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/Finset/LocallyFinite.lean | Finset.Ioc_eq_cons_Ioo | [
{
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"state_before": "ι : Type ?u.108656\nα : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : LocallyFiniteOrder α\na b c : α\nh : a < b\n⊢ Ioc a b = cons b (Ioo a b) (_ : ¬b ∈ Ioo a b)",
"tactic": "classical rw [cons_eq_insert, Ioo_insert_right h]"
},
{
"state_after": "no goa... | [
625,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
624,
1
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.C_1 | [] | [
214,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
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Mathlib/Data/Set/Intervals/Pi.lean | Set.pi_univ_Ico_subset | [] | [
84,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/Finite.lean | Set.Finite.toFinset_univ | [
{
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"tactic": "simp"
}
] | [
277,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
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Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.degrees_one | [] | [
137,
14
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136,
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Mathlib/RingTheory/FreeCommRing.lean | FreeRing.coe_surjective | [
{
"state_after": "no goals",
"state_before": "α : Type u\nx : FreeCommRing α\n⊢ ∃ a, ↑a = x",
"tactic": "induction x using FreeCommRing.induction_on with\n| hn1 =>\n use -1\n rfl\n| hb b =>\n exact ⟨FreeRing.of b, rfl⟩\n| ha _ _ hx hy =>\n rcases hx with ⟨x, rfl⟩; rcases hy with ⟨y, rfl⟩\n exact ⟨x... | [
377,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
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Mathlib/RingTheory/Polynomial/Dickson.lean | Polynomial.map_dickson | [
{
"state_after": "no goals",
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"tactic": "simp_rw [dickson_zero, Polynomial.map_sub, Polynomial.map_nat_cast, Polynomial.map_ofNat]"
},
{
... | [
104,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
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Mathlib/Algebra/Opposites.lean | MulOpposite.op_smul | [] | [
319,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
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Mathlib/Data/List/Count.lean | List.count_cons_self | [
{
"state_after": "no goals",
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"tactic": "simp [count_cons']"
}
] | [
192,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
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Mathlib/Data/SetLike/Basic.lean | SetLike.ext'_iff | [] | [
150,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
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Mathlib/Order/Filter/Archimedean.lean | Int.comap_cast_atTop | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.2256\nR : Type u_1\ninst✝¹ : StrictOrderedRing R\ninst✝ : Archimedean R\nr : R\nn : ℕ\nhn : r ≤ ↑n\n⊢ r ≤ ↑↑n",
"tactic": "exact_mod_cast hn"
}
] | [
48,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
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Mathlib/Data/Sym/Basic.lean | Sym.eq_replicate_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.30399\nn n' m : ℕ\ns : Sym α n\na b : α\n⊢ (↑Multiset.card ↑s = n ∧ ∀ (b : α), b ∈ ↑s → b = a) ↔ ∀ (b : α), b ∈ s → b = a",
"state_before": "α : Type u_1\nβ : Type ?u.30399\nn n' m : ℕ\ns : Sym α n\na b : α\n⊢ s = replicate n a ↔ ∀ (b : α), b ∈ s → b = a",
"ta... | [
295,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.stronglyMeasurable_of_isEmpty | [] | [
157,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
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Mathlib/Data/Finset/Sups.lean | Finset.disjSups_disjSups_disjSups_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝³ : DecidableEq α\ninst✝² : DistribLattice α\ninst✝¹ : OrderBot α\ninst✝ : DecidableRel Disjoint\ns t u v : Finset α\n⊢ s ○ t ○ (u ○ v) = s ○ u ○ (t ○ v)",
"tactic": "simp_rw [← disjSups_assoc, disjSups_right_comm]"
