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/LinearAlgebra/Basic.lean | Submodule.mem_right_iff_eq_zero_of_disjoint | [] | [
674,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
672,
1
] |
Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | coplanar_of_finrank_eq_two | [
{
"state_after": "k : Type u_2\nV : Type u_3\nP : Type u_1\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\ns : Set P\nh : finrank k V = 2\nthis : FiniteDimensional k V\n⊢ Coplanar k s",
"state_before": "k : Type u_2\nV : Type u_3\nP : Type u_1\ninst✝³ : Divis... | [
739,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
736,
1
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Mathlib/Topology/Constructions.lean | prod_generateFrom_generateFrom_eq | [
{
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646,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
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Mathlib/Algebra/Order/CompleteField.lean | LinearOrderedField.inducedMap_inv_self | [
{
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247,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/FieldTheory/Subfield.lean | Subfield.coe_top | [] | [
466,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
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Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.Disjoint.pow_disjoint_pow | [] | [
199,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
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Mathlib/Order/Cover.lean | Covby.eq_of_between | [] | [
457,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
1
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Mathlib/Analysis/NormedSpace/Extend.lean | ContinuousLinearMap.extendTo𝕜'_apply | [] | [
132,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
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Mathlib/Order/Basic.lean | lt_iff_lt_of_le_iff_le' | [] | [
511,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
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Mathlib/Analysis/Calculus/Deriv/Basic.lean | hasDerivAt_id' | [] | [
645,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
644,
1
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Mathlib/Order/Filter/AtTopBot.lean | Filter.eventually_iff_seq_eventually | [
{
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1872,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1864,
1
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Mathlib/Geometry/Manifold/ChartedSpace.lean | ChartedSpaceCore.open_target | [
{
"state_after": "H : Type u\nH' : Type ?u.57399\nM : Type u_1\nM' : Type ?u.57405\nM'' : Type ?u.57408\ninst✝ : TopologicalSpace H\nc : ChartedSpaceCore H M\ne : LocalEquiv M H\nhe : e ∈ c.atlas\nE : e.target ∩ ↑(LocalEquiv.symm e) ⁻¹' e.source = e.target\n⊢ IsOpen e.target",
"state_before": "H : Type u\nH... | [
800,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
1
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Mathlib/Analysis/Complex/Isometry.lean | LinearIsometry.re_apply_eq_re | [
{
"state_after": "case h₃\nf : ℂ →ₗᵢ[ℝ] ℂ\nh : ↑f 1 = 1\nz : ℂ\n⊢ ∀ (z : ℂ), z + ↑(starRingEnd ℂ) z = ↑f z + ↑(starRingEnd ((fun x => ℂ) z)) (↑f z)",
"state_before": "f : ℂ →ₗᵢ[ℝ] ℂ\nh : ↑f 1 = 1\nz : ℂ\n⊢ (↑f z).re = z.re",
"tactic": "apply LinearIsometry.re_apply_eq_re_of_add_conj_eq"
},
{
"st... | [
125,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.aeval_zero' | [] | [
1520,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1518,
1
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Mathlib/Algebra/Free.lean | FreeSemigroup.tail_mul | [] | [
479,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
1
] |
Mathlib/CategoryTheory/Extensive.lean | CategoryTheory.IsVanKampenColimit.of_iso | [
