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/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.cast_rat | [
{
"state_after": "no goals",
"state_before": "u : Lean.Level\nR✝ : Type ?u.334202\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝¹ : CommSemiring R✝\nn : ℤ\nd : ℕ\nR : Type u_1\ninst✝ : DivisionRing R\na : R\ninv✝ : Invertible ↑d\ne : a = ↑n * ⅟↑d\n⊢ a = Rat.rawCast n d + 0",
"tactic": "simp [e, div_eq... | [
841,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
840,
1
] |
Mathlib/LinearAlgebra/Matrix/Symmetric.lean | Matrix.isSymm_transpose_add_self | [] | [
73,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/CategoryTheory/Limits/Presheaf.lean | CategoryTheory.coconeOfRepresentable_pt | [] | [
336,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Pointwise.lean | Subalgebra.coe_pointwise_smul | [] | [
90,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Tower.lean | Subalgebra.restrictScalars_top | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nA : Type w\nB : Type u₁\nM : Type v₁\ninst✝¹⁰ : CommSemiring R\ninst✝⁹ : CommSemiring S\ninst✝⁸ : Semiring A\ninst✝⁷ : Semiring B\ninst✝⁶ : Algebra R S\ninst✝⁵ : Algebra S A\ninst✝⁴ : Algebra R A\ninst✝³ : Algebra S B\ninst✝² : Algebra R ... | [
106,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Algebra/Module/Submodule/Bilinear.lean | Submodule.map₂_bot_left | [
{
"state_after": "ι : Sort uι\nR : Type u_1\nM : Type u_2\nN : Type u_4\nP : Type u_3\ninst✝⁶ : CommSemiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : AddCommMonoid N\ninst✝³ : AddCommMonoid P\ninst✝² : Module R M\ninst✝¹ : Module R N\ninst✝ : Module R P\nf : M →ₗ[R] N →ₗ[R] P\nq : Submodule R N\nm : M\nhm : m = 0\... | [
97,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | RingHom.isIntegral_quotient_of_isIntegral | [
{
"state_after": "case mk\nR : Type u_2\nA : Type ?u.1581561\nB : Type ?u.1581564\nS : Type u_1\nT : Type ?u.1581570\ninst✝⁸ : CommRing R\ninst✝⁷ : CommRing A\ninst✝⁶ : CommRing B\ninst✝⁵ : CommRing S\ninst✝⁴ : CommRing T\ninst✝³ : Algebra A B\ninst✝² : Algebra R B\nf : R →+* S\ng : S →+* T\ninst✝¹ : Algebra R ... | [
1086,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1081,
1
] |
Mathlib/NumberTheory/Padics/PadicNorm.lean | padicNorm.sum_le | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\nα : Type u_1\nF : α → ℚ\nt : ℚ\ns : Finset α\n⊢ ∀ ⦃a : α⦄ {s : Finset α},\n ¬a ∈ s →\n (Finset.Nonempty s → (∀ (i : α), i ∈ s → padicNorm p (F i) ≤ t) → padicNorm p (∑ i in s, F i) ≤ t) →\n Finset.Nonempty (insert a s) →\n (∀ (i : α), i ∈... | [
342,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.monic_of_c_eq_one | [
{
"state_after": "R : Type u_1\nS : Type ?u.564413\nF : Type ?u.564416\nK : Type ?u.564419\nP Q : Cubic R\na b c d a' b' c' d' : R\ninst✝ : Semiring R\nha : P.a = 0\nhb : P.b = 0\nhc : P.c = 1\n✝ : Nontrivial R\n⊢ Monic (toPoly P)",
"state_before": "R : Type u_1\nS : Type ?u.564413\nF : Type ?u.564416\nK : ... | [
264,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/Data/Nat/GCD/Basic.lean | Nat.coprime_mul_right_add_left | [
{
"state_after": "no goals",
"state_before": "m n k : ℕ\n⊢ coprime (k * n + m) n ↔ coprime m n",
"tactic": "rw [coprime, coprime, gcd_mul_right_add_left]"
}
] | [
184,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Order/Filter/Pi.lean | Filter.coprodᵢ_eq_bot_iff' | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : ι → Type u_2\nf f₁ f₂ : (i : ι) → Filter (α i)\ns : (i : ι) → Set (α i)\n⊢ Filter.coprodᵢ f = ⊥ ↔ (∃ i, IsEmpty (α i)) ∨ f = ⊥",
"tactic": "simpa only [not_neBot, not_and_or, funext_iff, not_forall, not_exists, not_nonempty_iff]\n using co... | [
225,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Tactic/Ring/RingNF.lean | Mathlib.Tactic.RingNF.add_assoc_rev | [] | [
110,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.toAddSubmonoid_strictMono | [] | [
140,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Order/FixedPoints.lean | OrderHom.nextFixed_le | [] | [
224,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | UniformContinuous.inf_rng | [] | [
1380,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1377,
1
] |
Mathlib/Algebra/Lie/Nilpotent.lean | LieModule.iInf_max_gen_zero_eigenspace_eq_top_of_nilpotent | [
{
"state_after": "case h\nR : Type u\nL : Type v\nM : Type w\ninst✝⁷ : CommRing R\ninst✝⁶ : LieRing L\ninst✝⁵ : LieAlgebra R L\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\ninst✝² : LieRingModule L M\ninst✝¹ : LieModule R L M\nk : ℕ\nN : LieSubmodule R L M\ninst✝ : IsNilpotent R L M\nm : M\n⊢ (m ∈ ⨅ (x : L), M... | [
232,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.map_fst_prod | [
{