}
] | [
554,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
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Mathlib/LinearAlgebra/Quotient.lean | Submodule.mapQ_mkQ | [
{
"state_after": "case h\nR : Type u_1\nM : Type u_3\nr : R\nx✝ y : M\ninst✝⁵ : Ring R\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\np p' : Submodule R M\nR₂ : Type u_2\nM₂ : Type u_4\ninst✝² : Ring R₂\ninst✝¹ : AddCommGroup M₂\ninst✝ : Module R₂ M₂\nτ₁₂ : R →+* R₂\nq : Submodule R₂ M₂\nf : M →ₛₗ[τ₁₂] M₂\nh : ... | [
419,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/GroupTheory/GroupAction/Group.lean | inv_smul_smul | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝¹ : Group α\ninst✝ : MulAction α β\nc : α\nx : β\n⊢ c⁻¹ • c • x = x",
"tactic": "rw [smul_smul, mul_left_inv, one_smul]"
}
] | [
39,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/Analysis/BoxIntegral/DivergenceTheorem.lean | BoxIntegral.hasIntegral_GP_divergence_of_forall_hasDerivWithinAt | [
{
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287,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/IsTensorProduct.lean | IsTensorProduct.equiv_symm_apply | [
{
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97,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
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Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.order_X | [
{
"state_after": "no goals",
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"tactic": "simpa only [Nat.cast_one] using order_monomial_of_ne_zero 1 (1 : R) one_ne_zero"
}
] | [
2492,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2491,
1
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Mathlib/Analysis/InnerProductSpace/PiL2.lean | Orthonormal.exists_orthonormalBasis_extension_of_card_eq | [
{
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802,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
785,
1
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Mathlib/Topology/UniformSpace/UniformEmbedding.lean | uniformEmbedding_comap | [] | [
410,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
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] |
Mathlib/Analysis/NormedSpace/Complemented.lean | Subspace.coe_prodEquivOfClosedCompl | [] | [
107,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.comap_le_comap_iff_of_surjective | [] | [
930,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
929,
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] |
Mathlib/Data/Int/Bitwise.lean | Int.shiftl_neg | [] | [
372,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.Presieve.isSheafFor_iso | [
{
"state_after": "C : Type u₁\ninst✝ : Category C\nP Q U : Cᵒᵖ ⥤ Type w\nX Y : C\nS : Sieve X\nR : Presieve X\nJ J₂ : GrothendieckTopology C\nP' : Cᵒᵖ ⥤ Type w\ni : P ≅ P'\nh : IsSheafFor P R\nx : FamilyOfElements P' R\nhx : FamilyOfElements.Compatible x\n⊢ ∃! t, FamilyOfElements.IsAmalgamation x t",
"state... | [
681,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
670,
1
] |
Mathlib/Analysis/InnerProductSpace/GramSchmidtOrtho.lean | gramSchmidt_inv_triangular | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Group/Pi.lean | Pi.mulSingle_commute | [
{
"state_after": "ι : Type ?u.68984\nα : Type ?u.68987\nI : Type u\nf : I → Type v\nx✝ y✝ : (i : I) → f i\ni✝ j✝ : I\ninst✝¹ : DecidableEq I\ninst✝ : (i : I) → MulOneClass (f i)\ni j : I\nhij : i ≠ j\nx : f i\ny : f j\n⊢ Commute (mulSingle i x) (mulSingle j y)",
"state_before": "ι : Type ?u.68984\nα : Type ... | [
552,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
1
] |
Std/Data/Int/DivMod.lean | Int.le_of_dvd | [] | [
847,
97
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
844,
1
] |
Mathlib/Data/Nat/Factorization/PrimePow.lean | isPrimePow_iff_minFac_pow_factorization_eq | [] | [
42,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/Analysis/InnerProductSpace/l2Space.lean | OrthogonalFamily.hasSum_linearIsometry | [] | [
232,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
11
