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/Polynomial/FieldDivision.lean | Polynomial.prime_of_degree_eq_one | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nk : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝ : Field R\np q : R[X]\nhp1 : degree p = 1\nhp0 : p = 0\n⊢ ¬degree 0 = 1",
"tactic": "simp"
}
] | [
480,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.forall_sups_iff | [] | [
109,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.inj_on_iUnion_of_directed | [
{
"state_after": "α : Type u_1\nβ : Type u_3\nγ : Type ?u.191837\nι : Sort u_2\nι' : Sort ?u.191843\nι₂ : Sort ?u.191846\nκ : ι → Sort ?u.191851\nκ₁ : ι → Sort ?u.191856\nκ₂ : ι → Sort ?u.191861\nκ' : ι' → Sort ?u.191866\ns : ι → Set α\nhs : Directed (fun x x_1 => x ⊆ x_1) s\nf : α → β\nhf : ∀ (i : ι), InjOn f ... | [
1575,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1569,
1
] |
Mathlib/Computability/Partrec.lean | Computable.comp | [] | [
531,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
8
] |
Mathlib/Order/BoundedOrder.lean | sup_eq_bot_iff | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type ?u.26825\nδ : Type ?u.26828\ninst✝¹ : SemilatticeSup α\ninst✝ : OrderBot α\na b : α\n⊢ a ≤ ⊥ ∧ b ≤ ⊥ ↔ a = ⊥ ∧ b = ⊥",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.26825\nδ : Type ?u.26828\ninst✝¹ : SemilatticeSup α\ninst✝ : OrderBot α\na b : α\n⊢ a... | [
481,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/Data/Set/Finite.lean | Set.infinite_of_forall_exists_lt | [] | [
1417,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1416,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.map_pow | [
{
"state_after": "case zero\nR : Type u_1\ninst✝¹⁸ : CommSemiring R\nR' : Type ?u.980529\ninst✝¹⁷ : Monoid R'\nR'' : Type ?u.980535\ninst✝¹⁶ : Semiring R''\nM : Type u_2\nN : Type u_3\nP : Type ?u.980547\nQ : Type ?u.980550\nS : Type ?u.980553\ninst✝¹⁵ : AddCommMonoid M\ninst✝¹⁴ : AddCommMonoid N\ninst✝¹³ : Add... | [
788,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
784,
11
] |
Mathlib/Data/Finset/NAry.lean | Finset.card_image₂_iff | [
{
"state_after": "α : Type u_2\nα' : Type ?u.9016\nβ : Type u_3\nβ' : Type ?u.9022\nγ : Type u_1\nγ' : Type ?u.9028\nδ : Type ?u.9031\nδ' : Type ?u.9034\nε : Type ?u.9037\nε' : Type ?u.9040\nζ : Type ?u.9043\nζ' : Type ?u.9046\nν : Type ?u.9049\ninst✝⁷ : DecidableEq α'\ninst✝⁶ : DecidableEq β'\ninst✝⁵ : Decidab... | [
65,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Data/Set/BoolIndicator.lean | Set.not_mem_iff_boolIndicator | [
{
"state_after": "α : Type u_1\ns : Set α\nx : α\n⊢ ¬x ∈ s ↔ (if x ∈ s then true else false) = false",
"state_before": "α : Type u_1\ns : Set α\nx : α\n⊢ ¬x ∈ s ↔ boolIndicator s x = false",
"tactic": "unfold boolIndicator"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns : S... | [
37,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/Order/SymmDiff.lean | symmDiff_symmDiff_left | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.68209\nα : Type u_1\nβ : Type ?u.68215\nπ : ι → Type ?u.68220\ninst✝ : GeneralizedBooleanAlgebra α\na b c d : α\n⊢ a \\ (b ⊔ c) ⊔ b \\ (a ⊔ c) ⊔ (c \\ (a ⊔ b) ⊔ c ⊓ a ⊓ b) = a \\ (b ⊔ c) ⊔ b \\ (a ⊔ c) ⊔ c \\ (a ⊔ b) ⊔ a ⊓ b ⊓ c",
"tactic": "ac_r... | [
465,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
Mathlib/Topology/UniformSpace/Compact.lean | Continuous.uniformContinuous_of_tendsto_cocompact | [
{
"state_after": "case intro.intro.intro\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.44329\ninst✝¹ : UniformSpace α\ninst✝ : UniformSpace β\nf : α → β\nx : β\nh_cont : Continuous f\nhx : Tendsto f (cocompact α) (𝓝 x)\nr : Set (β × β)\nhr : r ∈ 𝓤 β\nt : Set (β × β)\nht : t ∈ 𝓤 β\nhtsymm : SymmetricRel t\nhtr : t... | [
