file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.derivFamily_zero | [] | [
167,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
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Mathlib/Data/MvPolynomial/Expand.lean | MvPolynomial.expand_X | [] | [
48,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
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Mathlib/MeasureTheory/Covering/Differentiation.lean | VitaliFamily.ae_tendsto_rnDeriv_of_absolutelyContinuous | [
{
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706,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
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Mathlib/Order/GaloisConnection.lean | OrderIso.to_galoisConnection | [] | [
70,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.exists_dropn_of_mem | [
{
"state_after": "case mk.intro\nα : Type u\nβ : Type v\nγ : Type w\ns : WSeq α\na : α\nh✝ : a ∈ s\nn : ℕ\nh : some a ∈ get? s n\no : Option (α × WSeq α)\nom : o ∈ destruct (drop s n)\n⊢ ∃ s', some (a, s') ∈ destruct (drop s n)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : WSeq α\na : α\nh✝ : a... | [
1036,
19
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1024,
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_top | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.53924\ninst✝¹ : Preorder α\ninst✝ : OrderTop α\na : α\n⊢ Icc a ⊤ = Ici a",
"tactic": "simp [← Ici_inter_Iic]"
}
] | [
998,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
998,
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Mathlib/Analysis/Calculus/ContDiff.lean | LinearIsometry.norm_iteratedFDeriv_comp_left | [
{
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300,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
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Mathlib/Data/Real/ENNReal.lean | ENNReal.inv_three_add_inv_three | [
{
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"state_before": "α : Type ?u.313809\nβ : Type ?u.313812\na b c d : ℝ≥0∞\nr p q : ℝ≥0\n⊢ 3⁻¹ + 3⁻¹ + 3⁻¹ = 3 * 3⁻¹",
"tactic": "ring"
},
{
"state_after": "no goals",
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... | [
1725,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1723,
1
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Mathlib/Algebra/GroupWithZero/Commute.lean | Ring.mul_inverse_rev' | [
{
"state_after": "case pos\nα : Type ?u.47\nM₀ : Type u_1\nG₀ : Type ?u.53\nM₀' : Type ?u.56\nG₀' : Type ?u.59\nF : Type ?u.62\nF' : Type ?u.65\ninst✝ : MonoidWithZero M₀\na b : M₀\nh : Commute a b\nhab : IsUnit (a * b)\n⊢ inverse (a * b) = inverse b * inverse a\n\ncase neg\nα : Type ?u.47\nM₀ : Type u_1\nG₀ : ... | [
36,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
29,
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Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.smul_imK | [] | [
374,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
9
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Mathlib/Data/Polynomial/Expand.lean | Polynomial.expand_one | [
{
"state_after": "no goals",
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"tactic": "rw [expand_C]"
},
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝¹ : CommSemiring R\nS :... | [
88,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.coeff_monomial_mul | [] | [
714,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
712,
1
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Mathlib/Algebra/Order/ToIntervalMod.lean | toIocMod_sub_zsmul' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ\na b : α\nm : ℤ\n⊢ toIocMod hp (a - m • p) b = toIocMod hp a b - m • p",
"tactic": "simp_rw [sub_eq_add_neg, ← neg_smul, toIocMod_add_zsmul']"
}
] | [
469,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
467,
1
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Mathlib/Data/Set/Intervals/Disjoint.lean | Set.Ico_disjoint_Ico | [
{
"state_after": "no goals",
"state_before": "ι : Sort u\nα : Type v\nβ : Type w\ninst✝ : LinearOrder α\na₁ a₂ b₁ b₂ : α\n⊢ Disjoint (Ico a₁ a₂) (Ico b₁ b₂) ↔ min a₂ b₂ ≤ max a₁ b₁",
"tactic": "simp_rw [Set.disjoint_iff_inter_eq_empty, Ico_inter_Ico, Ico_eq_empty_iff, inf_eq_min, sup_eq_max,\n not_lt]"... | [
135,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
