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/LinearAlgebra/Alternating.lean | AlternatingMap.smul_apply | [] | [
260,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Topology/Algebra/Order/Compact.lean | ContinuousOn.image_Icc | [] | [
426,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/Data/Set/Basic.lean | Set.ssubset_singleton_iff | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns✝ s₁ s₂ t t₁ t₂ u s : Set α\nx : α\n⊢ s = ∅ → s ≠ {x}",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns✝ s₁ s₂ t t₁ t₂ u s : Set α\nx : α\n⊢ s ⊂ {x} ↔ s = ∅",
"tactic": "rw [ssubset_iff_subset_ne, sub... | [
1507,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1504,
1
] |
Mathlib/Algebra/EuclideanDomain/Basic.lean | EuclideanDomain.lcm_zero_left | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝¹ : EuclideanDomain R\ninst✝ : DecidableEq R\nx : R\n⊢ lcm 0 x = 0",
"tactic": "rw [lcm, zero_mul, zero_div]"
}
] | [
301,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.mk_mem_graph | [] | [
87,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Data/Sum/Order.lean | Sum.Lex.inl_mono | [] | [
406,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
1
] |
Mathlib/Analysis/SpecialFunctions/Polynomials.lean | Polynomial.tendsto_atTop_of_leadingCoeff_nonneg | [] | [
64,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Data/List/MinMax.lean | List.not_lt_of_mem_argmin | [] | [
137,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.conjTranspose_zsmul | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.986278\nm : Type u_1\nn : Type u_2\no : Type ?u.986287\nm' : o → Type ?u.986292\nn' : o → Type ?u.986297\nR : Type ?u.986300\nS : Type ?u.986303\nα : Type v\nβ : Type w\nγ : Type ?u.986310\ninst✝¹ : AddGroup α\ninst✝ : StarAddMonoid α\nc : ℤ\nM : Mat... | [
2200,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2198,
1
] |
Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean | SimpleGraph.sum_incMatrix_apply | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nα : Type u_1\nG : SimpleGraph α\ninst✝³ : Fintype α\ninst✝² : NonAssocSemiring R\na b : α\ne : Sym2 α\ninst✝¹ : DecidableEq α\ninst✝ : DecidableRel G.Adj\n⊢ ∑ e : Sym2 α, incMatrix R G a e = ↑(degree G a)",
"tactic": "simp [incMatrix_apply', su... | [
125,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | TendstoLocallyUniformlyOn.unique | [] | [
782,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
780,
1
] |
Mathlib/Topology/PartitionOfUnity.lean | BumpCovering.exists_isSubordinate_of_prop | [
{
"state_after": "case intro.intro.intro.intro\nι : Type u\nX : Type v\ninst✝² : TopologicalSpace X\ns : Set X\nf : BumpCovering ι X s\ninst✝¹ : NormalSpace X\ninst✝ : ParacompactSpace X\np : (X → ℝ) → Prop\nh01 :\n ∀ (s t : Set X),\n IsClosed s → IsClosed t → Disjoint s t → ∃ f, p ↑f ∧ EqOn (↑f) 0 s ∧ EqOn... | [
342,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/Data/Num/Bitwise.lean | SNum.bit_one | [
{
"state_after": "no goals",
"state_before": "b : Bool\n⊢ (b::zero (decide ¬b = true)) = nz (msb b)",
"tactic": "cases b <;> rfl"
}
] | [
334,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/Algebra/Lie/OfAssociative.lean | AlgHom.to_lieHom_comp | [] | [
197,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/CategoryTheory/SingleObj.lean | CategoryTheory.SingleObj.mapHom_comp | [] | [
143,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Std/Data/List/Lemmas.lean | List.isInfix.eq_of_length | [] | [
1651,
25
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1650,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | AddSubmonoid.mem_inv_pointwise_smul_iff | [] | [
424,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.coeff_map | [
{
"state_after": "case h_C\nR : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type u_1\na a' a₁ a₂ : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S₁\np q : MvPolynomial σ R\nf : R →+* S₁\n⊢ ∀ (a : R) (m : σ →₀ ℕ), coeff m (↑(map f) (↑C a)) = ↑f (coeff m (↑C a))\n\ncase h_add... | [
