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/RingTheory/Ideal/MinimalPrime.lean | Ideal.minimalPrimes_eq_subsingleton | [
{
"state_after": "case h\nR : Type u_1\nS : Type ?u.121108\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nI J✝ : Ideal R\nhI : IsPrimary I\nJ : Ideal R\n⊢ J ∈ Ideal.minimalPrimes I ↔ J ∈ {radical I}",
"state_before": "R : Type u_1\nS : Type ?u.121108\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nI J : Ideal R\nhI : ... | [
207,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/MeasureTheory/Function/L2Space.lean | MeasureTheory.L2.add_left' | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.99640\n𝕜 : Type u_3\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : MeasurableSpace α\nμ : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : NormedAddCommGroup F\nf f' g : { x // x ∈ Lp E 2 }\n⊢ (∫ (a : α), inner (↑↑(f + f') a) (↑↑g a) ∂μ... | [
209,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
9
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioo_union_Ici_eq_Ioi | [] | [
1263,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1262,
1
] |
Mathlib/LinearAlgebra/Finrank.lean | coe_basisOfTopLeSpanOfCardEqFinrank | [] | [
463,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
460,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_eq_zero_add | [] | [
980,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
978,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | AddSubmonoid.smul_bot | [] | [
387,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/Order/Max.lean | IsTop.fst | [] | [
425,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/Topology/ContinuousFunction/Algebra.lean | ContinuousMap.summable_apply | [] | [
436,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.bijective | [] | [
555,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
11
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.coe_pow | [] | [
587,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
586,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.coeff_rescale | [] | [
1765,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1763,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.smul_set_mem_smul_filter | [] | [
1192,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1191,
1
] |
Mathlib/Topology/MetricSpace/IsometricSMul.lean | dist_smul | [] | [
339,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/RingTheory/Ideal/Over.lean | Ideal.comap_ne_bot_of_root_mem | [] | [
256,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/Data/Polynomial/Laurent.lean | Polynomial.toLaurent_C_mul_T | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nn : ℕ\nr : R\n⊢ Finsupp.mapDomain Nat.cast (↑(monomial n) r).toFinsupp = ↑C r * T ↑n",
"tactic": "rw [toFinsupp_monomial, Finsupp.mapDomain_single, single_eq_C_mul_T]"
}
] | [
215,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_nat_mul_pi | [] | [
269,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Std/Data/BinomialHeap.lean | Std.BinomialHeapImp.Heap.WellFormed.tail? | [
{
"state_after": "α : Type u_1\ns : Heap α\nle : α → α → Bool\nn : Nat\ntl : Heap α\nhwf : WellFormed le n s\n⊢ Option.map (fun x => x.snd) (Heap.deleteMin le s) = some tl → WellFormed le 0 tl",
"state_before": "α : Type u_1\ns : Heap α\nle : α → α → Bool\nn : Nat\ntl : Heap α\nhwf : WellFormed le n s\n⊢ He... | [
504,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
499,
1
] |
Mathlib/Analysis/Convex/Slope.lean | ConvexOn.secant_mono_aux3 | [
{
"state_after": "𝕜 : Type u_1\ninst✝ : LinearOrderedField 𝕜\ns : Set 𝕜\nf : 𝕜 → 𝕜\nhf : ConvexOn 𝕜 s f\nx y z : 𝕜\nhx : x ∈ s\nhz : z ∈ s\nhxy : x < y\nhyz : y < z\nhyz' : 0 < z - y\n⊢ (f z - f x) / (z - x) ≤ (f z - f y) / (z - y)",
"state_before": "𝕜 : Type u_1\ninst✝ : LinearOrderedField 𝕜\ns : ... | [
274,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Data/Fintype/Fin.lean | Fin.Iio_last_eq_map | [
{
"state_after": "case a\nα : Type ?u.6717\nβ : Type ?u.6720\nn : ℕ\n⊢ map valEmbedding (Iio (last n)) = map valEmbedding (map castSucc.toEmbedding univ)",
"state_before": "α : Type ?u.6717\nβ : Type ?u.6720\nn : ℕ\n⊢ Iio (last n) = map castSucc.toEmbedding univ",
"tactic": "apply Finset.map_injective F... | [
51,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Order/Monotone/Monovary.lean | AntivaryOn.subset | [] | [
92,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
11
] |
Mathlib/SetTheory/Ordinal/CantorNormalForm.lean | Ordinal.CNF_lt_snd | [
{
"state_after": "b o✝ : Ordinal\nx : Ordinal × Ordinal\no : Ordinal\nho : o ≠ 0\nIH : x ∈ CNF b (o % b ^ log b o) → 0 < x.snd\n⊢ x ∈ CNF b o → 0 < x.snd",
"state_before": "b o : Ordinal\nx : Ordinal × Ordinal\n⊢ x ∈ CNF b o → 0 < x.snd",
