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/Topology/Order/Basic.lean | exists_seq_strictMono_tendsto_nhdsWithin | [] | [
2149,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2145,
1
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Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.smul_dirac_apply | [
{
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"tactic": "simp only [smul_apply, smul_eq_mul, dirac_apply, ←... | [
529,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
527,
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Mathlib/SetTheory/Ordinal/Principal.lean | Ordinal.add_omega_opow | [
{
"state_after": "a b : Ordinal\nh : a < ω ^ b\n⊢ a + ω ^ b ≤ ω ^ b",
"state_before": "a b : Ordinal\nh : a < ω ^ b\n⊢ a + ω ^ b = ω ^ b",
"tactic": "refine' le_antisymm _ (le_add_left _ _)"
},
{
"state_after": "case H₁\na b : Ordinal\nh✝ : a < ω ^ b\nh : a < ω ^ 0\n⊢ a + ω ^ 0 ≤ ω ^ 0\n\ncase H... | [
213,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
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Mathlib/RingTheory/Localization/InvSubmonoid.lean | IsLocalization.toInvSubmonoid_eq_mk' | [
{
"state_after": "R : Type u_1\ninst✝⁴ : CommRing R\nM : Submonoid R\nS : Type u_2\ninst✝³ : CommRing S\ninst✝² : Algebra R S\nP : Type ?u.210005\ninst✝¹ : CommRing P\ninst✝ : IsLocalization M S\nx : { x // x ∈ M }\n⊢ ↑(↑(toInvSubmonoid M S) x) * ↑(algebraMap R S) ↑x = mk' S 1 x * ↑(algebraMap R S) ↑x",
"st... | [
102,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
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Mathlib/Data/Polynomial/UnitTrinomial.lean | Polynomial.trinomial_monic | [
{
"state_after": "R : Type u_1\ninst✝ : Semiring R\nk m n : ℕ\nu v w : R\nhkm : k < m\nhmn : m < n\n✝ : Nontrivial R\n⊢ Monic (trinomial k m n u v 1)",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nk m n : ℕ\nu v w : R\nhkm : k < m\nhmn : m < n\n⊢ Monic (trinomial k m n u v 1)",
"tactic": "nontrivi... | [
110,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
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Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.ofReal_set_integral_one_of_measure_ne_top | [
{
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199,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
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Mathlib/Data/List/Basic.lean | List.dropSlice_eq | [
{
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4341,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4338,
1
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Mathlib/Data/Int/Parity.lean | Int.natAbs_even | [
{
"state_after": "no goals",
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"tactic": "simp [even_iff_two_dvd, dvd_natAbs, coe_nat_dvd_left.symm]"
}
] | [
213,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.inv_mul_eq_iff_eq_mul_of_invertible | [
{
"state_after": "no goals",
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"tactic": "rw [← h, mul_inv_cancel_left_of_invertible]"... | [
377,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
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Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.card_le_nat | [] | [
1577,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1576,
1
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Mathlib/Data/Sum/Basic.lean | Sum.Not_isRight | [
{
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"tactic": "simp"
}
] | [
144,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
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Mathlib/CategoryTheory/Monoidal/End.lean | CategoryTheory.μ_naturalityᵣ | [
{
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166,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Control/Basic.lean | guard_true | [
{
"state_after": "no goals",
"state_before": "α β γ : Type u\nF : Type → Type v\ninst✝ : Alternative F\nh : Decidable True\n⊢ guard True = pure ()",
"tactic": "simp [guard, if_pos]"
}
] | [
201,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
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Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.toRingEquiv_eq_coe | [] | [