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Mathlib/Order/Bounds/Basic.lean | nonempty_of_not_bddBelow | [] | [
914,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
913,
1
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Mathlib/Data/Real/CauSeqCompletion.lean | CauSeq.lim_le | [] | [
450,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.WalkingPair.swap_symm_apply_ff | [] | [
81,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Analysis/InnerProductSpace/Adjoint.lean | ContinuousLinearMap.adjointAux_inner_right | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.269290\ninst✝⁸ : IsROrC 𝕜\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedAddCommGroup G\ninst✝⁴ : InnerProductSpace 𝕜 E\ninst✝³ : InnerProductSpace 𝕜 F\ninst✝² : InnerProduc... | [
91,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Dynamics/Ergodic/Ergodic.lean | Ergodic.ae_empty_or_univ_of_ae_le_preimage | [] | [
174,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/MeasureTheory/Function/UniformIntegrable.lean | MeasureTheory.uniformIntegrable_subsingleton | [] | [
785,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
783,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.sub | [
{
"state_after": "no goals",
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1115,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1114,
1
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.finite_support | [] | [
237,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
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Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | Ideal.mem_homogeneousCore_of_homogeneous_of_mem | [] | [
203,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Combinatorics/SimpleGraph/Clique.lean | SimpleGraph.cliqueFree_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nG H : SimpleGraph α\nm n✝ : ℕ\ns : Finset α\nn : ℕ\n⊢ CliqueFree G n ↔ IsEmpty (⊤ ↪g G)",
"tactic": "rw [← not_iff_not, not_cliqueFree_iff, not_isEmpty_iff]"
}
] | [
201,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Topology/Semicontinuous.lean | LowerSemicontinuousWithinAt.mono | [] | [
136,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Data/Real/GoldenRatio.lean | one_sub_gold | [
{
"state_after": "no goals",
"state_before": "⊢ 1 - ψ = φ",
"tactic": "linarith [gold_add_goldConj]"
}
] | [
86,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Data/Real/GoldenRatio.lean | Real.coe_fib_eq | [
{
"state_after": "no goals",
"state_before": "⊢ ∀ (n : ℕ), ↑(Nat.fib n) = (φ ^ n - ψ ^ n) / sqrt 5",
"tactic": "rw [← Function.funext_iff, Real.coe_fib_eq']"
}
] | [
236,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/Algebra/Order/LatticeGroup.lean | LatticeOrderedCommGroup.sup_eq_mul_pos_div | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : Lattice α\ninst✝¹ : CommGroup α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b : α\n⊢ a ⊔ b = b * (a / b) ⊔ b * 1",
"tactic": "rw [mul_one b, div_eq_mul_inv, mul_comm a, mul_inv_cancel_left]"
},
{
"s... | [
311,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/Topology/NoetherianSpace.lean | TopologicalSpace.noetherian_univ_iff | [] | [
150,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
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Mathlib/Data/Set/Prod.lean | Set.pi_eq_empty_iff | [
{
"state_after": "ι : Type u_1\nα : ι → Type u_2\nβ : ι → Type ?u.122847\ns s₁ s₂ : Set ι\nt t₁ t₂ : (i : ι) → Set (α i)\ni : ι\n⊢ (¬∀ (i : ι), ∃ x, i ∈ s → x ∈ t i) ↔ ∃ i, IsEmpty (α i) ∨ i ∈ s ∧ t i = ∅",
"state_before": "ι : Type u_1\nα : ι → Type u_2\nβ : ι → Type ?u.122847\ns s₁ s₂ : Set ι\nt t₁ t₂ : (... | [
695,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.sup_prod_eq_top | [
{
"state_after": "no goals",
"state_before": "R : Type u\nι : Type u_1\ninst✝ : CommSemiring R\nI J✝ K L : Ideal R\ns : Finset ι\nJ : ι → Ideal R\nh : ∀ (i : ι), i ∈ s → I ⊔ J i = ⊤\n⊢ (fun J => I ⊔ J = ⊤) 1",
"tactic": "simp_rw [one_eq_top, sup_top_eq]"
}
] | [
707,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
1
] |
Mathlib/Analysis/Complex/Basic.lean | IsROrC.re_tsum | [] | [
535,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Iso.reachable_iff | [] | [
