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/MeasureTheory/Measure/Regular.lean | MeasureTheory.Measure.InnerRegular.isCompact_isClosed | [
{
"state_after": "α : Type ?u.57900\nβ : Type ?u.57903\ninst✝⁴ : MeasurableSpace α\ninst✝³ : TopologicalSpace α\nμ✝ : Measure α\np q : Set α → Prop\nU s : Set α\nε r✝ : ℝ≥0∞\nX : Type u_1\ninst✝² : TopologicalSpace X\ninst✝¹ : SigmaCompactSpace X\ninst✝ : MeasurableSpace X\nμ : Measure X\nF : Set X\nhF : IsClos... | [
463,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
Mathlib/Algebra/Category/ModuleCat/Projective.lean | ModuleCat.projective_of_free | [] | [
55,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.smul_finset_symmDiff | [] | [
2004,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2003,
1
] |
Mathlib/Order/Monotone/Monovary.lean | Monovary.symm | [] | [
383,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
11
] |
Mathlib/Topology/Connected.lean | connectedComponents_lift_unique' | [] | [
1520,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1518,
1
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Mathlib/Logic/Basic.lean | exists_or_eq_left' | [] | [
796,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
9
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Mathlib/MeasureTheory/Constructions/Pi.lean | generateFrom_pi_eq | [
{
"state_after": "case intro\nι : Type u_2\nι' : Type ?u.642179\nα : ι → Type u_1\ninst✝¹ : Finite ι\ninst✝ : Finite ι'\nC : (i : ι) → Set (Set (α i))\nhC : ∀ (i : ι), IsCountablySpanning (C i)\nval✝ : Encodable ι\n⊢ MeasurableSpace.pi = generateFrom (Set.pi univ '' Set.pi univ C)",
"state_before": "ι : Typ... | [
131,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Data/Nat/Choose/Basic.lean | Nat.choose_one_right | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ choose n 1 = n",
"tactic": "induction n <;> simp [*, choose, add_comm]"
}
] | [
91,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Analysis/Convex/Between.lean | sbtw_comm | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nV : Type u_2\nV' : Type ?u.146841\nP : Type u_3\nP' : Type ?u.146847\ninst✝⁶ : OrderedRing R\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module R V\ninst✝³ : AddTorsor V P\ninst✝² : AddCommGroup V'\ninst✝¹ : Module R V'\ninst✝ : AddTorsor V' P'\nx y z : P\n... | [
282,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/Data/Finset/Sort.lean | Finset.orderEmbOfFin_last | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.44950\ninst✝ : LinearOrder α\ns : Finset α\nk : ℕ\nh : card s = k\nhz : 0 < k\n⊢ ↑(orderEmbOfFin s h) { val := k - 1, isLt := (_ : k - 1 < k) } = max' s (_ : Finset.Nonempty s)",
"tactic": "simp [orderEmbOfFin_apply, max'_eq_sorted_... | [
204,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
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Mathlib/LinearAlgebra/TensorProduct.lean | LinearMap.lTensor_add | [] | [
1038,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1037,
1
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Mathlib/Order/ConditionallyCompleteLattice/Finset.lean | Set.Nonempty.cInf_mem | [] | [
67,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/LinearAlgebra/Matrix/Hermitian.lean | Matrix.IsHermitian.ext | [
{
"state_after": "α : Type u_2\nβ : Type ?u.2918\nm : Type ?u.2921\nn : Type u_1\nA✝ : Matrix n n α\ninst✝¹ : Star α\ninst✝ : Star β\nA : Matrix n n α\nh : ∀ (i j : n), star (A j i) = A i j\n⊢ IsHermitian A",
"state_before": "α : Type u_2\nβ : Type ?u.2918\nm : Type ?u.2921\nn : Type u_1\nA✝ : Matrix n n α\... | [
57,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
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Mathlib/Order/Hom/Basic.lean | WithTop.toDualBotEquiv_symm_top | [] | [
1301,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1300,
1
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Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.center_toSubsemiring | [] | [
1354,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1353,
1
] |
Mathlib/Topology/Order/Basic.lean | tendsto_nhds_bot_mono | [] | [
1170,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1168,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.integral_comp_smul_deriv_Ioi | [
{
