file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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values | start list |
|---|---|---|---|---|---|---|
Mathlib/Algebra/Field/Basic.lean | toDual_rat_cast | [] | [
382,
6
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381,
1
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Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.mulVecLin_one | [
{
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251,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
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Mathlib/Data/Polynomial/Reverse.lean | Polynomial.reverse_zero | [] | [
264,
6
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263,
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Mathlib/Analysis/Convex/Extrema.lean | IsMinOn.of_isLocalMinOn_of_convexOn_Icc | [
{
"state_after": "E : Type ?u.1907\nβ : Type u_1\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : TopologicalSpace E\ninst✝⁵ : Module ℝ E\ninst✝⁴ : TopologicalAddGroup E\ninst✝³ : ContinuousSMul ℝ E\ninst✝² : OrderedAddCommGroup β\ninst✝¹ : Module ℝ β\ninst✝ : OrderedSMul ℝ β\ns : Set E\nf : ℝ → β\na b : ℝ\na_lt_b : a < b\nh... | [
51,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Complex/Exponential.lean | Real.one_lt_exp_iff | [
{
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"tactic": "rw [← exp_zero, exp_lt_exp]"
}
] | [
1543,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1543,
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Mathlib/Analysis/SpecificLimits/Basic.lean | summable_geometric_two_encode | [] | [
210,
67
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.le_trim | [
{
"state_after": "α : Type u_1\nβ : Type ?u.3497107\nγ : Type ?u.3497110\nδ : Type ?u.3497113\nι : Type ?u.3497116\nR : Type ?u.3497119\nR' : Type ?u.3497122\nm m0 : MeasurableSpace α\nμ : Measure α\ns : Set α\nhm : m ≤ m0\n⊢ ↑↑μ s ≤ ↑↑(OuterMeasure.toMeasure ↑μ (_ : m ≤ OuterMeasure.caratheodory ↑μ)) s",
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4377,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4375,
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Mathlib/Topology/MetricSpace/Infsep.lean | Set.einfsep_ne_top_iff | [] | [
281,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.edgeSet_injective | [] | [
504,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
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Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.self_trans_symm | [] | [
371,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
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Mathlib/Probability/CondCount.lean | ProbabilityTheory.pred_true_of_condCount_eq_one | [
{
"state_after": "Ω : Type u_1\ninst✝¹ : MeasurableSpace Ω\ninst✝ : MeasurableSingletonClass Ω\ns t u : Set Ω\nh : ↑↑(condCount s) t = 1\nhsf : Set.Finite s\n⊢ s ⊆ t",
"state_before": "Ω : Type u_1\ninst✝¹ : MeasurableSpace Ω\ninst✝ : MeasurableSingletonClass Ω\ns t u : Set Ω\nh : ↑↑(condCount s) t = 1\n⊢ s... | [
128,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
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Mathlib/Data/Set/Ncard.lean | Set.Finite_of_ncard_ne_zero | [] | [
121,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
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Mathlib/Algebra/Order/Sub/Basic.lean | AddHom.le_map_tsub | [
{
"state_after": "α : Type u_2\nβ : Type u_1\ninst✝⁷ : Preorder α\ninst✝⁶ : Add α\ninst✝⁵ : Sub α\ninst✝⁴ : OrderedSub α\na✝ b✝ c d : α\ninst✝³ : Preorder β\ninst✝² : Add β\ninst✝¹ : Sub β\ninst✝ : OrderedSub β\nf : AddHom α β\nhf : Monotone ↑f\na b : α\n⊢ ↑f a ≤ ↑f (a - b + b)",
"state_before": "α : Type u... | [
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Mathlib/Algebra/Order/Field/Power.lean | div_pow_le | [] | [
92,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
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Mathlib/Topology/SubsetProperties.lean | IsClopen.preimage | [] | [
1617,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1615,
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Mathlib/Data/Set/Basic.lean | Set.compl_inter_self | [] | [
1655,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/Basic.lean | Set.diff_self_inter | [] | [
2040,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/PathCategory.lean | CategoryTheory.Paths.ext_functor | [
{
"state_after": "case h_obj\nV : Type u₁\ninst✝¹ : Quiver V\nC : Type u_1\ninst✝ : Category C\nF G : Paths V ⥤ C\nh_obj : F.obj = G.obj\nh :\n ∀ (a b : V) (e : a ⟶ b),\n F.map (Quiver.Hom.toPath e) =\n eqToHom (_ : F.obj a = G.obj a) ≫ G.map (Quiver.Hom.toPath e) ≫ eqToHom (_ : G.obj b = F.obj b)\n⊢ ∀... | [
138,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
