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/Analysis/NormedSpace/Exponential.lean | exp_zsmul | [
{
"state_after": "case intro.inl\n𝕂 : Type u_2\n𝔸 : Type u_1\ninst✝³ : IsROrC 𝕂\ninst✝² : NormedDivisionRing 𝔸\ninst✝¹ : NormedAlgebra 𝕂 𝔸\ninst✝ : CompleteSpace 𝔸\nx : 𝔸\nn : ℕ\n⊢ exp 𝕂 (↑n • x) = exp 𝕂 x ^ ↑n\n\ncase intro.inr\n𝕂 : Type u_2\n𝔸 : Type u_1\ninst✝³ : IsROrC 𝕂\ninst✝² : NormedDivisio... | [
610,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
607,
1
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Mathlib/Analysis/NormedSpace/Banach.lean | ContinuousLinearMap.nonlinearRightInverseOfSurjective_nnnorm_pos | [
{
"state_after": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nf✝ : E →L[𝕜] F\ninst✝¹ : CompleteSpace F\ninst✝ : CompleteSpace E\nf : E →L[𝕜] F\nhsurj : Linear... | [
317,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Convex/Combination.lean | convexHull_basis_eq_stdSimplex | [
{
"state_after": "case refine'_1\nR : Type u_1\nE : Type ?u.418534\nF : Type ?u.418537\nι : Type u_2\nι' : Type ?u.418543\nα : Type ?u.418546\ninst✝⁸ : LinearOrderedField R\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : AddCommGroup F\ninst✝⁵ : LinearOrderedAddCommGroup α\ninst✝⁴ : Module R E\ninst✝³ : Module R F\ninst✝² :... | [
452,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
1
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Mathlib/Analysis/Calculus/FDeriv/Bilinear.lean | ContinuousLinearMap.hasFDerivWithinAt_of_bilinear | [] | [
134,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
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Mathlib/Analysis/NormedSpace/Dual.lean | NormedSpace.dualPairing_apply | [] | [
121,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
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Mathlib/MeasureTheory/Integral/IntegrableOn.lean | integrableOn_Ici_iff_integrableOn_Ioi | [
{
"state_after": "α : Type u_1\nβ : Type ?u.4570798\nE : Type u_2\nF : Type ?u.4570804\ninst✝⁴ : MeasurableSpace α\ninst✝³ : NormedAddCommGroup E\ninst✝² : PartialOrder α\ninst✝¹ : MeasurableSingletonClass α\nf : α → E\nμ : MeasureTheory.Measure α\na b : α\ninst✝ : NoAtoms μ\n⊢ 0 ≠ ⊤",
"state_before": "α : ... | [
704,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
702,
1
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Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | Convex.combo_affine_apply | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : Ring 𝕜\ninst✝³ : AddCommGroup E\ninst✝² : AddCommGroup F\ninst✝¹ : Module 𝕜 E\ninst✝ : Module 𝕜 F\nx y : E\na b : 𝕜\nf : E →ᵃ[𝕜] F\nh : a + b = 1\n⊢ ↑f (b • (y -ᵥ x) + x) = b • (↑f y -ᵥ ↑f x) + ↑f x",
"state_before": "𝕜 : Type u_1\n... | [
873,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
870,
1
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Mathlib/Analysis/Calculus/FDeriv/Mul.lean | DifferentiableOn.clm_comp | [] | [
94,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
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Mathlib/Analysis/Calculus/Deriv/Linear.lean | ContinuousLinearMap.hasStrictDerivAt | [] | [
57,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
11
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Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean | MvPolynomial.weightedHomogeneousComponent_isWeightedHomogeneous | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nM : Type u_2\ninst✝¹ : CommSemiring R\nσ : Type u_3\ninst✝ : AddCommMonoid M\nw : σ → M\nn : M\nφ ψ : MvPolynomial σ R\n⊢ IsWeightedHomogeneous w (↑(weightedHomogeneousComponent w n) φ) n",
