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/Computability/Partrec.lean | Nat.mem_rfind | [
{
"state_after": "p : ℕ →. Bool\nn : ℕ\nx✝ : true ∈ p n ∧ ∀ {m : ℕ}, m < n → false ∈ p m\nh₁ : true ∈ p n\nh₂ : ∀ {m : ℕ}, m < n → false ∈ p m\nm : ℕ\nhm : m ∈ rfind p\n⊢ n ∈ rfind p",
"state_before": "p : ℕ →. Bool\nn : ℕ\nx✝ : true ∈ p n ∧ ∀ {m : ℕ}, m < n → false ∈ p m\nh₁ : true ∈ p n\nh₂ : ∀ {m : ℕ}, m... | [
112,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.apply_update₂ | [
{
"state_after": "case pos\nα✝ : Sort u\nβ✝ : α✝ → Sort v\nα' : Sort w\ninst✝² : DecidableEq α✝\ninst✝¹ : DecidableEq α'\nf✝ g✝ : (a : α✝) → β✝ a\na : α✝\nb : β✝ a\nι : Sort u_1\ninst✝ : DecidableEq ι\nα : ι → Sort u_2\nβ : ι → Sort u_3\nγ : ι → Sort u_4\nf : (i : ι) → α i → β i → γ i\ng : (i : ι) → α i\nh✝ : (... | [
657,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
651,
1
] |
Std/Data/RBMap/WF.lean | Std.RBNode.All_and | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\np q : α → Prop\nt : RBNode α\n⊢ All (fun a => p a ∧ q a) t ↔ All p t ∧ All q t",
"tactic": "induction t <;> simp [*, and_assoc, and_left_comm]"
}
] | [
28,
53
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
27,
1
] |
Mathlib/Order/CompleteLattice.lean | sSup_diff_singleton_bot | [] | [
525,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Basis.lean | AffineBasis.ind | [] | [
84,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | coe_nnnorm' | [] | [
888,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
887,
1
] |
Mathlib/Analysis/SpecialFunctions/Arsinh.lean | HasFDerivWithinAt.arsinh | [] | [
255,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/Order/Basic.lean | strongLT_of_le_of_strongLT | [] | [
842,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
841,
1
] |
Mathlib/Data/Real/Cardinality.lean | Cardinal.mk_Ici_real | [] | [
250,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/CategoryTheory/Subobject/FactorThru.lean | CategoryTheory.Subobject.factorThru_add_sub_factorThru_left | [
{
"state_after": "case h\nC : Type u₁\ninst✝² : Category C\nX✝ Y✝ Z : C\nD : Type u₂\ninst✝¹ : Category D\ninst✝ : Preadditive C\nX Y : C\nP : Subobject Y\nf g : X ⟶ Y\nw : Factors P (f + g)\nwf : Factors P f\n⊢ (factorThru P (f + g) w - factorThru P f wf) ≫ arrow P = factorThru P g (_ : Factors P g) ≫ arrow P"... | [
224,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigOWith.trans | [
{
"state_after": "α : Type u_1\nβ : Type ?u.73759\nE : Type u_2\nF : Type u_3\nG : Type u_4\nE' : Type ?u.73771\nF' : Type ?u.73774\nG' : Type ?u.73777\nE'' : Type ?u.73780\nF'' : Type ?u.73783\nG'' : Type ?u.73786\nR : Type ?u.73789\nR' : Type ?u.73792\n𝕜 : Type ?u.73795\n𝕜' : Type ?u.73798\ninst✝¹² : Norm E... | [
466,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
Mathlib/Data/List/Basic.lean | List.choose_spec | [] | [
3975,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3974,
1
] |
Mathlib/Analysis/Complex/PhragmenLindelof.lean | PhragmenLindelof.eq_zero_on_horizontal_strip | [] | [
249,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Std/Data/Int/Lemmas.lean | Int.natAbs_lt_natAbs_of_nonneg_of_lt | [] | [
1359,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1356,
1
] |
Mathlib/Algebra/Star/Basic.lean | eq_star_iff_eq_star | [] | [
