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/MeasureSpace.lean | MeasureTheory.Measure.ae_sum_eq | [] | [
2091,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2090,
1
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Mathlib/Data/Finset/Image.lean | Function.Commute.finset_map | [] | [
153,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Logic/Basic.lean | forall_imp_iff_exists_imp | [
{
"state_after": "ι : Sort ?u.14066\nα : Sort u_1\nκ : ι → Sort ?u.14068\np q : α → Prop\nb : Prop\nha : Nonempty α\na : α\n⊢ (∀ (x : α), p x) → b ↔ ∃ x, p x → b",
"state_before": "ι : Sort ?u.14066\nα : Sort u_1\nκ : ι → Sort ?u.14068\np q : α → Prop\nb : Prop\nha : Nonempty α\n⊢ (∀ (x : α), p x) → b ↔ ∃ x... | [
710,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
707,
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Mathlib/Analysis/Calculus/ContDiff.lean | ContDiff.prod_map | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹⁴ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝¹³ : NormedAddCommGroup D\ninst✝¹² : NormedSpace 𝕜 D\nE : Type uE\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁹ : NormedAddCommGroup F\ninst✝⁸ : NormedSpace 𝕜 F\nG : Type uG\ninst✝⁷ : No... | [
1635,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1632,
1
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Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.bind₁_comp_rename | [
{
"state_after": "case hf\nσ : Type u_3\nτ : Type u_4\nR : Type u_2\nS : Type ?u.645310\nT : Type ?u.645313\ninst✝² : CommSemiring R\ninst✝¹ : CommSemiring S\ninst✝ : CommSemiring T\nf✝ : σ → MvPolynomial τ R\nυ : Type u_1\nf : τ → MvPolynomial υ R\ng : σ → τ\ni : σ\n⊢ ↑(AlgHom.comp (bind₁ f) (rename g)) (X i) ... | [
268,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
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Mathlib/GroupTheory/Submonoid/Operations.lean | OneMemClass.coe_one | [] | [
522,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
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Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.IntegrableOn.integrable | [] | [
105,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
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Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.smul_mk | [] | [
383,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.inl_inr_pushoutAssoc_inv | [
{
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"state_before": "C : Type u\ninst✝⁵ : Category C\nD : Type u₂\ninst✝⁴ : Category D\nW X Y Z X₁ X₂ X₃ Z₁ Z₂ : C\ng₁ : Z₁ ⟶ X₁\ng₂ : Z₁ ⟶ X₂\ng₃ : Z₂ ⟶ X₂\ng₄ : Z₂ ⟶ X₃\ninst✝³ : HasPushout g₁ g₂\ninst✝² : HasPushout g₃ g₄\ninst✝¹ : HasPushout (g₃ ≫ pushout.inr) g₄\ninst✝ : HasPus... | [
2644,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2641,
1
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Mathlib/Data/Int/Log.lean | Int.neg_log_inv_eq_clog | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹ : LinearOrderedSemifield R\ninst✝ : FloorSemiring R\nb : ℕ\nr : R\n⊢ -log b r⁻¹ = clog b r",
"tactic": "rw [log_inv, neg_neg]"
}
] | [
227,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.floor_eq_iff | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.36879\nα : Type u_1\nβ : Type ?u.36885\ninst✝¹ : LinearOrderedSemiring α\ninst✝ : FloorSemiring α\na : α\nn : ℕ\nha : 0 ≤ a\n⊢ ⌊a⌋₊ = n ↔ ↑n ≤ a ∧ a < ↑n + 1",
"tactic": "rw [← le_floor_iff ha, ← Nat.cast_one, ← Nat.cast_add, ← floor_lt ha, Nat.l... | [
242,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.SimpleFunc.coe_toLargerSpace_eq | [] | [
1738,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1737,
1
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Mathlib/Data/Nat/Bits.lean | Nat.div2_bit1 | [] | [
62,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.neg_im | [] | [