191,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Analysis/LocallyConvex/Basic.lean | Absorbs.neg | [] | [
222,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Combinatorics/SimpleGraph/Hasse.lean | SimpleGraph.hasse_prod | [
{
"state_after": "case Adj.h.h.a\nα : Type u_1\nβ : Type u_2\ninst✝¹ : PartialOrder α\ninst✝ : PartialOrder β\nx y : α × β\n⊢ Adj (hasse (α × β)) x y ↔ Adj (hasse α □ hasse β) x y",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝¹ : PartialOrder α\ninst✝ : PartialOrder β\n⊢ hasse (α × β) = hasse α □ hass... | [
77,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | invOf_pow | [] | [
58,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.coeFn_injective | [] | [
143,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Data/SetLike/Basic.lean | SetLike.le_def | [] | [
189,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | continuousAt_cpow | [
{
"state_after": "α : Type ?u.293132\np : ℂ × ℂ\nhp_fst : 0 < p.fst.re ∨ p.fst.im ≠ 0\nhp_fst_ne_zero : p.fst ≠ 0\n⊢ ContinuousAt (fun x => Complex.exp (Complex.log x.fst * x.snd)) p",
"state_before": "α : Type ?u.293132\np : ℂ × ℂ\nhp_fst : 0 < p.fst.re ∨ p.fst.im ≠ 0\nhp_fst_ne_zero : p.fst ≠ 0\n⊢ Continu... | [
103,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
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Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.zero_compLinearMap | [] | [
418,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_lt_rpow_iff | [] | [
429,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.symm_image_target_eq_source | [] | [
542,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.max_singleton | [
{
"state_after": "F : Type ?u.312871\nα : Type u_1\nβ : Type ?u.312877\nγ : Type ?u.312880\nι : Type ?u.312883\nκ : Type ?u.312886\ninst✝ : LinearOrder α\na : α\n⊢ Finset.max (insert a ∅) = ↑a",
"state_before": "F : Type ?u.312871\nα : Type u_1\nβ : Type ?u.312877\nγ : Type ?u.312880\nι : Type ?u.312883\nκ ... | [
1177,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1175,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.coe_div | [] | [
722,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
721,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.nondegenerateRestrictOfDisjointOrthogonal | [
{
"state_after": "case mk\nR : Type ?u.1488672\nM : Type ?u.1488675\ninst✝¹⁶ : Semiring R\ninst✝¹⁵ : AddCommMonoid M\ninst✝¹⁴ : Module R M\nR₁ : Type u_1\nM₁ : Type u_2\ninst✝¹³ : Ring R₁\ninst✝¹² : AddCommGroup M₁\ninst✝¹¹ : Module R₁ M₁\nR₂ : Type ?u.1489323\nM₂ : Type ?u.1489326\ninst✝¹⁰ : CommSemiring R₂\ni... | [
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35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1333,
1
] |
Mathlib/Data/Polynomial/Coeff.lean | Polynomial.coeff_mul | [
{
"state_after": "case ofFinsupp\nR : Type u\nS : Type v\na b : R\nn✝ m : ℕ\ninst✝ : Semiring R\np✝ q✝ r q : R[X]\nn : ℕ\np : AddMonoidAlgebra R ℕ\n⊢ coeff ({ toFinsupp := p } * q) n = ∑ x in Nat.antidiagonal n, coeff { toFinsupp := p } x.fst * coeff q x.snd",
"state_before": "R : Type u\nS : Type v\na b : ... | [
126,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | StrictMono.tendsto_atTop | [] | [
602,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
601,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.StronglyMeasurable.separableSpace_range_union_singleton | [] | [
615,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
611,
1
] |
Mathlib/Data/Set/Function.lean | Function.Semiconj.bijOn_range | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.112998\nι : Sort ?u.113001\nπ : α → Type ?u.113006\nfa : α → α\nfb : β → β\nf : α → β\ng : β → γ\ns t : Set α\nh : Semiconj f fa fb\nha : Bijective fa\nhf : Injective f\n⊢ BijOn fb (f '' univ) (f '' univ)",
"state_before": "α : Type u_1\nβ : Type u_2... | [
1661,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1658,
1
] |
Mathlib/Computability/Partrec.lean | Computable.id | [] | [
301,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
11
] |
Mathlib/Data/PNat/Factors.lean | PrimeMultiset.prod_ofPrime | [] | [
153,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Std/Data/PairingHeap.lean | Std.PairingHeapImp.Heap.WF.tail | [