"tactic": "classical\nintro d hd\ncontrapose! hd\nrw [... | [
357,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
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Mathlib/Algebra/Order/Field/Basic.lean | div_le_div_of_le_left | [
{
"state_after": "ι : Type ?u.62267\nα : Type u_1\nβ : Type ?u.62273\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nha : 0 ≤ a\nhc : 0 < c\nh : c ≤ b\n⊢ a * b⁻¹ ≤ a * c⁻¹",
"state_before": "ι : Type ?u.62267\nα : Type u_1\nβ : Type ?u.62273\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n :... | [
353,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/BooleanAlgebra.lean | disjoint_sdiff_iff_le | [
{
"state_after": "α : Type u\nβ : Type ?u.13662\nw x y z : α\ninst✝ : GeneralizedBooleanAlgebra α\nhz : z ≤ y\nhx : x ≤ y\nH : Disjoint z (y \\ x)\n⊢ z ⊔ y \\ x ≤ y",
"state_before": "α : Type u\nβ : Type ?u.13662\nw x y z : α\ninst✝ : GeneralizedBooleanAlgebra α\nhz : z ≤ y\nhx : x ≤ y\nH : Disjoint z (y \... | [
254,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
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Mathlib/Data/Set/Intervals/Pi.lean | Set.image_update_uIcc | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : ι → Type u_2\ninst✝¹ : (i : ι) → Lattice (α i)\ninst✝ : DecidableEq ι\nf : (i : ι) → α i\ni : ι\na b : α i\n⊢ Icc (update f i (a ⊓ b)) (update f i (a ⊔ b)) = uIcc (update f i a) (update f i b)",
"tactic": "simp_rw [uIcc, update_sup, update_... | [
296,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | nonneg_of_mul_nonpos_left | [] | [
1188,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1187,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | contDiffAt_prod | [] | [
1426,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1424,
1
] |
Mathlib/Data/List/Perm.lean | List.map_append_bind_perm | [
{
"state_after": "no goals",
"state_before": "α : Type uu\nβ : Type vv\nl₁ l₂ l : List α\nf : α → β\ng : α → List β\n⊢ map f l ++ List.bind l g ~ List.bind l fun x => f x :: g x",
"tactic": "simpa [← map_eq_bind] using bind_append_perm l (fun x => [f x]) g"
}
] | [
1103,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1101,
1
] |
Std/Data/Int/Lemmas.lean | Int.mul_le_mul | [] | [
1176,
98
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1174,
11
] |
Mathlib/GroupTheory/GroupAction/Pi.lean | Function.update_smul | [] | [
251,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Std/Data/Int/DivMod.lean | Int.div_zero | [
{
"state_after": "no goals",
"state_before": "a✝ : Nat\n⊢ ofNat (a✝ / 0) = 0",
"tactic": "simp"
}
] | [
43,
18
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
41,
19
] |
Mathlib/Data/Polynomial/Degree/Lemmas.lean | Polynomial.degree_pos_of_eval₂_root | [] | [
279,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Analysis/NormedSpace/Basic.lean | closure_ball | [
{
"state_after": "α : Type ?u.32233\nβ : Type ?u.32236\nγ : Type ?u.32239\nι : Type ?u.32242\ninst✝⁶ : NormedField α\ninst✝⁵ : SeminormedAddCommGroup β\nE : Type u_1\ninst✝⁴ : SeminormedAddCommGroup E\ninst✝³ : NormedSpace α E\nF : Type ?u.32273\ninst✝² : SeminormedAddCommGroup F\ninst✝¹ : NormedSpace α F\ninst... | [
124,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Order/Directed.lean | Antitone.directed_ge | [] | [
123,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/CategoryTheory/DiscreteCategory.lean | CategoryTheory.Discrete.functor_map | [
{
"state_after": "no goals",
"state_before": "α : Type u₁\nC : Type u₂\ninst✝ : Category C\nI : Type u₁\nF : I → C\ni : Discrete I\nf : i ⟶ i\n⊢ (functor F).map f = 𝟙 (F i.as)",