"state_after": "case a\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.16299\nδ : Type ?u.16302\nι : Sort ?u.16305\ns✝ : Set α\nt : Set β\nf✝ : Filter α\ng✝ : Filter β\nf : Filter α\ng : Filter β\ninst✝ : NeBot g\ns : Set α\n⊢ s ∈ map Prod.fst (f ×ˢ g) ↔ s ∈ f",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : T... | [
273,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.not_bot_adj | [] | [
365,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.comap_comp_apply | [] | [
616,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
614,
1
] |
Mathlib/Data/List/Sort.lean | List.insertionSort_cons_eq_take_drop | [] | [
222,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Algebra/BigOperators/Intervals.lean | Finset.sum_Ico_by_parts | [
{
"state_after": "R : Type u_2\nM : Type u_1\ninst✝² : Ring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nf : ℕ → R\ng : ℕ → M\nm n : ℕ\nhmn : m < n\nh₁ : ∑ i in Ico (m + 1) n, f i • ∑ i in range i, g i = ∑ i in Ico m (n - 1), f (i + 1) • ∑ i in range (i + 1), g i\n⊢ ∑ i in Ico m n, f i • g i =\n f (n - 1)... | [
307,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/NumberTheory/Padics/PadicVal.lean | padicValRat.sum_pos_of_pos | [
{
"state_after": "case zero\np : ℕ\nhp : Fact (Nat.Prime p)\nn : ℕ\nF : ℕ → ℚ\nhF✝ : ∀ (i : ℕ), i < n → 0 < padicValRat p (F i)\nhn0✝ : ∑ i in Finset.range n, F i ≠ 0\nhF : ∀ (i : ℕ), i < zero → 0 < padicValRat p (F i)\nhn0 : ∑ i in Finset.range zero, F i ≠ 0\n⊢ 0 < padicValRat p (∑ i in Finset.range zero, F i)... | [
397,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Data/Set/Basic.lean | Set.ite_mono | [] | [
2296,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2294,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.comap_principal | [] | [
2139,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2137,
1
] |
Mathlib/Order/Hom/Lattice.lean | InfTopHom.coe_comp | [] | [
954,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
953,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.image_inter_of_injOn | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.87546\ninst✝¹ : DecidableEq β\nf✝ g : α → β\ns✝ : Finset α\nt✝ : Finset β\na : α\nb c : β\ninst✝ : DecidableEq α\nf : α → β\ns t : Finset α\nhf : Set.InjOn f (↑s ∪ ↑t)\n⊢ f '' (↑s ∩ ↑t) = f '' ↑s ∩ f '' ↑t",
"state_before": "α : Type u_1\nβ : Type u_... | [
490,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.submatrix_apply | [] | [
2385,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2383,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | derivWithin_const | [] | [
704,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.mul_prod_erase | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.794748\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na✝ : α\nf✝ g : α → β\ninst✝¹ : CommMonoid β\ninst✝ : DecidableEq α\ns : Finset α\nf : α → β\na : α\nh : a ∈ s\n⊢ f a * ∏ x in erase s a, f x = ∏ x in s, f x",
"tactic": "rw [← prod_... | [
1657,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1655,
1
] |
Mathlib/CategoryTheory/Monoidal/End.lean | CategoryTheory.μ_inv_naturality | [] | [
140,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/CategoryTheory/Category/Bipointed.lean | Bipointed.swapEquiv_symm | [] | [
125,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/CategoryTheory/IsConnected.lean | CategoryTheory.isConnected_zigzag | [] | [
312,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/CategoryTheory/Preadditive/Basic.lean | CategoryTheory.Preadditive.mono_of_kernel_iso_zero | [] | [
285,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Std/Data/Int/Lemmas.lean | Int.add_neg_cancel_left | [
{
"state_after": "no goals",
"state_before": "a b : Int\n⊢ a + (-a + b) = b",
"tactic": "rw [← Int.add_assoc, Int.add_right_neg, Int.zero_add]"
}
] | [
321,
56
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
320,
11
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.edges_nodup_of_support_nodup | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v : V\np : Walk G u v\nh : List.Nodup (support p)\n⊢ List.Nodup (edges p)",
"tactic": "induction p with\n| nil => simp\n| cons _ p' ih =>\n simp only [ed... | [
828,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
822,
1
] |
Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.quotMapCMapSpanMkEquivQuotMapCQuotMapSpanMk_symm_quotQuotMk | [] | [
780,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
776,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.measure_toMeasurable_add_inter_right | [
{
"state_after": "α : Type u_1\nβ : Type ?u.141288\nγ : Type ?u.141291\nδ : Type ?u.141294\nι : Type ?u.141297\nR : Type ?u.141300\nR' : Type ?u.141303\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t✝ s t : Set α\nhs : MeasurableSet s\nh... | [
948,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
945,
1
] |