"tactic": "refine' CNFRec b (by simp) (fun o ho IH ↦ _) o"
},
... | [
148,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Data/Finset/Prod.lean | Finset.diag_insert | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.128864\nγ : Type ?u.128867\ninst✝ : DecidableEq α\ns t : Finset α\nx : α × α\na : α\n⊢ diag (insert a s) = insert (a, a) (diag s)",
"tactic": "rw [insert_eq, insert_eq, diag_union, diag_singleton]"
}
] | [
417,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/LinearAlgebra/BilinearMap.lean | LinearMap.map_smulₛₗ₂ | [] | [
179,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.count_cons | [] | [
2376,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2374,
1
] |
Mathlib/CategoryTheory/Generator.lean | CategoryTheory.isCodetector_def | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nX Y : C\nf : X ⟶ Y\nH : C\nh : X ⟶ H\nhG : IsCodetector H\nhf : ∀ (h : X ⟶ H), ∃! h', f ≫ h' = h\nhH : H ∈ {H}\n⊢ ∃! h', f ≫ h' = h",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nG : C... | [
504,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.le_sum_caratheodory | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nι : Type u_1\nm : ι → OuterMeasure α\ns : Set α\nh : MeasurableSet s\nt : Set α\n⊢ ↑(sum m) t = ↑(sum m) (t ∩ s) + ↑(sum m) (t \\ s)",
"tactic": "simp [fun i => MeasurableSpace.measurableSet_iInf.1 h i t, ENNReal.tsum_add]"
}
] | [
1116,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1114,
1
] |
Mathlib/Analysis/Normed/Group/Pointwise.lean | infEdist_inv | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\ninst✝ : SeminormedCommGroup E\nε δ : ℝ\ns✝ t : Set E\nx✝ y x : E\ns : Set E\n⊢ infEdist x⁻¹ s = infEdist x s⁻¹",
"tactic": "rw [← infEdist_inv_inv, inv_inv]"
}
] | [
71,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Dynamics/Ergodic/MeasurePreserving.lean | MeasureTheory.MeasurePreserving.restrict_preimage | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.52351\nδ : Type ?u.52354\ninst✝³ : MeasurableSpace α\ninst✝² : MeasurableSpace β\ninst✝¹ : MeasurableSpace γ\ninst✝ : MeasurableSpace δ\nμa : Measure α\nμb : Measure β\nμc : Measure γ\nμd : Measure δ\nf : α → β\nhf : Measu... | [
76,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Algebra/Order/LatticeGroup.lean | LatticeOrderedCommGroup.abs_abs_div_abs_le | [
{
"state_after": "α : Type u\ninst✝² : Lattice α\ninst✝¹ : CommGroup α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b : α\n⊢ abs a / abs b ≤ abs (a / b) ∧ (abs a / abs b)⁻¹ ≤ abs (a / b)",
"state_before": "α : Type u\ninst✝² : Lattice α\ninst✝¹ : CommGroup α\ninst✝ : CovariantC... | [
594,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
585,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.Tape.move_right_nth | [
{
"state_after": "Γ : Type u_1\ninst✝ : Inhabited Γ\nT : Tape Γ\ni : ℤ\n⊢ nth (move Dir.right T) i = nth (move Dir.left (move Dir.right T)) (i + 1)",
"state_before": "Γ : Type u_1\ninst✝ : Inhabited Γ\nT : Tape Γ\ni : ℤ\n⊢ nth (move Dir.right T) i = nth T (i + 1)",
"tactic": "conv => rhs; rw [← T.move_r... | [
648,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
645,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.mem_cons_of_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nδ : Type w\na : α\ns : Stream' α\nb : α\nx✝ : a ∈ s\nn : ℕ\nh : (fun b => a = b) (nth s n)\n⊢ (fun b => a = b) (nth (b :: s) (succ n))",
"tactic": "rw [nth_succ, tail_cons, h]"
}
] | [
126,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.unitsEquivAut_apply | [] | [
2373,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2372,
1
] |
Mathlib/Order/CompactlyGenerated.lean | exists_setIndependent_of_sSup_atoms_eq_top | [] | [
612,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
609,
1
] |
Mathlib/Algebra/Order/Sub/Defs.lean | add_tsub_add_eq_tsub_right | [
{
"state_after": "case refine'_1\nα : Type u_1\nβ : Type ?u.53321\ninst✝⁵ : PartialOrder α\ninst✝⁴ : AddCommSemigroup α\ninst✝³ : Sub α\ninst✝² : OrderedSub α\na✝ b✝ c✝ d : α\ninst✝¹ : CovariantClass α α (fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1\ninst✝ : ContravariantClass α α (fun x x_1 => x + x_1) fun x x_1... | [
395,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.smul_eq_cast | [
{
"state_after": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na : ℕ\nb : R\n⊢ a • b = ↑a * b",
"state_before": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na : ℕ\na' b c : R\nx✝¹ : ↑a = a'\nx✝ : a' * b = ... | [
507,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_list_eq_sum_pow | [
{
"state_after": "no goals",
"state_before": "α✝ β α : Type u\n⊢ (#(n : ℕ) × Vector α n) = sum fun n => (#α) ^ n",
"tactic": "simp"
