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/Analysis/NormedSpace/WeakDual.lean | NormedSpace.Dual.coe_toWeakDual | [] | [
126,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Data/List/Lattice.lean | List.mem_union_right | [] | [
95,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Topology/UniformSpace/Equicontinuity.lean | UniformInducing.equicontinuousAt_iff | [
{
"state_after": "ι : Type u_3\nκ : Type ?u.129520\nX : Type u_4\nY : Type ?u.129526\nZ : Type ?u.129529\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.129538\n𝓕 : Type ?u.129541\ninst✝⁵ : TopologicalSpace X\ninst✝⁴ : TopologicalSpace Y\ninst✝³ : TopologicalSpace Z\ninst✝² : UniformSpace α\ninst✝¹ : UniformSpace β\n... | [
345,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.mem_mk | [] | [
98,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.neg_eq_bot_iff | [] | [
783,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
782,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | ContinuousWithinAt.nnnorm' | [] | [
1238,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1236,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.sameCycle_pow_left | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.142827\nα : Type u_1\nβ : Type ?u.142833\nf g : Perm α\np : α → Prop\nx y z : α\nn : ℕ\n⊢ SameCycle f (↑(f ^ n) x) y ↔ SameCycle f x y",
"tactic": "rw [← zpow_ofNat, sameCycle_zpow_left]"
}
] | [
175,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Order/Hom/Lattice.lean | BoundedLatticeHom.id_apply | [] | [
1282,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1281,
1
] |
Mathlib/CategoryTheory/Endomorphism.lean | CategoryTheory.isUnit_iff_isIso | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX : C\nf : End X\nh : IsIso f\n⊢ f * inv f = 1",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX : C\nf : End X\nh : IsIso f\n⊢ inv f * f = 1",
"tactic": "sim... | [
119,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.findMax'_all | [] | [
630,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
628,
1
] |
Mathlib/Combinatorics/Additive/Etransform.lean | Finset.mulEtransformRight_one | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Group α\ne : α\nx : Finset α × Finset α\n⊢ mulEtransformRight 1 x = x",
"tactic": "simp [mulEtransformRight]"
}
] | [
140,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Algebra/CharZero/Quotient.lean | AddSubgroup.zsmul_mem_zmultiples_iff_exists_sub_div | [
{
"state_after": "R : Type u_1\ninst✝¹ : DivisionRing R\ninst✝ : CharZero R\np r : R\nz : ℤ\nhz : z ≠ 0\n⊢ (∃ k, k • p = z • r) ↔ ∃ k, r - ↑k • (p / ↑z) ∈ zmultiples p",
"state_before": "R : Type u_1\ninst✝¹ : DivisionRing R\ninst✝ : CharZero R\np r : R\nz : ℤ\nhz : z ≠ 0\n⊢ z • r ∈ zmultiples p ↔ ∃ k, r - ... | [
43,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
23,
1
] |
Std/Data/List/Lemmas.lean | List.not_mem_of_not_mem_cons | [] | [
98,
90
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
98,
1
] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.derivative_X_sub_C_sq | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝ : CommRing R\nc : R\n⊢ ↑derivative ((X - ↑C c) ^ 2) = ↑C 2 * (X - ↑C c)",
"tactic": "rw [derivative_sq, derivative_X_sub_C, mul_one]"
}
] | [
670,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
669,
1
] |
Mathlib/Topology/Inseparable.lean | Inducing.inseparable_iff | [
{
"state_after": "no goals",
"state_before": "X : Type u_1\nY : Type u_2\nZ : Type ?u.32496\nα : Type ?u.32499\nι : Type ?u.32502\nπ : ι → Type ?u.32507\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace Y\ninst✝¹ : TopologicalSpace Z\ninst✝ : (i : ι) → TopologicalSpace (π i)\nx y z : X\ns : Set X\nf :... | [