256,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
9
] |
Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.lower_mem_Icc | [] | [
216,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
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Mathlib/Order/Filter/Basic.lean | Filter.EventuallyEq.exists_mem | [] | [
1460,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1458,
1
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Mathlib/Order/Disjoint.lean | codisjoint_self | [] | [
266,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.IsEquivalence.ofIso_refl | [
{
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650,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
645,
1
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.le_iff_mem_closure | [
{
"state_after": "R : Type u_1\nA : Type u_2\ninst✝³ : CommSemiring R\ninst✝² : CommRing A\ninst✝¹ : Algebra R A\n𝒜 : ℕ → Submodule R A\ninst✝ : GradedAlgebra 𝒜\nx y : ProjectiveSpectrum 𝒜\n⊢ x.asHomogeneousIdeal ≤ y.asHomogeneousIdeal ↔ ↑x.asHomogeneousIdeal ⊆ ↑y.asHomogeneousIdeal",
"state_before": "R ... | [
502,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
] |
Mathlib/Data/Nat/PSub.lean | Nat.ppred_eq_some | [
{
"state_after": "no goals",
"state_before": "m : ℕ\n⊢ ppred 0 = some m ↔ succ m = 0",
"tactic": "constructor <;> intro h <;> contradiction"
},
{
"state_after": "no goals",
"state_before": "m n : ℕ\n⊢ ppred (n + 1) = some m ↔ succ m = n + 1",
"tactic": "constructor <;> intro h <;> inject... | [
68,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/LinearAlgebra/Orientation.lean | Orientation.map_eq_iff_det_pos | [
{
"state_after": "case inl\nR : Type u_1\ninst✝³ : LinearOrderedField R\nM : Type u_2\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\nι : Type u_3\ninst✝ : Fintype ι\n_i : FiniteDimensional R M\nx : Orientation R M ι\nf : M ≃ₗ[R] M\nh : Fintype.card ι = finrank R M\nh✝ : IsEmpty ι\n⊢ ↑(map ι f) x = x ↔ 0 < ↑Line... | [
379,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Std/Data/Int/DivMod.lean | Int.div_def' | [] | [
82,
83
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
81,
9
] |
Mathlib/RingTheory/JacobsonIdeal.lean | Ideal.jacobson_mono | [
{
"state_after": "R : Type u\nS : Type v\ninst✝¹ : Ring R\ninst✝ : Ring S\nI✝ I J : Ideal R\nh : I ≤ J\nx : R\nhx : x ∈ jacobson I\n⊢ x ∈ jacobson J",
"state_before": "R : Type u\nS : Type v\ninst✝¹ : Ring R\ninst✝ : Ring S\nI✝ I J : Ideal R\n⊢ I ≤ J → jacobson I ≤ jacobson J",
"tactic": "intro h x hx"
... | [
237,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Order/Filter/Cofinite.lean | Filter.Tendsto.exists_forall_ge | [] | [
189,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Data/Setoid/Partition.lean | Setoid.mem_classes | [] | [
78,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Computability/PartrecCode.lean | Nat.Partrec.Code.comp_prim | [] | [
256,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.mem_span_singleton_self | [] | [
503,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | Filter.Tendsto.op_one_isBoundedUnder_le | [] | [
1178,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1175,
1
] |
Mathlib/CategoryTheory/Closed/Monoidal.lean | CategoryTheory.MonoidalClosed.curry_eq_iff | [] | [
212,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Std/Data/String/Lemmas.lean | String.Pos.mk_zero | [] | [
88,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
88,
9
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContinuousLinearEquiv.iteratedFDerivWithin_comp_right | [
{
"state_after": "case zero\n𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝⁹ : NormedAddCommGroup D\ninst✝⁸ : NormedSpace 𝕜 D\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst... | [