}
] | [
1962,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1959,
1
] |
Mathlib/Topology/Algebra/OpenSubgroup.lean | OpenSubgroup.coe_inf | [] | [
222,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Analysis/Calculus/LocalExtr.lean | posTangentConeAt_mono | [
{
"state_after": "case intro.intro.intro.intro\nE : Type u\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : E → ℝ\na : E\nf' : E →L[ℝ] ℝ\ns t : Set E\nhst : s ≤ t\ny : E\nc : ℕ → ℝ\nd : ℕ → E\nhd : ∀ᶠ (n : ℕ) in atTop, a + d n ∈ s\nhc : Tendsto c atTop atTop\nhcd : Tendsto (fun n => c n • d n) atTop... | [
89,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | Submonoid.coe_pointwise_smul | [] | [
240,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_le_one_iff_of_pos | [
{
"state_after": "no goals",
"state_before": "x y z : ℝ\nhx : 0 < x\n⊢ x ^ y ≤ 1 ↔ 1 ≤ x ∧ y ≤ 0 ∨ x ≤ 1 ∧ 0 ≤ y",
"tactic": "rw [rpow_def_of_pos hx, exp_le_one_iff, mul_nonpos_iff, log_nonneg_iff hx, log_nonpos_iff hx]"
}
] | [
614,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
613,
1
] |
Mathlib/Analysis/Asymptotics/SuperpolynomialDecay.lean | Asymptotics.superpolynomialDecay_mul_const_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nl : Filter α\nk f g g' : α → β\ninst✝² : TopologicalSpace β\ninst✝¹ : Field β\ninst✝ : ContinuousMul β\nc : β\nhc0 : c ≠ 0\nh : SuperpolynomialDecay l k fun n => f n * c\nx : α\n⊢ f x * c * c⁻¹ = f x",
"tactic": "simp [mul_assoc, ... | [
206,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tsum_top | [] | [
882,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
880,
11
] |
Mathlib/Init/Logic.lean | let_eq | [
{
"state_after": "no goals",
"state_before": "a b c d : Prop\np : ?m.30637\nα : Sort v\nβ : Sort u\na₁ a₂ : α\nb₁ b₂ : α → β\nh₁ : a₁ = a₂\nh₂ : ∀ (x : α), b₁ x = b₂ x\n⊢ (let x := a₁;\n b₁ x) =\n let x := a₂;\n b₂ x",
"tactic": "simp [h₁, h₂]"
}
] | [
455,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
1
] |
Mathlib/Order/Lattice.lean | le_inf_iff | [] | [
429,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.fst_sumFinsuppEquivProdFinsupp | [] | [
1350,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1348,
1
] |
Mathlib/Data/Sum/Order.lean | Sum.Lex.inr_lt_inr_iff | [] | [
360,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.trans_apply | [] | [
368,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
] |
Mathlib/Data/TypeVec.lean | TypeVec.append1_drop_last | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nα : TypeVec (n + 1)\ni : Fin2 (n + 1)\n⊢ (drop α ::: last α) i = α i",
"tactic": "cases i <;> rfl"
}
] | [
131,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.zero_add | [] | [
116,
42
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
114,
19
] |
Mathlib/MeasureTheory/Group/Integration.lean | MeasureTheory.integrable_comp_div_left | [
{
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185,
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181,
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Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.trans_symm_eq_symm_trans_symm | [
{
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705,
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704,
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Mathlib/Data/List/MinMax.lean | List.argmax_nil | [] | [
112,
6
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111,
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Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.not_measurable | [] | [
106,
23
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105,
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Mathlib/Data/Num/Lemmas.lean | ZNum.of_nat_cast | [
{
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}
] | [
1570,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1569,
1
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Mathlib/Algebra/CharP/Two.lean | CharTwo.add_mul_self | [
{
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] | [
94,
47
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93,
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Mathlib/Order/Chain.lean | isChain_empty | [] | [
68,
23
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67,
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Mathlib/Analysis/Complex/UnitDisc/Basic.lean | Complex.UnitDisc.mk_neg | [] | [
98,
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Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_one_div | [
{
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] | [
444,
38
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443,
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Mathlib/NumberTheory/Padics/RingHoms.lean | PadicInt.toZMod_spec | [