316,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/Algebra/AddTorsor.lean | Prod.snd_vsub | [] | [
326,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/LinearAlgebra/Matrix/Trace.lean | Matrix.trace_fin_zero | [] | [
187,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | toMul_multiset_sum | [
{
"state_after": "ι : Type ?u.997971\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf g : α → β\ninst✝ : CommMonoid α\ns : Multiset (Additive α)\n⊢ Multiset.sum s = Multiset.prod s",
"state_before": "ι : Type ?u.997971\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf g : ... | [
2328,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2327,
1
] |
Mathlib/LinearAlgebra/Matrix/SpecialLinearGroup.lean | Matrix.SpecialLinearGroup.coe_toGL | [] | [
227,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csInf_image2_eq_csInf_csSup | [] | [
1419,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1416,
1
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | Subgroup.conj_smul_subgroupOf | [
{
"state_after": "case refine'_1\nα : Type ?u.110756\nG : Type u_1\nA : Type ?u.110762\nS : Type ?u.110765\ninst✝³ : Group G\ninst✝² : AddGroup A\ns : Set G\ninst✝¹ : Monoid α\ninst✝ : MulDistribMulAction α G\nP H : Subgroup G\nhP : P ≤ H\nh : { x // x ∈ H }\n⊢ ↑MulAut.conj h • subgroupOf P H ≤ subgroupOf (↑Mul... | [
329,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/Order/RelClasses.lean | not_subset_of_ssubset | [] | [
730,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
729,
1
] |
Mathlib/Data/QPF/Univariate/Basic.lean | Qpf.liftp_iff' | [
{
"state_after": "case mp\nF : Type u → Type u\ninst✝ : Functor F\nq : Qpf F\nα : Type u\np : α → Prop\nx : F α\n⊢ Liftp p x → ∃ u, abs u = x ∧ ∀ (i : PFunctor.B (P F) u.fst), p (Sigma.snd u i)\n\ncase mpr\nF : Type u → Type u\ninst✝ : Functor F\nq : Qpf F\nα : Type u\np : α → Prop\nx : F α\n⊢ (∃ u, abs u = x ∧... | [
134,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Matrix.lean | AffineBasis.isUnit_toMatrix | [] | [
133,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Algebra/Order/Monoid/MinMax.lean | max_mul_mul_right | [] | [
77,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Data/Fintype/Card.lean | Fintype.card_ofSubsingleton | [] | [
220,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Topology/UniformSpace/Completion.lean | UniformSpace.Completion.uniformContinuous_extension | [] | [
545,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
544,
1
] |
Mathlib/Data/PEquiv.lean | PEquiv.le_def | [] | [
430,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.mem_span_pair | [] | [
366,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Data/List/Pairwise.lean | List.pairwise_join | [
{
"state_after": "case nil\nα : Type u_1\nβ : Type ?u.29811\nR S T : α → α → Prop\na : α\nl : List α\n⊢ Pairwise R (join []) ↔\n (∀ (l : List α), l ∈ [] → Pairwise R l) ∧ Pairwise (fun l₁ l₂ => ∀ (x : α), x ∈ l₁ → ∀ (y : α), y ∈ l₂ → R x y) []\n\ncase cons\nα : Type u_1\nβ : Type ?u.29811\nR S T : α → α → Pr... | [
264,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | Real.volume_val | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.117408\ninst✝ : Fintype ι\ns : Set ℝ\n⊢ ↑↑volume s = ↑↑(StieltjesFunction.measure StieltjesFunction.id) s",
"tactic": "simp [volume_eq_stieltjes_id]"
}
] | [
79,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Analysis/NormedSpace/WeakDual.lean | WeakDual.coe_toNormedDual | [] | [
174,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Independent.lean | Affine.Simplex.centroid_eq_of_range_eq | [
{