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.eq_zero_of_le_zero | [] | [
302,
32
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
301,
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Mathlib/Analysis/Convex/Star.lean | starConvex_pi | [] | [
151,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tendsto_nat_nhds_top | [] | [
183,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Topology/UniformSpace/Pi.lean | uniformContinuous_pi | [
{
"state_after": "no goals",
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"tactic": "simp only [UniformContinuous, Pi.uniformity, tendsto... | [
47,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
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] |
Std/Classes/Order.lean | Ordering.swap_swap | [
{
"state_after": "no goals",
"state_before": "o : Ordering\n⊢ swap (swap o) = o",
"tactic": "cases o <;> rfl"
}
] | [
11,
90
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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Mathlib/Algebra/Order/Ring/Cone.lean | Ring.PositiveCone.one_pos | [] | [
53,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
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Mathlib/Order/Heyting/Basic.lean | snd_himp | [] | [
118,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Submodule.dualAnnihilator_sup_eq | [] | [
903,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
901,
1
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Mathlib/Analysis/SpecialFunctions/Pow/Asymptotics.lean | tendsto_rpow_neg_atTop | [] | [
54,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.biUnion_congr | [
{
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"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.50636... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/List/Forall2.lean | Relator.RightUnique.forall₂ | [] | [
155,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
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Mathlib/Topology/Connected.lean | connectedComponentIn_mem_nhds | [
{
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"state_before": "α : Type u\nβ : ... | [
1146,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/List/Cycle.lean | Cycle.coe_cons_eq_coe_append | [
{
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"tactic": "rw [rotate_cons_succ, rotate_zero]"
}
] | [
483,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
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] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.degree_pos_iff_exists_adj | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.269390\n𝕜 : Type ?u.269393\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v w : V\ne : Sym2 V\ninst✝ : Fintype ↑(neighborSet G v)\n⊢ 0 < degree G v ↔ ∃ w, Adj G v w",
"tactic": "simp only [degree, card_pos, F... | [
1387,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Lie/Basic.lean | LieHom.coe_id | [] | [
342,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
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Std/Data/List/Lemmas.lean | List.not_mem_nil | [] | [
58,
55
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
58,
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Mathlib/GroupTheory/GroupAction/BigOperators.lean | Finset.smul_sum | [] | [
57,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
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Mathlib/Algebra/Opposites.lean | MulOpposite.op_unop | [] | [
106,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoMod_sub' | [
{
"state_after": "no goals",
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"tactic": "simpa only [one_zsmul] using toIcoMod_sub_zsmul' hp a b 1"
}
] | [
519,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
518,
1
] |
Std/Data/Int/Lemmas.lean | Int.natAbs_zero | [] | [
140,
66
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
140,
9
] |
Mathlib/Algebra/Order/Archimedean.lean | existsUnique_zsmul_near_of_pos | [
{
