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/Data/Fin/Basic.lean | Fin.mk_le_mk | [] | [
320,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/MeasureTheory/Measure/NullMeasurable.lean | MeasureTheory.Measure.isComplete_iff | [] | [
456,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
1
] |
Mathlib/Data/Int/Units.lean | Int.units_eq_one_or | [
{
"state_after": "no goals",
"state_before": "u : ℤˣ\n⊢ u = 1 ∨ u = -1",
"tactic": "simpa only [Units.ext_iff, units_natAbs] using natAbs_eq u"
}
] | [
33,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
] |
Mathlib/Data/Set/Sigma.lean | Set.image_sigmaMk_preimage_sigmaMap | [
{
"state_after": "ι : Type u_2\nι' : Type u_3\nα : ι → Type u_4\nβ✝ : ι → Type ?u.1906\ns✝ s₁ s₂ : Set ι\nt t₁ t₂ : (i : ι) → Set (α i)\nu : Set ((i : ι) × α i)\nx : (i : ι) × α i\ni✝ j : ι\na : α i✝\nβ : ι' → Type u_1\nf : ι → ι'\nhf : Function.Injective f\ng : (i : ι) → α i → β (f i)\ni : ι\ns : Set (β (f i))... | [
52,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisConnection.u_inf | [] | [
279,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Std/Logic.lean | or_iff_left_of_imp | [] | [
291,
78
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
291,
1
] |
Std/Data/String/Lemmas.lean | String.extract.go₁_zero_utf8Len | [
{
"state_after": "no goals",
"state_before": "s : List Char\n⊢ go₂ s { byteIdx := 0 } { byteIdx := utf8Len s } = s",
"tactic": "simpa using go₂_append_left s [] 0 (utf8Len s) rfl"
}
] | [
431,
55
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
429,
1
] |
Mathlib/Data/Nat/Factorization/PrimePow.lean | IsPrimePow.minFac_pow_factorization_eq | [
{
"state_after": "case intro.intro.intro.intro\nR : Type ?u.14\ninst✝ : CommMonoidWithZero R\nn p✝ : R\nk✝ p k : ℕ\nhp : Prime p\nhk : 0 < k\n⊢ Nat.minFac (p ^ k) ^ ↑(Nat.factorization (p ^ k)) (Nat.minFac (p ^ k)) = p ^ k",
"state_before": "R : Type ?u.14\ninst✝ : CommMonoidWithZero R\nn✝ p : R\nk n : ℕ\nh... | [
27,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
23,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.preimage_mul_left_singleton | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.671388\nα : Type u_1\nβ : Type ?u.671394\nγ : Type ?u.671397\ninst✝ : Group α\ns t : Finset α\na b : α\n⊢ preimage {b} ((fun x x_1 => x * x_1) a)\n (_ : Set.InjOn ((fun x x_1 => x * x_1) a) ((fun x x_1 => x * x_1) a ⁻¹' ↑{b})) =\n {a⁻¹ * b}",... | [
1214,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1212,
1
] |
Mathlib/Algebra/Group/OrderSynonym.lean | ofLex_one | [] | [
249,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_sub | [] | [
1100,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1100,
9
] |
Mathlib/Data/Sum/Basic.lean | Sum.LiftRel.lex | [
{
"state_after": "case inl\nα : Type u\nα' : Type w\nβ : Type v\nβ' : Type x\nγ : Type ?u.30404\nδ : Type ?u.30407\nr r₁ r₂ : α → α → Prop\ns s₁ s₂ : β → β → Prop\na a₁ a₂ : α\nb b₁ b₂ : β\nx y : α ⊕ β\na✝¹ c✝ : α\na✝ : r a✝¹ c✝\n⊢ Lex r s (inl a✝¹) (inl c✝)\n\ncase inr\nα : Type u\nα' : Type w\nβ : Type v\nβ' ... | [
505,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
11
] |
Mathlib/Data/Set/Intervals/Pi.lean | Set.piecewise_mem_Icc' | [] | [
59,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq1.map_id | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\na : α\ns : Seq α\n⊢ map id (a, s) = (a, s)",
"tactic": "simp [map]"
}
] | [
928,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
927,
1
] |
Mathlib/CategoryTheory/Category/Preorder.lean | CategoryTheory.Equivalence.toOrderIso_symm_apply | [] | [
194,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | borel_eq_generateFrom_Ioc | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.674070\nβ : Type ?u.674073\nγ : Type ?u.674076\nγ₂ : Type ?u.674079\nδ : Type ?u.674082\nι : Sort y\ns t u : Set α✝\ninst✝²⁰ : TopologicalSpace α✝\ninst✝¹⁹ : MeasurableSpace α✝\ninst✝¹⁸ : OpensMeasurableSpace α✝\ninst✝¹⁷ : TopologicalSpace β\ninst✝¹... | [
657,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
652,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | Submodule.isClosed_topologicalClosure | [] | [
168,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.pos_of_ne_zero | [] | [
37,
94
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
37,
11
] |
Mathlib/Topology/IsLocallyHomeomorph.lean | IsLocallyHomeomorph.isOpenMap | [] | [
127,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
11
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.HasZeroObject.zeroIsoIsTerminal_hom | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝³ : Category C\nD : Type u'\ninst✝² : Category D\ninst✝¹ : HasZeroObject C\ninst✝ : HasZeroMorphisms C\nX : C\nt : IsTerminal X\n⊢ (zeroIsoIsTerminal t).hom = 0",