"state_after": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nn : ℕ\ns₁ s₂ : Simplex k P n\nh✝ : s₁.points '' Set.univ = s₂.points '' Set.univ\nh : s₁.points '' ↑Finset.univ = s₂.points '' ↑Finset.univ\n⊢ Finset.centro... | [
974,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
967,
1
] |
Mathlib/Data/List/Basic.lean | List.getLast_replicate_succ | [
{
"state_after": "ι : Type ?u.33399\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nm : ℕ\na : α\n⊢ getLast (replicate m a ++ [a]) (_ : replicate m a ++ [a] ≠ []) = a",
"state_before": "ι : Type ?u.33399\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nm : ℕ\na : α\n⊢ getLas... | [
760,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
757,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.norm_eq | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.981248\nα : Type u\nβ : Type v\nγ : Type w\ninst✝¹ : TopologicalSpace α\ninst✝ : SeminormedAddCommGroup β\nf✝ g : α →ᵇ β\nx : α\nC : ℝ\nf : α →ᵇ β\n⊢ ‖f‖ = sInf {C | 0 ≤ C ∧ ∀ (x : α), ‖↑f x‖ ≤ C}",
"tactic": "simp [norm_def, BoundedContinuousFun... | [
800,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
799,
1
] |
Mathlib/Algebra/GCDMonoid/Multiset.lean | Multiset.lcm_cons | [] | [
53,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.insertNth_apply_succAbove | [
{
"state_after": "m n : ℕ\nα : Fin (n + 1) → Type u\nβ : Type v\ni : Fin (n + 1)\nx : α i\np : (j : Fin n) → α (↑(succAbove i) j)\nj : Fin n\n⊢ (if h : ↑castSucc j < i then\n (_ : ↑(succAbove i) (castLT (↑(succAbove i) j) (_ : ↑(↑(succAbove i) j) < n)) = ↑(succAbove i) j) ▸\n p (castLT (↑(succAbove ... | [
680,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
669,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Pretrivialization.mk_mem_target | [] | [
239,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | norm_iteratedFDerivWithin_clm_apply_const | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝⁹ : NormedAddCommGroup D\ninst✝⁸ : NormedSpace 𝕜 D\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : Normed... | [
2747,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2737,
1
] |
Mathlib/Data/Set/NAry.lean | Set.image3_congr | [
{
"state_after": "case h\nα : Type u_1\nα' : Type ?u.30846\nβ : Type u_2\nβ' : Type ?u.30852\nγ : Type u_3\nγ' : Type ?u.30858\nδ : Type u_4\nδ' : Type ?u.30864\nε : Type ?u.30867\nε' : Type ?u.30870\nζ : Type ?u.30873\nζ' : Type ?u.30876\nν : Type ?u.30879\nf f' : α → β → γ\ng g' : α → β → γ → δ\ns s' : Set α\... | [
247,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.sin_two_mul | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ ↑(sin (2 * x)) = ↑(2 * sin x * cos x)",
"tactic": "simp [sin_two_mul]"
}
] | [
1291,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1290,
8
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.Adj.adj_sub | [] | [
119,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
11
] |
Mathlib/Data/Real/Sqrt.lean | Real.real_sqrt_le_nat_sqrt_succ | [
{
"state_after": "a : ℕ\n⊢ 0 ≤ ↑(Nat.sqrt a) + 1 ∧ ↑a ≤ (↑(Nat.sqrt a) + 1) ^ 2",
"state_before": "a : ℕ\n⊢ sqrt ↑a ≤ ↑(Nat.sqrt a) + 1",
"tactic": "rw [Real.sqrt_le_iff]"
},
{
"state_after": "case left\na : ℕ\n⊢ 0 ≤ ↑(Nat.sqrt a) + 1\n\ncase right\na : ℕ\n⊢ ↑a ≤ (↑(Nat.sqrt a) + 1) ^ 2",
"s... | [
467,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
1
] |
Mathlib/Order/SupIndep.lean | Finset.SupIndep.sup | [
{
"state_after": "α : Type u_3\nβ : Type ?u.19950\nι : Type u_1\nι' : Type u_2\ninst✝² : DistribLattice α\ninst✝¹ : OrderBot α\ns✝ : Finset ι\nf✝ : ι → α\ninst✝ : DecidableEq ι\ns : Finset ι'\ng : ι' → Finset ι\nf : ι → α\nhs : Set.PairwiseDisjoint ↑s fun i => Finset.sup (g i) f\nhg : ∀ (i' : ι'), i' ∈ s → Set.... | [