{
"state_after": "α : Type u_1\ns : Heap α\nle : α → α → Bool\nhwf : WF le s\n⊢ WF le (Option.getD (Heap.tail? le s) Heap.nil)",
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"tactic": "simp only [Heap.tail]"
},
{
"state_after": "no goals... | [
267,
34
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
263,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | MonoidHom.mker_one | [
{
"state_after": "case h\nM : Type u_1\nN : Type u_2\nP : Type ?u.140375\ninst✝³ : MulOneClass M\ninst✝² : MulOneClass N\ninst✝¹ : MulOneClass P\nS : Submonoid M\nA : Type ?u.140396\ninst✝ : SetLike A M\nhA : SubmonoidClass A M\nS' : A\nF : Type ?u.140420\nmc : MonoidHomClass F M N\nx✝ : M\n⊢ x✝ ∈ mker 1 ↔ x✝ ∈... | [
1211,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1209,
1
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Mathlib/Order/Atoms.lean | OrderIso.isSimpleOrder_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝³ : PartialOrder α\ninst✝² : PartialOrder β\ninst✝¹ : BoundedOrder α\ninst✝ : BoundedOrder β\nf : α ≃o β\n⊢ IsSimpleOrder α ↔ IsSimpleOrder β",
"tactic": "rw [isSimpleOrder_iff_isAtom_top, isSimpleOrder_iff_isAtom_top, ← f.is... | [
818,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
815,
1
] |
Mathlib/GroupTheory/PGroup.lean | IsPGroup.of_equiv | [] | [
98,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
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Mathlib/Algebra/Order/Kleene.lean | Prod.fst_kstar | [] | [
317,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | orderOf_abs_ne_one | [
{
"state_after": "G : Type u\nA : Type v\nx y : G\na b : A\nn m : ℕ\ninst✝ : LinearOrderedRing G\nh : abs x ≠ 1\n⊢ ∀ (n : ℕ), 0 < n → x ^ n ≠ 1",
"state_before": "G : Type u\nA : Type v\nx y : G\na b : A\nn m : ℕ\ninst✝ : LinearOrderedRing G\nh : abs x ≠ 1\n⊢ orderOf x = 0",
"tactic": "rw [orderOf_eq_ze... | [
1088,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1082,
1
] |
Mathlib/Order/Minimal.lean | minimals_empty | [] | [
59,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | nonempty_of_finprod_mem_ne_one | [] | [
756,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
755,
1
] |
Mathlib/Data/Int/Bitwise.lean | Int.testBit_lxor | [
{
"state_after": "no goals",
"state_before": "m n : ℤ\nk : ℕ\n⊢ testBit (lxor' m n) k = xor (testBit m k) (testBit n k)",
"tactic": "rw [← bitwise_xor, testBit_bitwise]"
}
] | [
361,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.lift_mk_compr₂ | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹⁴ : CommSemiring R\nR' : Type ?u.620874\ninst✝¹³ : Monoid R'\nR'' : Type ?u.620880\ninst✝¹² : Semiring R''\nM : Type u_3\nN : Type u_2\nP : Type u_4\nQ : Type ?u.620895\nS : Type ?u.620898\ninst✝¹¹ : AddCommMonoid M\ninst✝¹⁰ : AddCommMonoid N... | [
508,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
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] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.le_coe_iff | [] | [
712,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
712,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atTop_add_nonneg_right | [] | [
641,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
639,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.equiv_symm_neg | [] | [
807,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
806,
1
] |
Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | SeminormFamily.basisSets_smul_left | [
{
"state_after": "case intro.intro.intro\n𝕜 : Type u_2\n𝕜₂ : Type ?u.68753\n𝕝 : Type ?u.68756\n𝕝₂ : Type ?u.68759\nE : Type u_1\nF : Type ?u.68765\nG : Type ?u.68768\nι : Type u_3\nι' : Type ?u.68774\ninst✝³ : NormedField 𝕜\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\np : SeminormFamily 𝕜 E ι\ninst✝ : ... | [
180,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | InnerProductGeometry.inner_eq_neg_mul_norm_iff_angle_eq_pi | [
{
"state_after": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx✝ y✝ x y : V\nhx : x ≠ 0\nhy : y ≠ 0\nh : inner x y = -(‖x‖ * ‖y‖)\n⊢ angle x y = π",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx✝ y✝ x y : V\nhx : x ≠ 0\nhy : y ... | [