221,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.of_thinkN_terminates | [] | [
426,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/Data/Polynomial/Laurent.lean | LaurentPolynomial.degree_C_mul_T | [
{
"state_after": "R : Type u_1\ninst✝ : Semiring R\nn : ℤ\na : R\na0 : a ≠ 0\n⊢ Finset.max (↑C a * T n).support = ↑n",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nn : ℤ\na : R\na0 : a ≠ 0\n⊢ degree (↑C a * T n) = ↑n",
"tactic": "rw [degree]"
},
{
"state_after": "R : Type u_1\ninst✝ : Semi... | [
511,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/Analysis/LocallyConvex/BalancedCoreHull.lean | balancedCore_nonempty_iff | [] | [
138,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSpace.map_inf | [] | [
171,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Analysis/NormedSpace/IndicatorFunction.lean | norm_indicator_le_norm_self | [
{
"state_after": "α : Type u_2\nE : Type u_1\ninst✝ : SeminormedAddCommGroup E\ns t : Set α\nf : α → E\na : α\n⊢ indicator s (fun a => ‖f a‖) a ≤ ‖f a‖",
"state_before": "α : Type u_2\nE : Type u_1\ninst✝ : SeminormedAddCommGroup E\ns t : Set α\nf : α → E\na : α\n⊢ ‖indicator s f a‖ ≤ ‖f a‖",
"tactic": ... | [
49,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.sup'_congr | [
{
"state_after": "F : Type ?u.262044\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.262053\nι : Type ?u.262056\nκ : Type ?u.262059\ninst✝ : SemilatticeSup α\nf✝ : β → α\nt : Finset β\nf g : β → α\nH : Finset.Nonempty t\nh₂ : ∀ (x : β), x ∈ t → f x = g x\n⊢ sup' t H f = sup' t (_ : Finset.Nonempty t) g",
"state_be... | [
880,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
876,
1
] |
Mathlib/Algebra/DirectSum/Ring.lean | DirectSum.mulHom_apply | [] | [
207,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.eq_iInf | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.61688\nγ : Type ?u.61691\nι : Sort u_2\nι' : Sort ?u.61697\nl l' : Filter α\np : ι → Prop\ns : ι → Set α\nt : Set α\ni : ι\np' : ι' → Prop\ns' : ι' → Set α\ni' : ι'\nh : HasBasis l (fun x => True) s\n⊢ l = ⨅ (i : ι), 𝓟 (s i)",
"tac... | [
758,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
757,
1
] |
Mathlib/Analysis/InnerProductSpace/GramSchmidtOrtho.lean | gramSchmidtOrthonormalBasis_apply | [] | [
353,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.le_comap_of_map_le | [] | [
1427,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1426,
1
] |
Mathlib/Order/InitialSeg.lean | PrincipalSeg.codRestrict_apply | [] | [
404,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurable_of_Iic | [
{
"state_after": "case hf\nα : Type u_2\nβ : Type ?u.1088754\nγ : Type ?u.1088757\nγ₂ : Type ?u.1088760\nδ : Type u_1\nι : Sort y\ns t u : Set α\ninst✝¹² : TopologicalSpace α\ninst✝¹¹ : MeasurableSpace α\ninst✝¹⁰ : BorelSpace α\ninst✝⁹ : TopologicalSpace β\ninst✝⁸ : MeasurableSpace β\ninst✝⁷ : BorelSpace β\nins... | [
1066,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1063,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | orderOf_dvd_iff_pow_eq_one | [
{
"state_after": "no goals",
"state_before": "G : Type u\nA : Type v\nx y : G\na b : A\nn✝ m : ℕ\ninst✝¹ : Monoid G\ninst✝ : AddMonoid A\nn : ℕ\nh : orderOf x ∣ n\n⊢ x ^ n = 1",
"tactic": "rw [pow_eq_mod_orderOf, Nat.mod_eq_zero_of_dvd h, _root_.pow_zero]"
}
] | [
248,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.prod_le_prod_iff_le | [
{
"state_after": "case intro\nα : Type u_1\ninst✝² : CancelCommMonoidWithZero α\ndec_irr : (p : Associates α) → Decidable (Irreducible p)\ninst✝¹ : UniqueFactorizationMonoid α\ninst✝ : Nontrivial α\np q : Multiset (Associates α)\nhp : ∀ (a : Associates α), a ∈ p → Irreducible a\nhq : ∀ (a : Associates α), a ∈ q... | [
1391,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1376,