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Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.roots_map_of_injective_of_card_eq_natDegree | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\nA : Type u_1\nB : Type u_2\ninst✝³ : CommRing A\ninst✝² : CommRing B\ninst✝¹ : IsDomain A\ninst✝ : IsDomain B\np : A[X]\nf : A →+* B\nhf : Function.Injective ↑f\nhroots : ↑Multiset.card (roots p) = natDegree p\n⊢ ↑Multiset.card (roots (map f ... | [
1213,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1209,
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Mathlib/Algebra/Group/TypeTags.lean | toMul_add | [] | [
164,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
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Mathlib/RepresentationTheory/Action.lean | Action.tensorHom | [] | [
506,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Basic.lean | all_mem_nhds_filter | [] | [
1022,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1020,
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_eq_zero_iff_of_nonneg_ae | [
{
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1230,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/Pointwise/SMul.lean | Set.Nonempty.zero_smul | [
{
"state_after": "no goals",
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"tactic": "simpa [mem_smul] using ht"
}
] | [
806,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
805,
1
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src/lean/Init/Data/Nat/SOM.lean | Nat.SOM.Poly.add_denote | [
{
"state_after": "no goals",
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"tactic": "simp! [append_denote]"
},
{
"state_after": "case succ\nctx : Context\np₁✝ p₂✝ : Poly\nn✝ : Nat\nih : ∀ (p₁ p₂ : Poly), denot... | [
143,
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] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
127,
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Mathlib/Algebra/AddTorsor.lean | Prod.mk_vadd_mk | [] | [
316,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
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Mathlib/GroupTheory/Submonoid/Operations.lean | MonoidHom.prod_map_comap_prod' | [] | [
1219,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1216,
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.coeff_X_mul' | [
{
"state_after": "R : 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✝² : CommSemiring R\ninst✝¹ : CommSemiring S₁\np✝ q : MvPolynomial σ R\ninst✝ : DecidableEq σ\nm : σ →₀ ℕ\ns : σ\np : MvPolynomial σ R\n⊢ (if Finsupp.single s 1 ≤ m then 1 * coeff... | [
804,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
800,
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Mathlib/RingTheory/Localization/Integral.lean | IsLocalization.coeffIntegerNormalization_of_not_mem_support | [
{
"state_after": "no goals",
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"tacti... | [
62,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Data/Nat/Prime.lean | Nat.coprime_pow_primes | [] | [
680,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
678,
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src/lean/Init/WF.lean | Nat.strongInductionOn | [] | [
173,
28
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
169,
11
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Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_neg_iff | [] | [
178,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.derivative_X_pow | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\nA : Type z\na b : R\nn✝ : ℕ\ninst✝ : Semiring R\nn : ℕ\n⊢ ↑derivative (X ^ n) = ↑C ↑n * X ^ (n - 1)",
"tactic": "convert derivative_C_mul_X_pow (1 : R) n <;> simp"
}
] | [
115,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | RingHom.range_top_iff_surjective | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\ninst✝² : Ring R\ninst✝¹ : Ring S\ninst✝ : Ring T\ns : Subring R\nf : R →+* S\n⊢ ↑(range f) = ↑⊤ ↔ Set.range ↑f = Set.univ",
"tactic": "rw [coe_range, coe_top]"
}
] | [
1214,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1212,
1
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Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.mkUnits_eq | [] | [
478,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
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Mathlib/Data/Int/ModEq.lean | Int.ModEq.cancel_right_div_gcd | [
{
"state_after": "m n a b c d✝ : ℤ\nhm : 0 < m\nh : a * c ≡ b * c [ZMOD m]\nd : ℕ := gcd m c\n⊢ a ≡ b [ZMOD m / ↑(gcd m c)]",
"state_before": "m n a b c d : ℤ\nhm : 0 < m\nh : a * c ≡ b * c [ZMOD m]\n⊢ a ≡ b [ZMOD m / ↑(gcd m c)]",
"tactic": "letI d := gcd m c"
},
{
"state_after": "m n a b c d✝ ... | [
236,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.sup_inf | [] | [
606,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
604,
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Mathlib/Data/Finset/NAry.lean | Finset.subset_image₂ | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Setoid/Basic.lean | Setoid.eqvGen_mono | [] | [