1910,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1908,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.val_two | [] | [
784,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
783,
1
] |
Mathlib/Data/List/Basic.lean | List.map_foldl_erase | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.427557\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁✝ l₂✝ : List α\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\nf : α → β\nfinj : Injective f\nl₁ l₂ : List α\n⊢ map f (foldl List.erase l₁ l₂) = foldl (fun l a => List.erase l (f a)) (map f l₁... | [
3751,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3749,
1
] |
Mathlib/Algebra/Hom/Ring.lean | RingHom.coe_addMonoidHom_mk | [] | [
499,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Basis.lean | AffineBasis.reindex_refl | [] | [
115,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
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Mathlib/Order/RelClasses.lean | ne_of_irrefl | [] | [
136,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.mem_inf_principal' | [
{
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"tactic": "simp only [← le_principal_iff, (isCompl_principal s).le_left_iff, disjoint_assoc, inf_prin... | [
1000,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
998,
1
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Mathlib/Algebra/CharP/MixedCharZero.lean | EqualCharZero.of_not_mixedCharZero | [
{
"state_after": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : CharZero R\nh : ∀ (p : ℕ), p > 0 → ¬MixedCharZero R p\nI : Ideal R\nhI_ne_top : I ≠ ⊤\n⊢ CharZero (R ⧸ I)",
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265,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Data/Real/NNReal.lean | Real.le_toNNReal_iff_coe_le' | [
{
"state_after": "no goals",
"state_before": "r : ℝ≥0\np : ℝ\nhr : 0 < r\nhp : p < 0\n⊢ r ≤ toNNReal p ↔ ↑r ≤ p",
"tactic": "simp only [(hp.trans_le r.coe_nonneg).not_le, toNNReal_eq_zero.2 hp.le, hr.not_le]"
}
] | [
683,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
681,
1
] |
Mathlib/Control/Traversable/Basic.lean | ApplicativeTransformation.comp_assoc | [] | [
199,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Data/Bitvec/Lemmas.lean | Bitvec.toFin_ofFin | [
{
"state_after": "no goals",
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"tactic": "simp [toFin_val, ofFin, toNat_ofNat, Nat.mod_eq_of_lt, i.is_lt]"
}
] | [
168,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Analysis/Calculus/FDerivMeasurable.lean | stronglyMeasurable_deriv | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nE : Type ?u.404351\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\nF : Type u_2\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace 𝕜 F\nf✝ : E → F\nK : Set (E →L[𝕜] F)\ninst✝⁵ : MeasurableSpace E\ninst✝⁴ : OpensMeasurableSpace... | [
440,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
] |
Mathlib/Analysis/Convex/StrictConvexSpace.lean | StrictConvexSpace.ofNormAddNeTwo | [
{
"state_after": "𝕜 : Type ?u.32392\nE : Type u_1\ninst✝³ : NormedLinearOrderedField 𝕜\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : NormedSpace ℝ E\nh : ∀ ⦃x y : E⦄, ‖x‖ = 1 → ‖y‖ = 1 → x ≠ y → ‖x + y‖ ≠ 2\nx y : E\nhx : ‖x‖ = 1\nhy : ‖y‖ = 1\nhne : x ≠ y\n⊢ ‖(1 / 2) • x + (1 / 2) • y‖ ≠... | [
135,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
src/lean/Init/Data/Array/Basic.lean | Array.ext' | [
{
"state_after": "case mk\nα : Type u_1\nbs : Array α\ndata✝ : List α\nh : { data := data✝ }.data = bs.data\n⊢ { data := data✝ } = bs",
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"tactic": "cases as"
},
{
"state_after": "case mk.mk\nα : Type u_1\ndata✝¹ da... | [
736,
40
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
735,
1
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Mathlib/NumberTheory/Padics/PadicNorm.lean | padicNorm.div | [
{
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},
{
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167,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_comp_mul_sub | [
{
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803,
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Mathlib/Algebra/Algebra/Unitization.lean | Unitization.algHom_ext' | [