1
] |
Mathlib/Data/Nat/Choose/Basic.lean | Nat.ascFactorial_eq_factorial_mul_choose | [
{
"state_after": "n k : ℕ\n⊢ ascFactorial n k = choose (n + k) k * k !",
"state_before": "n k : ℕ\n⊢ ascFactorial n k = k ! * choose (n + k) k",
"tactic": "rw [mul_comm]"
},
{
"state_after": "n k : ℕ\n⊢ ascFactorial n k * (n + k - k)! = choose (n + k) k * k ! * (n + k - k)!",
"state_before":... | [
244,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Tactic/Ring/RingNF.lean | Mathlib.Tactic.RingNF.nat_rawCast_0 | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : CommSemiring R\n⊢ Nat.rawCast 0 = 0",
"tactic": "simp"
}
] | [
114,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.not_isFiniteMeasure_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.604437\nγ : Type ?u.604440\nδ : Type ?u.604443\nι : Type ?u.604446\nR : Type ?u.604449\nR' : Type ?u.604452\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set α\nh : ¬IsFiniteMeasure μ\n⊢ ↑↑μ... | [
3042,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3039,
1
] |
Mathlib/Algebra/Algebra/Tower.lean | Submodule.span_algebraMap_image_of_tower | [] | [
340,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/Algebra/DirectSum/Decomposition.lean | DirectSum.decompose_smul | [] | [
248,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | eq_one_of_inv_eq' | [] | [
1129,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1121,
1
] |
Mathlib/Topology/MetricSpace/Gluing.lean | Metric.Sigma.dist_ne | [] | [
336,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.translationNumber_eq_of_tendsto_aux | [] | [
653,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
651,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.preimage_closure | [] | [
1842,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1841,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisInsertion.leftInverse_l_u | [] | [
522,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.mul_inv_cancel | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝² : LinearOrderedField α\ninst✝¹ : DivisionRing β\nabv : β → α\ninst✝ : IsAbsoluteValue abv\nf : CauSeq β abv\nhf : ¬LimZero f\nε : α\nε0 : ε > 0\nK : α\nK0 : K > 0\ni : ℕ\nH : ∀ (j : ℕ), j ≥ i → K ≤ abv (↑f j)\nj : ℕ\nij : j ≥ i... | [
646,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
644,
1
] |
Mathlib/Order/CompleteLattice.lean | disjoint_sSup_left | [] | [
1950,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1948,
1
] |
Mathlib/Data/Set/Pointwise/Finite.lean | Group.card_pow_eq_card_pow_card_univ | [
{
"state_after": "F : Type ?u.35675\nα : Type ?u.35678\nβ : Type ?u.35681\nγ : Type ?u.35684\nG : Type u_1\ninst✝² : Group G\ninst✝¹ : Fintype G\nS : Set G\ninst✝ : (k : ℕ) → DecidablePred fun x => x ∈ S ^ k\nhG : 0 < Fintype.card G\n⊢ ∀ (k : ℕ), Fintype.card G ≤ k → Fintype.card ↑(S ^ k) = Fintype.card ↑(S ^ F... | [
203,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.balancedSz_down | [] | [
217,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Data/Pi/Algebra.lean | Pi.one_comp | [] | [
69,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Topology/LocallyConstant/Algebra.lean | LocallyConstant.coe_inv | [] | [
46,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.AEDisjoint.preimage | [] | [
2674,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2672,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.op_norm_neg | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\n𝕜₂ : Type u_2\n𝕜₃ : Type ?u.285603\nE : Type u_3\nEₗ : Type ?u.285609\nF : Type u_4\nFₗ : Type ?u.285615\nG : Type ?u.285618\nGₗ : Type ?u.285621\n𝓕 : Type ?u.285624\ninst✝¹⁵ : SeminormedAddCommGroup E\ninst✝¹⁴ : SeminormedAddCommGroup Eₗ\ninst... | [