"state_after": "E : Type u_1\nf✝ : ℝ → E\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\nf f' : ℝ → ℝ\ng : ℝ → E\na : ℝ\nhf : ContinuousOn f (Ici a)\nhft : Tendsto f atTop atTop\nhff' : ∀ (x : ℝ), x ∈ Ioi a → HasDerivWithinAt f (f' x) (Ioi x) x\nhg_cont : ContinuousOn g (f '... | [
832,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
808,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPullback.isoPullback_hom_fst | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\nP X Y Z : C\nfst : P ⟶ X\nsnd : P ⟶ Y\nf : X ⟶ Z\ng : Y ⟶ Z\nh : IsPullback fst snd f g\ninst✝ : HasPullback f g\n⊢ (limit.isoLimitCone { cone := PullbackCone.mk fst snd (_ : fst ≫ f = snd ≫ g), isLimit := isLimit h }).inv ≫\n pullback.fst =\n fst",
... | [
291,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
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Mathlib/RingTheory/Subsemiring/Basic.lean | RingHom.rangeS_eq_map | [
{
"state_after": "case h\nR : Type u\nS : Type v\nT : Type w\ninst✝² : NonAssocSemiring R\nM : Submonoid R\ninst✝¹ : NonAssocSemiring S\ninst✝ : NonAssocSemiring T\ng : S →+* T\nf✝ f : R →+* S\nx✝ : S\n⊢ x✝ ∈ rangeS f ↔ x✝ ∈ Subsemiring.map f ⊤",
"state_before": "R : Type u\nS : Type v\nT : Type w\ninst✝² :... | [
613,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
611,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.dropn_add | [] | [
737,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
735,
1
] |
Mathlib/Data/Set/Intervals/OrdConnectedComponent.lean | Set.ordConnectedComponent_inter | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrder α\ns✝ t✝ : Set α\nx✝ y z : α\ns t : Set α\nx : α\n⊢ ordConnectedComponent (s ∩ t) x = ordConnectedComponent s x ∩ ordConnectedComponent t x",
"tactic": "simp [ordConnectedComponent, setOf_and]"
}
] | [
81,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.castSucc_one | [] | [
1281,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1280,
1
] |
Mathlib/Algebra/Group/Commute.lean | Commute.units_inv_left | [] | [
235,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | rank_eq_zero | [
{
"state_after": "no goals",
"state_before": "K : Type u\nV : Type v\ninst✝² : DivisionRing K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nS : Submodule K V\nh : S = ⊥\n⊢ Module.rank K { x // x ∈ S } = 0",
"tactic": "rw [h, rank_bot]"
}
] | [
679,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
673,
1
] |
Mathlib/Topology/MetricSpace/Contracting.lean | ContractingWith.fixedPoint_unique' | [] | [
289,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biproduct.conePointUniqueUpToIso_hom | [] | [
889,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
886,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mk_list_eq_mk | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Infinite α\nH1 : ℵ₀ ≤ (#α)\nx✝ : α\n⊢ ∀ ⦃a₂ : α⦄, (fun a => [a]) x✝ = (fun a => [a]) a₂ → x✝ = a₂",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Infinite α\nH1 : ℵ₀ ≤ (#α)\n⊢ (sum fun x... | [
1000,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
993,
1
] |
Mathlib/Deprecated/Group.lean | MonoidHom.coe_of | [] | [
129,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.const_apply | [] | [
236,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalMaxOn.on_subset | [] | [
112,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.factorization_lcm | [
{
"state_after": "a b : ℕ\nha : a ≠ 0\nhb : b ≠ 0\n⊢ factorization a + factorization b = factorization a ⊓ factorization b + factorization a ⊔ factorization b",
"state_before": "a b : ℕ\nha : a ≠ 0\nhb : b ≠ 0\n⊢ factorization (lcm a b) = factorization a ⊔ factorization b",
"tactic": "rw [← add_right_in... | [
698,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
692,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.pow_succ' | [
{
"state_after": "no goals",
"state_before": "m n : Nat\n⊢ m ^ succ n = m * m ^ n",
"tactic": "rw [Nat.pow_succ, Nat.mul_comm]"
}
] | [
795,
34
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
794,
1
] |
Mathlib/Analysis/LocallyConvex/Basic.lean | absorbent_iff_forall_absorbs_singleton | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\n𝕝 : Type ?u.6901\nE : Type u_2\nι : Sort ?u.6907\nκ : ι → Sort ?u.6912\ninst✝¹ : SeminormedRing 𝕜\ninst✝ : SMul 𝕜 E\ns t u v A B : Set E\n⊢ Absorbent 𝕜 A ↔ ∀ (x : E), Absorbs 𝕜 A {x}",