{
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653,
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648,
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Mathlib/Algebra/Invertible.lean | invOf_units | [] | [
208,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
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Mathlib/RingTheory/JacobsonIdeal.lean | Ideal.jacobson_idem | [] | [
72,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
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Mathlib/Analysis/InnerProductSpace/PiL2.lean | OrthonormalBasis.toBasis_map | [] | [
480,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
11
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Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Finsupp.log_prod | [] | [
345,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
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Mathlib/Data/Multiset/Sum.lean | Multiset.disjSum_strictMono_right | [] | [
104,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
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Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.monic_normalize | [
{
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417,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
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Mathlib/Analysis/Calculus/Deriv/Inverse.lean | HasStrictDerivAt.hasStrictFDerivAt_equiv | [] | [
55,
5
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
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Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.lift_comp_of | [] | [
299,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
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Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometry.id_toAffineMap | [] | [
228,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
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Mathlib/Algebra/DirectSum/Module.lean | DirectSum.IsInternal.collectedBasis_mem | [
{
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375,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
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Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.isSkewAdjoint_iff_neg_self_adjoint | [
{
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590,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
1
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Mathlib/Computability/Primrec.lean | Nat.Primrec'.of_eq | [] | [
1398,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1397,
1
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Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.mk'_spec | [] | [
262,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
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Mathlib/Algebra/GroupWithZero/Basic.lean | mul_left_inj' | [] | [
171,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
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Mathlib/Algebra/Algebra/Hom.lean | AlgHom.coe_fn_injective | [] | [
195,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
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Mathlib/Algebra/Module/LocalizedModule.lean | LocalizedModule.mul_by_divBy | [
{
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530,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
522,
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left | [] | [
940,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
938,
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Mathlib/LinearAlgebra/Dimension.lean | LinearMap.rank_le_of_injective | [] | [
139,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
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Mathlib/Algebra/Order/ToIntervalMod.lean | toIocMod_le_right | [] | [
111,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
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Mathlib/RingTheory/Ideal/Basic.lean | Ideal.mem_span_insert' | [] | [
672,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
671,
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Mathlib/Data/Multiset/Basic.lean | Multiset.pair_comm | [] | [