Mathlib/Data/Nat/Parity.lean | Nat.not_even_one | [] | [
111,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
9
] |
Mathlib/Topology/Algebra/ContinuousMonoidHom.lean | ContinuousMonoidHom.toContinuousMap_injective | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.14417\nA : Type u_1\nB : Type u_2\nC : Type ?u.14426\nD : Type ?u.14429\nE : Type ?u.14432\ninst✝¹⁰ : Monoid A\ninst✝⁹ : Monoid B\ninst✝⁸ : Monoid C\ninst✝⁷ : Monoid D\ninst✝⁶ : CommGroup E\ninst✝⁵ : TopologicalSpace A\ninst✝⁴ : TopologicalSpace B\ni... | [
137,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.support_pow_coprime | [
{
"state_after": "case intro\nα : Type u\nβ : Type v\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nσ : Perm α\nn : ℕ\nh : Nat.coprime n (orderOf σ)\nm : ℕ\nhm : (σ ^ n) ^ m = σ\n⊢ support (σ ^ n) = support σ",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nσ : Perm α\nn : ... | [
206,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Combinatorics/SimpleGraph/Density.lean | SimpleGraph.edgeDensity_empty_right | [] | [
417,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/Data/Rat/Defs.lean | Rat.den_zero | [] | [
413,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.ofReal_ofNat | [] | [
483,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
482,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.sizeOf_lt_sizeOf_of_mem | [
{
"state_after": "case mk\nα : Type u_1\nβ : Type ?u.287378\nγ : Type ?u.287381\ninst✝ : SizeOf α\nx : α\nval✝ : Multiset α\nnodup✝ : Nodup val✝\nhx : x ∈ { val := val✝, nodup := nodup✝ }\n⊢ SizeOf.sizeOf x < SizeOf.sizeOf { val := val✝, nodup := nodup✝ }",
"state_before": "α : Type u_1\nβ : Type ?u.287378\... | [
2402,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2396,
1
] |
Mathlib/Algebra/Lie/Solvable.lean | LieAlgebra.derivedSeriesOfIdeal_succ_le | [] | [
106,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.coe_div | [] | [
559,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
1
] |
Mathlib/NumberTheory/VonMangoldt.lean | Nat.ArithmeticFunction.vonMangoldt_eq_zero_iff | [] | [
107,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Data/Set/Image.lean | Set.preimage_mono | [] | [
76,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.map_map | [] | [
527,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
526,
1
] |
Mathlib/Topology/Order/Basic.lean | continuousWithinAt_Icc_iff_Iic | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝⁴ : TopologicalSpace α\ninst✝³ : LinearOrder α\ninst✝² : OrderClosedTopology α\na✝ b✝ : α\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace β\na b : α\nf : α → β\nh : a < b\n⊢ ContinuousWithinAt f (Icc a b) b ↔ Conti... | [
605,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
1
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Mathlib/Topology/Algebra/Order/ExtendFrom.lean | continuousOn_Icc_extendFrom_Ioo | [
{
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33,
26
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23,
1
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Mathlib/Data/List/Forall2.lean | List.rel_mem | [
{
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243,
52
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239,
1
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Mathlib/Topology/TietzeExtension.lean | ContinuousMap.exists_restrict_eq_forall_mem_of_closed | [] | [
408,
30
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403,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Arctan.lean | Real.arcsin_eq_arctan | [
{
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171,
95
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168,
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Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.natDegree_le_of_dvd | [
{
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171,
59
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169,
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Std/Logic.lean | ite_not | [] | [
708,
39
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707,
9
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Mathlib/Order/JordanHolder.lean | CompositionSeries.step | [] | [
160,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.finStronglyMeasurable_iff_measurable | [] | [
1967,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1965,
1
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Mathlib/Algebra/GroupPower/Ring.lean | add_sq | [
{
"state_after": "no goals",
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}
] | [
174,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
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Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.Monic.irreducible_iff_natDegree' | [
{