436,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/Analysis/Calculus/Deriv/ZPow.lean | Differentiable.zpow | [] | [
173,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | nsmul_eq_mul' | [
{
"state_after": "no goals",
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"tactic": "induction' n with n ih <;> [rw [zero_nsmul, Nat.cast_zero, mul_zero]... | [
505,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.updateRow_transpose | [
{
"state_after": "case a.h\nl : Type ?u.1225606\nm : Type u_2\nn : Type u_1\no : Type ?u.1225615\nm' : o → Type ?u.1225620\nn' : o → Type ?u.1225625\nR : Type ?u.1225628\nS : Type ?u.1225631\nα : Type v\nβ : Type w\nγ : Type ?u.1225638\nM : Matrix m n α\ni : m\nj : n\nb : n → α\nc : m → α\ninst✝ : DecidableEq n... | [
2818,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2815,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Images.lean | CategoryTheory.Limits.IsImage.e_isoExt_inv | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX Y : C\nf : X ⟶ Y\nF F' : MonoFactorisation f\nhF : IsImage F\nhF' : IsImage F'\n⊢ F'.e ≫ (isoExt hF hF').inv = F.e",
"tactic": "simp"
}
] | [
232,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/GroupTheory/SpecificGroups/Quaternion.lean | QuaternionGroup.xa_pow_four | [
{
"state_after": "n : ℕ\ni : ZMod (2 * n)\n⊢ a (↑n + ↑n) = 1",
"state_before": "n : ℕ\ni : ZMod (2 * n)\n⊢ xa i ^ 4 = 1",
"tactic": "rw [pow_succ, pow_succ, sq, xa_mul_xa, xa_mul_a, xa_mul_xa, add_sub_cancel, add_sub_assoc,\n add_sub_cancel']"
},
{
"state_after": "n : ℕ\ni : ZMod (2 * n)\n⊢ a ↑... | [
209,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.exists_mem_eq_sup | [] | [
1132,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1130,
1
] |
Mathlib/Order/Compare.lean | Ordering.swap_orElse | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.9939\nβ : Type ?u.9942\no₁ o₂ : Ordering\n⊢ swap (orElse o₁ o₂) = orElse (swap o₁) (swap o₂)",
"tactic": "cases o₁ <;> rfl"
}
] | [
145,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Algebra/GroupWithZero/Units/Basic.lean | IsUnit.mk0 | [] | [
253,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.mem_inf_iff_superset | [] | [
446,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | symmetrize_mono | [] | [
227,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.commute_of_normal_of_disjoint | [
{
"state_after": "case a\nG : Type u_1\nG' : Type ?u.717622\ninst✝³ : Group G\ninst✝² : Group G'\nA : Type ?u.717631\ninst✝¹ : AddGroup A\nN : Type ?u.717637\ninst✝ : Group N\nH₁ H₂ : Subgroup G\nhH₁ : Normal H₁\nhH₂ : Normal H₂\nhdis : Disjoint H₁ H₂\nx y : G\nhx : x ∈ H₁\nhy : y ∈ H₂\n⊢ x * y * x⁻¹ * y⁻¹ ∈ H₁... | [
3630,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3615,
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] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_const_mul_Ioi | [] | [
607,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
606,
1
] |
Mathlib/GroupTheory/SpecificGroups/Alternating.lean | alternatingGroup.normalClosure_swap_mul_swap_five | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.143668\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\n⊢ ↑sign (swap 0 4 * swap 1 3) = 1",
"tactic": "decide"
},
{
"state_after": "α : Type ?u.143668\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\ng1 : { x // x ∈ alternatingGroup (Fin 5) } :=\n ... | [
274,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/CategoryTheory/Monoidal/Opposite.lean | CategoryTheory.MonoidalOpposite.unmop_mop | [] | [
75,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Restrict.lean | AffineSubspace.nonempty_map | [
{
"state_after": "case intro.mk\nk : Type u_1\nV₁ : Type u_2\nP₁ : Type u_3\nV₂ : Type u_4\nP₂ : Type u_5\ninst✝⁶ : Ring k\ninst✝⁵ : AddCommGroup V₁\ninst✝⁴ : AddCommGroup V₂\ninst✝³ : Module k V₁\ninst✝² : Module k V₂\ninst✝¹ : AddTorsor V₁ P₁\ninst✝ : AddTorsor V₂ P₂\nE : AffineSubspace k P₁\nEne : Nonempty {... | [