"tactic": "ext"
}
] | [
312,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Data/List/Basic.lean | List.nthLe_of_mem | [] | [
1239,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1238,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.coe_top | [] | [
617,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
616,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.monic_of_subsingleton | [] | [
81,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.neg_nsmul | [] | [
210,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.mul_rpow_of_ne_zero | [
{
"state_after": "no goals",
"state_before": "x y : ℝ≥0∞\nhx : x ≠ 0\nhy : y ≠ 0\nz : ℝ\n⊢ (x * y) ^ z = x ^ z * y ^ z",
"tactic": "simp [*, mul_rpow_eq_ite]"
}
] | [
514,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
513,
1
] |
Mathlib/Topology/Order/Basic.lean | IsCompact.bddBelow_image | [] | [
824,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
822,
1
] |
Mathlib/Data/ZMod/Coprime.lean | ZMod.ne_zero_of_gcd_eq_one | [] | [
35,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.aecover_Icc_of_Ioc | [] | [
269,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/RingTheory/Ideal/Over.lean | Ideal.IntegralClosure.eq_bot_of_comap_eq_bot | [] | [
362,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/Logic/Nonempty.lean | Nonempty.forall | [] | [
111,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Data/Set/Basic.lean | Set.mem_of_mem_inter_right | [] | [
907,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
906,
1
] |
Std/Data/Int/DivMod.lean | Int.mod_one | [
{
"state_after": "no goals",
"state_before": "a : Int\n⊢ mod a 1 = 0",
"tactic": "simp [mod_def, Int.div_one, Int.one_mul, Int.sub_self]"
}
] | [
347,
57
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
346,
9
] |
src/lean/Init/Control/Lawful.lean | StateT.run'_eq | [] | [
246,
6
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
245,
9
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.cycleOf_mem_cycleFactorsFinset_iff | [
{
"state_after": "ι : Type ?u.2742928\nα : Type u_1\nβ : Type ?u.2742934\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf✝ f : Perm α\nx : α\n⊢ (IsCycle (cycleOf f x) ∧ ∀ (a : α), a ∈ support (cycleOf f x) → ↑(cycleOf f x) a = ↑f a) ↔ x ∈ support f",
"state_before": "ι : Type ?u.2742928\nα : Type u_1\nβ : Type... | [
1432,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1416,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | EMetric.infEdist_le_hausdorffEdist_of_mem | [
{
"state_after": "ι : Sort ?u.37567\nα : Type u\nβ : Type v\ninst✝¹ : PseudoEMetricSpace α\ninst✝ : PseudoEMetricSpace β\nx y : α\ns t u : Set α\nΦ : α → β\nh : x ∈ s\n⊢ infEdist x t ≤ (⨆ (x : α) (_ : x ∈ s), infEdist x t) ⊔ ⨆ (y : α) (_ : y ∈ t), infEdist y s",
"state_before": "ι : Sort ?u.37567\nα : Type ... | [
304,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.map_iSup_comap_of_surjective | [] | [
1584,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1583,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieHom.range_eq_top | [
{
"state_after": "R : Type u\nL : Type v\nL' : Type w₂\nM : Type w\nM' : Type w₁\ninst✝¹² : CommRing R\ninst✝¹¹ : LieRing L\ninst✝¹⁰ : LieAlgebra R L\ninst✝⁹ : LieRing L'\ninst✝⁸ : LieAlgebra R L'\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³ : AddCo... | [
991,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
989,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.edist_lt_top | [] | [
157,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | eq_of_forall_edist_le | [] | [
1024,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1023,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.coe_prodCongr | [] | [
479,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
Mathlib/RingTheory/Algebraic.lean | Subalgebra.isAlgebraic_iff | [
{
"state_after": "R : Type u\nA : Type v\ninst✝² : CommRing R\ninst✝¹ : Ring A\ninst✝ : Algebra R A\nS : Subalgebra R A\n⊢ (∀ (x : A), x ∈ S → _root_.IsAlgebraic R x) ↔ ∀ (x : { x // x ∈ S }), _root_.IsAlgebraic R x",
"state_before": "R : Type u\nA : Type v\ninst✝² : CommRing R\ninst✝¹ : Ring A\ninst✝ : Alg... | [
74,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Analysis/SpecialFunctions/Exponential.lean | hasStrictDerivAt_exp | [] | [
202,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Data/Rat/Cast.lean | Rat.cast_add_of_ne_zero | [
{
"state_after": "F : Type ?u.7925\nι : Type ?u.7928\nα : Type u_1\nβ : Type ?u.7934\ninst✝ : DivisionRing α\nn₁ : ℤ\nd₁ : ℕ\nh₁ : d₁ ≠ 0\nc₁ : Nat.coprime (Int.natAbs n₁) d₁\nn₂ : ℤ\nd₂ : ℕ\nh₂ : d₂ ≠ 0\nc₂ : Nat.coprime (Int.natAbs n₂) d₂\nd₁0 : ↑d₁ ≠ 0\nd₂0 : ↑d₂ ≠ 0\nd₁0' : ↑d₁ ≠ 0\n⊢ ↑(mk' n₁ d₁ + mk' n₂ d... | [