109,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | reflection_bot | [
{
"state_after": "case h\n𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.748584\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : InnerProductSpace ℝ F\nK : Submodule 𝕜 E\ninst✝ : CompleteSpace { x // x ∈ K }\nx✝ : E\n⊢ ↑(reflection ⊥) x✝ = ↑... | [
726,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
725,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.set_biInter_insert | [] | [
2054,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2052,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | Padic.norm_eq_pow_val | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\nx : ℚ_[p]\nf : CauSeq ℚ (padicNorm p)\nhf : Quotient.mk'' f ≠ 0\n⊢ ‖Quotient.mk'' f‖ = ↑p ^ (-valuation (Quotient.mk'' f))",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nx : ℚ_[p]\n⊢ x ≠ 0 → ‖x‖ = ↑p ^ (-valuation x)",
"tactic": "refine Quotient.indu... | [
1063,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1052,
1
] |
Mathlib/Order/WithBot.lean | WithTop.none_eq_top | [] | [
597,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
596,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.singleton_apply | [
{
"state_after": "no goals",
"state_before": "ι✝ : Type ?u.609084\nι' : Type ?u.609087\nR✝ : Type ?u.609090\nR₂ : Type ?u.609093\nK : Type ?u.609096\nM : Type ?u.609099\nM' : Type ?u.609102\nM'' : Type ?u.609105\nV : Type u\nV' : Type ?u.609110\ninst✝⁶ : Semiring R✝\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Modul... | [
824,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
823,
1
] |
Mathlib/Topology/Algebra/Module/LocallyConvex.lean | locallyConvexSpace_iff | [] | [
56,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | Differentiable.neg | [] | [
447,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
] |
Mathlib/Order/SuccPred/LinearLocallyFinite.lean | LinearLocallyFiniteOrder.succFn_le_of_lt | [
{
"state_after": "ι : Type u_1\ninst✝ : LinearOrder ι\ni j : ι\nhij : i < j\nh : IsGLB (Set.Ioi i) (succFn i)\n⊢ succFn i ≤ j",
"state_before": "ι : Type u_1\ninst✝ : LinearOrder ι\ni j : ι\nhij : i < j\n⊢ succFn i ≤ j",
"tactic": "have h := succFn_spec i"
},
{
"state_after": "ι : Type u_1\ninst... | [
109,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/GroupTheory/Coset.lean | QuotientGroup.rightRel_eq | [
{
"state_after": "α : Type u_1\ninst✝ : Group α\ns : Subgroup α\n⊢ ∀ (a b : α), Setoid.r a b ↔ b * a⁻¹ ∈ s",
"state_before": "α : Type u_1\ninst✝ : Group α\ns : Subgroup α\n⊢ ∀ (a b : α), Setoid.r a b = (b * a⁻¹ ∈ s)",
"tactic": "simp only [eq_iff_iff]"
},
{
"state_after": "no goals",
"state... | [
391,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/Order/Basic.lean | lt_trans' | [] | [
79,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Data/Nat/Choose/Basic.lean | Nat.choose_mul | [
{
"state_after": "no goals",
"state_before": "n k s : ℕ\nhkn : k ≤ n\nhsk : s ≤ k\n⊢ (n - k)! * (k - s)! * s ! ≠ 0",
"tactic": "apply_rules [factorial_ne_zero, mul_ne_zero]"
},
{
"state_after": "no goals",
"state_before": "n k s : ℕ\nhkn : k ≤ n\nhsk : s ≤ k\nh : (n - k)! * (k - s)! * s ! ≠ ... | [
165,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.mem_range_iff | [
{