365,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
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Mathlib/Algebra/Hom/Units.lean | IsUnit.div_left_inj | [
{
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406,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
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Mathlib/Data/Nat/Dist.lean | Nat.dist_succ_succ | [
{
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"tactic": "simp [dist.def, succ_sub_succ]"
}
] | [
117,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
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Mathlib/Data/Polynomial/Laurent.lean | LaurentPolynomial.induction_on | [
{
"state_after": "case h.e'_1\nR : Type u_1\ninst✝ : Semiring R\nM : R[T;T⁻¹] → Prop\np : R[T;T⁻¹]\nh_C : ∀ (a : R), M (↑C a)\nh_add : ∀ {p q : R[T;T⁻¹]}, M p → M q → M (p + q)\nh_C_mul_T : ∀ (n : ℕ) (a : R), M (↑C a * T ↑n) → M (↑C a * T (↑n + 1))\nh_C_mul_T_Z : ∀ (n : ℕ) (a : R), M (↑C a * T (-↑n)) → M (↑C a ... | [
302,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
11
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Mathlib/Logic/Equiv/Basic.lean | Equiv.subtypeEquiv_apply | [] | [
1114,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1111,
1
] |
Mathlib/Topology/Order/Hom/Esakia.lean | PseudoEpimorphism.coe_id_orderHom | [] | [
165,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
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src/lean/Init/Control/StateCps.lean | StateCpsT.runK_modify | [] | [
57,
156
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
57,
9
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | exp_sum | [
{
"state_after": "case h\n𝕂 : Type u_3\n𝔸 : Type u_2\ninst✝³ : IsROrC 𝕂\ninst✝² : NormedCommRing 𝔸\ninst✝¹ : NormedAlgebra 𝕂 𝔸\ninst✝ : CompleteSpace 𝔸\nι : Type u_1\ns : Finset ι\nf : ι → 𝔸\n⊢ Set.Pairwise ↑s fun i j => Commute (f i) (f j)\n\ncase h\n𝕂 : Type u_3\n𝔸 : Type u_2\ninst✝³ : IsROrC 𝕂\nin... | [
637,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
635,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_mul_cos_add_sin_mul_I_eq_toIocMod | [
{
"state_after": "r : ℝ\nhr : 0 < r\nθ : ℝ\nhi : toIocMod two_pi_pos (-π) θ ∈ Set.Ioc (-π) π\n⊢ arg (↑r * (cos ↑θ + sin ↑θ * I)) = toIocMod two_pi_pos (-π) θ",
"state_before": "r : ℝ\nhr : 0 < r\nθ : ℝ\n⊢ arg (↑r * (cos ↑θ + sin ↑θ * I)) = toIocMod two_pi_pos (-π) θ",
"tactic": "have hi : toIocMod Real.... | [
436,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | NonarchAddGroupSeminorm.coe_smul | [] | [
720,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
719,
1
] |
Mathlib/Order/Hom/Set.lean | OrderIso.preimage_image | [] | [
65,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Ordered.lean | lineMap_lt_right_iff_lt | [
{
"state_after": "no goals",
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"tactic":... | [
100,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.eval_prod | [] | [
1164,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1162,
1
] |
Mathlib/Data/List/Sort.lean | List.Sorted.insertionSort_eq | [
{
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"state_before": "α : Type uu\nr : α → α ... | [
258,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.Integrable.tendsto_integralSum_sum_integral | [
{
"state_after": "ι : Type u\nE : Type v\nF : Type w\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace ℝ F\nI J : Box ι\nπ : TaggedPrepartition I\ninst✝¹ : Fintype ι\nl : IntegrationParams\nf g : (ι → ℝ) → E\nvol : ι →ᵇᵃ[⊤] E →L[ℝ] F\ny y' : F\nc c₁ c₂... | [
640,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
633,
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] |
Mathlib/Topology/Algebra/Group/Basic.lean | TopologicalGroup.of_comm_of_nhds_one | [
{
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"state_before": "α : Type u\nβ : Type v\nG✝ : Type w\nH : Type x\ninst✝⁵ : TopologicalSpace G✝\ninst✝⁴ : Group G✝\ninst✝³ : TopologicalGroup G✝\ninst✝² : TopologicalSpace α\nf : α → G✝\ns : Set α\nx : α\nG : Type u\ninst✝¹ : CommGroup G\ninst✝ : TopologicalSpace G\nhmul : Tendst... | [
956,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
952,
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] |