"tactic": "simp_rw [Absorbs, Absorbent, singleton_sub... | [
137,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Data/Sigma/Basic.lean | Function.Injective.sigma_map | [
{
"state_after": "α : Type ?u.6398\nα₁ : Type u_1\nα₂ : Type u_2\nβ : α → Type ?u.6409\nβ₁ : α₁ → Type u_3\nβ₂ : α₂ → Type u_4\nf₁ : α₁ → α₂\nf₂ : (a : α₁) → β₁ a → β₂ (f₁ a)\nh₁ : Injective f₁\nh₂ : ∀ (a : α₁), Injective (f₂ a)\ni : α₁\nx y : β₁ i\nh : Sigma.map f₁ f₂ { fst := i, snd := x } = Sigma.map f₁ f₂ {... | [
119,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean | MvPolynomial.IsWeightedHomogeneous.inj_right | [
{
"state_after": "case intro\nR : Type u_1\nM : Type u_3\ninst✝¹ : CommSemiring R\nσ : Type u_2\ninst✝ : AddCommMonoid M\nφ ψ : MvPolynomial σ R\nm n : M\nw : σ → M\nhφ : φ ≠ 0\nhm : IsWeightedHomogeneous w φ m\nhn : IsWeightedHomogeneous w φ n\nd : σ →₀ ℕ\nhd : coeff d φ ≠ 0\n⊢ m = n",
"state_before": "R :... | [
261,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.le_floor_iff' | [
{
"state_after": "case inl\nF : Type ?u.28566\nα : Type u_1\nβ : Type ?u.28572\ninst✝¹ : LinearOrderedSemiring α\ninst✝ : FloorSemiring α\na : α\nn : ℕ\nhn : n ≠ 0\nha : a ≤ 0\n⊢ n ≤ ⌊a⌋₊ ↔ ↑n ≤ a\n\ncase inr\nF : Type ?u.28566\nα : Type u_1\nβ : Type ?u.28572\ninst✝¹ : LinearOrderedSemiring α\ninst✝ : FloorSem... | [
201,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.forall_fin_succ | [] | [
1751,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1750,
1
] |
Std/Data/Int/DivMod.lean | Int.mul_ediv_mul_of_pos | [
{
"state_after": "a b c : Int\nthis : ∀ (m k : Nat) (b : Int), ↑(succ m) * b / (↑(succ m) * ↑k) = b / ↑k\nm k : Nat\nH : 0 < ↑(succ m)\n⊢ -(↑(succ m) * b / (↑(succ m) * ↑k)) = -(b / ↑k)",
"state_before": "a b c : Int\nthis : ∀ (m k : Nat) (b : Int), ↑(succ m) * b / (↑(succ m) * ↑k) = b / ↑k\nm k : Nat\nH : ... | [
536,
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] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
514,
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] |
Mathlib/Data/PEquiv.lean | PEquiv.trans_refl | [
{
"state_after": "case h.a\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nf : α ≃. β\nx✝ : α\na✝ : β\n⊢ a✝ ∈ ↑(PEquiv.trans f (PEquiv.refl β)) x✝ ↔ a✝ ∈ ↑f x✝",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nf : α ≃. β\n⊢ PEquiv.trans f (PEquiv.refl β) = f",
"tactic": "ext"
},
{
... | [
174,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
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] |
Mathlib/Data/Sum/Basic.lean | Sum.lex_inr_inl | [] | [
493,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
1
] |
Std/Logic.lean | Decidable.not_iff_comm | [
{
"state_after": "a b : Prop\ninst✝¹ : Decidable a\ninst✝ : Decidable b\n⊢ (¬a → b) ∧ (b → ¬a) ↔ (¬b → a) ∧ (a → ¬b)",
"state_before": "a b : Prop\ninst✝¹ : Decidable a\ninst✝ : Decidable b\n⊢ (¬a ↔ b) ↔ (¬b ↔ a)",
"tactic": "rw [@iff_def (¬a), @iff_def (¬b)]"
},
{
"state_after": "no goals",
... | [
580,
79
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
579,
1
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Mathlib/Algebra/Order/Group/Defs.lean | div_le_div_right' | [] | [
722,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
721,
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] |
Mathlib/Topology/Algebra/Group/Basic.lean | Filter.HasBasis.nhds_of_one | [
{
"state_after": "α : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝³ : TopologicalSpace G\ninst✝² : Group G\ninst✝¹ : TopologicalGroup G\ninst✝ : TopologicalSpace α\nf : α → G\ns✝ : Set α\nx✝ : α\nι : Sort u_1\np : ι → Prop\ns : ι → Set G\nhb : HasBasis (𝓝 1) p s\nx : G\n⊢ HasBasis (Filter.comap (fun y => ... | [
847,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
842,
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Mathlib/Order/Ideal.lean | Order.Ideal.coe_sup | [] | [
407,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
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] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | Antitone.mul_strictAnti' | [] | [
1499,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1495,
1
] |
Mathlib/Data/List/Basic.lean | List.take_append_eq_append_take | [
{