39,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
] |
Mathlib/Data/Int/GCD.lean | Int.lcm_self | [
{
"state_after": "i : ℤ\n⊢ Nat.lcm (natAbs i) (natAbs i) = natAbs i",
"state_before": "i : ℤ\n⊢ lcm i i = natAbs i",
"tactic": "rw [Int.lcm]"
},
{
"state_after": "no goals",
"state_before": "i : ℤ\n⊢ Nat.lcm (natAbs i) (natAbs i) = natAbs i",
"tactic": "apply Nat.lcm_self"
}
] | [
480,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.aeval_unique | [
{
"state_after": "case hf\nR : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type u_1\na a' a₁ a₂ : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝³ : CommSemiring R\ninst✝² : CommSemiring S₁\np q : MvPolynomial σ R\ninst✝¹ : Algebra R S₁\ninst✝ : CommSemiring S₂\nf : σ → S₁\nφ : MvPolynomial σ R →ₐ[R] S₁\ni : σ\n⊢ ↑... | [
1455,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1453,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.lt_log_iff_exp_lt | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\nhy : 0 < y\n⊢ x < log y ↔ exp x < y",
"tactic": "rw [← exp_lt_exp, exp_log hy]"
}
] | [
167,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_same | [] | [
473,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | Submodule.coe_subtypeₗᵢ | [] | [
466,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/Topology/Instances/AddCircle.lean | AddCircle.equivIccQuot_comp_mk_eq_toIocMod | [
{
"state_after": "𝕜 : Type u_1\nB : Type ?u.328688\ninst✝³ : LinearOrderedAddCommGroup 𝕜\ninst✝² : TopologicalSpace 𝕜\ninst✝¹ : OrderTopology 𝕜\np a : 𝕜\nhp : Fact (0 < p)\ninst✝ : Archimedean 𝕜\n⊢ (fun x =>\n Quot.mk (EndpointIdent p a)\n { val := toIcoMod (_ : 0 < p) a x, property := (_ : to... | [
609,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
601,
1
] |
Mathlib/Order/Atoms.lean | IsSimpleOrder.eq_top_of_lt | [] | [
513,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
512,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.Bijective.of_comp_iff' | [] | [
272,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.norm_eq_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u\nL L₁ L₂ L₃ L₄ : List (α × Bool)\ninst✝ : DecidableEq α\nx : FreeGroup α\n⊢ norm x = 0 ↔ x = 1",
"tactic": "simp only [norm, List.length_eq_zero, toWord_eq_nil_iff]"
}
] | [
1417,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1416,
1
] |
Mathlib/Algebra/Lie/Free.lean | FreeLieAlgebra.Rel.subRight | [
{
"state_after": "no goals",
"state_before": "R : Type u\nX : Type v\ninst✝ : CommRing R\na b c : lib R X\nh : Rel R X a b\n⊢ Rel R X (a - c) (b - c)",
"tactic": "simpa only [sub_eq_add_neg] using h.add_right (-c)"
}
] | [
108,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/CategoryTheory/Monoidal/CoherenceLemmas.lean | CategoryTheory.MonoidalCategory.leftUnitor_tensor | [
{
"state_after": "no goals",
"state_before": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : MonoidalCategory C\nX Y : C\n⊢ (λ_ (X ⊗ Y)).hom = (α_ (𝟙_ C) X Y).inv ≫ ((λ_ X).hom ⊗ 𝟙 Y)",
"tactic": "coherence"
}
] | [
40,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.PushoutCocone.mk_ι_app_zero | [] | [
850,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
849,
1
] |
Mathlib/Data/Polynomial/Expand.lean | Polynomial.of_irreducible_expand | [] | [
286,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/Algebra/Hom/GroupAction.lean | MulSemiringActionHom.map_smul | [] | [
537,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
536,
11
] |
Mathlib/Topology/MetricSpace/GromovHausdorffRealized.lean | GromovHausdorff.candidatesBDist_mem_candidatesB | [] | [
234,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | mul_lt_of_lt_one_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na b c d : α\ninst✝³ : MulOneClass α\ninst✝² : Zero α\ninst✝¹ : Preorder α\ninst✝ : PosMulStrictMono α\nha : 0 < a\nh : b < 1\n⊢ a * b < a",