119,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.comap_neg_atBot | [] | [
839,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
838,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | PadicSeq.norm_const | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\nq : ℚ\nhq : q = 0\nthis : const (padicNorm p) q ≈ 0\n⊢ norm (const (padicNorm p) q) = padicNorm p q",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nq : ℚ\nhq : q = 0\n⊢ norm (const (padicNorm p) q) = padicNorm p q",
"tactic": "have : const (padicNorm ... | [
315,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | abs_one_div | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.201202\nα : Type u_1\nβ : Type ?u.201208\ninst✝ : LinearOrderedField α\na✝ b c d : α\nn : ℤ\na : α\n⊢ abs (1 / a) = 1 / abs a",
"tactic": "rw [abs_div, abs_one]"
}
] | [
1008,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1008,
1
] |
Mathlib/Topology/UniformSpace/UniformEmbedding.lean | completeSpace_congr | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝² : UniformSpace α\ninst✝¹ : UniformSpace β\ninst✝ : UniformSpace γ\ne : α ≃ β\nhe : UniformEmbedding ↑e\n⊢ CompleteSpace α ↔ CompleteSpace β",
"tactic": "rw [completeSpace_iff_isComplete_range he.toUniformInducing, e... | [
320,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | LocalHomeomorph.isLocalStructomorphWithinAt_source_iff | [
{
"state_after": "no goals",
"state_before": "H : Type u_1\nM : Type ?u.71024\nH' : Type ?u.71027\nM' : Type ?u.71030\nX : Type ?u.71033\ninst✝⁷ : TopologicalSpace H\ninst✝⁶ : TopologicalSpace M\ninst✝⁵ : ChartedSpace H M\ninst✝⁴ : TopologicalSpace H'\ninst✝³ : TopologicalSpace M'\ninst✝² : ChartedSpace H' ... | [
651,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
645,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.image₂_singleton_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nα' : Type ?u.29712\nβ : Type u_3\nβ' : Type ?u.29718\nγ : Type u_1\nγ' : Type ?u.29724\nδ : Type ?u.29727\nδ' : Type ?u.29730\nε : Type ?u.29733\nε' : Type ?u.29736\nζ : Type ?u.29739\nζ' : Type ?u.29742\nν : Type ?u.29745\ninst✝⁷ : DecidableEq α'\... | [
160,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Topology/Constructions.lean | ContinuousAt.snd' | [] | [
390,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/CategoryTheory/StructuredArrow.lean | CategoryTheory.StructuredArrow.mk_left | [] | [
70,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.bot_toSubalgebra | [
{
"state_after": "F : Type ?u.698810\nR : Type u_2\nA : Type u_1\nB : Type ?u.698819\ninst✝⁹ : CommSemiring R\ninst✝⁸ : StarRing R\ninst✝⁷ : Semiring A\ninst✝⁶ : Algebra R A\ninst✝⁵ : StarRing A\ninst✝⁴ : StarModule R A\ninst✝³ : Semiring B\ninst✝² : Algebra R B\ninst✝¹ : StarRing B\ninst✝ : StarModule R B\n⊢ A... | [
701,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
699,
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Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSpace.comap_iSup | [] | [
161,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
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Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | InnerProductGeometry.sin_angle_add_mul_norm_of_inner_eq_zero | [
{
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191,
101
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182,
1
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Mathlib/GroupTheory/FreeProduct.lean | FreeProduct.NeWord.prod_singleton | [
{
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] | [
607,
33
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606,
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Mathlib/Data/Fintype/Card.lean | Fintype.card_pos_iff | [] | [
539,
91
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538,
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Mathlib/ModelTheory/FinitelyGenerated.lean | FirstOrder.Language.Equiv.fg_iff | [] | [
267,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
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Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.principal_add_ord | [
{
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},
{
... | [
859,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
856,
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Mathlib/Data/List/Perm.lean | List.nodup_permutations'Aux_iff | [
{
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},
{... | [
1445,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.sum_C | [] | [
367,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