"tactic": "aesop_cat"
}
] | [
190,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Data/Nat/Bits.lean | Nat.binaryRec_eq' | [
{
"state_after": "n✝ : ℕ\nC : ℕ → Sort u_1\nz : C 0\nf : (b : Bool) → (n : ℕ) → C n → C (bit b n)\nb : Bool\nn : ℕ\nh : f false 0 z = z ∨ (n = 0 → b = true)\n⊢ (if n0 : bit b n = 0 then Eq.mpr (_ : C (bit b n) = C 0) z\n else\n let n' := div2 (bit b n);\n let_fun _x := (_ : bit (bodd (bit b n)) (di... | [
185,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
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Mathlib/Algebra/Module/LinearMap.lean | LinearMap.copy_eq | [] | [
251,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | mem_nhds_uniformity_iff_right | [
{
"state_after": "case refine'_1\nα : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.56643\ninst✝ : UniformSpace α\nx : α\ns : Set α\n⊢ s ∈ 𝓝 x → {p | p.fst = x → p.snd ∈ s} ∈ 𝓤 α\n\ncase refine'_2\nα : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.56643\ninst✝ : UniformSpace α\nx :... | [
703,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
689,
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Mathlib/CategoryTheory/Sites/Sheafification.lean | CategoryTheory.Meq.condition | [] | [
72,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/LinearAlgebra/Determinant.lean | LinearMap.det_id | [] | [
257,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | mul_lt_mul_of_pos_of_pos | [] | [
243,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
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] |
Mathlib/Analysis/Calculus/FormalMultilinearSeries.lean | FormalMultilinearSeries.ne_iff | [] | [
90,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
11
] |
Mathlib/Data/Sum/Order.lean | OrderIso.sumDualDistrib_symm_inl | [] | [
627,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
626,
1
] |
Mathlib/Algebra/Module/Zlattice.lean | Zspan.repr_ceil_apply | [
{
"state_after": "no goals",
"state_before": "E : Type u_3\nι : Type u_2\nK : Type u_1\ninst✝⁴ : NormedLinearOrderedField K\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace K E\nb : Basis ι K E\ninst✝¹ : FloorRing K\ninst✝ : Fintype ι\nm : E\ni : ι\n⊢ ↑(↑b.repr ↑(ceil b m)) i = ↑⌈↑(↑b.repr m) i⌉",
"... | [
89,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/RingTheory/Derivation/Basic.lean | Derivation.eqOn_adjoin | [
{
"state_after": "no goals",
"state_before": "R : Type u_3\ninst✝⁵ : CommSemiring R\nA : Type u_1\ninst✝⁴ : CommSemiring A\ninst✝³ : Algebra R A\nM : Type u_2\ninst✝² : AddCommMonoid M\ninst✝¹ : Module A M\ninst✝ : Module R M\nD D1 D2 : Derivation R A M\nr : R\na b : A\ns : Set A\nh : Set.EqOn (↑D1) (↑D2) s... | [
171,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
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Mathlib/Topology/MetricSpace/Completion.lean | UniformSpace.Completion.dist_comm | [
{
"state_after": "case refine'_1\nα : Type u\nβ : Type v\ninst✝ : PseudoMetricSpace α\nx y : Completion α\n⊢ IsClosed {x | dist x.fst x.snd = dist x.snd x.fst}\n\ncase refine'_2\nα : Type u\nβ : Type v\ninst✝ : PseudoMetricSpace α\nx y : Completion α\n⊢ ∀ (a b : α), dist (↑α a) (↑α b) = dist (↑α b) (↑α a)",
... | [
75,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
11
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mul_eq_max_of_aleph0_le_left | [
{
"state_after": "case inl\na b : Cardinal\nh : ℵ₀ ≤ a\nh' : b ≠ 0\nhb : ℵ₀ ≤ b\n⊢ a * b = max a b\n\ncase inr\na b : Cardinal\nh : ℵ₀ ≤ a\nh' : b ≠ 0\nhb : b < ℵ₀\n⊢ a * b = max a b",
"state_before": "a b : Cardinal\nh : ℵ₀ ≤ a\nh' : b ≠ 0\n⊢ a * b = max a b",