"tactic": "simpa only [mul_one] using mul_lt_mul_of_pos_left h ha"
}
] | [
694,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
693,
1
] |
Mathlib/Data/Set/Intervals/Pi.lean | Set.pi_univ_Iic | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : ι → Type u_2\ninst✝ : (i : ι) → Preorder (α i)\nx y✝ y : (i : ι) → α i\n⊢ (y ∈ pi univ fun i => Iic (x i)) ↔ y ∈ Iic x",
"tactic": "simp [Pi.le_def]"
}
] | [
42,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Algebra/Star/Unitary.lean | unitary.coe_neg | [] | [
197,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.image_add_left_Ioc | [
{
"state_after": "ι : Type ?u.239108\nα : Type u_1\ninst✝³ : OrderedCancelAddCommMonoid α\ninst✝² : ExistsAddOfLE α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : DecidableEq α\na b c : α\n⊢ image ((fun x x_1 => x + x_1) c) (Ioc a b) = image (↑(addLeftEmbedding c)) (Ioc a b)",
"state_before": "ι : Type ?u.239108\n... | [
1113,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1111,
1
] |
Mathlib/Analysis/InnerProductSpace/Orientation.lean | Orientation.volumeForm_robust_neg | [
{
"state_after": "case zero\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : InnerProductSpace ℝ E\n_i : Fact (finrank ℝ E = Nat.zero)\no : Orientation ℝ E (Fin Nat.zero)\nb : OrthonormalBasis (Fin Nat.zero) ℝ E\nhb : Basis.orientation (OrthonormalBasis.toBasis b) ≠ o\n⊢ volumeForm o = -Basis.det (Orthonor... | [
239,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.eval_nodal_derivative_eval_node_eq | [
{
"state_after": "F : Type u_2\ninst✝¹ : Field F\nι : Type u_1\ns : Finset ι\nv : ι → F\ni : ι\nr : ι → F\nx : F\ninst✝ : DecidableEq ι\nhi : i ∈ s\n⊢ ∑ x in Finset.erase s i, eval (v i) (nodal (Finset.erase s x) v) = 0",
"state_before": "F : Type u_2\ninst✝¹ : Field F\nι : Type u_1\ns : Finset ι\nv : ι → F... | [
555,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
550,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.logb_pos_of_base_lt_one | [
{
"state_after": "b x y : ℝ\nb_pos : 0 < b\nb_lt_one : b < 1\nhx : 0 < x\nhx' : x < 1\n⊢ x < 1",
"state_before": "b x y : ℝ\nb_pos : 0 < b\nb_lt_one : b < 1\nhx : 0 < x\nhx' : x < 1\n⊢ 0 < logb b x",
"tactic": "rw [logb_pos_iff_of_base_lt_one b_pos b_lt_one hx]"
},
{
"state_after": "no goals",
... | [
294,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Data/Int/GCD.lean | Int.lcm_zero_left | [
{
"state_after": "i : ℤ\n⊢ Nat.lcm (natAbs 0) (natAbs i) = 0",
"state_before": "i : ℤ\n⊢ lcm 0 i = 0",
"tactic": "rw [Int.lcm]"
},
{
"state_after": "no goals",
"state_before": "i : ℤ\n⊢ Nat.lcm (natAbs 0) (natAbs i) = 0",
"tactic": "apply Nat.lcm_zero_left"
}
] | [
456,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.ncard_exchange' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.21433\ns t : Set α\na b x y : α\nf : α → β\nha : ¬a ∈ s\nhb : b ∈ s\n⊢ ncard (insert a s \\ {b}) = ncard s",
"tactic": "rw [← ncard_exchange ha hb, ← singleton_union, ← singleton_union, union_diff_distrib,\n @diff_singleton_eq_self... | [
230,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Deriv.lean | Real.hasSum_pow_div_log_of_abs_lt_1 | [
{
"state_after": "x : ℝ\nh : abs x < 1\n⊢ Tendsto (fun n => ∑ i in Finset.range n, x ^ (i + 1) / (↑i + 1)) atTop (𝓝 (-log (1 - x)))\n\nx : ℝ\nh : abs x < 1\n⊢ Summable fun n => x ^ (n + 1) / (↑n + 1)",
"state_before": "x : ℝ\nh : abs x < 1\n⊢ HasSum (fun n => x ^ (n + 1) / (↑n + 1)) (-log (1 - x))",
"t... | [
294,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Algebra/Order/Floor.lean | round_two_inv | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.280191\nα : Type u_1\nβ : Type ?u.280197\ninst✝¹ : LinearOrderedField α\ninst✝ : FloorRing α\n⊢ round 2⁻¹ = 1",