{
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{
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282,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
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Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.tmul_mul_tmul | [] | [
469,
6
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Mathlib/Data/Matrix/Block.lean | Matrix.toBlock_apply | [] | [
198,
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196,
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Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.map_smul_left | [
{
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805,
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803,
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Mathlib/Topology/PathConnected.lean | Path.trans_pi_eq_pi_trans | [
{
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597,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Limits/Constructions/LimitsOfProductsAndEqualizers.lean | CategoryTheory.Limits.hasFiniteLimits_of_hasTerminal_and_pullbacks | [] | [
245,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
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Mathlib/Logic/Basic.lean | eq_iff_eq_cancel_left | [
{
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] | [
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45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Real/ENNReal.lean | ENNReal.ofReal_coe_nat | [
{
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] | [
682,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
682,
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Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquivClass.map_ne_one_iff | [] | [
159,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
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Mathlib/Algebra/Order/Group/Abs.lean | abs_zero | [] | [
132,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
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Mathlib/Algebra/Order/Rearrangement.lean | Monovary.sum_comp_perm_smul_lt_sum_smul_iff | [
{
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288,
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286,
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Mathlib/Data/Finset/Prod.lean | Finset.product_image_snd | [
{
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85,
27
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Mathlib/Order/Hom/Basic.lean | Codisjoint.map_orderIso | [
{
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1219,
29
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1216,
1
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Mathlib/Order/Lattice.lean | Ne.lt_sup_or_lt_sup | [] | [
310,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
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Mathlib/Order/Disjoint.lean | codisjoint_iff_le_sup | [] | [
309,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_eq_zero_iff_cos_eq | [
{
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"state_before": "x : ℝ\n⊢ sin x = 0 ↔ cos x = 1 ∨ cos x = -1",
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},
{
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526,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
524,
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Mathlib/Topology/ContinuousOn.lean | continuousOn_empty | [] | [
667,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
667,
1
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Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | ext_chart_model_space_apply | [] | [
1287,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1286,
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_union_le_aleph0 | [
{
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}
] | [
2137,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2134,
1
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Std/Data/List/Lemmas.lean | List.isPrefix.subset | [] | [
1610,
20
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1609,
11
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Mathlib/Computability/Halting.lean | Nat.Partrec'.comp' | [
{
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}
] | [
363,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
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Mathlib/Algebra/Ring/Prod.lean | NonUnitalRingHom.fst_comp_prod | [] | [
145,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
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Mathlib/Computability/Halting.lean | ComputablePred.rice₂ | [
{
"state_after": "no goals",