"tactic": "cases' le_or_lt ℵ₀ b with hb hb... | [
620,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
612,
1
] |
Mathlib/Order/Bounds/Basic.lean | upperBounds_Ico | [] | [
780,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
779,
1
] |
Mathlib/Algebra/GroupWithZero/Units/Lemmas.lean | div_helper | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.13686\nM₀ : Type ?u.13689\nG₀ : Type u_1\nM₀' : Type ?u.13695\nG₀' : Type ?u.13698\nF : Type ?u.13701\nF' : Type ?u.13704\ninst✝¹ : MonoidWithZero M₀\ninst✝ : CommGroupWithZero G₀\na b✝ c d b : G₀\nh : a ≠ 0\n⊢ 1 / (a * b) * a = 1 / b",
"tactic":... | [
202,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Data/ENat/Basic.lean | ENat.toNat_add | [
{
"state_after": "case intro\nm✝ n✝ n : ℕ∞\nhn : n ≠ ⊤\nm : ℕ\n⊢ ↑toNat (↑m + n) = ↑toNat ↑m + ↑toNat n",
"state_before": "m✝ n✝ m n : ℕ∞\nhm : m ≠ ⊤\nhn : n ≠ ⊤\n⊢ ↑toNat (m + n) = ↑toNat m + ↑toNat n",
"tactic": "lift m to ℕ using hm"
},
{
"state_after": "case intro.intro\nm✝ n✝ : ℕ∞\nm n : ℕ\... | [
170,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Analysis/Calculus/FDerivAnalytic.lean | HasFPowerSeriesOnBall.differentiableOn | [] | [
71,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/GroupTheory/FreeAbelianGroup.lean | FreeAbelianGroup.mul_def | [] | [
413,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.Reaches₀.tail | [] | [
802,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
800,
1
] |
Mathlib/Topology/Constructions.lean | Filter.Eventually.prod_nhds | [] | [
582,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
580,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | IsLinearMap.isLinearMap_smul' | [] | [
701,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
699,
1
] |
Mathlib/Order/Heyting/Hom.lean | BiheytingHom.id_apply | [] | [
560,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
559,
1
] |
Mathlib/Order/WithBot.lean | WithTop.ofDual_lt_ofDual_iff | [] | [
911,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
910,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.SimpleFunc.exists_forall_norm_le | [] | [
294,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | IsBoundedBilinearMap.isBoundedLinearMap_left | [] | [
433,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/Topology/Category/TopCat/Limits/Products.lean | TopCat.sigmaIsoSigma_hom_ι_apply | [] | [
133,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.Measure.toENNRealVectorMeasure_zero | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.147666\nm : MeasurableSpace α\ni : Set α\n⊢ MeasurableSet i → ↑(toENNRealVectorMeasure 0) i = ↑0 i",
"state_before": "α : Type u_1\nβ : Type ?u.147666\nm : MeasurableSpace α\n⊢ toENNRealVectorMeasure 0 = 0",
"tactic": "ext i"
},
{
"state_after"... | [
508,
7
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506,
1
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Mathlib/Data/Finset/Image.lean | Finset.map_disjUnion' | [] | [
209,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
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Mathlib/Topology/Basic.lean | DenseRange.subset_closure_image_preimage_of_isOpen | [
{
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... | [
1835,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1832,
1
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Mathlib/Topology/Basic.lean | mem_closure_iff_nhds' | [
{
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"tactic": "simp only [mem_closure_iff_nhds, Set.inter_nonempty_iff_exi... | [
1337,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1336,
1