"tactic": "simp only [round_eq, ← one_div, add_halves', floor_one]"
}
] | [
1454,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1453,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.Tendsto.atTop_mul_atBot | [
{
"state_after": "ι : Type ?u.196199\nι' : Type ?u.196202\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.196211\ninst✝ : StrictOrderedRing α\nl : Filter β\nf g : β → α\nhf : Tendsto f l atTop\nhg : Tendsto g l atBot\nthis : Tendsto (fun x => f x * (Neg.neg ∘ g) x) l atTop\n⊢ Tendsto (fun x => f x * g x) l atBot",
... | [
909,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
906,
1
] |
Mathlib/LinearAlgebra/TensorAlgebra/Basic.lean | TensorAlgebra.ι_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝² : CommSemiring R\nM : Type u_2\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nx : M\n⊢ ↑(ι R) x = 0 ↔ x = 0",
"tactic": "rw [← ι_inj R x 0, LinearMap.map_zero]"
}
] | [
259,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzOnWith.mk_one | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝² : PseudoMetricSpace α\ninst✝¹ : PseudoMetricSpace β\ninst✝ : PseudoMetricSpace γ\nK : ℝ≥0\ns : Set α\nf : α → β\nh : ∀ (x : α), x ∈ s → ∀ (y : α), y ∈ s → dist (f x) (f y) ≤ dist x y\n⊢ ∀ (x : α), x ∈ s → ∀ ... | [
541,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
11
] |
Mathlib/GroupTheory/GroupAction/SubMulAction.lean | SetLike.smul_def | [] | [
99,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Topology/DenseEmbedding.lean | isClosed_property3 | [] | [
332,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | Orthonormal.orthonormal_of_forall_eq_or_eq_neg | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.2146112\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nι : Type u_3\ndec_ι : DecidableEq ι\nv w : ι → E\nhv : Orthonormal 𝕜 v\nhw... | [
924,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
916,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_comp_div_sub | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.14935768\n𝕜 : Type ?u.14935771\nE : Type u_1\nF : Type ?u.14935777\nA : Type ?u.14935780\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\na b c d✝ : ℝ\nf : ℝ → E\nhc : c ≠ 0\nd : ℝ\n⊢ (∫ (x : ℝ) in a..b, f (x / c - ... | [
829,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
827,
1
] |
Mathlib/CategoryTheory/Preadditive/Injective.lean | CategoryTheory.Injective.projective_iff_injective_op | [] | [
189,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.prod.associator_naturality | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\nX Y : C\ninst✝ : HasBinaryProducts C\nX₁ X₂ X₃ Y₁ Y₂ Y₃ : C\nf₁ : X₁ ⟶ Y₁\nf₂ : X₂ ⟶ Y₂\nf₃ : X₃ ⟶ Y₃\n⊢ map (map f₁ f₂) f₃ ≫ (associator Y₁ Y₂ Y₃).hom = (associator X₁ X₂ X₃).hom ≫ map f₁ (map f₂ f₃)",
"tactic": "simp"
}
] | [
1045,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1041,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Monad.lean | Pmf.bind_pure | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.61522\nγ : Type ?u.61525\np : Pmf α\nf : α → Pmf β\ng : β → Pmf γ\nx y : α\nhy : y ≠ x\n⊢ ↑p y * ↑(pure y) x = 0",
"tactic": "rw [pure_apply_of_ne _ _ hy.symm, MulZeroClass.mul_zero]"
},
{
"state_after": "no goals",
"sta... | [
145,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.to_has_basis' | [
{
"state_after": "α : Type u_1\nβ : Type ?u.16192\nγ : Type ?u.16195\nι : Sort u_2\nι' : Sort u_3\nl l' : Filter α\np : ι → Prop\ns : ι → Set α\nt✝ : Set α\ni : ι\np' : ι' → Prop\ns' : ι' → Set α\ni' : ι'\nhl : HasBasis l p s\nh : ∀ (i : ι), p i → ∃ i', p' i' ∧ s' i' ⊆ s i\nh' : ∀ (i' : ι'), p' i' → s' i' ∈ l\n... | [
351,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.vadd_ball | [] | [
774,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
772,
1
] |