1286,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1269,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | set_integral_withDensity_eq_set_integral_smul | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.4658033\nE : Type u_2\nF : Type ?u.4658039\ninst✝⁹ : MeasurableSpace α\nι : Type ?u.4658045\ninst✝⁸ : NormedAddCommGroup E\nμ : MeasureTheory.Measure α\n𝕜 : Type ?u.4772853\ninst✝⁷ : IsROrC 𝕜\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : Norme... | [
1283,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1280,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.destruct_nil | [] | [
629,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
628,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.mrange_inl | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\nN : Type u_2\nP : Type ?u.149993\ninst✝³ : MulOneClass M\ninst✝² : MulOneClass N\ninst✝¹ : MulOneClass P\nS : Submonoid M\nA : Type ?u.150014\ninst✝ : SetLike A M\nhA : SubmonoidClass A M\nS' : A\n⊢ mrange (inl M N) = prod ⊤ ⊥",
"tactic": "simp... | [
1288,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1288,
1
] |
Mathlib/NumberTheory/LegendreSymbol/MulCharacter.lean | MulChar.pow_apply_coe | [
{
"state_after": "case zero\nR : Type u\ninst✝¹ : CommMonoid R\nR' : Type v\ninst✝ : CommMonoidWithZero R'\nχ : MulChar R R'\na : Rˣ\n⊢ ↑(χ ^ Nat.zero) ↑a = ↑χ ↑a ^ Nat.zero\n\ncase succ\nR : Type u\ninst✝¹ : CommMonoid R\nR' : Type v\ninst✝ : CommMonoidWithZero R'\nχ : MulChar R R'\na : Rˣ\nn : ℕ\nih : ↑(χ ^ n... | [
409,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infiniteNeg_of_tendsto_bot | [
{
"state_after": "f : ℕ → ℝ\nhf : Tendsto f atTop atBot\nr : ℝ\nhf' : ∀ (b : ℝ), ∃ i, ∀ (a : ℕ), i ≤ a → f a ≤ b\ni : ℕ\nhi : ∀ (a : ℕ), i ≤ a → f a ≤ r - 1\nhi' : ∀ (a : ℕ), r - 1 < f a → a < i\n⊢ {a | r ≤ f a} ⊆ {a | a ≤ i}",
"state_before": "f : ℕ → ℝ\nhf : Tendsto f atTop atBot\nr : ℝ\nhf' : ∀ (b : ℝ), ... | [
601,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
] |
Mathlib/Algebra/Hom/Freiman.lean | FreimanHom.const_apply | [] | [
301,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Real.hasStrictDerivAt_sin | [] | [
580,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
] |
Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.inf_eq_map_pullback | [] | [
472,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/Algebra/Associated.lean | not_irreducible_zero | [] | [
203,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Computability/Partrec.lean | Partrec.sum_casesOn_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_4\nβ : Type u_1\nγ : Type u_2\nσ : Type u_3\ninst✝³ : Primcodable α\ninst✝² : Primcodable β\ninst✝¹ : Primcodable γ\ninst✝ : Primcodable σ\nf : α → β ⊕ γ\ng : α → β →. σ\nh : α → γ → σ\nhf : Computable f\nhg : Partrec₂ g\nhh : Computable₂ h\na : α\n⊢ ... | [
810,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
806,
1
] |
Mathlib/Order/Filter/FilterProduct.lean | Filter.Germ.const_min | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nφ : Ultrafilter α\ninst✝ : LinearOrder β\nx y : β\n⊢ ↑(min x y) = min ↑x ↑y",
"tactic": "rw [min_def, map₂_const]"
}
] | [
247,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.setToFun_mono_left' | [
{
"state_after": "case pos\nα : Type u_1\nE : Type u_2\nF : Type ?u.1515415\nF' : Type ?u.1515418\nG : Type ?u.1515421\n𝕜 : Type ?u.1515424\np : ℝ≥0∞\ninst✝¹² : NormedAddCommGroup E\ninst✝¹¹ : NormedSpace ℝ E\ninst✝¹⁰ : NormedAddCommGroup F\ninst✝⁹ : NormedSpace ℝ F\ninst✝⁸ : NormedAddCommGroup F'\ninst✝⁷ : No... | [
1475,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1469,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.comap_equiv_eq_map_symm | [] | [
