\n⊢ extend γ (min 1 1) = b",
"tactic": "rw... | [
702,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | HasFDerivWithinAt.nhdsWithin | [] | [
495,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
11
] |
Mathlib/Computability/PartrecCode.lean | Nat.Partrec.Code.prec_prim | [] | [
267,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Init/Data/Nat/Bitwise.lean | Nat.shiftr_add | [] | [
330,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/SetTheory/Cardinal/Continuum.lean | Cardinal.continuum_ne_zero | [] | [
102,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.Iic_principal | [] | [
650,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
649,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.supports_singleton | [
{
"state_after": "no goals",
"state_before": "S : Finset Λ'\nq : Λ'\n⊢ Supports {q} S ↔ TM2.SupportsStmt S (tr q)",
"tactic": "simp [Supports]"
}
] | [
1922,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1922,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | abs_add_eq_add_abs_iff | [
{
"state_after": "case inl\nα : Type u_1\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝ : LinearOrderedAddCommGroup α\na✝ b✝ a b : α\nab : a ≤ b\n⊢ abs (a + b) = abs a + abs b ↔ 0 ≤ a ∧ 0 ≤ b ∨ a ≤ 0 ∧ b ≤ 0\n\ncase inr\nα : Type u_1\nM : Type u\nN : Typ... | [
489,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
Mathlib/Algebra/Star/BigOperators.lean | star_sum | [] | [
31,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.normSq_div | [] | [
827,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
826,
1
] |
Mathlib/Data/List/NatAntidiagonal.lean | List.Nat.antidiagonal_zero | [] | [
62,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.set_integral_dirac' | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.1491744\n𝕜 : Type ?u.1491747\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace ℝ E\ninst✝⁹ : CompleteSpace E\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : NormedSpace 𝕜 E\ninst✝⁶ : SMulCommClass ℝ 𝕜 E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : Nor... | [
1608,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1602,
1
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.le_of_lt_minimalPeriod_of_iterate_eq | [
{
"state_after": "α : Type u_1\nβ : Type ?u.23726\nf fa : α → α\nfb : β → β\nx y : α\nm✝ n✝ m n : ℕ\nhm : m < minimalPeriod f x\nhmn : (f^[m]) x = (f^[n]) x\nhmn' : n < m\n⊢ False",
"state_before": "α : Type u_1\nβ : Type ?u.23726\nf fa : α → α\nfb : β → β\nx y : α\nm✝ n✝ m n : ℕ\nhm : m < minimalPeriod f x... | [
354,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/Data/Fintype/Card.lean | Finite.Preorder.wellFounded_gt | [] | [
919,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
918,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.cos_add_nat_mul_two_pi | [] | [
1240,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1239,
1
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Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.eq_one_div_of_mul_eq_one_right | [
{
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1183,
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1166,
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Mathlib/Topology/Separation.lean | singleton_mem_nhdsWithin_of_mem_discrete | [
{
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"state_before": "α : Type u\nβ : Type v\ninst✝¹ : TopologicalSpace α\ns : Set α\ninst✝ ... | [
816,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
812,
1
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.reverseAux_eq_reverse_append | [
{
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}
] | [
352,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
11
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Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_le_mulIndicator_of_subset | [] | [
827,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
823,
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Mathlib/Order/Monotone/Monovary.lean | antivary_toDual_right | [] | [
264,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
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Mathlib/ModelTheory/Types.lean | FirstOrder.Language.Theory.CompleteType.iInter_setOf_subset | [
{
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"state_before": "L : Language\nT : Theory L\nα : Type w\nι : Type u_1\nS : ι → Theory (L[[α]])\n⊢ (⋂ (i : ι)... | [
164,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | IntervalIntegrable.mono | [] | [
194,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.compl_map | [] | [
1050,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1049,
1
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Mathlib/Algebra/GroupWithZero/Units/Basic.lean | Ring.inverse_mul_eq_iff_eq_mul | [
{
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"tactic": "rw [← h1, mul_inverse_cance... | [
134,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
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Mathlib/Analysis/InnerProductSpace/Calculus.lean | ContDiffAt.norm | [] | [
182,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
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Mathlib/Data/Fintype/Card.lean | Fintype.card_le_one_iff | [
{
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"state_before": "α : Type u_1\nβ : Type ?u.22499\nγ : Type ?u.22502\ninst✝¹ : Fintype α... | [