"state_after": "α : Type u_1\ninst✝¹ : LinearOrderedAddCommGroup α\ninst✝ : Archimedean α\na : α\nha : 0 < a\ng : α\ns : Set ℤ := {n | n • a ≤ g}\n⊢ ∃! k, k • a ≤ g ∧ g < (k + 1) • a",
"state_before": "α : Type u_1\ninst✝¹ : LinearOrderedAddCommGroup α\ninst✝ : Archimedean α\na : α\nha : 0 < a\ng : α\n⊢ ∃... | [
76,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Algebra/Algebra/Basic.lean | Algebra.algebraMap_pUnit | [] | [
478,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Mathlib/FieldTheory/Laurent.lean | RatFunc.laurent_C | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : CommRing R\nhdomain : IsDomain R\nr s : R\np q : R[X]\nf : RatFunc R\nx : R\n⊢ ↑(laurent r) (↑C x) = ↑C x",
"tactic": "rw [← algebraMap_C, laurent_algebraMap, taylor_C]"
}
] | [
107,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.commute_X_pow | [] | [
619,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
1
] |
Mathlib/Order/SymmDiff.lean | bihimp_of_le | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.38067\nα : Type u_1\nβ : Type ?u.38073\nπ : ι → Type ?u.38078\ninst✝ : GeneralizedHeytingAlgebra α\na✝ b✝ c d a b : α\nh : a ≤ b\n⊢ a ⇔ b = b ⇨ a",
"tactic": "rw [bihimp, himp_eq_top_iff.2 h, inf_top_eq]"
}
] | [
263,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_mem_eq_prod | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.195249\nι : Type ?u.195252\nG : Type ?u.195255\nM : Type u_2\nN : Type ?u.195261\ninst✝¹ : CommMonoid M\ninst✝ : CommMonoid N\nf : α → M\ns : Set α\nhf : Set.Finite (s ∩ mulSupport f)\n⊢ (s ∩ mulSupport fun i => f i) = ↑(Finite.toFinset... | [
492,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/Data/MvPolynomial/CommRing.lean | MvPolynomial.hom_C | [] | [
147,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Analysis/Convex/Hull.lean | LinearMap.convexHull_image | [] | [
181,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Topology/MetricSpace/Baire.lean | eventually_residual | [
{
"state_after": "case h.e'_2.h.e'_2.h.a\nα : Type u_1\nβ : Type ?u.15155\nγ : Type ?u.15158\nι : Type ?u.15161\ninst✝¹ : TopologicalSpace α\ninst✝ : BaireSpace α\np : α → Prop\nx✝ : Set α\n⊢ (IsGδ x✝ ∧ Dense x✝ ∧ ∀ (x : α), x ∈ x✝ → p x) ↔ ∃ x, IsGδ x✝ ∧ Dense x✝",
"state_before": "α : Type u_1\nβ : Type ?... | [
248,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.ord_proj_dvd_ord_proj_iff_dvd | [
{
"state_after": "a b : ℕ\nha0 : a ≠ 0\nhb0 : b ≠ 0\nh : ∀ (p : ℕ), p ^ ↑(factorization a) p ∣ p ^ ↑(factorization b) p\n⊢ a ∣ b",
"state_before": "a b : ℕ\nha0 : a ≠ 0\nhb0 : b ≠ 0\n⊢ (∀ (p : ℕ), p ^ ↑(factorization a) p ∣ p ^ ↑(factorization b) p) ↔ a ∣ b",
"tactic": "refine' ⟨fun h => _, fun hab p =>... | [
609,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
602,
1
] |
Mathlib/Data/Real/Cardinality.lean | Cardinal.mk_univ_real | [
{
"state_after": "no goals",
"state_before": "c : ℝ\nf g : ℕ → Bool\nn : ℕ\n⊢ (#↑Set.univ) = 𝔠",
"tactic": "rw [mk_univ, mk_real]"
}
] | [
217,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Analysis/NormedSpace/ENorm.lean | ENorm.finite_norm_eq | [] | [
237,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | LinearMap.toMatrix'_comp | [
{
"state_after": "R : Type u_2\ninst✝⁴ : CommSemiring R\nk : Type ?u.752944\nl : Type u_1\nm : Type u_4\nn : Type u_3\ninst✝³ : Fintype n\ninst✝² : DecidableEq n\ninst✝¹ : Fintype l\ninst✝ : DecidableEq l\nf : (n → R) →ₗ[R] m → R\ng : (l → R) →ₗ[R] n → R\n⊢ comp f g = ↑toLin' (↑toMatrix' f ⬝ ↑toMatrix' g)",
... | [
401,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
1
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.mem_prod | [] | [
1548,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1547,
1
] |
Mathlib/Topology/UrysohnsLemma.lean | Urysohns.CU.approx_le_succ | [
{
"state_after": "case zero\nX : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : NormalSpace X\nc✝ : CU X\nx : X\nc : CU X\n⊢ approx Nat.zero c x ≤ approx (Nat.zero + 1) c x\n\ncase succ\nX : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : NormalSpace X\nc✝ : CU X\nx : X\nn : ℕ\nihn : ∀ (c : CU X), approx n c x ≤... | [