Mathlib/Logic/Embedding/Set.lean | Equiv.asEmbedding_range | [
{
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"tactic": "simp"
}
] | [
29,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
27,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | mul_lt_of_lt_of_le_one' | [] | [
747,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
745,
1
] |
Mathlib/Algebra/Hom/Units.lean | IsUnit.inv | [
{
"state_after": "case intro\nF : Type ?u.55988\nG : Type ?u.55991\nα : Type u_1\nM : Type ?u.55997\nN : Type ?u.56000\ninst✝ : DivisionMonoid α\na b c : α\nu : αˣ\nhu : ↑u = a\n⊢ IsUnit a⁻¹",
"state_before": "F : Type ?u.55988\nG : Type ?u.55991\nα : Type u_1\nM : Type ?u.55997\nN : Type ?u.56000\ninst✝ : ... | [
392,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
] |
Mathlib/Algebra/Algebra/Unitization.lean | Unitization.fst_star | [] | [
527,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
526,
1
] |
Mathlib/Data/Real/Irrational.lean | irrational_div_int_iff | [
{
"state_after": "no goals",
"state_before": "q : ℚ\nm : ℤ\nn : ℕ\nx : ℝ\n⊢ Irrational (x / ↑m) ↔ m ≠ 0 ∧ Irrational x",
"tactic": "rw [← cast_coe_int, irrational_div_rat_iff, Int.cast_ne_zero]"
}
] | [
649,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
648,
1
] |
Mathlib/Logic/Function/Basic.lean | cast_inj | [] | [
1029,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1028,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.tendstoUniformly_iff | [
{
"state_after": "α : Type u\nβ : Type v\nX : Type ?u.82769\nι✝ : Type ?u.82772\ninst✝ : PseudoMetricSpace α\nx y z : α\nδ ε ε₁ ε₂ : ℝ\ns : Set α\nι : Type u_1\nF : ι → β → α\nf : β → α\np : Filter ι\n⊢ (∀ (ε : ℝ), ε > 0 → ∀ᶠ (n : ι) in p, ∀ (x : β), x ∈ univ → dist (f x) (F n x) < ε) ↔\n ∀ (ε : ℝ), ε > 0 → ... | [
932,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
929,
1
] |
Mathlib/Data/Polynomial/Coeff.lean | Polynomial.update_eq_add_sub_coeff | [
{
"state_after": "case a\nR✝ : Type u\nS : Type v\na✝ b : R✝\nn✝¹ m : ℕ\ninst✝¹ : Semiring R✝\np✝ q r : R✝[X]\nR : Type u_1\ninst✝ : Ring R\np : R[X]\nn : ℕ\na : R\nn✝ : ℕ\n⊢ coeff (update p n a) n✝ = coeff (p + ↑C (a - coeff p n) * X ^ n) n✝",
"state_before": "R✝ : Type u\nS : Type v\na✝ b : R✝\nn✝ m : ℕ\n... | [
369,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Analysis/LocallyConvex/BalancedCoreHull.lean | balancedCoreAux_subset | [
{
"state_after": "no goals",
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"tactic": "simpa only [one_smul] using mem_balancedCoreAux_iff.1 hx 1 norm_... | [
172,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.top_mul | [] | [
559,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
559,
9
] |
Mathlib/Logic/Function/Iterate.lean | List.foldl_const | [
{
"state_after": "case nil\nα : Type u\nβ : Type v\nf : α → α\na✝ a : α\n⊢ foldl (fun b x => f b) a [] = (f^[length []]) a\n\ncase cons\nα : Type u\nβ : Type v\nf : α → α\na✝ : α\nb : β\nl : List β\nH : ∀ (a : α), foldl (fun b x => f b) a l = (f^[length l]) a\na : α\n⊢ foldl (fun b x => f b) a (b :: l) = (f^[le... | [
250,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.cos_two_neg | [
{
"state_after": "case h.h.ha\n\n⊢ 0 ≤ cos 1\n\ncase h.h.hab\n\n⊢ cos 1 ≤ 2 / 3",
"state_before": "⊢ 2 * cos 1 ^ 2 - 1 ≤ 2 * (2 / 3) ^ 2 - 1",
"tactic": "gcongr"
},
{
"state_after": "no goals",
"state_before": "case h.h.ha\n\n⊢ 0 ≤ cos 1",
"tactic": "exact cos_one_pos.le"
},
{
"s... | [
1927,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1920,
1
] |
Std/Data/List/Lemmas.lean | List.get?_range | [
{
"state_after": "no goals",
"state_before": "m n : Nat\nh : m < n\n⊢ get? (range n) m = some m",
"tactic": "simp [range_eq_range', get?_range' _ _ h]"
}
] | [
1921,
44
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1920,
1
] |
Mathlib/Data/Int/GCD.lean | Nat.xgcdAux_succ | [] | [
55,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Analysis/Calculus/Dslope.lean | DifferentiableWithinAt.of_dslope | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\na b : 𝕜\ns : Set 𝕜\nh : DifferentiableWithinAt 𝕜 (dslope f a) s b\n⊢ DifferentiableWithinAt 𝕜 f s b",
"tactic": "simpa ... | [
133,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
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