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Std/Data/List/Basic.lean | List.insertNthTR_go_eq | [
{
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},
{
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573,
78
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioo_subset_Ioo_union_Ico | [] | [
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84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/BigOperators/Intervals.lean | Finset.prod_Ioc_succ_top | [
{
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87,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
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Mathlib/Data/Int/Basic.lean | Int.ediv_of_neg_of_pos | [
{
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243,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
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Mathlib/Analysis/InnerProductSpace/Adjoint.lean | LinearMap.isAdjointPair_inner | [
{
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500,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
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Mathlib/Algebra/Module/Basic.lean | smul_right_inj | [] | [
682,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
680,
1
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Mathlib/GroupTheory/Submonoid/Pointwise.lean | AddSubmonoid.smul_closure | [] | [
396,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
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] |
Mathlib/Algebra/Hom/Group.lean | MulHom.toFun_eq_coe | [] | [
601,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
601,
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] |
Mathlib/Algebra/Order/Floor.lean | Int.floor_le | [] | [
661,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
660,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.IsZero.eq_zero_of_src | [] | [
182,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.single_left_inj | [] | [
428,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/RingTheory/GradedAlgebra/Radical.lean | Ideal.IsHomogeneous.isPrime_of_homogeneous_mem_or_mem | [
{
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145,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
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Mathlib/Data/Multiset/Lattice.lean | Multiset.inf_ndunion | [
{
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167,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
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Mathlib/Data/Set/Lattice.lean | Set.iInter_false | [] | [
666,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
665,
1
] |
Mathlib/SetTheory/Ordinal/Principal.lean | Ordinal.principal_iff_principal_swap | [
{
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}
] | [
57,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Combinatorics/Additive/SalemSpencer.lean | mulSalemSpencer_mul_left_iff | [
{
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201,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
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Mathlib/Analysis/SpecialFunctions/Bernstein.lean | bernstein_nonneg | [
{
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"tactic": "simp only [bernstein_apply]"
},
{
"state_after": "n ν : ℕ\nx : ↑I\nh₁ : 0 ≤ ↑x\n⊢ 0 ≤ ↑(Nat.choose n ν) * ↑x ^ ν * (1 - ↑x) ^ (n - ν)... | [
74,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
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Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.IndepSets.union_iff | [] | [
216,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
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Mathlib/Algebra/ModEq.lean | AddCommGroup.nat_cast_modEq_nat_cast | [
{
"state_after": "no goals",
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"tactic": "simp_rw [← Int.coe_nat_modEq_iff, ← modEq_iff_int_modEq, ← @int_cast_modEq_int_cast α,\n Int.cast_ofNat]"
}
] | [
330,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.cospanExt_app_left | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nX Y Z X' Y' Z' : C\niX : X ≅ X'\niY : Y ≅ Y'\niZ : Z ≅ Z'\nf : X ⟶ Z\ng : Y ⟶ Z\nf' : X' ⟶ Z'\ng' : Y' ⟶ Z'\nwf : iX.hom ≫ f' = f ≫ iZ.hom\nwg : iY.hom ≫ g' = g ≫ iZ.hom\n⊢ (cospanExt iX iY iZ wf ... | [
401,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
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src/lean/Init/Core.lean | Ne.irrefl | [] | [
573,
47
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
573,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.spanCompIso_hom_app_right | [] | [
360,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/Order/GaloisConnection.lean | sInf_image2_eq_sInf_sInf | [
{