1183,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1181,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.le_mul_self | [
{
"state_after": "no goals",
"state_before": "m n✝ k l n : ℕ\n⊢ n + 1 ≤ (n + 1) * (n + 1)",
"tactic": "simp"
}
] | [
303,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/Data/Nat/Choose/Dvd.lean | Nat.Prime.dvd_choose_add | [
{
"state_after": "p a b k : ℕ\nhp : Prime p\nhap : a < p\nhbp : b < p\nh : p ≤ a + b\nh₁ : p ∣ (a + b)!\n⊢ p ∣ choose (a + b) a",
"state_before": "p a b k : ℕ\nhp : Prime p\nhap : a < p\nhbp : b < p\nh : p ≤ a + b\n⊢ p ∣ choose (a + b) a",
"tactic": "have h₁ : p ∣ (a + b)! := hp.dvd_factorial.2 h"
},
... | [
32,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
27,
1
] |
Mathlib/RingTheory/MvPolynomial/Basic.lean | MvPolynomial.mem_restrictDegree | [
{
"state_after": "σ : Type u\nR : Type v\ninst✝ : CommRing R\np✝ m : ℕ\np : MvPolynomial σ R\nn : ℕ\n⊢ ↑p.support ⊆ {n_1 | ∀ (i : σ), ↑n_1 i ≤ n} ↔ ∀ (s : σ →₀ ℕ), s ∈ support p → ∀ (i : σ), ↑s i ≤ n",
"state_before": "σ : Type u\nR : Type v\ninst✝ : CommRing R\np✝ m : ℕ\np : MvPolynomial σ R\nn : ℕ\n⊢ p ∈ ... | [
99,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.dual_Icc | [] | [
251,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Order/Bounds/Basic.lean | IsGreatest.nonempty | [] | [
353,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Std/Data/List/Lemmas.lean | List.reverse_prefix | [
{
"state_after": "α✝ : Type u_1\nl₁ l₂ : List α✝\n⊢ reverse (reverse l₁) <:+ reverse (reverse l₂) ↔ l₁ <:+ l₂",
"state_before": "α✝ : Type u_1\nl₁ l₂ : List α✝\n⊢ reverse l₁ <+: reverse l₂ ↔ l₁ <:+ l₂",
"tactic": "rw [← reverse_suffix]"
},
{
"state_after": "no goals",
"state_before": "α✝ : T... | [
1623,
53
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1622,
9
] |
Mathlib/Topology/Sheaves/Stalks.lean | TopCat.Presheaf.stalkPushforward.stalkPushforward_iso_of_openEmbedding | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\ninst✝ : HasColimits C\nX Y Z : TopCat\nf : X ⟶ Y\nhf : OpenEmbedding ((forget TopCat).map f)\nF : Presheaf C X\nx : ↑X\nthis : Functor.Initial (IsOpenMap.functorNhds (_ : IsOpenMap ((forget TopCat).map f)) x)\n⊢ IsIso (stalkPushforward C f F x)",
"state_bef... | [
228,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Order/Hom/Basic.lean | le_map_inv_iff | [
{
"state_after": "case h.e'_2.h.e'_4\nF : Type u_2\nα : Type u_1\nβ : Type u_3\nγ : Type ?u.29401\nδ : Type ?u.29404\ninst✝² : LE α\ninst✝¹ : LE β\ninst✝ : OrderIsoClass F α β\nf : F\na : α\nb : β\n⊢ b = ↑f (EquivLike.inv f b)",
"state_before": "F : Type u_2\nα : Type u_1\nβ : Type u_3\nγ : Type ?u.29401\nδ... | [
194,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.coe_equivMapOfInjective_apply | [] | [
823,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
821,
1
] |
Mathlib/Data/Set/BoolIndicator.lean | Set.preimage_boolIndicator_eq_union | [
{
"state_after": "case h\nα : Type u_1\ns : Set α\nt : Set Bool\nx : α\n⊢ x ∈ boolIndicator s ⁻¹' t ↔ x ∈ (if true ∈ t then s else ∅) ∪ if false ∈ t then sᶜ else ∅",
"state_before": "α : Type u_1\ns : Set α\nt : Set Bool\n⊢ boolIndicator s ⁻¹' t = (if true ∈ t then s else ∅) ∪ if false ∈ t then sᶜ else ∅",
... | [
54,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisConnection.u_iInf | [] | [
300,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.balance_sz_dual | [
{
"state_after": "α : Type u_1\nl r : Ordnode α\nH : (∃ l', Raised (size l) l' ∧ BalancedSz l' (size r)) ∨ ∃ r', Raised r' (size r) ∧ BalancedSz (size l) r'\n⊢ (∃ l', Raised l' (size r) ∧ BalancedSz l' (size l)) ∨ ∃ r', Raised (size l) r' ∧ BalancedSz (size r) r'",
"state_before": "α : Type u_1\nl r : Ordno... | [
845,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
837,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_congr | [] | [
259,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.NeBot.of_div_left | [] | [