"state_after": "case mp\nR : Type u_1\ninst✝⁹ : Ring R\nE : Type u_2\ninst✝⁸ : AddCommGroup E\ninst✝⁷ : Module R E\nF : Type u_3\ninst✝⁶ : AddCommGroup F\ninst✝⁵ : Module R F\nG : Type ?u.585339\ninst✝⁴ : AddCommGroup G\ninst✝³ : Module R G\nM : Type ?u.585855\ninst✝² : Monoid M\ninst✝¹ : DistribMulAction M F... | [
873,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
860,
1
] |
Mathlib/Topology/Hom/Open.lean | ContinuousOpenMap.cancel_right | [] | [
159,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/LinearAlgebra/Determinant.lean | Basis.det_apply | [] | [
535,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
] |
Mathlib/Topology/Basic.lean | Dense.mono | [] | [
670,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
669,
1
] |
Mathlib/Topology/Category/TopCat/Opens.lean | TopologicalSpace.Opens.functor_map_eq_inf | [
{
"state_after": "case h\nX : TopCat\nU V : Opens ↑X\n⊢ ↑((IsOpenMap.functor (_ : IsOpenMap ((forget TopCat).map (inclusion U)))).obj ((map (inclusion U)).obj V)) = ↑(V ⊓ U)",
"state_before": "X : TopCat\nU V : Opens ↑X\n⊢ (IsOpenMap.functor (_ : IsOpenMap ((forget TopCat).map (inclusion U)))).obj ((map (in... | [
391,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.of_eq | [] | [
250,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Data/Real/Irrational.lean | irrational_rat_add_iff | [] | [
533,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.mem_iUnion₂_of_mem | [] | [
166,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.coe_constVSub | [] | [
731,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
730,
1
] |
Mathlib/NumberTheory/Padics/Hensel.lean | ncs_tendsto_const | [
{
"state_after": "case h.e'_3.h\np : ℕ\ninst✝ : Fact (Nat.Prime p)\nncs : CauSeq ℤ_[p] norm\nF : Polynomial ℤ_[p]\na : ℤ_[p]\nncs_der_val :\n ∀ (n : ℕ), ‖Polynomial.eval (↑ncs n) (↑Polynomial.derivative F)‖ = ‖Polynomial.eval a (↑Polynomial.derivative F)‖\nx✝ : ℕ\n⊢ ‖Polynomial.eval (↑ncs x✝) (↑Polynomial.deri... | [
69,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
9
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | hasDerivAtFilter_const | [] | [
679,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
678,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Filter.compl_mem_hyperfilter_of_finite | [] | [
499,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.TM2to1.trNormal_run | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\ninst✝² : DecidableEq K\nΓ : K → Type u_2\nΛ : Type u_4\ninst✝¹ : Inhabited Λ\nσ : Type u_3\ninst✝ : Inhabited σ\nk : K\ns : StAct k\nq : Stmt₂\n⊢ trNormal (stRun s q) = goto fun x x => go k s q",
"tactic": "cases s <;> rfl"
}
] | [
2531,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2529,
1
] |
Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.aeval_def | [] | [
190,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/RingTheory/Ideal/Prod.lean | Ideal.prod_top_top | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\ninst✝¹ : Ring R\ninst✝ : Ring S\nI I' : Ideal R\nJ J' : Ideal S\n⊢ ∀ (x : R × S), x ∈ prod ⊤ ⊤ ↔ x ∈ ⊤",
"tactic": "simp"
}
] | [
48,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | Matrix.toBilin_basisFun | [
{