165,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Order/Filter/Germ.lean | Filter.Germ.coe_eq | [] | [
180,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.insert_sdiff_of_not_mem | [
{
"state_after": "α : Type u_1\nβ : Type ?u.240257\nγ : Type ?u.240260\ninst✝ : DecidableEq α\ns✝ t✝ u v : Finset α\na b : α\ns t : Finset α\nx : α\nh : ¬x ∈ t\n⊢ insert x ↑s \\ ↑t = insert x (↑s \\ ↑t)",
"state_before": "α : Type u_1\nβ : Type ?u.240257\nγ : Type ?u.240260\ninst✝ : DecidableEq α\ns✝ t✝ u v... | [
2178,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2175,
1
] |
Mathlib/RingTheory/FiniteType.lean | AddMonoidAlgebra.finiteType_iff_fg | [
{
"state_after": "R : Type u_1\nM : Type u_2\ninst✝² : AddCommMonoid M\ninst✝¹ : CommRing R\ninst✝ : Nontrivial R\nh : FiniteType R (AddMonoidAlgebra R M)\n⊢ AddMonoid.FG M",
"state_before": "R : Type u_1\nM : Type u_2\ninst✝² : AddCommMonoid M\ninst✝¹ : CommRing R\ninst✝ : Nontrivial R\n⊢ FiniteType R (Add... | [
470,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Mathlib/Data/PEquiv.lean | Equiv.toPEquiv_refl | [] | [
482,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/Data/Nat/Bits.lean | Nat.bodd_bit1 | [] | [
52,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.mem_closure_iff | [] | [
901,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
899,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.symm_symm_apply | [] | [
2105,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2104,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.mul_add_mod_self | [
{
"state_after": "case inl\nα : Type ?u.265351\nβ : Type ?u.265354\nγ : Type ?u.265357\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\ny z : Ordinal\n⊢ (0 * y + z) % 0 = z % 0\n\ncase inr\nα : Type ?u.265351\nβ : Type ?u.265354\nγ : Type ?u.265357\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nx ... | [
1084,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1081,
1
] |
Mathlib/Topology/Order/Hom/Basic.lean | ContinuousOrderHom.id_comp | [] | [
187,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.degree_interpolate_lt | [
{
"state_after": "F : Type u_2\ninst✝¹ : Field F\nι : Type u_1\ninst✝ : DecidableEq ι\ns t : Finset ι\ni j : ι\nv r r' : ι → F\nhvs : Set.InjOn v ↑s\n⊢ degree (↑(interpolate s v) r) < ↑(card s)",
"state_before": "F : Type u_2\ninst✝¹ : Field F\nι : Type u_1\ninst✝ : DecidableEq ι\ns t : Finset ι\ni j : ι\nv... | [
350,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/Order/Disjoint.lean | Disjoint.inf_right' | [] | [
167,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Equiv.toHom_range | [
{
"state_after": "case h\nL : Language\nM : Type w\nN : Type u_1\nP : Type ?u.1142600\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nS : Substructure L M\nf : M ≃[L] N\nn : N\n⊢ n ∈ Hom.range (toHom f) ↔ n ∈ ⊤",
"state_before": "L : Language\nM : Type w\nN : Type u_1\nP : Type ?u.11... | [
993,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
990,
1
] |
Mathlib/Topology/Algebra/Monoid.lean | Inducing.continuousMul | [] | [
380,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
] |
src/lean/Init/Classical.lean | Classical.epsilon_spec | [] | [
101,
50
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
100,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.single_eq_pi_single | [] | [
637,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
1
] |
Mathlib/MeasureTheory/Measure/GiryMonad.lean | MeasureTheory.Measure.bind_apply | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝¹ : MeasurableSpace α\ninst✝ : MeasurableSpace β\nm : Measure α\nf : α → Measure β\ns : Set β\nhs : MeasurableSet s\nhf : Measurable f\n⊢ ↑↑(bind m f) s = ∫⁻ (a : α), ↑↑(f a) s ∂m",