187,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.unbounded_of_tendsto_atTop' | [] | [
1708,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1706,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.union_add_distrib | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.179823\nγ : Type ?u.179826\ninst✝ : DecidableEq α\ns✝ t✝ u✝ : Multiset α\na b : α\ns t u : Multiset α\n⊢ s + u - (t + u) = s - t",
"tactic": "rw [add_comm t, tsub_add_eq_tsub_tsub, add_tsub_cancel_right]"
}
] | [
1848,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1846,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.blockDiag_sub | [] | [
601,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
599,
1
] |
Mathlib/Algebra/GroupWithZero/Basic.lean | eq_of_zero_eq_one | [] | [
136,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Data/Set/Pointwise/BigOperators.lean | Set.list_prod_mem_list_prod | [
{
"state_after": "case nil\nι : Type u_1\nα : Type u_2\nβ : Type ?u.67083\nF : Type ?u.67086\ninst✝² : CommMonoid α\ninst✝¹ : CommMonoid β\ninst✝ : MonoidHomClass F α β\nt : List ι\nf : ι → Set α\ng : ι → α\nhg✝ : ∀ (i : ι), i ∈ t → g i ∈ f i\nhg : ∀ (i : ι), i ∈ [] → g i ∈ f i\n⊢ List.prod (List.map g []) ∈ Li... | [
105,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.sub_half | [
{
"state_after": "case intro\nα : Type ?u.327971\nβ : Type ?u.327974\nb c d : ℝ≥0∞\nr p q a : ℝ≥0\n⊢ ↑a - ↑a / 2 = ↑a / 2",
"state_before": "α : Type ?u.327971\nβ : Type ?u.327974\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nh : a ≠ ⊤\n⊢ a - a / 2 = a / 2",
"tactic": "lift a to ℝ≥0 using h"
},
{
"state_after":... | [
1764,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1762,
1
] |
Mathlib/RingTheory/Localization/Integral.lean | IsIntegralClosure.isFractionRing_of_algebraic | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.445070\ninst✝¹⁶ : CommRing R\nM : Submonoid R\nS : Type ?u.445277\ninst✝¹⁵ : CommRing S\ninst✝¹⁴ : Algebra R S\nP : Type ?u.445533\ninst✝¹³ : CommRing P\nA : Type u_1\nK : Type ?u.445542\ninst✝¹² : CommRing A\ninst✝¹¹ : IsDomain A\nL : Type u_2\ninst... | [
342,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | nnnorm_inv' | [] | [
935,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
934,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.curryFinFinset_symm_apply_const | [] | [
1887,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1884,
1
] |
Mathlib/CategoryTheory/Closed/Cartesian.lean | CategoryTheory.CartesianClosed.curry_id_eq_coev | [
{
"state_after": "C : Type u\ninst✝³ : Category C\nA✝ B X✝ X' Y Y' Z : C\ninst✝² : HasFiniteProducts C\ninst✝¹ : Exponentiable A✝\nA X : C\ninst✝ : Exponentiable A\n⊢ (exp.coev A).app ((𝟭 C).obj X) ≫ 𝟙 (A ⟹ A ⨯ (𝟭 C).obj X) = (exp.coev A).app X",
"state_before": "C : Type u\ninst✝³ : Category C\nA✝ B X✝ ... | [
237,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Std/Data/Rat/Lemmas.lean | Rat.normalize_zero | [
{
"state_after": "d : Nat\nnz : d ≠ 0\n⊢ mk' 0 1 = 0",
"state_before": "d : Nat\nnz : d ≠ 0\n⊢ normalize 0 d = 0",
"tactic": "simp [normalize, Int.zero_div, Int.natAbs_zero, Nat.div_self (Nat.pos_of_ne_zero nz)]"
},
{
"state_after": "no goals",
"state_before": "d : Nat\nnz : d ≠ 0\n⊢ mk' 0 1... | [
29,
93
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
28,
9
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq.map_id | [
{
"state_after": "case a\nα : Type u\nβ : Type v\nγ : Type w\ns : Stream' (Option α)\nal : IsSeq s\n⊢ ↑(map id { val := s, property := al }) = ↑{ val := s, property := al }",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : Stream' (Option α)\nal : IsSeq s\n⊢ map id { val := s, property := al } = { ... | [
707,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
704,
1
] |