"state_after": "case h.H\nR : Type ?u.1302880\nM✝ : Type ?u.1302883\ninst✝¹⁷ : Semiring R\ninst✝¹⁶ : AddCommMonoid M✝\ninst✝¹⁵ : Module R M✝\nR₁ : Type ?u.1302919\nM₁ : Type ?u.1302922\ninst✝¹⁴ : Ring R₁\ninst✝¹³ : AddCommGroup M₁\ninst✝¹² : Module R₁ M₁\nR₂ : Type u_1\nM₂ : Type ?u.1303534\ninst✝¹¹ : CommSem... | [
337,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.transpose_nonsing_inv | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.184059\nm : Type u\nn : Type u'\nα : Type v\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommRing α\nA B : Matrix n n α\n⊢ A⁻¹ᵀ = Aᵀ⁻¹",
"tactic": "rw [inv_def, inv_def, transpose_smul, det_transpose, adjugate_transpose]"
}
] | [
293,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.lift_eq_iff_equiv | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nc₁ c₂ : Computation α\nx✝ : LiftRel (fun x x_1 => x = x_1) c₁ c₂\na : α\nh1 : ∀ {a : α}, a ∈ c₁ → ∃ b, b ∈ c₂ ∧ (fun x x_1 => x = x_1) a b\nh2 : ∀ {b : α}, b ∈ c₂ → ∃ a, a ∈ c₁ ∧ (fun x x_1 => x = x_1) a b\na1 : a ∈ c₁\nb : α\nb2 : b ∈ c₂\nab : (fun x x_1 =>... | [
1062,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1055,
1
] |
Mathlib/Algebra/MonoidAlgebra/ToDirectSum.lean | DirectSum.toAddMonoidAlgebra_mul | [
{
"state_after": "ι : Type u_1\nR : Type ?u.136196\nM : Type u_2\nA : Type ?u.136202\ninst✝³ : DecidableEq ι\ninst✝² : AddMonoid ι\ninst✝¹ : Semiring M\ninst✝ : (m : M) → Decidable (m ≠ 0)\nf g : ⨁ (x : ι), M\n⊢ AddMonoidAlgebra.toDirectSum (toAddMonoidAlgebra (f * g)) =\n AddMonoidAlgebra.toDirectSum (toAdd... | [
184,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Topology/MetricSpace/Closeds.lean | EMetric.NonemptyCompacts.isClosed_in_closeds | [
{
"state_after": "α : Type u\ninst✝¹ : EMetricSpace α\ns : Set α\ninst✝ : CompleteSpace α\nthis : range NonemptyCompacts.toCloseds = {s | Set.Nonempty ↑s ∧ IsCompact ↑s}\n⊢ IsClosed (range NonemptyCompacts.toCloseds)",
"state_before": "α : Type u\ninst✝¹ : EMetricSpace α\ns : Set α\ninst✝ : CompleteSpace α\... | [
300,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Algebra/Associated.lean | associated_zero_iff_eq_zero | [
{
"state_after": "α : Type u_1\nβ : Type ?u.151491\nγ : Type ?u.151494\nδ : Type ?u.151497\ninst✝ : MonoidWithZero α\na : α\nh✝ : a ~ᵤ 0\nu : αˣ\nh : 0 * ↑u = a\n⊢ a = 0",
"state_before": "α : Type u_1\nβ : Type ?u.151491\nγ : Type ?u.151494\nδ : Type ?u.151497\ninst✝ : MonoidWithZero α\na : α\nh : a ~ᵤ 0\n... | [
441,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
1
] |
Std/Data/List/Lemmas.lean | List.eraseP_map | [
{
"state_after": "no goals",
"state_before": "β : Type u_1\nα : Type u_2\np : α → Bool\nf : β → α\nb : β\nl : List β\n⊢ eraseP p (map f (b :: l)) = map f (eraseP (p ∘ f) (b :: l))",
"tactic": "by_cases h : p (f b) <;> simp [h, eraseP_map f l, eraseP_cons_of_pos]"
}
] | [
1011,
85
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1009,
1
] |
Mathlib/Topology/Order.lean | generateFrom_union | [] | [
940,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
938,
1
] |
Mathlib/Topology/Inseparable.lean | Specializes.mem_closed | [] | [
132,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Data/QPF/Multivariate/Constructions/Fix.lean | MvQPF.Fix.rec_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 : F (α ::: Fix F α)\nthis : recF g ∘ fixToW = rec g\n⊢ rec g (mk x) = g ((TypeVec.id ::: rec g) <$$> x)",