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Mathlib/Algebra/EuclideanDomain/Basic.lean | EuclideanDomain.gcd_mul_lcm | [
{
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"state_before": "R : Type u\ninst✝¹ : EuclideanDomain R\ninst✝ : DecidableEq R\nx y : R\n⊢ gcd x y * lcm x y = x * y",
"tactic": "rw [lcm]"
},
{
"state_after": "case ... | [
336,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
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Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | Matrix.Nondegenerate.toLinearMap₂' | [
{
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693,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
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Mathlib/Topology/Sets/Closeds.lean | TopologicalSpace.Closeds.coe_sInf | [] | [
143,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
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Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.lift_unique | [
{
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1049,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1045,
1
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.conj_smul | [
{
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391,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
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Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.Ico_sub_Ico_right | [
{
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"tactic": "rw [Ico, Ico, Ico, ← Finset.sdiff_val, Finset.Ico_diff_Ico_right]"
}
] | [
280,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
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Mathlib/Init/Data/Nat/Lemmas.lean | Nat.bit1_succ_eq | [] | [
86,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
11
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Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.HomotopyWith.coe_toHomotopy | [] | [
470,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
469,
1
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Mathlib/Analysis/Quaternion.lean | Quaternion.continuous_re | [] | [
209,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_sub | [
{
"state_after": "α : Type u_2\nE : Type u_1\nF : Type ?u.913636\n𝕜 : Type ?u.913639\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : CompleteSpace E\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : SMulCommClass ℝ 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedS... | [
890,
69
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887,
1
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Mathlib/Order/Monotone/Basic.lean | StrictMono.maximal_of_maximal_image | [] | [
855,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
853,
1
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.support_add | [
{
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"state_before": "R : Type u\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q : R[X]\n⊢ su... | [
476,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
473,
1
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | summable_of_isBigO | [] | [
2162,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2159,
1
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Mathlib/CategoryTheory/Abelian/Images.lean | CategoryTheory.Abelian.coimage_image_factorisation | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝³ : Category C\ninst✝² : HasZeroMorphisms C\ninst✝¹ : HasKernels C\ninst✝ : HasCokernels C\nP Q : C\nf : P ⟶ Q\n⊢ coimage.π f ≫ coimageImageComparison f ≫ image.ι f = f",