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"tactic": "classical exact\n have ... | [
232,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
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Mathlib/Topology/Instances/ENNReal.lean | ENNReal.Tendsto.div | [
{
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544,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Filter/Germ.lean | Filter.Germ.map_coe | [] | [
193,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
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] |
Mathlib/MeasureTheory/Function/AEEqOfIntegral.lean | MeasureTheory.AEFinStronglyMeasurable.ae_eq_zero_of_forall_set_integral_eq_zero | [
{
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456,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
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Mathlib/Algebra/Module/DedekindDomain.lean | Submodule.exists_isInternal_prime_power_torsion | [] | [
86,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
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Mathlib/Algebra/Symmetrized.lean | SymAlg.unsym_smul | [] | [
235,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Init/Data/Ordering/Lemmas.lean | Ordering.ite_eq_lt_distrib | [
{
"state_after": "no goals",
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}
] | [
27,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
25,
1
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Mathlib/Order/WellFounded.lean | WellFounded.induction_bot | [] | [
281,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
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Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.prod_mk | [] | [
908,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
907,
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Mathlib/Topology/Algebra/InfiniteSum/Module.lean | ContinuousLinearEquiv.map_tsum | [
{
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105,
28
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11
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Mathlib/LinearAlgebra/AffineSpace/Ordered.lean | lineMap_le_map_iff_slope_le_slope_right | [] | [
258,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
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Mathlib/AlgebraicTopology/DoldKan/Faces.lean | AlgebraicTopology.DoldKan.HigherFacesVanish.of_succ | [
{
"state_after": "no goals",
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"tactic": "simpa only [← add_assoc] us... | [
63,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
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Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | modelWithCorners_prod_toLocalEquiv | [] | [
451,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
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Mathlib/GroupTheory/GroupAction/Defs.lean | smul_mul_smul | [
{
"state_after": "no goals",
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583,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
581,
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Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.mem_vars_rename | [
{
"state_after": "no goals",
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... | [
897,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
894,
1
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Mathlib/RingTheory/Subring/Basic.lean | Subring.sum_mem | [] | [
405,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
11
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Mathlib/Analysis/Calculus/DiffContOnCl.lean | DiffContOnCl.sub | [] | [
110,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Data/Finset/Card.lean | Multiset.toFinset_card_of_nodup | [] | [
193,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Data/Nat/Factorial/Basic.lean | Nat.pow_sub_lt_descFactorial | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ 2 ≤ 0 → 0 ≤ n → (n + 1 - 0) ^ 0 < descFactorial n 0",
"tactic": "rintro ⟨⟩"
},
{
"state_after": "n : ℕ\na✝ : 2 ≤ 1\n⊢ 1 ≤ n → (n + 1 - 1) ^ 1 < descFactorial n 1",
"state_before": "n : ℕ\n⊢ 2 ≤ 1 → 1 ≤ n → (n + 1 - 1) ^ 1 < descFactorial... | [
466,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
460,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.restrict_iInf_restrict | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nι : Sort u_1\ns : Set α\nm : ι → OuterMeasure α\n⊢ ↑(restrict s) (⨅ (i : ι), ↑(restrict s) (m i)) = ↑(restrict (range Subtype.val)) (⨅ (i : ι), ↑(restrict s) (m i))",
"tactic": "rw [Subtype.range_coe]"
}
] | [
1269,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1263,
1
] |
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