"tactic": "rw [bind, join_apply hs, lintegr... | [
179,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.map_comap_eq | [
{
"state_after": "no goals",
"state_before": "G : Type u_2\nG' : Type ?u.564457\ninst✝³ : Group G\ninst✝² : Group G'\nA : Type ?u.564466\ninst✝¹ : AddGroup A\nN : Type u_1\ninst✝ : Group N\nf : G →* N\nH : Subgroup N\n⊢ ↑(map f (comap f H)) = ↑(range f ⊓ H)",
"tactic": "rw [coe_map, coe_comap, Set.image... | [
3009,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3007,
1
] |
Mathlib/Topology/Semicontinuous.lean | upperSemicontinuous_iff_isClosed_preimage | [
{
"state_after": "α : Type u_1\ninst✝² : TopologicalSpace α\nβ : Type ?u.149869\ninst✝¹ : Preorder β\nf✝ g : α → β\nx : α\ns t : Set α\ny z : β\nγ : Type u_2\ninst✝ : LinearOrder γ\nf : α → γ\n⊢ (∀ (y : γ), IsOpen (f ⁻¹' Iio y)) ↔ ∀ (y : γ), IsClosed (f ⁻¹' Ici y)",
"state_before": "α : Type u_1\ninst✝² : T... | [
801,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
798,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | innerSLFlip_apply | [] | [
1813,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1812,
1
] |
Std/Data/String/Lemmas.lean | String.any_eq | [
{
"state_after": "no goals",
"state_before": "s : String\np : Char → Bool\n⊢ any s p = List.any s.data p",
"tactic": "simpa using anyAux_of_valid p [] s.1 []"
}
] | [
718,
42
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
717,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.cospanCompIso_hom_app_left | [] | [
304,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/Data/Set/Intervals/Monoid.lean | Set.Icc_add_bij | [
{
"state_after": "M : Type u_1\ninst✝¹ : OrderedCancelAddCommMonoid M\ninst✝ : ExistsAddOfLE M\na b c d : M\n⊢ BijOn (fun x => x + d) (Ici a ∩ Iic b) (Ici (a + d) ∩ Iic (b + d))",
"state_before": "M : Type u_1\ninst✝¹ : OrderedCancelAddCommMonoid M\ninst✝ : ExistsAddOfLE M\na b c d : M\n⊢ BijOn (fun x => x ... | [
51,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/Algebra/Module/Submodule/Pointwise.lean | Submodule.neg_inf | [] | [
118,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Data/Polynomial/Reverse.lean | Polynomial.revAtFun_invol | [
{
"state_after": "R : Type ?u.164\ninst✝ : Semiring R\nf : R[X]\nN i : ℕ\n⊢ (if (if i ≤ N then N - i else i) ≤ N then N - if i ≤ N then N - i else i else if i ≤ N then N - i else i) = i",
"state_before": "R : Type ?u.164\ninst✝ : Semiring R\nf : R[X]\nN i : ℕ\n⊢ revAtFun N (revAtFun N i) = i",
"tactic":... | [
50,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.not_mem_empty | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\na : α\nx✝ : a ∈ empty α\nn : ℕ\nh : (fun b => some a = b) (Stream'.nth (↑(empty α)) n)\n⊢ False",
"tactic": "contradiction"
}
] | [
402,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
1
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.toMulEquiv_eq_coe | [] | [
198,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/AlgebraicTopology/DoldKan/Degeneracies.lean | AlgebraicTopology.DoldKan.degeneracy_comp_PInfty | [
{
"state_after": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX : SimplicialObject C\nn : ℕ\nΔ' : SimplexCategory\nθ : [n] ⟶ Δ'\nhθ : ¬Function.Injective ↑(SimplexCategory.Hom.toOrderHom θ)\n⊢ X.map θ.op ≫ HomologicalComplex.Hom.f PInfty n = 0",
"state_before": "C : Type u_2\ninst✝¹ : Category... | [
141,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.pow_apply | [] | [
466,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/Algebra/Homology/Additive.lean | CategoryTheory.NatTrans.mapHomologicalComplex_comp | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nV : Type u\ninst✝⁶ : Category V\ninst✝⁵ : Preadditive V\nc✝ : ComplexShape ι\nC D E : HomologicalComplex V c✝\nf g : C ⟶ D\nh k : D ⟶ E\ni : ι\nW : Type u_3\ninst✝⁴ : Category W\ninst✝³ : Preadditive W\nc : ComplexShape ι\nF G H : V ⥤ W\ninst✝² : F... | [