"state_before": "n : ℕ\nF : TypeVec (n + 1) → Type u\ninst✝ : M... | [
242,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.one_smul | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹⁶ : CommSemiring R\nR' : Type u_4\ninst✝¹⁵ : Monoid R'\nR'' : Type ?u.221106\ninst✝¹⁴ : Semiring R''\nM : Type u_2\nN : Type u_3\nP : Type ?u.221118\nQ : Type ?u.221121\nS : Type ?u.221124\ninst✝¹³ : AddCommMonoid M\ninst✝¹² : AddCommMonoid N... | [
263,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
11
] |
Mathlib/Algebra/Order/WithZero.lean | mul_lt_mul₀ | [] | [
190,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Algebra/ContinuedFractions/Translations.lean | GeneralizedContinuedFraction.first_continuant_aux_eq_h_one | [] | [
128,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/RingTheory/FreeCommRing.lean | FreeCommRing.isSupported_add | [] | [
190,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/CategoryTheory/Monoidal/Mon_.lean | Mon_.mul_associator | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\ninst✝¹ : MonoidalCategory C\ninst✝ : BraidedCategory C\nM N P : Mon_ C\n⊢ tensor_μ C (M.X ⊗ N.X, P.X) (M.X ⊗ N.X, P.X) ≫\n (tensor_μ C (M.X, N.X) (M.X, N.X) ≫ (M.mul ⊗ N.mul) ⊗ P.mul) ≫ (α_ M.X N.X P.X).hom =\n ((α_ M.X N.X P.X).hom ⊗ (α_ M.X N.X P.X).... | [
460,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/AlgebraicTopology/DoldKan/GammaCompN.lean | AlgebraicTopology.DoldKan.N₁Γ₀_app | [
{
"state_after": "case w\nC : Type u_2\ninst✝² : Category C\ninst✝¹ : Preadditive C\ninst✝ : HasFiniteCoproducts C\nK : ChainComplex C ℕ\n⊢ (N₁Γ₀.app K).hom =\n ((Splitting.toKaroubiNondegComplexIsoN₁ (Γ₀.splitting K)).symm ≪≫\n (toKaroubi (ChainComplex C ℕ)).mapIso (Γ₀NondegComplexIso K)).hom",
"... | [
82,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Analysis/SpecificLimits/Basic.lean | tendsto_nat_floor_atTop | [
{
"state_after": "no goals",
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"tactic": "simp [Nat.le_floor_iff]"
}
] | [
574,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
572,
1
] |
Mathlib/Order/Filter/Bases.lean | Disjoint.exists_mem_filter_basis | [] | [
656,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
654,
1
] |
Mathlib/Order/SupIndep.lean | CompleteLattice.Independent.mono | [] | [
286,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | span_le_span_iff | [] | [
1103,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1101,
1
] |
Mathlib/Algebra/CharP/Basic.lean | sum_pow_char | [] | [
423,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/MeasureTheory/Function/EssSup.lean | meas_lt_essInf | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nm : MeasurableSpace α\nμ ν : MeasureTheory.Measure α\ninst✝³ : ConditionallyCompleteLinearOrder β\nx : β\nf : α → β\ninst✝² : TopologicalSpace β\ninst✝¹ : FirstCountableTopology β\ninst✝ : OrderTopology β\nhf : autoParam (IsBoundedUnder (fun x x_1 => x ≥ x_1) (Measu... | [
140,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Order/Heyting/Basic.lean | sdiff_sup_self | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.91987\nα : Type u_1\nβ : Type ?u.91993\ninst✝ : GeneralizedCoheytingAlgebra α\na✝ b✝ c d a b : α\n⊢ b \\ a ⊔ a = b ⊔ a",
"tactic": "rw [sup_comm, sup_sdiff_self, sup_comm]"
}
] | [