483,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
482,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.coeff_truncFun | [
{
"state_after": "no goals",
"state_before": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\nn m : σ →₀ ℕ\nφ : MvPowerSeries σ R\n⊢ MvPolynomial.coeff m (truncFun n φ) = if m < n then ↑(coeff R m) φ else 0",
"tactic": "simp [truncFun, MvPolynomial.coeff_sum]"
}
] | [
680,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
678,
1
] |
Mathlib/Topology/MetricSpace/IsometricSMul.lean | ediam_smul | [] | [
89,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Analysis/Convex/Side.lean | Wbtw.wSameSide₂₃ | [
{
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377,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/GroupTheory/GroupAction/ConjAct.lean | MulAut.conjNormal_symm_apply | [
{
"state_after": "α : Type ?u.89699\nM : Type ?u.89702\nG : Type u_1\nG₀ : Type ?u.89708\nR : Type ?u.89711\nK : Type ?u.89714\ninst✝¹ : Group G\nH : Subgroup G\ninst✝ : Normal H\ng : G\nh : { x // x ∈ H }\n⊢ ↑ofConjAct (↑(MulEquiv.toMonoidHom toConjAct) g)⁻¹ * ↑h * (↑(MulEquiv.toMonoidHom toConjAct) g)⁻¹⁻¹ = g... | [
347,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
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Mathlib/Data/Real/NNReal.lean | NNReal.half_lt_self | [] | [
877,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
876,
8
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Mathlib/Algebra/Ring/Pi.lean | Pi.nonUnitalRingHom_injective | [] | [
107,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
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Mathlib/Data/PNat/Prime.lean | PNat.Coprime.mul | [
{
"state_after": "k m n : ℕ+\n⊢ coprime ↑m ↑k → coprime ↑n ↑k → coprime ↑(m * n) ↑k",
"state_before": "k m n : ℕ+\n⊢ Coprime m k → Coprime n k → Coprime (m * n) k",
"tactic": "repeat' rw [← coprime_coe]"
},
{
"state_after": "k m n : ℕ+\n⊢ coprime ↑m ↑k → coprime ↑n ↑k → coprime (↑m * ↑n) ↑k",
... | [
180,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/RingTheory/Localization/Integer.lean | IsLocalization.isInteger_zero | [] | [
54,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_sub_lt | [
{
"state_after": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Ring R\np q : R[X]\nhd : degree p = degree q\nhp0 : p ≠ 0\nhlc : leadingCoeff p = leadingCoeff q\nhp : ↑(monomial (natDegree p)) (leadingCoeff p) + erase (natDegree p) p = p\nhq : ↑(monomial (natDegree q)) (leadingCoeff q) + erase (natDegre... | [
1316,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1301,
1
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Mathlib/CategoryTheory/Preadditive/OfBiproducts.lean | CategoryTheory.SemiadditiveOfBinaryBiproducts.distrib | [
{
"state_after": "C : Type u\ninst✝² : Category C\ninst✝¹ : HasZeroMorphisms C\ninst✝ : HasBinaryBiproducts C\nX Y : C\nf g h k : X ⟶ Y\ndiag : X ⊞ X ⟶ Y ⊞ Y := biprod.lift (biprod.desc f g) (biprod.desc h k)\n⊢ leftAdd X Y (rightAdd X Y f g) (rightAdd X Y h k) = rightAdd X Y (leftAdd X Y f h) (leftAdd X Y g k)... | [
97,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.IsNormal.apply_omega | [
{
"state_after": "no goals",
"state_before": "f : Ordinal → Ordinal\nhf : IsNormal f\n⊢ Ordinal.sup (f ∘ Nat.cast) = f ω",
"tactic": "rw [← sup_nat_cast, IsNormal.sup.{0, u, u} hf]"
}
] | [
2509,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2508,
1
] |
Mathlib/Init/Algebra/Classes.lean | symm_of | [] | [
304,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
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Mathlib/CategoryTheory/Limits/IsLimit.lean | CategoryTheory.Limits.IsLimit.existsUnique | [] | [
114,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.bypass_isPath | [
{
"state_after": "no goals",
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"tactic": "simp!"