268,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
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Mathlib/Data/Rel.lean | Rel.dom_inv | [
{
"state_after": "case h\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.1450\nr : Rel α β\nx : β\n⊢ x ∈ dom (inv r) ↔ x ∈ codom r",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.1450\nr : Rel α β\n⊢ dom (inv r) = codom r",
"tactic": "ext x"
},
{
"state_after": "no goals",
"state_before"... | [
88,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.Fork.app_one_eq_ι_comp_left | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX Y : C\nf g : X ⟶ Y\ns : Fork f g\n⊢ s.π.app one = ι s ≫ f",
"tactic": "rw [← s.app_zero_eq_ι, ← s.w left, parallelPair_map_left]"
}
] | [
341,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
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Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.toNonUnitalRingHom_commutes | [] | [
702,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
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Mathlib/Data/List/MinMax.lean | List.argmin_mem | [] | [
158,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
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Mathlib/Algebra/Module/LocalizedModule.lean | LocalizedModule.r.isEquiv | [
{
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"tactic": "rw [one_smul]"
},
... | [
68,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
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Mathlib/Algebra/Lie/Nilpotent.lean | LieModule.nilpotencyLength_eq_succ_iff | [
{
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283,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.list_prod_inv_reverse | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.356623\nm : Type u\nn : Type u'\nα : Type v\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommRing α\nA B : Matrix n n α\n⊢ (List.prod [])⁻¹ = List.prod (List.map Inv.inv (List.reverse []))",
"tactic": "rw [List.reverse_nil, List.map_nil, ... | [
599,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
595,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.degree_toSubring | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type ?u.91195\ninst✝¹ : Ring R\ninst✝ : Semiring S\nf : R →+* S\nx : S\np : R[X]\nT : Subring R\nhp : ↑(frange p) ⊆ ↑T\n⊢ degree (toSubring p T hp) = degree p",
"tactic": "simp [degree]"
}
] | [
379,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
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Mathlib/Order/Synonym.lean | OrderDual.forall | [] | [
136,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
11
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Std/Data/RBMap/Lemmas.lean | Std.RBNode.All.lowerBound? | [] | [
244,
27
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
243,
1
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Mathlib/RingTheory/MvPolynomial/Homogeneous.lean | MvPolynomial.isHomogeneous_X | [
{
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159,
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156,
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Mathlib/Order/Filter/Bases.lean | Filter.countable_biInf_principal_eq_seq_iInf | [] | [
1045,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1043,
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Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.linearMap_ext | [] | [
404,
59
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401,
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Mathlib/LinearAlgebra/Prod.lean | LinearMap.snd_apply | [] | [
84,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Data/Option/NAry.lean | Option.map₂_coe_coe | [] | [
57,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.eval₂_one | [] | [
972,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
971,
1
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Mathlib/Topology/UniformSpace/UniformEmbedding.lean | UniformInducing.mk' | [
{
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64,
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62,
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Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.lineMap_eq_right_iff | [
{
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587,
57
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585,
1
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Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.IsZero.of_mono_zero | [
{
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}
] | [
198,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
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Mathlib/LinearAlgebra/AdicCompletion.lean | adicCompletion.eval_comp_of | [] | [
249,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
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Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.measurePreserving_div_right | [