{
"state_after": "J : Type v'\ninst✝² : Category J\nC : Type u\ninst✝¹ : Category C\nX Y : C\nD : Type u''\ninst✝ : Category D\nF : J ⥤ C\nc c' : Cocone F\nH : IsVanKampenColimit c\ne : c ≅ c'\nF' : J ⥤ C\nc'' : Cocone F'\nα : F' ⟶ F\nf : c''.pt ⟶ c'.pt\nh : α ≫ c'.ι = c''.ι ≫ (Functor.const J).map f\nhα : NatT... | [
532,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
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Mathlib/CategoryTheory/Abelian/Pseudoelements.lean | CategoryTheory.Abelian.Pseudoelement.sub_of_eq_image | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\ninst✝ : Abelian C\nP Q : C\nf : P ⟶ Q\nx y : Pseudoelement P\na a' : Over P\nh : pseudoApply f (Quotient.mk (setoid P) a) = pseudoApply f (Quotient.mk (setoid P) a')\nR : C\np : R ⟶ ((fun g => app f g) a).left\nq : R ⟶ ((fun g => app f g) a').left\nep : Epi p\n... | [
456,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
1
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Mathlib/Data/Set/Ncard.lean | Set.ncard_diff_singleton_lt_of_mem | [
{
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"state_before": "α : Type u_1\nβ : Type ?u.15901\ns t : Set α\na b x y : α\nf : α → β\nh : a ∈ s\nhs : autoParam (Set.Finite s)... | [
200,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.zero_apply | [] | [
176,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_neg | [] | [
1262,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1261,
1
] |
Mathlib/Algebra/Group/Basic.lean | eq_mul_of_mul_inv_eq | [
{
"state_after": "no goals",
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"tactic": "simp [h.symm]"
}
] | [
648,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
648,
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.mem_ball_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.38658\nι : Type ?u.38661\ninst✝ : PseudoMetricSpace α\nx y z : α\nδ ε ε₁ ε₂ : ℝ\ns : Set α\n⊢ x ∈ ball y ε ↔ y ∈ ball x ε",
"tactic": "rw [mem_ball', mem_ball]"
}
] | [
573,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
573,
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Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.isUnit_of_right_inverse | [] | [
219,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
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Mathlib/Deprecated/Subfield.lean | IsSubfield.inter | [] | [
164,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.affineCombination_linear | [] | [
389,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Algebra/GCDMonoid/Finset.lean | Finset.lcm_mono_fun | [] | [
110,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Std/Data/Int/Lemmas.lean | Int.lt_add_of_neg_lt_sub_left | [] | [
1104,
63
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1103,
11
] |
Mathlib/MeasureTheory/Measure/Regular.lean | IsOpen.exists_lt_isCompact | [] | [
477,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
1
] |
Mathlib/GroupTheory/Submonoid/Membership.lean | SMulCommClass.of_mclosure_eq_top | [
{
"state_after": "case refine'_1\nM : Type u_3\nA : Type ?u.240612\nB : Type ?u.240615\nN : Type u_1\nα : Type u_2\ninst✝² : Monoid M\ninst✝¹ : SMul N α\ninst✝ : MulAction M α\ns : Set M\nhtop : Submonoid.closure s = ⊤\nhs : ∀ (x : M), x ∈ s → ∀ (y : N) (z : α), x • y • z = y • x • z\nx : M\n⊢ ∀ (n : N) (a : α)... | [
559,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
551,
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lift_mk_eq' | [] | [
329,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Concrete.lean | List.cycleType_formPerm | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\nl l' : List α\nhl : Nodup l\nhn : 2 ≤ length (attach l)\n⊢ cycleType (formPerm (attach l)) = {length l}",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\nl l' : List α\nhl : Nodup l\nhn : 2 ≤ length l\n⊢ cycleType (formPerm (attach l)) = {length l... | [