},
{
"state_after": "case cons\nV : Type u\nV' : Type v\nV'' ... | [
1375,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1368,
1
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Mathlib/RingTheory/Subring/Basic.lean | Subring.top_prod_top | [] | [
1130,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1129,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.singleton_div | [] | [
671,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
670,
1
] |
Std/Data/Int/Lemmas.lean | Int.add_neg_one | [] | [
96,
54
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
96,
1
] |
Mathlib/Data/Set/Function.lean | Set.EqOn.congr_strictMonoOn | [] | [
283,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/Algebra/Homology/Homotopy.lean | Homotopy.map_nullHomotopicMap | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.262154\nV : Type u\ninst✝⁴ : Category V\ninst✝³ : Preadditive V\nc : ComplexShape ι\nC D E : HomologicalComplex V c\nf g : C ⟶ D\nh k : D ⟶ E\ni✝ : ι\nW : Type ?u.262509\ninst✝² : Category W\ninst✝¹ : Preadditive W\nG : V ⥤ W\ninst✝ : Functor.Additiv... | [
320,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
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Mathlib/Data/Real/EReal.lean | EReal.coe_nsmul | [] | [
362,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.sub_eq_zero_of_le | [
{
"state_after": "no goals",
"state_before": "n m : Nat\nh : n ≤ m\n⊢ n - m = 0",
"tactic": "match le.dest h with\n| ⟨k, hk⟩ => rw [← hk, Nat.sub_self_add]"
},
{
"state_after": "no goals",
"state_before": "n m : Nat\nh : n ≤ m\nk : Nat\nhk : n + k = m\n⊢ n - m = 0",
"tactic": "rw [← hk, ... | [
640,
43
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
638,
11
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Mathlib/Analysis/Normed/Group/Basic.lean | nnnorm_div_le | [] | [
941,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
940,
1
] |
Mathlib/Data/Vector/Mem.lean | Vector.mem_cons_of_mem | [] | [
70,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Algebra/DirectLimit.lean | Module.DirectLimit.exists_of | [
{
"state_after": "no goals",
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135,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Comp.lean | HasFDerivAt.comp_hasFDerivWithinAt | [] | [
103,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Algebra/Hom/Group.lean | MulHom.mul_apply | [] | [
1461,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1460,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.pure_bind | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.232378\nι : Sort x\na : α\nm : α → Filter β\n⊢ bind (pure a) m = m a",
"tactic": "simp only [Bind.bind, bind, map_pure, join_pure]"
}
] | [
2000,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1999,
1
] |
Mathlib/Analysis/InnerProductSpace/Adjoint.lean | IsSelfAdjoint.isSymmetric | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.1318115\nG : Type ?u.1318118\ninst✝⁸ : IsROrC 𝕜\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedAddCommGroup G\ninst✝⁴ : InnerProductSpace 𝕜 E\ninst✝³ : InnerProductSpace 𝕜 F\ninst✝² : InnerProductSpace 𝕜 G\ninst✝¹ : Co... | [
289,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Data/List/BigOperators/Lemmas.lean | MulOpposite.unop_list_prod | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.28940\nα : Type ?u.28943\nM : Type u_1\nN : Type ?u.28949\nP : Type ?u.28952\nM₀ : Type ?u.28955\nG : Type ?u.28958\nR : Type ?u.28961\ninst✝ : Monoid M\nl : List Mᵐᵒᵖ\n⊢ unop (prod l) = prod (reverse (map unop l))",