219,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.mk_toAddMonoidHom | [] | [
165,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.span_singleton_mul_le_iff | [
{
"state_after": "R : Type u\nι : Type ?u.232307\ninst✝ : CommSemiring R\nI✝ J✝ K L : Ideal R\nx : R\nI J : Ideal R\n⊢ (∀ (r : R), x ∣ r → ∀ (s : R), s ∈ I → r * s ∈ J) ↔ ∀ (z : R), z ∈ I → x * z ∈ J",
"state_before": "R : Type u\nι : Type ?u.232307\ninst✝ : CommSemiring R\nI✝ J✝ K L : Ideal R\nx : R\nI J :... | [
560,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
552,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/InverseDeriv.lean | Real.hasDerivAt_arccos | [] | [
147,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/RingTheory/Ideal/LocalRing.lean | LocalRing.nonunits_add | [] | [
103,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/RingTheory/Adjoin/Basic.lean | Algebra.mem_adjoin_iff | [] | [
392,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/Data/Sym/Sym2.lean | Sym2.mem_and_mem_iff | [
{
"state_after": "case mp\nα : Type u_1\nβ : Type ?u.35991\nγ : Type ?u.35994\nx y : α\nz : Sym2 α\nhne : x ≠ y\n⊢ x ∈ z ∧ y ∈ z → z = Quotient.mk (Rel.setoid α) (x, y)\n\ncase mpr\nα : Type u_1\nβ : Type ?u.35991\nγ : Type ?u.35994\nx y : α\nz : Sym2 α\nhne : x ≠ y\n⊢ z = Quotient.mk (Rel.setoid α) (x, y) → x ... | [
380,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Topology/MetricSpace/Gluing.lean | Metric.toGlueL_isometry | [] | [
520,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.sign_ne_zero_iff | [
{
"state_after": "no goals",
"state_before": "θ : Angle\n⊢ sign θ ≠ 0 ↔ θ ≠ 0 ∧ θ ≠ ↑π",
"tactic": "rw [← not_or, ← sign_eq_zero_iff]"
}
] | [
898,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
897,
1
] |
Mathlib/Data/QPF/Multivariate/Constructions/Fix.lean | MvQPF.recF_eq' | [
{
"state_after": "n : ℕ\nF : TypeVec (n + 1) → Type u\ninst✝ : MvFunctor F\nq : MvQPF F\nα : TypeVec n\nβ : Type u\ng : F (α ::: β) → β\nx : MvPFunctor.W (P F) α\n⊢ ∀ (a : (P F).A) (f' : MvPFunctor.B (MvPFunctor.drop (P F)) a ⟹ α)\n (f : PFunctor.B (MvPFunctor.last (P F)) a → MvPFunctor.W (P F) α),\n recF... | [
78,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.cons_sub_of_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.160229\nγ : Type ?u.160232\ninst✝ : DecidableEq α\ns✝ t✝ u : Multiset α\na✝ b a : α\ns t : Multiset α\nh : t ≤ s\n⊢ a ::ₘ s - t = a ::ₘ (s - t)",
"tactic": "rw [← singleton_add, ← singleton_add, add_tsub_assoc_of_le h]"
}
] | [
1665,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1664,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Order.lean | tsum_pos | [
{
"state_after": "ι : Type u_2\nκ : Type ?u.47829\nα : Type u_1\ninst✝³ : OrderedAddCommGroup α\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalAddGroup α\ninst✝ : OrderClosedTopology α\nf g : ι → α\na₁ a₂ : α\ni✝ : ι\nhsum : Summable g\nhg : ∀ (i : ι), 0 ≤ g i\ni : ι\nhi : 0 < g i\n⊢ (∑' (x : ?m.49191), 0) <... | [
191,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.add_le_add_left | [] | [
635,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
633,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | OpenEmbedding.measurableEmbedding | [] | [
1034,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1032,
11
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.map_top | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nR : Type ?u.127541\nR' : Type ?u.127544\nms : Set (OuterMeasure α)\nm : OuterMeasure α\nf : α → β\ns : Set β\n⊢ ↑(↑(map f) ⊤) s = ↑(↑(restrict (range f)) ⊤) s",