564,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
552,
1
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Mathlib/Order/RelIso/Basic.lean | RelEmbedding.isAntisymm | [] | [
355,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
11
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Mathlib/CategoryTheory/Monad/Algebra.lean | CategoryTheory.Monad.Algebra.comp_eq_comp | [] | [
119,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
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Mathlib/LinearAlgebra/FreeModule/PID.lean | Submodule.basisOfPid_bot | [
{
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333,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
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Mathlib/Topology/Algebra/WithZeroTopology.lean | WithZeroTopology.nhds_eq_update | [] | [
52,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
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Mathlib/Analysis/NormedSpace/Exponential.lean | map_exp | [] | [
523,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
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Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.ext_fun | [
{
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200,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
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Mathlib/Data/Matrix/Kronecker.lean | Matrix.kroneckerMap_one_one | [
{
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155,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
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Mathlib/Data/Fintype/Card.lean | Finset.card_compl_lt_iff_nonempty | [] | [
282,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
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Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.mem_range | [] | [
794,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
794,
1
] |
Mathlib/Topology/Algebra/Module/WeakDual.lean | WeakSpace.coe_map | [] | [
337,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Star.lean | HasFDerivAt.star | [] | [
56,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
8
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Mathlib/Topology/Bornology/Basic.lean | Bornology.IsBounded.subset | [] | [
213,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_neg | [
{
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594,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
8
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioc_inter_Iic | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.180034\ninst✝ : SemilatticeInf α\na b c : α\n⊢ Ioc a b ∩ Iic c = Ioc a (b ⊓ c)",
"tactic": "rw [← Ioi_inter_Iic, ← Ioi_inter_Iic, inter_assoc, Iic_inter_Iic]"
}
] | [
1730,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1729,
1
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Mathlib/GroupTheory/Exponent.lean | Monoid.exponent_min' | [
{
"state_after": "G : Type u\ninst✝ : Monoid G\nn : ℕ\nhpos : 0 < n\nhG : ∀ (g : G), g ^ n = 1\n⊢ Nat.find ?hc ≤ n\n\ncase hc\nG : Type u\ninst✝ : Monoid G\nn : ℕ\nhpos : 0 < n\nhG : ∀ (g : G), g ^ n = 1\n⊢ ExponentExists G",
"state_before": "G : Type u\ninst✝ : Monoid G\nn : ℕ\nhpos : 0 < n\nhG : ∀ (g : G)... | [
134,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
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Mathlib/Analysis/Calculus/TangentCone.lean | uniqueDiffWithinAt_inter | [] | [
300,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/LinearAlgebra/ProjectiveSpace/Independence.lean | Projectivization.dependent_iff | [
{
"state_after": "case refine'_1\nι : Type u_1\nK : Type u_2\nV : Type u_3\ninst✝² : Field K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nf : ι → ℙ K V\n⊢ Dependent f → ¬LinearIndependent K (Projectivization.rep ∘ f)\n\ncase refine'_2\nι : Type u_1\nK : Type u_2\nV : Type u_3\ninst✝² : Field K\ninst✝¹ : AddCom... | [
96,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Formula.realize_equivSentence_symm | [] | [
759,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
754,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.tendsto_of_isEmpty | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.308632\nι : Sort x\ninst✝ : IsEmpty α\nf : α → β\nla : Filter α\nlb : Filter β\n⊢ Tendsto f la lb",
"tactic": "simp only [filter_eq_bot_of_isEmpty la, tendsto_bot]"
}
] | [
2867,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2866,
1
] |
Mathlib/GroupTheory/SchurZassenhaus.lean | Subgroup.SchurZassenhausInduction.step4 | [] | [
242,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
9
] |
Mathlib/MeasureTheory/Measure/NullMeasurable.lean | MeasureTheory.NullMeasurableSet.exists_measurable_subset_ae_eq | [] | [
251,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | dist_pi_le_iff' | [
{
"state_after": "case pos\nα : Type u\nβ : Type v\nX : Type ?u.395267\nι : Type ?u.395270\ninst✝³ : PseudoMetricSpace α\nπ : β → Type u_1\ninst✝² : Fintype β\ninst✝¹ : (b : β) → PseudoMetricSpace (π b)\ninst✝ : Nonempty β\nf g : (b : β) → π b\nr : ℝ\nhr : 0 ≤ r\n⊢ dist f g ≤ r ↔ ∀ (b : β), dist (f b) (g b) ≤ r... | [
2016,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2011,
1
] |
Mathlib/Order/Minimal.lean | IsLeast.minimals_eq | [] | [
226,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/MeasureTheory/Covering/Differentiation.lean | VitaliFamily.measure_le_of_frequently_le | [
{