"tactic": "simp [coimageImageComparison]"
}
] | [
129,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.map_surjective_of_surjective | [] | [
465,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
] |
Mathlib/GroupTheory/SemidirectProduct.lean | SemidirectProduct.hom_ext | [
{
"state_after": "N : Type u_2\nG : Type u_1\nH : Type u_3\ninst✝² : Group N\ninst✝¹ : Group G\ninst✝ : Group H\nφ : G →* MulAut N\nf₁ : N →* H\nf₂ : G →* H\nh :\n ∀ (g : G),\n MonoidHom.comp f₁ (MulEquiv.toMonoidHom (↑φ g)) = MonoidHom.comp (MulEquiv.toMonoidHom (↑MulAut.conj (↑f₂ g))) f₁\nf g : N ⋊[φ] G →... | [
259,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.tendsto_arg_nhdsWithin_im_nonneg_of_re_neg_of_im_zero | [
{
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"tactic": "simpa only [arg_eq_pi_iff.2 ⟨hre, him⟩] using\n (continuousWithinAt_arg_of_re_neg_of_im_zero hre him).tendsto"
}
] | [
603,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
600,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.add_biSup' | [
{
"state_after": "no goals",
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"tactic": ... | [
576,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
574,
1
] |
Mathlib/LinearAlgebra/Prod.lean | LinearMap.comap_prod_prod | [] | [
480,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
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Mathlib/Algebra/Bounds.lean | isLUB_inv | [] | [
60,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.union_mem_iff | [
{
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"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.11570\nf g : Ultrafilter α\ns t : Set α\np q : α → Prop\n⊢ s ∪ t ∈ f ↔ s ∈ f ∨ t ∈ f",
"tactic": "simp only [← mem_coe, ← le_principal_iff, ← sup_principal, le_sup_iff]"
}
] | [
179,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Data/Set/Image.lean | Subtype.preimage_coe_nonempty | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns t : Set α\n⊢ Set.Nonempty (val ⁻¹' t) ↔ Set.Nonempty (s ∩ t)",
"tactic": "rw [inter_comm, ← image_preimage_coe, nonempty_image_iff]"
}
] | [
1467,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1465,
1
] |
Mathlib/Data/Set/Basic.lean | Set.mem_of_mem_inter_left | [] | [
903,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
902,
1
] |
Mathlib/Algebra/Group/Semiconj.lean | SemiconjBy.units_inv_right_iff | [] | [
131,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Combinatorics/SimpleGraph/AdjMatrix.lean | Matrix.IsAdjMatrix.toGraph_compl_eq | [
{
"state_after": "case Adj.h.h.a\nV : Type u_2\nα : Type u_1\nβ : Type ?u.18379\ninst✝³ : DecidableEq α\ninst✝² : DecidableEq V\nA : Matrix V V α\ninst✝¹ : MulZeroOneClass α\ninst✝ : Nontrivial α\nh : IsAdjMatrix A\nv w : V\n⊢ Adj (toGraph (_ : IsAdjMatrix (Matrix.compl A))) v w ↔ Adj (toGraph hᶜ) v w",
"st... | [
140,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Order/Filter/Archimedean.lean | Filter.Tendsto.const_mul_atTop' | [
{
"state_after": "α : Type u_2\nR : Type u_1\nl : Filter α\nf : α → R\nr : R\ninst✝¹ : LinearOrderedSemiring R\ninst✝ : Archimedean R\nhr : 0 < r\nhf : Tendsto f l atTop\nb : R\n⊢ ∀ᶠ (a : α) in l, b ≤ r * f a",
"state_before": "α : Type u_2\nR : Type u_1\nl : Filter α\nf : α → R\nr : R\ninst✝¹ : LinearOrder... | [
158,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/CategoryTheory/Closed/Cartesian.lean | CategoryTheory.initial_mono | [
{
"state_after": "C : Type u\ninst✝³ : Category C\nA B✝ X X' Y Y' Z : C\ninst✝² : HasFiniteProducts C\ninst✝¹ : Exponentiable A\nI B : C\nt : IsInitial I\ninst✝ : CartesianClosed C\nZ✝ : C\ng h : Z✝ ⟶ I\nx✝ : g ≫ IsInitial.to t B = h ≫ IsInitial.to t B\nthis : IsIso g\n⊢ g = h",