"tactic": "rw [← op_inj, op_u... | [
153,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Data/Matrix/Kronecker.lean | Matrix.smul_kronecker | [] | [
317,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.ofDual_inf' | [] | [
1076,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1074,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.coe_refl | [] | [
298,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/Data/Polynomial/Reverse.lean | Polynomial.coeff_reflect | [
{
"state_after": "case ofFinsupp\nR : Type u_1\ninst✝ : Semiring R\nf✝ : R[X]\nN i : ℕ\nf : AddMonoidAlgebra R ℕ\n⊢ coeff (reflect N { toFinsupp := f }) i = coeff { toFinsupp := f } (↑(revAt N) i)",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nf✝ : R[X]\nN : ℕ\nf : R[X]\ni : ℕ\n⊢ coeff (reflect N f) i... | [
121,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Analysis/Convex/Between.lean | wbtw_zero_one_iff | [
{
"state_after": "R : Type u_1\nV : Type ?u.257226\nV' : Type ?u.257229\nP : Type ?u.257232\nP' : Type ?u.257235\ninst✝⁶ : OrderedRing R\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module R V\ninst✝³ : AddTorsor V P\ninst✝² : AddCommGroup V'\ninst✝¹ : Module R V'\ninst✝ : AddTorsor V' P'\nx : R\n⊢ (∃ x_1, x_1 ∈ Set.Icc ... | [
448,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
] |
Mathlib/LinearAlgebra/Matrix/MvPolynomial.lean | Matrix.det_mvPolynomialX_ne_zero | [
{
"state_after": "m : Type u_1\nn : Type ?u.39994\nR : Type u_2\nS : Type ?u.40000\ninst✝³ : DecidableEq m\ninst✝² : Fintype m\ninst✝¹ : CommRing R\ninst✝ : Nontrivial R\nh_det : det (mvPolynomialX m m R) = 0\n⊢ False",
"state_before": "m : Type u_1\nn : Type ?u.39994\nR : Type u_2\nS : Type ?u.40000\ninst✝... | [
83,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.toFinsupp_smul | [] | [
241,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/GroupTheory/Submonoid/Membership.lean | MulMemClass.mul_right_mem_add_closure | [
{
"state_after": "M : Type u_2\nA : Type ?u.256135\nB : Type ?u.256138\nR : Type u_1\ninst✝² : NonUnitalNonAssocSemiring R\ninst✝¹ : SetLike M R\ninst✝ : MulMemClass M R\nS : M\na : R\nha : a ∈ AddSubmonoid.closure ↑S\n⊢ ∀ {b : R}, b ∈ S → a * b ∈ AddSubmonoid.closure ↑S",
"state_before": "M : Type u_2\nA :... | [
653,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
645,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.inter_vsub_union_subset_union | [] | [
701,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
1
] |
Mathlib/Data/Multiset/Sum.lean | Multiset.disjSum_mono | [] | [
76,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.ToPartrec.Cont.then_eval | [
{
"state_after": "case comp\nk' : Cont\nv✝ : List ℕ\na✝¹ : Code\na✝ : Cont\nk_ih : ∀ {v : List ℕ}, eval (then a✝ k') v = eval a✝ v >>= eval k'\nv : List ℕ\n⊢ Code.eval a✝¹ v >>= eval (then a✝ k') = Code.eval a✝¹ v >>= fun x => eval a✝ x >>= eval k'\n\ncase fix\nk' : Cont\nv✝ : List ℕ\na✝¹ : Code\na✝ : Cont\nk_i... | [
556,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
552,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atTop_add_const_left | [] | [
811,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
809,
1
] |
Mathlib/Data/Rel.lean | Rel.preimage_union | [] | [
196,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Algebra/Group/Basic.lean | eq_div_of_mul_eq'' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.66484\nβ : Type ?u.66487\nG : Type u_1\ninst✝ : CommGroup G\na b c d : G\nh : c * a = b\n⊢ a = b / c",