Mathlib/Data/Set/Intervals/Disjoint.lean | Set.Iic_disjoint_Ici | [] | [
63,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup_image | [
{
"state_after": "α : Type u_3\nβ : Type u_2\nβ₂ : Type ?u.142348\nγ✝ : Type ?u.142351\nι : Sort ?u.142354\nι' : Sort ?u.142357\nκ : ι → Sort ?u.142362\nκ' : ι' → Sort ?u.142367\ninst✝ : CompleteLattice α\nf✝ g✝ s t✝ : ι → α\na b : α\nγ : Type u_1\nf : β → γ\ng : γ → α\nt : Set β\n⊢ sSup ((fun c => g c) ∘ f '' ... | [
1474,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1473,
1
] |
Mathlib/Algebra/Order/Monoid/Canonical/Defs.lean | self_le_mul_right | [] | [
170,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.diff_nonempty_of_ncard_lt_ncard | [
{
"state_after": "α : Type u_1\nβ : Type ?u.127640\ns t : Set α\na b x y : α\nf : α → β\nh : ncard s < ncard t\nhs : autoParam (Set.Finite s) _auto✝\n⊢ ¬t ⊆ s",
"state_before": "α : Type u_1\nβ : Type ?u.127640\ns t : Set α\na b x y : α\nf : α → β\nh : ncard s < ncard t\nhs : autoParam (Set.Finite s) _auto✝... | [
532,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.countp_cons_of_pos | [] | [
2211,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2210,
1
] |
Mathlib/Topology/LocallyConstant/Basic.lean | LocallyConstant.comap_const | [
{
"state_after": "case h.h\nX : Type u_2\nY : Type u_1\nZ : Type u_3\nα : Type ?u.34199\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nf : X → Y\ny : Y\nh : ∀ (x : X), f x = y\nx✝¹ : LocallyConstant Y Z\nx✝ : X\n⊢ ↑(comap f x✝¹) x✝ =\n ↑{ toFun := fun x => ↑x✝¹ y, isLocallyConstant := (_ : IsLocal... | [
502,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
1
] |
Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.Measure.map_inv_eq_self | [] | [
382,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.aleph'_le | [] | [
183,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Algebra/Order/Monoid/Units.lean | Units.val_le_val | [] | [
28,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
27,
1
] |
Mathlib/Order/Antichain.lean | IsStrongAntichain.swap | [] | [
313,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Data/BinaryHeap.lean | BinaryHeap.size_popMax | [] | [
122,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
9
] |
Std/Data/List/Lemmas.lean | List.suffix_cons_iff | [
{
"state_after": "case mp\nα✝ : Type u_1\nl₁ : List α✝\na : α✝\nl₂ : List α✝\n⊢ l₁ <:+ a :: l₂ → l₁ = a :: l₂ ∨ l₁ <:+ l₂\n\ncase mpr\nα✝ : Type u_1\nl₁ : List α✝\na : α✝\nl₂ : List α✝\n⊢ l₁ = a :: l₂ ∨ l₁ <:+ l₂ → l₁ <:+ a :: l₂",
"state_before": "α✝ : Type u_1\nl₁ : List α✝\na : α✝\nl₂ : List α✝\n⊢ l₁ <:+... | [
1689,
41
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1680,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.SimpleFunc.measure_support_lt_top | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nι : Type ?u.1439544\nE : Type ?u.1439547\nF : Type ?u.1439550\n𝕜 : Type ?u.1439553\ninst✝³ : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\nμ : Measure α\np : ℝ≥0∞\ninst✝ : Zero β\nf : α →ₛ β\nhf : ∀ (y : β), y ≠ 0 → ↑↑μ (↑f ⁻¹' {y... | [
410,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
1
] |
Mathlib/Topology/Constructions.lean | ContinuousAt.restrict | [] | [
1099,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1097,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.nnnorm_constOfIsEmpty | [] | [
539,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.comap_injective | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nG' : Type ?u.580217\ninst✝³ : Group G\ninst✝² : Group G'\nA : Type ?u.580226\ninst✝¹ : AddGroup A\nN : Type u_2\ninst✝ : Group N\nf✝ f : G →* N\nh : Surjective ↑f\nK L : Subgroup N\n⊢ comap f K = comap f L → K = L",
"tactic": "simp only [le_ant... | [
3058,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3057,
1
] |
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