Std/Data/String/Lemmas.lean | String.Iterator.ValidFor.out | [] | [
516,
17
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
515,
1
] |
Mathlib/Data/Nat/GCD/BigOperators.lean | Nat.coprime_prod_right | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nx : ℕ\ns : ι → ℕ\nt : Finset ι\n⊢ (fun y => coprime x y) 1",
"tactic": "simp"
}
] | [
33,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
31,
1
] |
Mathlib/Data/Rat/Lemmas.lean | Rat.inv_coe_int_num | [
{
"state_after": "no goals",
"state_before": "a : ℤ\n⊢ (↑a)⁻¹.num = Int.sign a",
"tactic": "induction a using Int.induction_on <;>\n simp [← Int.negSucc_coe', Int.negSucc_coe, -neg_add_rev, Rat.inv_neg, Int.ofNat_add_one_out,\n -Nat.cast_succ, inv_coe_nat_num_of_pos, -Int.cast_negSucc, @eq_comm ℤ 1,... | [
286,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | stronglyMeasurable_id | [] | [
643,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
641,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.Monic.ne_zero_of_ne | [
{
"state_after": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝¹ : Semiring R\np✝ q : R[X]\nι : Type ?u.646647\nh : 0 ≠ 1\np : R[X]\nhp : Monic p\ninst✝ : Nontrivial R\n⊢ p ≠ 0",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np✝ q : R[X]\nι : Type ?u.646647\nh : 0 ≠... | [
853,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
851,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.prime_ne_zero | [
{
"state_after": "no goals",
"state_before": "p q : ℕ\nhp : Fact (Nat.Prime p)\nhq : Fact (Nat.Prime q)\nhpq : p ≠ q\n⊢ ↑q ≠ 0",
"tactic": "rwa [← Nat.cast_zero, Ne.def, eq_iff_modEq_nat, Nat.modEq_zero_iff_dvd, ←\n hp.1.coprime_iff_not_dvd, Nat.coprime_primes hp.1 hq.1]"
}
] | [
1044,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1041,
1
] |
Mathlib/Deprecated/Submonoid.lean | powers.one_mem | [] | [
138,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Std/Data/Nat/Gcd.lean | Nat.coprime_self | [
{
"state_after": "no goals",
"state_before": "n : Nat\n⊢ coprime n n ↔ n = 1",
"tactic": "simp [coprime]"
}
] | [
365,
82
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
365,
9
] |
Mathlib/Combinatorics/SimpleGraph/Regularity/Uniform.lean | SimpleGraph.IsUniform.symm | [
{
"state_after": "α : Type u_1\n𝕜 : Type u_2\ninst✝¹ : LinearOrderedField 𝕜\nG : SimpleGraph α\ninst✝ : DecidableRel G.Adj\nε : 𝕜\ns✝ t✝ : Finset α\na b : α\ns t : Finset α\nh : IsUniform G ε s t\nt' : Finset α\nht' : t' ⊆ t\ns' : Finset α\nhs' : s' ⊆ s\nht : ↑(card t) * ε ≤ ↑(card t')\nhs : ↑(card s) * ε ≤ ... | [
73,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Data/List/Cycle.lean | Cycle.coe_toMultiset | [] | [
694,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
693,
1
] |
Mathlib/LinearAlgebra/Ray.lean | SameRay.map | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁵ : StrictOrderedCommSemiring R\nM : Type u_2\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nN : Type u_3\ninst✝² : AddCommMonoid N\ninst✝¹ : Module R N\nι : Type ?u.37832\ninst✝ : DecidableEq ι\nx y z : M\nf : M →ₗ[R] N\nh : SameRay R x y\nh... | [
168,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycleOn.exists_pow_eq' | [
{
"state_after": "case intro\nι : Type ?u.1917955\nα : Type u_1\nβ : Type ?u.1917961\nf g : Perm α\nt : Set α\na b x y : α\ns : Finset α\nhs : Set.Finite ↑s\nhf : IsCycleOn f ↑s\nha : a ∈ ↑s\nhb : b ∈ ↑s\n⊢ ∃ n, ↑(f ^ n) a = b",
"state_before": "ι : Type ?u.1917955\nα : Type u_1\nβ : Type ?u.1917961\nf g : ... | [
914,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
910,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.one_imJ | [] | [
199,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
9
] |
Mathlib/CategoryTheory/Sums/Basic.lean | CategoryTheory.sum_comp_inr | [] | [