"state_after": "α : Type u_1\ninst✝⁴ : MetricSpace α\nm0 : MeasurableSpace α\nμ : MeasureTheory.Measure α\nv : VitaliFamily μ\nE : Type ?u.713372\ninst✝³ : NormedAddCommGroup E\ninst✝² : SecondCountableTopology α\ninst✝¹ : BorelSpace α\nρ ν : MeasureTheory.Measure α\ninst✝ : IsLocallyFiniteMeasure ν\nhρ : ρ ≪... | [
157,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.not_and_self | [
{
"state_after": "no goals",
"state_before": "⊢ ∀ (x : Bool), (!x && x) = false",
"tactic": "decide"
}
] | [
252,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Data/Set/Basic.lean | Set.union_union_distrib_left | [] | [
1074,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1073,
1
] |
Std/Logic.lean | peirce' | [] | [
574,
71
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
574,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | le_ciInf | [] | [
813,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
812,
1
] |
Mathlib/CategoryTheory/Sites/Sheaf.lean | CategoryTheory.Presheaf.isSheaf_iff_multiequalizer | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\nA : Type u₂\ninst✝¹ : Category A\nJ : GrothendieckTopology C\nU : C\nR : Presieve U\nP : Cᵒᵖ ⥤ A\ninst✝ : ∀ (X : C) (S : GrothendieckTopology.Cover J X), HasMultiequalizer (GrothendieckTopology.Cover.index S P)\n⊢ (∀ (X : C) (S : GrothendieckTopology.Cover J X... | [
525,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
510,
1
] |
Std/Data/Int/Lemmas.lean | Int.negOfNat_add | [
{
"state_after": "no goals",
"state_before": "m n : Nat\n⊢ negOfNat m + negOfNat n = negOfNat (m + n)",
"tactic": "cases m <;> cases n <;> simp [Nat.succ_add] <;> rfl"
}
] | [
427,
54
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
426,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.card_nthRootsFinset | [
{
"state_after": "no goals",
"state_before": "M : Type ?u.3632058\nN : Type ?u.3632061\nG : Type ?u.3632064\nR : Type u_1\nS : Type ?u.3632070\nF : Type ?u.3632073\ninst✝⁴ : CommMonoid M\ninst✝³ : CommMonoid N\ninst✝² : DivisionCommMonoid G\nk l : ℕ\ninst✝¹ : CommRing R\nζ✝ : Rˣ\nh✝ : IsPrimitiveRoot ζ✝ k\n... | [
865,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
863,
1
] |
Mathlib/Algebra/Module/Basic.lean | smul_add_one_sub_smul | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.67416\nR✝ : Type ?u.67419\nk : Type ?u.67422\nS : Type ?u.67425\nM : Type u_2\nM₂ : Type ?u.67431\nM₃ : Type ?u.67434\nι : Type ?u.67437\ninst✝⁴ : Semiring R✝\ninst✝³ : AddCommMonoid M\ninst✝² : Module R✝ M\nr✝ s : R✝\nx y : M\nR : Type u_1\ninst✝¹ :... | [
210,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Algebra/Parity.lean | odd_abs | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.105789\nα : Type u_1\nβ : Type ?u.105795\nR : Type ?u.105798\ninst✝¹ : Ring α\na b : α\nn : ℕ\ninst✝ : LinearOrder α\n⊢ Odd (abs a) ↔ Odd a",
"tactic": "cases' abs_choice a with h h <;> simp only [h, odd_neg]"
}
] | [
459,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Mathlib/Data/Rel.lean | Rel.preimage_inter | [] | [
192,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Logic/Basic.lean | exists_const | [] | [
739,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
738,
9
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | HomologicalComplex.kernel_from_eq_kernel | [
{
"state_after": "ι : Type u_1\nV : Type u\ninst✝² : Category V\ninst✝¹ : HasZeroMorphisms V\nc : ComplexShape ι\nC : HomologicalComplex V c\ninst✝ : HasKernels V\ni j : ι\nr : ComplexShape.Rel c i j\n⊢ kernelSubobject (d C i j ≫ (xNextIso C r).inv) = kernelSubobject (d C i j)",
"state_before": "ι : Type u_... | [
462,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
Mathlib/Algebra/Order/SMul.lean | smul_le_smul_iff_of_pos | [] | [
244,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Analysis/Asymptotics/SuperpolynomialDecay.lean | Asymptotics.SuperpolynomialDecay.congr | [] | [
79,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Topology/Algebra/Order/MonotoneConvergence.lean | tendsto_atBot_ciInf | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.22872\nι : Type u_1\ninst✝³ : Preorder ι\ninst✝² : TopologicalSpace α\ninst✝¹ : ConditionallyCompleteLattice α\ninst✝ : InfConvergenceClass α\nf : ι → α\na : α\nh_mono : Monotone f\nhbdd : BddBelow (range f)\n⊢ Tendsto f atBot (𝓝 (⨅ (i... | [
146,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.count_mul_of_coprime' | [
{
"state_after": "case pos\nα : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ndec_irr : (p : Associates α) → Decidable (Irreducible p)\ninst✝ : UniqueFactorizationMonoid α\ndec : DecidableEq α\ndec' : DecidableEq (Associates α)\na b p : Associates α\nhp : Irreducible p\nhab : ∀ (d : Associates α), d ∣ a → d ∣ ... | [
1773,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1761,
1
] |
Mathlib/Analysis/NormedSpace/Extend.lean | ContinuousLinearMap.norm_extendTo𝕜' | [] | [
142,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/RingTheory/FreeCommRing.lean | FreeCommRing.lift_comp_of | [
{
"state_after": "no goals",
"state_before": "α : Type u\nR : Type v\ninst✝ : CommRing R\nf✝ : α → R\nf : FreeCommRing α →+* R\nx : FreeCommRing α\n⊢ ↑(↑lift (↑f ∘ of)) (-1) = ↑f (-1)",
"tactic": "rw [RingHom.map_neg, RingHom.map_one, f.map_neg, f.map_one]"
},
{
"state_after": "no goals",
"s... | [
154,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.mem_Lp_of_ae_bound | [] | [
411,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
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