"tactic": "rw [map_apply, restrict_apply, ← image_preimage_eq_inter_r... | [
642,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
639,
1
] |
Mathlib/Data/Set/NAry.lean | Set.Nonempty.of_image2_right | [] | [
171,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Order/Basic.lean | LT.lt.ne' | [] | [
312,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.transpose_transpose | [
{
"state_after": "case a.h\nl : Type ?u.923744\nm : Type u_1\nn : Type u_2\no : Type ?u.923753\nm' : o → Type ?u.923758\nn' : o → Type ?u.923763\nR : Type ?u.923766\nS : Type ?u.923769\nα : Type v\nβ : Type w\nγ : Type ?u.923776\nM : Matrix m n α\ni✝ : m\nx✝ : n\n⊢ Mᵀᵀ i✝ x✝ = M i✝ x✝",
"state_before": "l :... | [
1969,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1967,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.div_one | [
{
"state_after": "n : Nat\nthis : n % 1 + 1 * (n / 1) = n\n⊢ n / 1 = n",
"state_before": "n : Nat\n⊢ n / 1 = n",
"tactic": "have := mod_add_div n 1"
},
{
"state_after": "no goals",
"state_before": "n : Nat\nthis : n % 1 + 1 * (n / 1) = n\n⊢ n / 1 = n",
"tactic": "rwa [mod_one, Nat.zero_a... | [
259,
51
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
257,
19
] |
Mathlib/RingTheory/Valuation/Basic.lean | AddValuation.mem_supp_iff | [] | [
885,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
884,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiff.continuousLinearMap_comp | [] | [
234,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.prod_neBot | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.50863\nδ : Type ?u.50866\nι : Sort ?u.50869\ns : Set α\nt : Set β\nf✝ : Filter α\ng✝ : Filter β\nf : Filter α\ng : Filter β\n⊢ NeBot (f ×ˢ g) ↔ NeBot f ∧ NeBot g",
"tactic": "simp only [neBot_iff, Ne, prod_eq_bot, not_... | [
436,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
1
] |
Mathlib/NumberTheory/Padics/PadicNorm.lean | padicNorm.padicNorm_of_prime_of_ne | [
{
"state_after": "p✝ q : ℕ\np_prime : Fact (Nat.Prime p✝)\nq_prime : Fact (Nat.Prime q)\nneq : p✝ ≠ q\np : padicValRat p✝ ↑q = 0\n⊢ padicNorm p✝ ↑q = 1",
"state_before": "p q : ℕ\np_prime : Fact (Nat.Prime p)\nq_prime : Fact (Nat.Prime q)\nneq : p ≠ q\n⊢ padicNorm p ↑q = 1",
"tactic": "have p : padicVal... | [
105,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Data/Multiset/Bind.lean | Multiset.product_add | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.60368\nδ : Type ?u.60371\na✝ : α\nb : β\ns✝¹ : Multiset α\nt✝ : Multiset β\ns✝ : Multiset α\na : α\ns : Multiset α\nIH : ∀ (t u : Multiset β), s ×ˢ (t + u) = s ×ˢ t + s ×ˢ u\nt u : Multiset β\n⊢ map (Prod.mk a) (t + u) + (s ×ˢ t + s ×ˢ u) = (a ::ₘ s) ×ˢ ... | [
287,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.single_eq_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.58789\nγ : Type ?u.58792\nι : Type ?u.58795\nM : Type u_2\nM' : Type ?u.58801\nN : Type ?u.58804\nP : Type ?u.58807\nG : Type ?u.58810\nH : Type ?u.58813\nR : Type ?u.58816\nS : Type ?u.58819\ninst✝ : Zero M\na a' : α\nb : M\n⊢ single a... | [
442,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
1
] |
Mathlib/FieldTheory/Subfield.lean | RingHom.coe_rangeRestrictField | [] | [
868,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
867,
1
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | Submodule.pointed_toConvexCone | [] | [
549,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
1
] |
Mathlib/Analysis/LocallyConvex/ContinuousOfBounded.lean | LinearMap.continuous_of_locally_bounded | [] | [
181,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.