"state_after": "case nil\nι : Type ?u.163016\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂✝ l₂ : List α\nn : ℕ\n⊢ take n ([] ++ l₂) = take n [] ++ take (n - length []) l₂\n\ncase cons\nι : Type ?u.163016\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂✝ l₂ : List α\nhead✝ : α\ntail✝ : List α\nt... | [
1976,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1973,
1
] |
Mathlib/Control/Fold.lean | Traversable.foldrm.ofFreeMonoid_comp_of | [
{
"state_after": "case h\nα β γ : Type u\nt : Type u → Type u\ninst✝³ : Traversable t\ninst✝² : IsLawfulTraversable t\nm : Type u → Type u\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nf : β → α → m α\nx✝ : β\n⊢ (↑(foldrM.ofFreeMonoid f) ∘ FreeMonoid.of) x✝ = (foldrM.mk ∘ f) x✝",
"state_before": "α β γ : Type u... | [
333,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.eval₂_X | [
{
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"tactic": "simp... | [
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1
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Mathlib/Data/List/Zip.lean | List.zipWith_distrib_drop | [
{
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491,
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Mathlib/FieldTheory/Finite/Polynomial.lean | MvPolynomial.rank_R | [
{
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{
"state_after": "σ K ... | [
225,
54
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209,
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Mathlib/Data/Nat/Factors.lean | Nat.prime_of_mem_factors | [
{
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Mathlib/Algebra/Ring/Units.lean | Units.divp_add_divp_same | [
{
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] | [
64,
28
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63,
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Std/Data/Array/Init/Lemmas.lean | Array.toListRev_eq | [
{
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102,
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101,
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Mathlib/CategoryTheory/LiftingProperties/Adjunction.lean | CategoryTheory.Adjunction.hasLiftingProperty_iff | [
{
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137,
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131,
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Mathlib/Data/Matrix/Hadamard.lean | Matrix.hadamard_apply | [] | [
56,
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Ico_eq_empty_iff | [
{
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"tactic": "rw [← not_nonempty_iff_eq_empty, not_iff_not, nonempty_Ico]"
}
] | [
687,
62
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686,
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Mathlib/Data/PFunctor/Multivariate/W.lean | MvPFunctor.wpRec_eq | [] | [
168,
91
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165,
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.cons_copy | [
{
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165,
6
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162,
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Mathlib/Data/Set/Functor.lean | Set.fmap_eq_image | [] | [
42,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/BigOperators/Finprod.lean | finprod_emb_domain' | [
{
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Mathlib/Algebra/GeomSum.lean | Commute.mul_neg_geom_sum₂ | [
{
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183,
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.adj_incidenceSet_inter | [
{
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... | [
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42
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Mathlib/Data/Polynomial/Coeff.lean | Polynomial.int_cast_inj | [
{
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406,
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400,
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Mathlib/Order/Filter/Interval.lean | Filter.Tendsto.uIcc | [] | [
275,
72
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Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.IsAlt.isRefl | [
{
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285,
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Mathlib/Order/Concept.lean | Concept.sup_snd | [] | [
337,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