205,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.lift'_bot | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.36509\nι : Sort ?u.36512\nf f₁ f₂ : Filter α\nh h₁ h₂ : Set α → Set β\nhh : Monotone h\n⊢ Filter.lift' ⊥ h = 𝓟 (h ∅)",
"tactic": "rw [← principal_empty, lift'_principal hh]"
}
] | [
328,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | iteratedFDerivWithin_succ_apply_right | [
{
"state_after": "case zero\n𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nX : Type uX\ninst✝¹ ... | [
850,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
819,
1
] |
Mathlib/Analysis/InnerProductSpace/Adjoint.lean | ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.658805\nG : Type ?u.658808\ninst✝⁹ : IsROrC 𝕜\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedAddCommGroup G\ninst✝⁵ : InnerProductSpace 𝕜 E\ninst✝⁴ : InnerProductSpace 𝕜 F\ninst✝³ : InnerProductSpace 𝕜 G\ninst✝² : Comp... | [
164,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | sum_add_tsum_subtype_compl | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.770476\nδ : Type ?u.770479\ninst✝⁴ : AddCommGroup α\ninst✝³ : UniformSpace α\ninst✝² : UniformAddGroup α\nf✝ g : β → α\na a₁ a₂ : α\ninst✝¹ : CompleteSpace α\ninst✝ : T2Space α\nf : β → α\nhf : Summable f\ns : Finset β\n⊢ (∑ x in s, f x + ∑' (x : { x // ... | [
1241,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1237,
1
] |
Mathlib/RingTheory/Polynomial/Chebyshev.lean | Polynomial.Chebyshev.mul_T | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.100205\ninst✝¹ : CommRing R\ninst✝ : CommRing S\n⊢ ∀ (k : ℕ), 2 * T R 0 * T R (0 + k) = T R (2 * 0 + k) + T R k",
"tactic": "simp [two_mul, add_mul]"
},
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Typ... | [
268,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Data/MvPolynomial/Rename.lean | MvPolynomial.constantCoeff_rename | [
{
"state_after": "case h_C\nσ : Type u_2\nτ✝ : Type ?u.978943\nα : Type ?u.978946\nR : Type u_3\nS : Type ?u.978952\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S\nτ : Type u_1\nf : σ → τ\nφ : MvPolynomial σ R\n⊢ ∀ (a : R), ↑constantCoeff (↑(rename f) (↑C a)) = ↑constantCoeff (↑C a)\n\ncase h_add\nσ : Type u_... | [
336,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.finite_setOf_isRoot | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np✝ q p : R[X]\nhp : p ≠ 0\n⊢ Set.Finite {x | IsRoot p x}",
"tactic": "simpa only [← Finset.setOf_mem, Multiset.mem_toFinset, mem_roots hp]\n using p.roots.toFinset.... | [
604,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
602,
1
] |
Mathlib/Algebra/Category/GroupCat/EpiMono.lean | GroupCat.ker_eq_bot_of_mono | [] | [
83,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalMax.add | [] | [
374,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
8
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.sup_pow_eq_top | [
{
"state_after": "R : Type u\nι : Type ?u.280883\ninst✝ : CommSemiring R\nI J K L : Ideal R\nn : ℕ\nh : I ⊔ J = ⊤\n⊢ I ⊔ ∏ _x in Finset.range n, J = ⊤",
"state_before": "R : Type u\nι : Type ?u.280883\ninst✝ : CommSemiring R\nI J K L : Ideal R\nn : ℕ\nh : I ⊔ J = ⊤\n⊢ I ⊔ J ^ n = ⊤",
"tactic": "rw [← Fi... | [
729,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
727,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.coe_zero | [] | [
377,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
] |
Mathlib/RingTheory/FiniteType.lean | RingHom.FiniteType.of_surjective | [
{
"state_after": "A : Type u_1\nB : Type u_2\nC : Type ?u.122685\ninst✝² : CommRing A\ninst✝¹ : CommRing B\ninst✝ : CommRing C\nf : A →+* B\nhf : Surjective ↑f\n⊢ FiniteType (comp f (RingHom.id A))",
"state_before": "A : Type u_1\nB : Type u_2\nC : Type ?u.122685\ninst✝² : CommRing A\ninst✝¹ : CommRing B\ni... | [
233,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Std/Data/Int/DivMod.lean | Int.eq_one_of_mul_eq_one_left | [
{
"state_after": "no goals",
"state_before": "a b : Int\nH : 0 ≤ b\nH' : a * b = 1\n⊢ b * ?m.93792 H H' = 1",
"tactic": "rw [Int.mul_comm, H']"