562,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | LocalHomeomorph.continuousAt_extend_symm' | [] | [
858,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
856,
1
] |
Mathlib/Order/Heyting/Boundary.lean | Coheyting.boundary_le | [] | [
53,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | AddValuation.IsEquiv.of_eq | [] | [
842,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
841,
1
] |
Mathlib/LinearAlgebra/Projection.lean | Submodule.linear_proj_add_linearProjOfIsCompl_eq_self | [
{
"state_after": "R : Type u_2\ninst✝⁹ : Ring R\nE : Type u_1\ninst✝⁸ : AddCommGroup E\ninst✝⁷ : Module R E\nF : Type ?u.186731\ninst✝⁶ : AddCommGroup F\ninst✝⁵ : Module R F\nG : Type ?u.187247\ninst✝⁴ : AddCommGroup G\ninst✝³ : Module R G\np q : Submodule R E\nS : Type ?u.188210\ninst✝² : Semiring S\nM : Type ... | [
218,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Algebra/Tropical/Basic.lean | Tropical.untrop_add | [] | [
274,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Memℒp.toLp_const_smul | [] | [
541,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
1
] |
Std/Data/List/Basic.lean | List.unzip_eq_unzipTR | [
{
"state_after": "case h.h.h\nα : Type u_2\nβ : Type u_1\nl : List (α × β)\n⊢ unzip l = unzipTR l",
"state_before": "⊢ @unzip = @unzipTR",
"tactic": "funext α β l"
},
{
"state_after": "case h.h.h\nα : Type u_2\nβ : Type u_1\nl : List (α × β)\n⊢ unzip l = foldr (fun x x_1 => (x.fst :: x_1.fst, x.... | [
192,
57
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
191,
10
] |
Mathlib/Data/Set/Intervals/Infinite.lean | Set.Ici_infinite | [] | [
102,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/CategoryTheory/Monoidal/Mod_.lean | Mod_.id_hom' | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝¹ : Category C\ninst✝ : MonoidalCategory C\nA : Mon_ C\nM✝ M : Mod_ A\n⊢ (𝟙 M).hom = 𝟙 M.X",
"tactic": "rfl"
}
] | [
86,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.ae_eq_empty | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.101184\nγ : Type ?u.101187\nδ : Type ?u.101190\nι : Type ?u.101193\ninst✝ : MeasurableSpace α\nμ μ₁ μ₂ : Measure α\ns s₁ s₂ t : Set α\n⊢ (∀ᵐ (x : α) ∂μ, ¬x ∈ s) ↔ ↑↑μ s = 0",
"tactic": "simp only [ae_iff, Classical.not_not, setOf_me... | [
443,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/Algebra/Ring/Defs.lean | mul_one_add | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nR : Type x\ninst✝² : Add α\ninst✝¹ : MulOneClass α\ninst✝ : LeftDistribClass α\na b : α\n⊢ a * (1 + b) = a + a * b",
"tactic": "rw [mul_add, mul_one]"
}
] | [
170,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Geometry/Manifold/ChartedSpace.lean | StructureGroupoid.trans | [] | [
183,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Analysis/Convex/Body.lean | ConvexBody.coe_smul | [] | [
143,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Topology/Constructions.lean | embedding_subtype_val | [] | [
1003,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1002,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.trans_le | [] | [
581,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
580,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.SimpleFunc.setToSimpleFunc_congr' | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type u_3\nF' : Type ?u.191544\nG : Type ?u.191547\n𝕜 : Type ?u.191550\np : ℝ≥0∞\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ninst✝² : NormedAddCommGroup F'\ninst✝¹ : NormedSpace ℝ F'\ninst✝ :... | [