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Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ioc_insert_left | [
{
"state_after": "no goals",
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"tactic": "rw [← coe_inj, coe_insert, coe_Ioc, coe_Icc, Set.insert_eq, Set.union_comm, Set.... | [
571,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
570,
1
] |
Mathlib/Analysis/Complex/Circle.lean | coe_div_circle | [] | [
90,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
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Mathlib/Data/Fin/VecNotation.lean | Matrix.empty_val' | [] | [
160,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
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Mathlib/Data/Sum/Interval.lean | Sum.Icc_inr_inl | [] | [
179,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
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Mathlib/Algebra/Order/CompleteField.lean | LinearOrderedField.inducedMap_zero | [
{
"state_after": "no goals",
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"tactic":... | [
205,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
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Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.order_mul | [
{
"state_after": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nφ ψ : PowerSeries R\n⊢ multiplicity X (φ * ψ) = multiplicity X φ + multiplicity X ψ",
"state_before": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nφ ψ : PowerSeries R\n⊢ order (φ * ψ) = order φ + order ψ",
"tactic": "sim... | [
2515,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2513,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | Filter.EventuallyEq.fderiv_eq | [
{
"state_after": "no goals",
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976,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
975,
1
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Mathlib/MeasureTheory/MeasurableSpaceDef.lean | Set.Finite.measurableSet | [] | [
310,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Analysis/SpecificLimits/Basic.lean | hasSum_geometric_two | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.75182\nβ : Type ?u.75185\nι : Type ?u.75188\n⊢ HasSum (fun n => (1 / 2) ^ n) 2",
"tactic": "convert hasSum_geometric_of_lt_1 _ _ <;> norm_num"
}
] | [
201,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.BoundedFormula.not_ex_isAtomic | [
{
"state_after": "no goals",
"state_before": "L : Language\nL' : Language\nM : Type w\nN : Type ?u.110112\nP : Type ?u.110115\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nγ : Type ?u.110143\nn l : ℕ\nφ✝ ψ : BoundedFormula L α l\nθ : BoundedFormula L α (Na... | [
691,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
] |
Mathlib/Order/Hom/Lattice.lean | BoundedLatticeHom.coe_comp_inf_hom' | [] | [
1329,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1327,
1
] |
Mathlib/Data/Set/Intervals/WithBotTop.lean | WithBot.preimage_coe_Ioi | [] | [
149,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Combinatorics/SetFamily/Intersecting.lean | Set.Intersecting.ne_bot | [] | [
57,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Order/Lattice.lean | le_sup_right | [] | [
143,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Data/Complex/Module.lean | realPart_apply_coe | [
{
"state_after": "A : Type u_1\ninst✝³ : AddCommGroup A\ninst✝² : Module ℂ A\ninst✝¹ : StarAddMonoid A\ninst✝ : StarModule ℂ A\na : A\n⊢ ↑(↑(selfAdjointPart ℝ) a) = 2⁻¹ • (a + star a)",
"state_before": "A : Type u_1\ninst✝³ : AddCommGroup A\ninst✝² : Module ℂ A\ninst✝¹ : StarAddMonoid A\ninst✝ : StarModule ... | [
457,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
1
] |
Mathlib/Data/Real/Cardinality.lean | Cardinal.mk_Iio_real | [
{
"state_after": "c : ℝ\nf g : ℕ → Bool\nn : ℕ\na : ℝ\n⊢ 𝔠 ≤ (#↑(Iio a))",
"state_before": "c : ℝ\nf g : ℕ → Bool\nn : ℕ\na : ℝ\n⊢ (#↑(Iio a)) = 𝔠",
"tactic": "refine' le_antisymm (mk_real ▸ mk_set_le _) _"
},
{
"state_after": "c : ℝ\nf g : ℕ → Bool\nn : ℕ\na : ℝ\nh2 : (fun x => a + a - x) '' ... | [
258,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.coe_add | [] | [
209,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.IsImage.symm_image_eq | [] | [
409,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.coe_injective | [] | [
1689,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1688,