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310,
60
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299,
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Mathlib/Topology/MetricSpace/EMetricSpace.lean | MulOpposite.edist_op | [] | [
428,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
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Mathlib/Data/Set/Image.lean | Set.preimage_range_inter | [
{
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"tactic": "rw [inter_comm, preimage_inter_range]"
}
] | [
848,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
847,
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Mathlib/LinearAlgebra/FiniteDimensional.lean | FiniteDimensional.exists_nontrivial_relation_of_rank_lt_card | [
{
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482,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
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Std/Data/RBMap/Lemmas.lean | Std.RBNode.Stream.foldr_cons | [
{
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"state_before": "α : Type u_1\nt : RBNode.Stream α\nl : List α\n⊢ foldr (fun x x_1 => x :: x_1) t l = toList t ++ l",
"tactic": "unfold toList"
},
{
"s... | [
371,
83
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
370,
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Mathlib/Data/Set/Intervals/OrdConnected.lean | Set.ordConnected_biInter | [] | [
121,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
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Mathlib/Order/WellFoundedSet.lean | Set.isWf_union | [] | [
211,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
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Mathlib/Data/Finset/Pointwise.lean | Finset.coe_zpow | [
{
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999,
42
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995,
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Mathlib/Topology/MetricSpace/Isometry.lean | Isometry.uniformInducing | [] | [
125,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
11
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Mathlib/Analysis/Convex/Function.lean | ConvexOn.le_right_of_left_le | [
{
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756,
55
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753,
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Std/Data/Rat/Lemmas.lean | Rat.mkRat_mul_mkRat | [
{
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277,
101
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
274,
1
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Mathlib/Order/PFilter.lean | Order.PFilter.isPFilter | [] | [
87,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
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Mathlib/Algebra/Algebra/Unitization.lean | Unitization.snd_smul | [] | [
249,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
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Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.norm_mkPiAlgebra | [
{
"state_after": "case inl\n𝕜 : Type u\nι : Type v\nι' : Type v'\nn : ℕ\nE : ι → Type wE\nE₁ : ι → Type wE₁\nE' : ι' → Type wE'\nEi : Fin (Nat.succ n) → Type wEi\nG : Type wG\nG' : Type wG'\ninst✝¹⁷ : Fintype ι\ninst✝¹⁶ : Fintype ι'\ninst✝¹⁵ : NontriviallyNormedField 𝕜\ninst✝¹⁴ : (i : ι) → NormedAddCommGroup ... | [
830,
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825,
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Mathlib/FieldTheory/IsAlgClosed/Basic.lean | lift.SubfieldWithHom.compat | [
{
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236,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
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Mathlib/Order/CompleteLattice.lean | sInf_eq_of_forall_ge_of_forall_gt_exists_lt | [] | [
580,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
578,
1
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Mathlib/Data/Pi/Algebra.lean | Pi.div_apply | [] | [
205,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
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Mathlib/Data/Real/Basic.lean | Real.cauchy_intCast | [] | [
197,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
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Mathlib/Data/Rat/BigOperators.lean | Rat.cast_list_prod | [] | [
44,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
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Mathlib/Data/PFunctor/Univariate/M.lean | PFunctor.M.isPath_cons' | [
{
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"state_before": "F : PFunctor\nX : Type ?u.21403\nf✝ : X → Obj F X\nxs : Path F\n... | [
488,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
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Mathlib/Topology/Algebra/GroupWithZero.lean | ContinuousOn.zpow₀ | [] | [