380,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
] |
Mathlib/Analysis/ODE/PicardLindelof.lean | IsPicardLindelof.norm_le₀ | [] | [
382,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/Analysis/Convex/SpecificFunctions/Basic.lean | convexOn_zpow | [
{
"state_after": "n : ℕ\n⊢ ConvexOn ℝ (Ioi 0) fun x => x ^ n",
"state_before": "n : ℕ\n⊢ ConvexOn ℝ (Ioi 0) fun x => x ^ ↑n",
"tactic": "simp_rw [zpow_ofNat]"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ ConvexOn ℝ (Ioi 0) fun x => x ^ n",
"tactic": "exact (convexOn_pow n).s... | [
152,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/CategoryTheory/Bicategory/Coherence.lean | CategoryTheory.FreeBicategory.preinclusion_map₂ | [
{
"state_after": "case up.up\nB : Type u\ninst✝ : Quiver B\na b : B\nf g : Discrete (Path a b)\ndown✝ : f.as = g.as\n⊢ PrelaxFunctor.map₂ (preinclusion B) { down := { down := down✝ } } =\n eqToHom (_ : (↑(preinclusion B)).map f = (↑(preinclusion B)).map g)",
"state_before": "B : Type u\ninst✝ : Quiver B\... | [
101,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Algebra/Group/UniqueProds.lean | UniqueMul.mt | [
{
"state_after": "G✝ : Type ?u.271\nH : Type ?u.274\ninst✝² : Mul G✝\ninst✝¹ : Mul H\nA✝ B✝ : Finset G✝\na0✝ b0✝ : G✝\nG : Type u_1\ninst✝ : Mul G\nA B : Finset G\na0 b0 : G\nh : UniqueMul A B a0 b0\nx✝¹ x✝ : G\nha : x✝¹ ∈ A\nhb : x✝ ∈ B\nk : x✝¹ * x✝ = a0 * b0\n⊢ x✝¹ = a0 ∧ x✝ = b0",
"state_before": "G✝ : ... | [
59,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/GroupTheory/SpecificGroups/Cyclic.lean | isCyclic_of_prime_card | [
{
"state_after": "case intro\nα✝ : Type u\na : α✝\ninst✝² : Group α✝\nα : Type u\ninst✝¹ : Group α\ninst✝ : Fintype α\np : ℕ\nhp : Fact (Nat.Prime p)\nh : Fintype.card α = p\ng : α\nhg : g ≠ 1\n⊢ ∃ g, ∀ (x : α), x ∈ zpowers g",
"state_before": "α✝ : Type u\na : α✝\ninst✝² : Group α✝\nα : Type u\ninst✝¹ : Gr... | [
144,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.evalRingHom_zero | [] | [
1067,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1066,
1
] |
Mathlib/Analysis/NormedSpace/Banach.lean | ContinuousLinearMap.exists_preimage_norm_le | [
{
"state_after": "case intro.intro\n𝕜 : Type u_3\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_2\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nf : E →L[𝕜] F\ninst✝¹ : CompleteSpace F\ninst✝ : CompleteSpace E\nsurj : Surjec... | [
236,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Init/Algebra/Order.lean | le_or_lt | [] | [
345,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.reverse_induction_last | [
{
"state_after": "n✝ m n : ℕ\nC : Fin (n + 1) → Sort u_1\nh0 : C (last n)\nhs : (i : Fin n) → C (succ i) → C (↑castSucc i)\n⊢ (if hi : last n = last n then _root_.cast (_ : C (last n) = C (last n)) h0\n else\n let j := { val := ↑(last n), isLt := (_ : ↑(last n) < n) };\n let_fun x := (_ : n - ↑(las... | [
1803,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1800,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | Monotone.mul_const' | [] | [
1313,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1312,
1
] |
Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.iIndepFun.indepFun_prod | [