77,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Order/Heyting/Basic.lean | sdiff_le_sdiff_left | [] | [
670,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
669,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_ball_lt_top | [] | [
3960,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3958,
1
] |
Mathlib/CategoryTheory/Sites/Subsheaf.lean | CategoryTheory.GrothendieckTopology.imagePresheaf_comp_le | [] | [
385,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
1
] |
Mathlib/Topology/MetricSpace/MetricSeparated.lean | IsMetricSeparated.union_right | [] | [
100,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.property_index | [] | [
305,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/RingTheory/Polynomial/Chebyshev.lean | Polynomial.Chebyshev.T_eq_X_mul_T_sub_pol_U | [
{
"state_after": "R : Type u_1\nS : Type ?u.22740\ninst✝¹ : CommRing R\ninst✝ : CommRing S\n⊢ 2 * X * X - 1 = X * X - (1 - X ^ 2) * 1",
"state_before": "R : Type u_1\nS : Type ?u.22740\ninst✝¹ : CommRing R\ninst✝ : CommRing S\n⊢ T R (0 + 2) = X * T R (0 + 1) - (1 - X ^ 2) * U R 0",
"tactic": "simp only ... | [
153,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.inclusion_self | [] | [
1051,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1050,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.SameCycle.cycleOf_apply | [] | [
1001,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1000,
1
] |
Mathlib/Algebra/Hom/GroupAction.lean | MulSemiringActionHom.comp_apply | [] | [
562,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
561,
1
] |
Mathlib/Data/List/Sigma.lean | List.perm_dlookup | [
{
"state_after": "case a\nα : Type u\nβ : α → Type v\nl l₁✝ l₂✝ : List (Sigma β)\ninst✝ : DecidableEq α\na : α\nl₁ l₂ : List (Sigma β)\nnd₁ : NodupKeys l₁\nnd₂ : NodupKeys l₂\np : l₁ ~ l₂\nb : β a\n⊢ b ∈ dlookup a l₁ ↔ b ∈ dlookup a l₂",
"state_before": "α : Type u\nβ : α → Type v\nl l₁✝ l₂✝ : List (Sigma β... | [
241,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Std/Data/List/Lemmas.lean | List.modify_get?_length | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nf : α → α\nl : List α\n⊢ length (modifyHead f l) = length l",
"tactic": "cases l <;> rfl"
}
] | [
754,
53
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
753,
9
] |
Mathlib/Algebra/Order/Field/Basic.lean | one_div_lt_one_div | [] | [
478,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieIdeal.map_coeSubmodule | [
{
"state_after": "R : Type u\nL : Type v\nL' : Type w₂\nM : Type w\nM' : Type w₁\ninst✝¹² : CommRing R\ninst✝¹¹ : LieRing L\ninst✝¹⁰ : LieAlgebra R L\ninst✝⁹ : LieRing L'\ninst✝⁸ : LieAlgebra R L'\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³ : AddCo... | [
809,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
807,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.sUnion_iUnion | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.178747\nγ : Type ?u.178750\nι : Sort u_2\nι' : Sort ?u.178756\nι₂ : Sort ?u.178759\nκ : ι → Sort ?u.178764\nκ₁ : ι → Sort ?u.178769\nκ₂ : ι → Sort ?u.178774\nκ' : ι' → Sort ?u.178779\ns : ι → Set (Set α)\n⊢ (⋃₀ ⋃ (i : ι), s i) = ⋃ (i : ... | [
1368,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1367,
1
] |
src/lean/Init/Core.lean | eqRec_heq | [] | [
645,
25
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
644,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.div_bot | [] | [
459,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.image_subset_infs_right | [] | [
279,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/Logic/Nonempty.lean | nonempty_psigma | [] | [
55,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | fderivWithin_pi | [] | [
457,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Measure.lean | BoxIntegral.Box.measurableSet_Icc | [] | [