"state_after": "no goals",
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405,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
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Mathlib/Data/Fin/Basic.lean | Fin.pos_iff_nonempty | [] | [
154,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
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Mathlib/CategoryTheory/Generator.lean | CategoryTheory.isSeparating_unop_iff | [
{
"state_after": "no goals",
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"tactic": "rw [← isCoseparating_op_iff, Set.unop_op]"
}
] | [
116,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Computability/Encoding.lean | Computability.decode_encodeBool | [] | [
225,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Analysis/InnerProductSpace/Orientation.lean | Orientation.abs_volumeForm_apply_of_orthonormal | [
{
"state_after": "no goals",
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"tactic": "simpa [o.volumeForm_robust' v v] using ... | [
318,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
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Mathlib/Topology/MetricSpace/Infsep.lean | Set.Finite.einfsep | [
{
"state_after": "α : Type u_1\nβ : Type ?u.33000\ninst✝ : EDist α\nx y : α\ns t : Set α\nhs : Set.Finite s\nx✝ : ℝ≥0∞\n⊢ x✝ ≤ Set.einfsep s ↔ x✝ ≤ Finset.inf (Finite.toFinset (_ : Set.Finite (offDiag s))) (uncurry edist)",
"state_before": "α : Type u_1\nβ : Type ?u.33000\ninst✝ : EDist α\nx y : α\ns t : Se... | [
186,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/ModelTheory/Definability.lean | FirstOrder.Language.DefinableSet.not_mem_bot | [] | [
319,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Mathlib/Init/Algebra/Classes.lean | isStrictWeakOrder_of_isTotalPreorder | [] | [
390,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.map | [
{
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792,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
791,
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Mathlib/CategoryTheory/Limits/IsLimit.lean | CategoryTheory.Limits.IsLimit.lift_comp_conePointUniqueUpToIso_hom | [
{
"state_after": "no goals",
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"tactic": "simp... | [
173,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
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Mathlib/Topology/Instances/ENNReal.lean | Real.ediam_Icc | [
{
"state_after": "case inl\nα : Type ?u.556633\nβ : Type ?u.556636\nγ : Type ?u.556639\ninst✝ : PseudoEMetricSpace α\na b : ℝ\nh : a ≤ b\n⊢ EMetric.diam (Icc a b) = ENNReal.ofReal (b - a)\n\ncase inr\nα : Type ?u.556633\nβ : Type ?u.556636\nγ : Type ?u.556639\ninst✝ : PseudoEMetricSpace α\na b : ℝ\nh : b < a\n⊢... | [
1540,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1537,
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Mathlib/Computability/Halting.lean | Nat.Partrec'.bind | [
{
"state_after": "case refine'_2\nn : ℕ\nf : Vector ℕ n →. ℕ\ng : Vector ℕ (n + 1) →. ℕ\nhf : Partrec' f\nhg : Partrec' g\ni✝ : Fin (n + 1)\ni : Fin n\n⊢ Partrec' fun v => Part.some (Vector.get v i)",
"state_before": "n : ℕ\nf : Vector ℕ n →. ℕ\ng : Vector ℕ (n + 1) →. ℕ\nhf : Partrec' f\nhg : Partrec' g\ni... | [
331,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
11
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Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.ext | [] | [
173,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.map_disjUnion | [] | [
203,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieEquiv.injective | [] | [
666,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
665,
11
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.induction_on | [] | [
190,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.norm_sq_re_add_conj | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nE : Type ?u.7033014\ninst✝ : IsROrC K\nx : K\n⊢ ‖x + ↑(starRingEnd K) x‖ ^ 2 = ↑re (x + ↑(starRingEnd K) x) ^ 2",
"tactic": "rw [add_conj, ← ofReal_ofNat, ← ofReal_mul, norm_ofReal, sq_abs, ofReal_re]"
}
] | [
766,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
765,
1
] |
Mathlib/Analysis/SpecialFunctions/NonIntegrable.lean | not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_filter | [
{
"state_after": "E : Type u_1\nF : Type u_2\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : SecondCountableTopology E\ninst✝³ : CompleteSpace E\ninst✝² : NormedAddCommGroup F\nf : ℝ → E\ng : ℝ → F\na b : ℝ\nl : Filter ℝ\ninst✝¹ : NeBot l\ninst✝ : TendstoIxxClass Icc l l\nhl : [[a, b]] ∈ l\nh... | [
98,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
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