256,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.measurableSet_cut | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.22535\nδ : Type ?u.22538\ninst✝ : MeasurableSpace α\nr : α → β → Prop\nf : α →ₛ β\nh : ∀ (b : β), MeasurableSet {a | r a b}\nthis : {a | r a (↑f a)} = ⋃ (b : β) (_ : b ∈ range ↑f), {a | r a b} ∩ ↑f ⁻¹' {b}\n⊢ MeasurableSet {a | r a (↑f a)}",
"state_b... | [
205,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Order/Filter/Cofinite.lean | Finset.eventually_cofinite_nmem | [] | [
85,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.smul_finset_subset_smul_finset_iff₀ | [] | [
2049,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2048,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | ContinuousLinearMap.integral_comp_comm' | [
{
"state_after": "case pos\nα : Type u_4\nβ : Type ?u.1835818\nE : Type u_2\nF : Type u_3\ninst✝⁹ : MeasurableSpace α\nι : Type ?u.1835830\ninst✝⁸ : NormedAddCommGroup E\nμ : MeasureTheory.Measure α\n𝕜 : Type u_1\ninst✝⁷ : IsROrC 𝕜\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpac... | [
1118,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1111,
1
] |
Mathlib/GroupTheory/Subsemigroup/Center.lean | Set.center_units_eq | [] | [
102,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | BilinForm.toMatrix_toBilin | [] | [
355,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/Data/Nat/Hyperoperation.lean | hyperoperation_recursion | [
{
"state_after": "no goals",
"state_before": "n m k : ℕ\n⊢ hyperoperation (n + 1) m (k + 1) = hyperoperation n m (hyperoperation (n + 1) m k)",
"tactic": "rw [hyperoperation]"
}
] | [
60,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.ceil_intCast | [
{
"state_after": "F : Type ?u.47671\nα✝ : Type ?u.47674\nβ : Type ?u.47677\ninst✝³ : LinearOrderedSemiring α✝\ninst✝² : FloorSemiring α✝\na✝ : α✝\nn : ℕ\nα : Type u_1\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorSemiring α\nz : ℤ\na : ℕ\n⊢ ↑z ≤ ↑a ↔ z ≤ ↑a",
"state_before": "F : Type ?u.47671\nα✝ : Type ?u.4... | [
311,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/Data/List/Basic.lean | List.pmap_append' | [] | [
3226,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3222,
1
] |
Mathlib/Data/Fintype/Card.lean | Fintype.card_punit | [] | [
359,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
Mathlib/Probability/CondCount.lean | ProbabilityTheory.condCount_empty_meas | [
{
"state_after": "no goals",
"state_before": "Ω : Type u_1\ninst✝ : MeasurableSpace Ω\n⊢ condCount ∅ = 0",
"tactic": "simp [condCount]"
}
] | [
61,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Combinatorics/SimpleGraph/StronglyRegular.lean | SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_not_adj_compl | [
{
"state_after": "V : Type u\ninst✝² : Fintype V\ninst✝¹ : DecidableEq V\nG : SimpleGraph V\ninst✝ : DecidableRel G.Adj\nn k ℓ μ : ℕ\nh : IsSRGWith G n k ℓ μ\nv w : V\nhn : v ≠ w\nhna : ¬Adj (Gᶜ) v w\n⊢ Finset.card (neighborFinset G vᶜ \\ {v} ∩ (neighborFinset G wᶜ \\ {w})) = n - (2 * k - ℓ)",
"state_before... | [
168,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Data/MvPolynomial/Division.lean | MvPolynomial.coeff_modMonomial_of_not_le | [
{
"state_after": "case intro\nσ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\ns : σ →₀ ℕ\nx : MvPolynomial σ R\nd : σ →₀ ℕ\nh : ¬s ≤ s + d\n⊢ False",
"state_before": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\ns' s : σ →₀ ℕ\nx : MvPolynomial σ R\nh : ¬s ≤ s'\n⊢ ¬∃ d, s' = s + d",
"tactic": ... | [
114,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.lift_id | [] | [
577,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
576,
1
] |
Mathlib/GroupTheory/Complement.lean | Subgroup.card_right_transversal | [] | [
290,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.mul_cases | [
{
"state_after": "q : ℚ\nx y : ℝ\n⊢ ¬x * y ∈ Set.range Rat.cast → ¬x ∈ Set.range Rat.cast ∨ ¬y ∈ Set.range Rat.cast",
"state_before": "q : ℚ\nx y : ℝ\n⊢ Irrational (x * y) → Irrational x ∨ Irrational y",
"tactic": "delta Irrational"
},
{
"state_after": "q : ℚ\nx y : ℝ\n⊢ x ∈ Set.range Rat.cast ∧... | [
336,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
Mathlib/Topology/SubsetProperties.lean | SigmaCompactSpace.of_countable | [] | [