66,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/GroupTheory/QuotientGroup.lean | QuotientGroup.equivQuotientZPowOfEquiv_refl | [
{
"state_after": "case h\nG : Type u\ninst✝⁴ : Group G\nN : Subgroup G\nnN : Subgroup.Normal N\nH : Type v\ninst✝³ : Group H\nφ : G →* H\nA B C : Type u\ninst✝² : CommGroup A\ninst✝¹ : CommGroup B\ninst✝ : CommGroup C\nf : A →* B\ng : B →* A\ne : A ≃* B\nd : B ≃* C\nn : ℤ\nx : A ⧸ range (zpowGroupHom n)\n⊢ ↑(Mu... | [
547,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
1
] |
Mathlib/Order/Heyting/Basic.lean | sdiff_le | [] | [
514,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
513,
1
] |
Mathlib/GroupTheory/SemidirectProduct.lean | SemidirectProduct.map_inl | [
{
"state_after": "no goals",
"state_before": "N : Type u_3\nG : Type u_4\nH : Type ?u.240686\ninst✝⁴ : Group N\ninst✝³ : Group G\ninst✝² : Group H\nφ : G →* MulAut N\nN₁ : Type u_1\nG₁ : Type u_2\ninst✝¹ : Group N₁\ninst✝ : Group G₁\nφ₁ : G₁ →* MulAut N₁\nf₁ : N →* N₁\nf₂ : G →* G₁\nh : ∀ (g : G), MonoidHom... | [
296,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/CategoryTheory/Closed/Cartesian.lean | CategoryTheory.pre_map | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝⁵ : Category C\nA B X X' Y Y' Z : C\ninst✝⁴ : HasFiniteProducts C\ninst✝³ : Exponentiable A\nA₁ A₂ A₃ : C\ninst✝² : Exponentiable A₁\ninst✝¹ : Exponentiable A₂\ninst✝ : Exponentiable A₃\nf : A₁ ⟶ A₂\ng : A₂ ⟶ A₃\n⊢ pre (f ≫ g) = pre g ≫ pre f",
... | [
307,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.order_mul | [
{
"state_after": "case a\nΓ✝ : Type ?u.1293056\nR : Type u_2\ninst✝³ : OrderedCancelAddCommMonoid Γ✝\nΓ : Type u_1\ninst✝² : LinearOrderedCancelAddCommMonoid Γ\ninst✝¹ : NonUnitalNonAssocSemiring R\ninst✝ : NoZeroDivisors R\nx y : HahnSeries Γ R\nhx : x ≠ 0\nhy : y ≠ 0\n⊢ order (x * y) ≤ order x + order y\n\nca... | [
917,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
909,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.sumAddHom_apply | [
{
"state_after": "case mk'.mk.mk\nι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝² : (i : ι) → AddZeroClass (β i)\ninst✝¹ : (i : ι) → (x : β i) → Decidable (x ≠ 0)\ninst✝ : AddCommMonoid γ\nφ : (i : ι) → β i →+ γ\nf : (i : ι) → β i\nsupport'✝ : Trunc { s //... | [
1934,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1925,
1
] |
Mathlib/Analysis/SpecialFunctions/ImproperIntegrals.lean | integral_exp_Iic | [
{
"state_after": "c : ℝ\n⊢ Tendsto (fun i => ∫ (x : ℝ) in id i..c, exp x) atBot (𝓝 (exp c))",
"state_before": "c : ℝ\n⊢ (∫ (x : ℝ) in Iic c, exp x) = exp c",
"tactic": "refine'\n tendsto_nhds_unique\n (intervalIntegral_tendsto_integral_Iic _ (integrableOn_exp_Iic _) tendsto_id) _"
},
{
"sta... | [
49,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/Topology/Order/LowerTopology.lean | WithLowerTopology.toLower_ofLower | [] | [
87,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.smul_im | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nE : Type ?u.2153398\ninst✝ : IsROrC K\nr : ℝ\nz : K\n⊢ ↑im (r • z) = r * ↑im z",
"tactic": "rw [real_smul_eq_coe_mul, ofReal_mul_im]"
}
] | [
290,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/MeasureTheory/Group/Prod.lean | MeasureTheory.measurePreserving_prod_inv_mul | [] | [
129,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Algebra/Divisibility/Units.lean | Units.dvd_mul_left | [
{
"state_after": "α : Type u_1\ninst✝ : CommMonoid α\na b : α\nu : αˣ\n⊢ a ∣ b * ↑u ↔ a ∣ b",
"state_before": "α : Type u_1\ninst✝ : CommMonoid α\na b : α\nu : αˣ\n⊢ a ∣ ↑u * b ↔ a ∣ b",
"tactic": "rw [mul_comm]"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : CommMono... | [
57,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.