"tactic": "simp [h.symm]"
}
] | [
915,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
915,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.not_lt_of_le | [] | [
378,
93
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
378,
11
] |
Mathlib/CategoryTheory/Monoidal/Braided.lean | CategoryTheory.rightUnitor_monoidal | [
{
"state_after": "C : Type u₁\ninst✝⁸ : Category C\ninst✝⁷ : MonoidalCategory C\ninst✝⁶ : BraidedCategory C\nD : Type u₂\ninst✝⁵ : Category D\ninst✝⁴ : MonoidalCategory D\ninst✝³ : BraidedCategory D\nE : Type u₃\ninst✝² : Category E\ninst✝¹ : MonoidalCategory E\ninst✝ : BraidedCategory E\nX₁ X₂ : C\n⊢ (ρ_ X₁).h... | [
600,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
587,
1
] |
src/lean/Init/Control/Lawful.lean | StateT.run_modify | [] | [
261,
119
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
261,
9
] |
Mathlib/ModelTheory/Order.lean | FirstOrder.Language.orderedStructure_iff | [] | [
174,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/MeasureTheory/Function/UniformIntegrable.lean | MeasureTheory.UniformIntegrable.unifIntegrable | [] | [
88,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
11
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.adj_of_mem_edges | [] | [
681,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
680,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.take_theorem | [
{
"state_after": "α : Type u\nβ : Type v\nδ : Type w\ns₁ s₂ : Stream' α\nh : ∀ (n : ℕ), take n s₁ = take n s₂\n⊢ s₁ = s₂",
"state_before": "α : Type u\nβ : Type v\nδ : Type w\ns₁ s₂ : Stream' α\n⊢ (∀ (n : ℕ), take n s₁ = take n s₂) → s₁ = s₂",
"tactic": "intro h"
},
{
"state_after": "case a\nα :... | [
635,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
627,
1
] |
Mathlib/Topology/FiberBundle/Constructions.lean | Trivialization.baseSet_prod | [] | [
255,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.smul_apply | [] | [
265,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/Deprecated/Subgroup.lean | IsGroupHom.inv_ker_one' | [
{
"state_after": "G : Type u_1\nH : Type u_2\nA : Type ?u.77638\na✝ a₁ a₂ b✝ c : G\ninst✝¹ : Group G\ninst✝ : Group H\nf : G → H\nhf : IsGroupHom f\na b : G\nh : f a = f b\nthis : (f a)⁻¹ * f b = 1\n⊢ f (a⁻¹ * b) = 1",
"state_before": "G : Type u_1\nH : Type u_2\nA : Type ?u.77638\na✝ a₁ a₂ b✝ c : G\ninst✝¹... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
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] |
Mathlib/Analysis/Convex/Hull.lean | affineSpan_convexHull | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.45458\ninst✝⁴ : OrderedRing 𝕜\ninst✝³ : AddCommGroup E\ninst✝² : AddCommGroup F\ninst✝¹ : Module 𝕜 E\ninst✝ : Module 𝕜 F\ns : Set E\n⊢ affineSpan 𝕜 (↑(convexHull 𝕜).toOrderHom s) ≤ affineSpan 𝕜 s",
"state_before": "𝕜 : Type u_2\nE : Type u_1\... | [
225,
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222,
1
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Mathlib/CategoryTheory/Bicategory/Basic.lean | CategoryTheory.Bicategory.unitors_inv_equal | [
{
"state_after": "no goals",
"state_before": "B : Type u\ninst✝ : Bicategory B\na b c d e : B\n⊢ (λ_ (𝟙 a)).inv = (ρ_ (𝟙 a)).inv",
"tactic": "simp [Iso.inv_eq_inv]"
}
] | [
490,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
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