1279,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1277,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.comp_cons | [
{
"state_after": "case h\nm n : ℕ\nα✝ : Fin (n + 1) → Type u\nx : α✝ 0\nq✝ : (i : Fin (n + 1)) → α✝ i\np : (i : Fin n) → α✝ (succ i)\ni : Fin n\ny✝ : α✝ (succ i)\nz : α✝ 0\nα : Type u_1\nβ : Type u_2\ng : α → β\ny : α\nq : Fin n → α\nj : Fin (n + 1)\n⊢ (g ∘ cons y q) j = cons (g y) (g ∘ q) j",
"state_before... | [
244,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.carrier_eq_coe | [] | [
432,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/Algebra/Homology/Single.lean | ChainComplex.single₀_obj_X_0 | [] | [
149,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Algebra/CharP/Two.lean | CharTwo.list_sum_sq | [] | [
100,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/LinearAlgebra/Prod.lean | LinearMap.inl_apply | [] | [
186,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/LinearAlgebra/Projection.lean | LinearMap.ofIsCompl_eq' | [] | [
254,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Data/Sym/Sym2.lean | Sym2.isDiag_iff_proj_eq | [] | [
446,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
] |
Mathlib/LinearAlgebra/Projection.lean | LinearMap.coe_equivProdOfSurjectiveOfIsCompl | [] | [
333,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.CompactOpens.coe_sup | [] | [
544,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_const_one | [] | [
1313,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1312,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | dist_le_pi_dist | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.398493\nι : Type ?u.398496\ninst✝² : PseudoMetricSpace α\nπ : β → Type u_1\ninst✝¹ : Fintype β\ninst✝ : (b : β) → PseudoMetricSpace (π b)\nf g : (b : β) → π b\nb : β\n⊢ dist (f b) (g b) ≤ dist f g",
"tactic": "simp only [d... | [
2044,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2043,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.closure_union | [] | [
998,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
997,
1
] |
Mathlib/Order/BooleanAlgebra.lean | disjoint_sdiff_sdiff | [] | [
167,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Data/Set/Basic.lean | Set.not_mem_subset | [] | [
389,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.toWithTop_natCast' | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nh : Decidable (↑n).Dom\n⊢ toWithTop ↑n = ↑n",
"tactic": "rw [toWithTop_natCast n]"
}
] | [
585,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
] |
Mathlib/FieldTheory/IsAlgClosed/Spectrum.lean | spectrum.pow_image_subset | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u\nA : Type v\ninst✝² : Field 𝕜\ninst✝¹ : Ring A\ninst✝ : Algebra 𝕜 A\na : A\nn : ℕ\n⊢ (fun x => x ^ n) '' σ a ⊆ σ (a ^ n)",
"tactic": "simpa only [eval_pow, eval_X, aeval_X_pow] using subset_polynomial_aeval a (X ^ n : 𝕜[X])"
}
] | [
137,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Analysis/PSeries.lean | Real.not_summable_one_div_nat_cast | [
{
"state_after": "no goals",
"state_before": "⊢ ¬Summable fun n => 1 / ↑n",
"tactic": "simpa only [inv_eq_one_div] using Real.not_summable_nat_cast_inv"
}
] | [
257,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.coe_inf | [] | [
539,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.affineSpan_pair_parallel_iff_vectorSpan_eq | [
{
"state_after": "no goals",
"state_before": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\np₁ p₂ p₃ p₄ : P\n⊢ affineSpan k {p₁, p₂} ∥ affineSpan k {p₃, p₄} ↔ vectorSpan k {p₁, p₂} = vectorSpan k {p₃, p₄}",
"tactic": "si... | [
1803,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1799,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.constantCoeff_one | [] | [
514,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
513,
1
] |
Mathlib/Topology/Sheaves/Sheaf.lean | TopCat.Sheaf.id_app | [] | [
162,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Data/Set/Intervals/Instances.lean | Set.Ioc.coe_ne_one | [] | [
273,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.ofBijective_apply | [] | [
527,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