{
"state_after": "no goals",
"state_before": "Ω : Type u_1\nι✝ : Type ?u.3447382\nβ✝ : Type ?u.3447385\nβ' : Type ?u.3447388\nγ : Type ?u.3447391\nγ' : Type ?u.3447394\nmΩ : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\nf✝ : Ω → β✝\ng : Ω → β'\ninst✝ : IsProbabilityMeasure μ\nι : Type u_2\nβ : ι → Type u_... | [
848,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
823,
1
] |
Mathlib/Data/Nat/SuccPred.lean | Nat.succ_iterate | [
{
"state_after": "a n : ℕ\n⊢ (succ ∘ succ^[n]) a = succ (a + n)",
"state_before": "a n : ℕ\n⊢ (succ^[n + 1]) a = a + (n + 1)",
"tactic": "rw [Function.iterate_succ', add_succ]"
},
{
"state_after": "no goals",
"state_before": "a n : ℕ\n⊢ (succ ∘ succ^[n]) a = succ (a + n)",
"tactic": "exa... | [
62,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Data/List/Rotate.lean | List.cyclicPermutations_rotate | [
{
"state_after": "α : Type u\nl✝ l' l : List α\nk : ℕ\nthis : length (cyclicPermutations (rotate l k)) = length (rotate (cyclicPermutations l) k)\nn : ℕ\nhn : n < length (cyclicPermutations (rotate l k))\nhn' : n < length (rotate (cyclicPermutations l) k)\n⊢ nthLe (cyclicPermutations (rotate l k)) n hn = nthLe ... | [
680,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
672,
1
] |
Mathlib/Analysis/Convex/Complex.lean | convex_halfspace_re_lt | [] | [
23,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
22,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.coe_apply_coe_coe_symm_apply | [] | [
329,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/Analysis/Asymptotics/SpecificAsymptotics.lean | pow_div_pow_eventuallyEq_atTop | [
{
"state_after": "𝕜 : Type u_1\ninst✝ : LinearOrderedField 𝕜\np q : ℕ\n⊢ ∀ (x : 𝕜), 0 < x → (fun x => x ^ p / x ^ q) x = (fun x => x ^ (↑p - ↑q)) x",
"state_before": "𝕜 : Type u_1\ninst✝ : LinearOrderedField 𝕜\np q : ℕ\n⊢ (fun x => x ^ p / x ^ q) =ᶠ[atTop] fun x => x ^ (↑p - ↑q)",
"tactic": "apply ... | [
48,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | deriv_fderiv | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type w\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf f₀ f₁ g : 𝕜 → F\nf' f₀' f₁' g' : F\nx : 𝕜\ns t : Set 𝕜\nL L₁ L₂ : Fi... | [
477,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Mathlib/Analysis/LocallyConvex/AbsConvex.lean | with_gaugeSeminormFamily | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.88243\nG : Type ?u.88246\nι : Type ?u.88249\ninst✝¹⁰ : IsROrC 𝕜\ninst✝⁹ : AddCommGroup E\ninst✝⁸ : TopologicalSpace E\ninst✝⁷ : Module 𝕜 E\ninst✝⁶ : Module ℝ E\ninst✝⁵ : IsScalarTower ℝ 𝕜 E\ninst✝⁴ : ContinuousSMul ℝ E\ninst✝³ : TopologicalAddGroup E... | [
186,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Order/RelIso/Set.lean | subrel_val | [] | [
63,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.single_injective | [
{
"state_after": "α : Type u_2\nβ : Type ?u.49306\nγ : Type ?u.49309\nι : Type ?u.49312\nM : Type u_1\nM' : Type ?u.49318\nN : Type ?u.49321\nP : Type ?u.49324\nG : Type ?u.49327\nH : Type ?u.49330\nR : Type ?u.49333\nS : Type ?u.49336\ninst✝ : Zero M\na✝ a' : α\nb : M\na : α\nb₁ b₂ : M\neq : single a b₁ = sing... | [
381,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
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