}
] | [
857,
59
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
856,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.filter_union | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.368807\nγ : Type ?u.368810\np q : α → Prop\ninst✝² : DecidablePred p\ninst✝¹ : DecidablePred q\ninst✝ : DecidableEq α\ns₁ s₂ : Finset α\nx✝ : α\n⊢ x✝ ∈ filter p (s₁ ∪ s₂) ↔ x✝ ∈ filter p s₁ ∪ filter p s₂",
"tactic": "simp only [mem_... | [
2813,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2812,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.lift_type_le | [] | [
737,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
730,
1
] |
Mathlib/Data/List/Perm.lean | List.Perm.nil_eq | [] | [
164,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/CategoryTheory/Monoidal/Free/Basic.lean | CategoryTheory.FreeMonoidalCategory.mk_tensor | [] | [
196,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_coe_angle_eq_iff_eq_toReal | [
{
"state_after": "no goals",
"state_before": "z : ℂ\nθ : Angle\n⊢ ↑(arg z) = θ ↔ arg z = Angle.toReal θ",
"tactic": "rw [← Real.Angle.toReal_inj, arg_coe_angle_toReal_eq_arg]"
}
] | [
499,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.pred_le | [] | [
219,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isNat_pow | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Semiring α\nn✝¹ n✝ : ℕ\n⊢ ↑n✝¹ ^ ↑n✝ = ↑(Nat.pow n✝¹ n✝)",
"tactic": "simp"
}
] | [
427,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.eq_one_of_pos_of_log_eq_zero | [] | [
230,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigOWith.add_isLittleO | [] | [
1096,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1094,
1
] |
Std/Data/Int/DivMod.lean | Int.eq_ediv_of_mul_eq_right | [] | [
753,
48
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
751,
11
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.constantCoeff_X | [] | [
1562,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1561,
1
] |
Mathlib/CategoryTheory/Monad/Algebra.lean | CategoryTheory.Monad.Algebra.comp_f | [] | [
134,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.centralizer_toSubsemiring | [] | [
862,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
860,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.erase_subset | [] | [
1079,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1078,
1
] |
Mathlib/Analysis/Normed/MulAction.lean | edist_smul_le | [] | [
54,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Topology/Basic.lean | DenseRange.nonempty_iff | [] | [
1854,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1853,
8
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiff.clm_apply | [] | [
897,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
895,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioc_subset_Ioc_right | [] | [
493,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.mem_vsub | [] | [
1089,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1088,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.coe_snd | [] | [
1091,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1090,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.map_eq_cons | [
{
"state_after": "case mp\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.122604\ninst✝ : DecidableEq α\nf : α → β\ns : Multiset α\nt : Multiset β\nb : β\n⊢ (∃ a, a ∈ s ∧ f a = b ∧ map f (erase s a) = t) → map f s = b ::ₘ t\n\ncase mpr\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.122604\ninst✝ : DecidableEq α\nf : α → β\n... | [
1270,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1257,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_le_nnreal_smul_snorm_of_ae_le_mul | [
{
"state_after": "case pos\nα : Type u_1\nE : Type ?u.5059288\nF : Type u_2\nG : Type u_3\nm m0 : MeasurableSpace α\np✝ : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf : α → F\ng : α → G\nc : ℝ≥0\nh : ∀ᵐ (x : α) ∂μ, ‖f x‖₊ ≤ c * ‖g x‖... | [
1285,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1277,
1
] |
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