525,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.ae_eq_set_compl | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.112006\nγ : Type ?u.112009\nδ : Type ?u.112012\nι : Type ?u.112015\ninst✝ : MeasurableSpace α\nμ μ₁ μ₂ : Measure α\ns✝ s₁ s₂ t✝ s t : Set α\n⊢ sᶜ =ᵐ[μ] t ↔ s =ᵐ[μ] tᶜ",
"tactic": "rw [← ae_eq_set_compl_compl, compl_compl]"
}
] | [
498,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | contDiff_zero | [
{
"state_after": "𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\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 : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nX : Type uX\ninst✝¹ : NormedAdd... | [
1444,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1442,
1
] |
Mathlib/Data/List/Pairwise.lean | List.pairwise_filter | [
{
"state_after": "α : Type u_1\nβ : Type ?u.15897\nR S T : α → α → Prop\na : α\nl✝ : List α\np : α → Prop\ninst✝ : DecidablePred p\nl : List α\n⊢ Pairwise\n (fun a a' =>\n ∀ (b : α),\n b ∈ Option.guard (fun x => decide (p x) = true) a →\n ∀ (b' : α), b' ∈ Option.guard (fun x => d... | [
225,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.tsum_indicator_apply_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.356681\nγ : Type ?u.356684\nδ : Type ?u.356687\nι : Type ?u.356690\nR : Type ?u.356693\nR' : Type ?u.356696\nm0 : MeasurableSpace α\ninst✝³ : MeasurableSpace β\ninst✝² : MeasurableSpace γ\nμ✝ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t : S... | [
2156,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2149,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | div_lt_one_of_neg | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.155573\nα : Type u_1\nβ : Type ?u.155579\ninst✝ : LinearOrderedField α\na b c d : α\nn : ℤ\nhb : b < 0\n⊢ a / b < 1 ↔ b < a",
"tactic": "rw [div_lt_iff_of_neg hb, one_mul]"
}
] | [
816,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
816,
1
] |
Mathlib/Algebra/Order/LatticeGroup.lean | LatticeOrderedCommGroup.m_neg_abs | [
{
"state_after": "case refine'_1\nα : 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 : α\n⊢ abs a⁻ ≤ 1\n\ncase refine'_2\nα : 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... | [
355,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/Data/Multiset/Pi.lean | Multiset.pi_zero | [] | [
109,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.aeval_algHom_apply | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nA : Type z\nA' : Type ?u.893198\nB' : Type ?u.893201\na b : R\nn : ℕ\ninst✝⁷ : CommSemiring A'\ninst✝⁶ : Semiring B'\ninst✝⁵ : CommSemiring R\np✝¹ q✝ : R[X]\ninst✝⁴ : Semiring A\ninst✝³ : Algebra R A\nB : Type u_2\ninst✝² : Semiring B\ninst✝¹ : Algebra R B\n... | [
285,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | le_div_iff_mul_le' | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : CommGroup α\ninst✝¹ : LE α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b c d : α\n⊢ b ≤ c / a ↔ a * b ≤ c",
"tactic": "rw [le_div_iff_mul_le, mul_comm]"
}
] | [
810,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
810,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | uniformity_pseudoedist | [] | [
166,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Std/Data/Nat/Gcd.lean | Nat.coprime.mul | [] | [
292,
38
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
291,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.disjoint_sup_left | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.157856\nα : Type u_1\nβ : Type ?u.157862\nγ : Type ?u.157865\nι : Type u_2\nκ : Type ?u.157871\ninst✝¹ : DistribLattice α\ninst✝ : OrderBot α\ns : Finset ι\nt : Finset κ\nf : ι → α\ng : κ → α\na : α\n⊢ _root_.Disjoint (sup s f) a ↔ ∀ ⦃i : ι⦄, i ∈ s →... | [
532,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
11
] |
Mathlib/Order/Filter/SmallSets.lean | Filter.smallSets_bot | [
{
"state_after": "α : Type u_1\nβ : Type ?u.2653\nι : Sort ?u.2656\nl l' la : Filter α\nlb : Filter β\n⊢ Monotone powerset",
"state_before": "α : Type u_1\nβ : Type ?u.2653\nι : Sort ?u.2656\nl l' la : Filter α\nlb : Filter β\n⊢ smallSets ⊥ = pure ∅",
"tactic": "rw [smallSets, lift'_bot, powerset_empty,... | [
100,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
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