347,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.simpleFunc_bot | [
{
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"state_before": "α✝ : Type ?u.20769\nβ : Type u_2\nγ : Type ?u.20... | [
184,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
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Mathlib/Data/Set/Lattice.lean | Set.compl_sInter | [
{
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1249,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1248,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioc_union_Ioc_eq_Ioc | [] | [
1598,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1595,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.zero_nmem_multiset_map_X_add_C | [] | [
1398,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1395,
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] |
Mathlib/Computability/Primrec.lean | Primrec.list_indexOf | [] | [
1139,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1138,
1
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Mathlib/GroupTheory/GroupAction/Defs.lean | Function.End.smul_def | [] | [
1111,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1110,
1
] |
Mathlib/Algebra/Module/LocalizedModule.lean | LocalizedModule.liftOn₂_mk | [
{
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139,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
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Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Algebra.mem_bot | [
{
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"state_before": "R : Type u\nA : Type... | [
897,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
893,
1
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Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.id_zero | [
{
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"tactic": "apply HasZeroObject.from_zero_ext"
}
] | [
373,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
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Mathlib/Data/Finset/LocallyFinite.lean | Finset.uIcc_subset_uIcc | [
{
"state_after": "ι : Type ?u.184228\nα : Type u_1\ninst✝¹ : Lattice α\ninst✝ : LocallyFiniteOrder α\na a₁ a₂ b b₁ b₂ c x : α\nh₁ : a₂ ⊓ b₂ ≤ a₁ ∧ a₁ ≤ a₂ ⊔ b₂\nh₂ : a₂ ⊓ b₂ ≤ b₁ ∧ b₁ ≤ a₂ ⊔ b₂\n⊢ [[a₁, b₁]] ⊆ [[a₂, b₂]]",
"state_before": "ι : Type ?u.184228\nα : Type u_1\ninst✝¹ : Lattice α\ninst✝ : Locall... | [
935,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
932,
1
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Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.restrict_of_comp_subtype | [] | [
409,
5
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
] |
Mathlib/Order/Disjoint.lean | IsCompl.le_right_iff | [] | [
543,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.cons_eq_cons | [] | [
110,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
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Mathlib/CategoryTheory/Arrow.lean | CategoryTheory.Arrow.w | [] | [
131,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
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Mathlib/Order/RelClasses.lean | IsPartialOrder.swap | [] | [
108,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.lift_pred | [
{
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"state_before": "α : Type ?u.88270\nβ : Type ?u.88273\nγ : Type ?u.88276\nr : α → α → Prop\ns : β → β ... | [
233,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | IntervalIntegrable.comp_sub_left | [
{
"state_after": "no goals",
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348,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
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Mathlib/Algebra/Free.lean | Magma.AssocQuotient.quot_mk_assoc_left | [] | [
361,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.pullbackArrows_comm | [
{
"state_after": "case h\nC : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nF : C ⥤ D\nX✝ Y✝ Z : C\nf✝ : Y✝ ⟶ X✝\nS R✝ : Sieve X✝\ninst✝ : HasPullbacks C\nX Y : C\nf : Y ⟶ X\nR : Presieve X\nW : C\n⊢ ∀ (f_1 : W ⟶ Y), (generate (Presieve.pullbackArrows f R)).arrows f_1 ↔ (pullback f (generate R... | [
576,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
565,
1
] |
Mathlib/Data/Real/ConjugateExponents.lean | Real.IsConjugateExponent.conj_eq | [
{
"state_after": "p q : ℝ\nh : IsConjugateExponent p q\nthis : 1 / p + 1 / q = 1\n⊢ q = p / (p - 1)",
"state_before": "p q : ℝ\nh : IsConjugateExponent p q\n⊢ q = p / (p - 1)",
"tactic": "have := h.inv_add_inv_conj"
},
{
"state_after": "p q : ℝ\nh : IsConjugateExponent p q\nthis : q = (1 - 1 / p... | [
77,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
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