1
] |
Mathlib/Data/Polynomial/Degree/Lemmas.lean | Polynomial.natDegree_sub_le_iff_left | [
{
"state_after": "R : Type u\nS : Type v\nι : Type w\na b : R\nm n : ℕ\ninst✝ : Ring R\np q : R[X]\nqn : natDegree (-q) ≤ n\n⊢ natDegree (p - q) ≤ n ↔ natDegree p ≤ n",
"state_before": "R : Type u\nS : Type v\nι : Type w\na b : R\nm n : ℕ\ninst✝ : Ring R\np q : R[X]\nqn : natDegree q ≤ n\n⊢ natDegree (p - q... | [
303,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Std/Logic.lean | or_iff_left | [] | [
301,
75
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
301,
1
] |
Mathlib/Data/Rat/Defs.lean | Rat.num_ne_zero_of_ne_zero | [] | [
426,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/LinearAlgebra/Ray.lean | sameRay_smul_left_iff | [] | [
547,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.sup_eq_lsub | [] | [
1585,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1583,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.exists_concat_eq_cons | [] | [
317,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/CategoryTheory/Functor/LeftDerived.lean | CategoryTheory.NatTrans.leftDerived_id | [
{
"state_after": "C : Type u\ninst✝¹² : Category C\nD : Type u_2\ninst✝¹¹ : Category D\ninst✝¹⁰ : Preadditive C\ninst✝⁹ : HasZeroObject C\ninst✝⁸ : HasEqualizers C\ninst✝⁷ : HasImages C\ninst✝⁶ : HasProjectiveResolutions C\ninst✝⁵ : Preadditive D\ninst✝⁴ : HasEqualizers D\ninst✝³ : HasCokernels D\ninst✝² : HasI... | [
142,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/GroupTheory/GroupAction/Quotient.lean | Subgroup.normalCore_eq_ker | [
{
"state_after": "case a\nα : Type u\nβ : Type v\nγ : Type w\nG : Type u_1\ninst✝ : Group G\nH : Subgroup G\n⊢ normalCore H ≤ MonoidHom.ker (MulAction.toPermHom G (G ⧸ H))\n\ncase a\nα : Type u\nβ : Type v\nγ : Type w\nG : Type u_1\ninst✝ : Group G\nH : Subgroup G\n⊢ MonoidHom.ker (MulAction.toPermHom G (G ⧸ H)... | [
370,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/CategoryTheory/Monoidal/Opposite.lean | CategoryTheory.mop_tensorObj | [] | [
211,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/CategoryTheory/Limits/Opposites.lean | CategoryTheory.Limits.pushoutIsoUnopPullback_inl_hom | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝³ : Category C\nJ : Type u₂\ninst✝² : Category J\nX✝ : Type v₂\nX Y Z : C\nf : X ⟶ Z\ng : X ⟶ Y\ninst✝¹ : HasPushout f g\ninst✝ : HasPullback f.op g.op\n⊢ (PullbackCone.unop (limit.cone (cospan f.op g.op))).ι.app WalkingSpan.left = pullback.fst... | [
682,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
678,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.range_normSq | [
{
"state_after": "no goals",
"state_before": "x : ℝ\nhx : x ∈ Ici 0\n⊢ ↑normSq ↑(Real.sqrt x) = x",
"tactic": "rw [normSq_ofReal, Real.mul_self_sqrt hx]"
}
] | [
632,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.degreeOf_mul_X_eq | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.318009\nr : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝ : CommSemiring R\np q : MvPolynomial σ R\nj : σ\nf : MvPolynomial σ R\n⊢ degreeOf j (f * X j) ≤ degreeOf j f + 1",
"tactic": "classical\nrepeat' rw [degreeOf]\... | [
575,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
1
] |
Mathlib/Topology/Order/Basic.lean | right_nhdsWithin_Ico_neBot | [] | [
2430,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2429,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.L1.SimpleFunc.integral_eq_norm_posPart_sub | [
{
"state_after": "α : Type u_1\nE : Type ?u.361821\nF : Type ?u.361824\n𝕜 : Type ?u.361827\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedAddCommGroup F\nm : MeasurableSpace α\nμ : Measure α\ninst✝⁸ : NormedField 𝕜\ninst✝⁷ : NormedSpace 𝕜 E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : SMulCommClass ℝ 𝕜 E\nF' : Type... | [
636,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
615,
1
] |
Mathlib/Data/PFunctor/Univariate/M.lean | PFunctor.M.dest_corec | [
{
"state_after": "no goals",
"state_before": "F : PFunctor\nX : Type ?u.72575\nf : X → Obj F X\nP : PFunctor\nα : Type u\ng : α → Obj P α\nx : α\n⊢ dest (M.corec g x) = M.corec g <$> g x",
"tactic": "rw [corec_def, dest_mk]"
}
] | [
724,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
723,
1
] |
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