{
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"tactic": "si... | [
270,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
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Mathlib/Data/Fin/Basic.lean | Fin.succ_zero_eq_one' | [] | [
920,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
919,
1
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.cospanCompIso_hom_app_one | [] | [
313,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
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Mathlib/Data/Sym/Basic.lean | Sym.coe_erase | [] | [
220,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
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Mathlib/Order/Filter/Basic.lean | Filter.comap_id | [] | [
2067,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2066,
1
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Mathlib/CategoryTheory/Opposites.lean | CategoryTheory.unop_inv | [
{
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},
... | [
171,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
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Mathlib/Data/Finset/Basic.lean | Finset.mem_biUnion | [
{
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"tactic": "simp only [mem_def, biUnion_val, mem_dedup, mem_bind, exists_prop]"
}
] | [
3541,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3540,
1
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.weightedSMul_zero_measure | [
{
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"state_before": "α : Type u_1\nE : Type ?u.1... | [
179,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
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Mathlib/Analysis/Convex/Between.lean | Sbtw.left_mem_affineSpan | [] | [
764,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
763,
1
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Mathlib/Algebra/Regular/Basic.lean | IsRightRegular.ne_zero | [
{
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"tactic": "rintro rfl"
},
{
"state_after": "case intro.in... | [
250,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
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Mathlib/Order/Interval.lean | NonemptyInterval.toDualProd_injective | [] | [
79,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
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Mathlib/Analysis/Complex/RealDeriv.lean | HasDerivWithinAt.complexToReal_fderiv | [
{
"state_after": "no goals",
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"tactic": "simpa only [Complex.restrictScalars_one_smulR... | [
133,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
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Mathlib/Algebra/Homology/ImageToKernel.lean | homology.map_comp | [
{
"state_after": "case p\nι : Type ?u.138713\nV : Type u\ninst✝¹⁹ : Category V\ninst✝¹⁸ : HasZeroMorphisms V\nA B C : V\nf : A ⟶ B\ninst✝¹⁷ : HasImage f\ng : B ⟶ C\ninst✝¹⁶ : HasKernel g\nw : f ≫ g = 0\nA' B' C' : V\nf' : A' ⟶ B'\ninst✝¹⁵ : HasImage f'\ng' : B' ⟶ C'\ninst✝¹⁴ : HasKernel g'\nw' : f' ≫ g' = 0\nα ... | [
319,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.neg_ne_self_iff | [
{
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] | [
226,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
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Mathlib/Topology/Maps.lean | quotientMap_iff_closed | [
{
"state_after": "no goals",
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"tactic": "simp only... | [
284,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
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Mathlib/Data/Finset/Pointwise.lean | Finset.mul_add_subset | [] | [
1075,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1074,
1
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Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csSup_le_csSup | [] | [
467,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
Mathlib/Combinatorics/Derangements/Finite.lean | card_derangements_fin_add_two | [
{
"state_after": "α : Type ?u.2521\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nn : ℕ\nh1 : ∀ (a : Fin (n + 1)), card ↑({a}ᶜ) = card (Fin n)\n⊢ card ↑(derangements (Fin (n + 2))) =\n (n + 1) * card ↑(derangements (Fin n)) + (n + 1) * card ↑(derangements (Fin (n + 1)))",
"state_before": "α : Type ?u.2521\n... | [
66,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
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Mathlib/Data/Fin/Tuple/Basic.lean | Fin.find_spec | [
{
"state_after": "m n✝ n : ℕ\np : Fin (n + 1) → Prop\nI : DecidablePred p\ni : Fin (n + 1)\nhi :\n i ∈\n Option.casesOn (find fun i => p (castLT i (_ : ↑i < Nat.succ n))) (if x : p (last n) then some (last n) else none)\n fun i => some (castLT i (_ : ↑i < Nat.succ n))\n⊢ p i",
"state_before": "m n✝... | [
864,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
849,
1