"state_before": "C : Type u\... | [
390,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/Data/List/Forall2.lean | List.forall₂_iff_zip | [
{
"state_after": "case intro\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.40478\nδ : Type ?u.40481\nR S : α → β → Prop\nP : γ → δ → Prop\nRₐ : α → α → Prop\nl₁ : List α\nl₂ : List β\nh₁ : length l₁ = length l₂\nh₂ : ∀ {a : α} {b : β}, (a, b) ∈ zip l₁ l₂ → R a b\n⊢ Forall₂ R l₁ l₂",
"state_before": "α : Type u_1... | [
210,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Algebra/Order/Rearrangement.lean | AntivaryOn.sum_smul_lt_sum_smul_comp_perm_iff | [
{
"state_after": "no goals",
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214,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.sum_centroidWeights_eq_one_of_cast_card_ne_zero | [
{
"state_after": "no goals",
"state_before": "k : Type u_1\nV : Type ?u.465735\nP : Type ?u.465738\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι : Type u_2\ns : Finset ι\nι₂ : Type ?u.466257\ns₂ : Finset ι₂\nh : ↑(card s) ≠ 0\n⊢ ∑ i in s, centroidWeights ... | [
808,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
807,
1
] |
Mathlib/Topology/ContinuousFunction/Compact.lean | ContinuousMap.dist_lt_iff_of_nonempty | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nE : Type ?u.76000\ninst✝⁴ : TopologicalSpace α\ninst✝³ : CompactSpace α\ninst✝² : MetricSpace β\ninst✝¹ : NormedAddCommGroup E\nf g : C(α, β)\nC : ℝ\ninst✝ : Nonempty α\n⊢ dist f g < C ↔ ∀ (x : α), dist (↑f x) (↑g x) < C",
"tactic... | [
148,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Algebra/Hom/Group.lean | MulHom.coe_mk | [] | [
596,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
596,
1
] |
Mathlib/Algebra/Group/Commute.lean | Commute.self_pow | [] | [
194,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Topology/Algebra/GroupWithZero.lean | ContinuousOn.div | [] | [
186,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Analysis/Normed/Group/AddCircle.lean | AddCircle.norm_eq' | [
{
"state_after": "p : ℝ\nhp : 0 < p\nx : ℝ\n⊢ ‖↑x‖ = abs p * abs (p⁻¹ * x - ↑(round (p⁻¹ * x)))",
"state_before": "p : ℝ\nhp : 0 < p\nx : ℝ\n⊢ ‖↑x‖ = p * abs (p⁻¹ * x - ↑(round (p⁻¹ * x)))",
"tactic": "conv_rhs =>\n congr\n rw [← abs_eq_self.mpr hp.le]"
},
{
"state_after": "no goals",
"sta... | [
128,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Std/Data/Nat/Gcd.lean | Nat.coprime.dvd_of_dvd_mul_right | [
{
"state_after": "k n m : Nat\nH1 : coprime k n\nH2 : k ∣ m * n\nt : k ∣ gcd (m * k) (m * n) := dvd_gcd (Nat.dvd_mul_left k m) H2\n⊢ k ∣ m",
"state_before": "k n m : Nat\nH1 : coprime k n\nH2 : k ∣ m * n\n⊢ k ∣ m",
"tactic": "let t := dvd_gcd (Nat.dvd_mul_left k m) H2"
},
{
"state_after": "no go... | [
250,
54
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
248,
1
] |
Mathlib/Topology/List.lean | List.tendsto_prod | [
{
"state_after": "case nil\nα : Type u_1\nβ : Type ?u.56124\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : Monoid α\ninst✝ : ContinuousMul α\n⊢ Tendsto prod (𝓝 []) (𝓝 (prod []))\n\ncase cons\nα : Type u_1\nβ : Type ?u.56124\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹... | [
174,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.locally_const_basicOpen | [
{
"state_after": "case intro.intro.intro.intro.intro.intro\nR : Type u\ninst✝ : CommRing R\nU : Opens ↑(PrimeSpectrum.Top R)\ns : ↑((structureSheaf R).val.obj U.op)\nx : { x // x ∈ U }\nV : Opens ↑(PrimeSpectrum.Top R)\nhxV : ↑x ∈ V.carrier\niVU : V ⟶ U\nf g : R\nhVDg : V ≤ PrimeSpectrum.basicOpen g\ns_eq : con... | [