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Mathlib/Data/ENat/Basic.lean | ENat.add_one_le_iff | [
{
"state_after": "no goals",
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}
] | [
193,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.edges_append | [
{
"state_after": "no goals",
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"tactic": "simp [edges]"
}
] | [
762,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
761,
1
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Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.nnnorm_zero | [
{
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"state_before": "α : Type u... | [
313,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.iterate_eq_of_map_eq_add_int | [
{
"state_after": "no goals",
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"tactic": "simpa only [nsmul_eq_mul, add_right_iterate] using (f.commute_add_int m).iterate_eq_of_map_eq n h"
}
] | [
585,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
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Mathlib/Data/Quot.lean | true_equivalence | [] | [
449,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/Topology/Algebra/UniformGroup.lean | uniformity_eq_comap_nhds_one_swapped | [
{
"state_after": "α : Type u_1\nβ : Type ?u.164871\ninst✝² : UniformSpace α\ninst✝¹ : Group α\ninst✝ : UniformGroup α\n⊢ comap ((fun x => x.snd / x.fst) ∘ Prod.swap) (𝓝 1) = comap (fun x => x.fst / x.snd) (𝓝 1)",
"state_before": "α : Type u_1\nβ : Type ?u.164871\ninst✝² : UniformSpace α\ninst✝¹ : Group α\... | [
286,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.sdiff_adj | [] | [
291,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Module.DualBases.lc_def | [] | [
691,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
690,
1
] |
Mathlib/Order/RelClasses.lean | ssubset_of_ne_of_subset | [] | [
765,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
764,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.continuous' | [] | [
1170,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1167,
11
] |
Mathlib/Order/Hom/Basic.lean | OrderIso.isCompl | [] | [
1369,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1368,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.coe_prod | [
{
"state_after": "case empty\nK : Type u_3\nL : Type u_2\nL' : Type ?u.112045\ninst✝⁵ : Field K\ninst✝⁴ : Field L\ninst✝³ : Field L'\ninst✝² : Algebra K L\ninst✝¹ : Algebra K L'\nS : IntermediateField K L\nι : Type u_1\ninst✝ : Fintype ι\nf : ι → { x // x ∈ S }\n⊢ ↑(∏ i in ∅, f i) = ∏ i in ∅, ↑(f i)\n\ncase ins... | [
362,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_add_eq_right_of_degree_lt | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q : R[X]\nι : Type ?u.530544\nh : degree p < degree q\n⊢ degree (p + q) = degree q",
"tactic": "rw [add_comm, degree_add_eq_left_of_degree_lt h]"
}
] | [
698,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
697,
1
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Mathlib/AlgebraicTopology/AlternatingFaceMapComplex.lean | AlgebraicTopology.AlternatingFaceMapComplex.obj_X | [] | [
134,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
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Mathlib/Data/List/Func.lean | List.Func.get_pointwise | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝² : Inhabited α\ninst✝¹ : Inhabited β\ninst✝ : Inhabited γ\nf : α → β → γ\nh1 : f default default = default\nk : ℕ\n⊢ get k (pointwise f [] []) = f (get k []) (get k [])",
"tactic": "simp only [h1, get_nil, pointwise,... | [
301,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.leadingCoeff_C_mul_X | [
{
"state_after": "no goals",
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"tactic": "simpa only [pow_one] using leadingCoeff_C_mul_X_pow a 1"
}
] | [
807,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
806,
1
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Mathlib/Analysis/Normed/Group/Pointwise.lean | div_ball | [
{
"state_after": "no goals",
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"tactic": "simp [div_eq_mul_inv]"
}
] | [
238,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Data/Sym/Sym2.lean | Sym2.Rel.symm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.124\nγ : Type ?u.127\nx y : α × α\n⊢ Rel α x y → Rel α y x",
"tactic": "aesop (rule_sets [Sym2])"
}
] | [
76,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Data/Multiset/FinsetOps.lean | Multiset.coe_ndinsert | [] | [
39,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
Mathlib/Algebra/Group/OrderSynonym.lean | ofDual_mul | [] | [
119,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.coeFn_abs | [] | [
1564,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1564,
1
] |
Std/Logic.lean | false_imp_iff | [] | [
118,
83
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
118,
1
] |
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