722,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
1
] |
Mathlib/MeasureTheory/Integral/VitaliCaratheodory.lean | MeasureTheory.exists_upperSemicontinuous_le_lintegral_le | [
{
"state_after": "case intro.intro\nα : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : MeasurableSpace α\ninst✝¹ : BorelSpace α\nμ : Measure α\ninst✝ : WeaklyRegular μ\nf : α → ℝ≥0\nint_f : (∫⁻ (x : α), ↑(f x) ∂μ) ≠ ⊤\nε : ℝ≥0∞\nε0 : ε ≠ 0\nfs : α →ₛ ℝ≥0\nfs_le_f : ∀ (x : α), ↑fs x ≤ f x\nint_fs : (∫⁻ (x : α),... | [
422,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.filterMap_some | [] | [
2169,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2168,
1
] |
Mathlib/Geometry/Manifold/ChartedSpace.lean | ChartedSpace.locallyCompact | [
{
"state_after": "H : Type u\nH' : Type ?u.45087\nM : Type u_1\nM' : Type ?u.45093\nM'' : Type ?u.45096\ninst✝³ : TopologicalSpace H\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\ninst✝ : LocallyCompactSpace H\nthis :\n ∀ (x : M),\n HasBasis (𝓝 x) (fun s => s ∈ 𝓝 (↑(chartAt H x) x) ∧ IsCompact s... | [
612,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Diagonal.lean | CategoryTheory.Limits.diagonalObjPullbackFstIso_hom_fst_fst | [
{
"state_after": "C : Type u_2\ninst✝⁵ : Category C\nX✝ Y✝ Z✝ : C\ninst✝⁴ : HasPullbacks C\nS T : C\nf✝ : X✝ ⟶ T\ng✝ : Y✝ ⟶ T\ni : T ⟶ S\ninst✝³ : HasPullback i i\ninst✝² : HasPullback f✝ g✝\ninst✝¹ : HasPullback (f✝ ≫ i) (g✝ ≫ i)\ninst✝ :\n HasPullback (diagonal i)\n (map (f✝ ≫ i) (g✝ ≫ i) i i f✝ g✝ (𝟙 S)... | [
309,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | norm_iteratedFDeriv_clm_apply_const | [
{
"state_after": "𝕜 : 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✝³ : Normed... | [
2755,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2750,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.map_mul | [
{
"state_after": "R : Type u_2\ninst✝⁶ : CommRing R\nS : Submonoid R\nP : Type u_3\ninst✝⁵ : CommRing P\ninst✝⁴ : Algebra R P\nloc : IsLocalization S P\nP' : Type u_1\ninst✝³ : CommRing P'\ninst✝² : Algebra R P'\nloc' : IsLocalization S P'\nP'' : Type ?u.565642\ninst✝¹ : CommRing P''\ninst✝ : Algebra R P''\nloc... | [
786,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
784,
1
] |
Mathlib/Data/List/Count.lean | List.one_le_count_iff_mem | [] | [
249,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Data/Set/Intervals/SurjOn.lean | surjOn_Ico_of_monotone_surjective | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrder α\ninst✝ : PartialOrder β\nf : α → β\nh_mono : Monotone f\nh_surj : Surjective f\na b : α\nhab : a < b\n⊢ SurjOn f (Ico a b) (Ico (f a) (f b))\n\ncase inr\nα : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrder α\ninst✝ : PartialOrder β\nf :... | [
48,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/Combinatorics/SimpleGraph/Prod.lean | SimpleGraph.Walk.ofBoxProdLeft_boxProdLeft | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.57688\nG : SimpleGraph α\nH : SimpleGraph β\nb : β\ninst✝¹ : DecidableEq β\ninst✝ : DecidableRel G.Adj\na₁ a₂ x z y : α\nh : Adj G x y\nw : Walk G y z\n⊢ cons (_ : Adj G (x, b).fst (↑(Embedding.toHom (boxProdLeft G H b)) y).fst) (ofBoxProdLeft (Walk.boxP... | [
154,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Data/Int/Parity.lean | Int.odd_add' | [
{
"state_after": "no goals",
"state_before": "m n : ℤ\n⊢ Odd (m + n) ↔ (Odd n ↔ Even m)",
"tactic": "rw [add_comm, odd_add]"
}
] | [
180,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
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