120,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Data/Sym/Basic.lean | Sym.replicate_right_injective | [] | [
345,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
Mathlib/Data/Nat/Bits.lean | Nat.bit_cases_on_injective | [
{
"state_after": "n : ℕ\nC : ℕ → Sort u\nH₁ H₂ : (b : Bool) → (n : ℕ) → C (bit b n)\nh : (fun H n => bitCasesOn n H) H₁ = (fun H n => bitCasesOn n H) H₂\n⊢ H₁ = H₂",
"state_before": "n : ℕ\nC : ℕ → Sort u\n⊢ Function.Injective fun H n => bitCasesOn n H",
"tactic": "intro H₁ H₂ h"
},
{
"state_aft... | [
144,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.domLCongr_refl | [] | [
621,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
620,
1
] |
Mathlib/Data/Nat/Multiplicity.lean | Nat.Prime.dvd_choose_pow | [
{
"state_after": "case inl\np n k : ℕ\nhp : Prime p\nhk : k ≠ 0\nhkp✝ : k ≠ p ^ n\nhkp : p ^ n < k\n⊢ p ∣ choose (p ^ n) k\n\ncase inr\np n k : ℕ\nhp : Prime p\nhk : k ≠ 0\nhkp✝ : k ≠ p ^ n\nhkp : k < p ^ n\n⊢ p ∣ choose (p ^ n) k",
"state_before": "p n k : ℕ\nhp : Prime p\nhk : k ≠ 0\nhkp : k ≠ p ^ n\n⊢ p ... | [
256,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.ofPowerSeries_X_pow | [
{
"state_after": "Γ : Type u_2\nR✝ : Type ?u.2401544\ninst✝² : Semiring R✝\ninst✝¹ : StrictOrderedSemiring Γ\nR : Type u_1\ninst✝ : CommSemiring R\nn : ℕ\n⊢ ↑(ofPowerSeries Γ R) PowerSeries.X ^ n = ↑(single ↑n) 1",
"state_before": "Γ : Type u_2\nR✝ : Type ?u.2401544\ninst✝² : Semiring R✝\ninst✝¹ : StrictOrd... | [
1230,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1223,
1
] |
Mathlib/Order/RelClasses.lean | subset_antisymm_iff | [] | [
657,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
656,
1
] |
Mathlib/Algebra/MonoidAlgebra/Degree.lean | AddMonoidAlgebra.sup_support_multiset_prod_le | [
{
"state_after": "case h\nR : Type u_3\nA : Type u_2\nT : Type ?u.70204\nB : Type u_1\nι : Type ?u.70210\ninst✝¹¹ : SemilatticeSup B\ninst✝¹⁰ : OrderBot B\ninst✝⁹ : SemilatticeInf T\ninst✝⁸ : OrderTop T\ninst✝⁷ : CommSemiring R\ninst✝⁶ : AddCommMonoid A\ninst✝⁵ : AddCommMonoid B\ninst✝⁴ : CovariantClass B B (fu... | [
149,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Prod.lean | QuadraticForm.Equivalent.prod | [] | [
74,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | irreducible_iff_prime_of_exists_unique_irreducible_factors | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : CancelCommMonoidWithZero α\neif : ∀ (a : α), a ≠ 0 → ∃ f, (∀ (b : α), b ∈ f → Irreducible b) ∧ Multiset.prod f ~ᵤ a\nuif :\n ∀ (f g : Multiset α),\n (∀ (x : α), x ∈ f → Irreducible x) →\n (∀ (x : α), x ∈ g → Irreducible x) → Multis... | [
421,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
1
] |
Mathlib/Topology/Basic.lean | ClusterPt.of_le_nhds' | [] | [
1120,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1118,
1
] |
Mathlib/Data/Multiset/Bind.lean | Multiset.singleton_join | [] | [
66,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Data/Finset/Fold.lean | Finset.lt_fold_min | [] | [
231,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/Data/List/Basic.lean | List.bind_congr | [] | [
1819,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1817,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | HasStrictFDerivAt.rpow | [] | [
429,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
1
] |
Mathlib/Data/QPF/Univariate/Basic.lean | Qpf.mem_supp | [
{
"state_after": "F : Type u → Type u\ninst✝ : Functor F\nq : Qpf F\nα : Type u\nx : F α\nu : α\n⊢ u ∈ {y | ∀ ⦃p : α → Prop⦄, Liftp p x → p y} ↔\n ∀ (a : (P F).A) (f : PFunctor.B (P F) a → α), abs { fst := a, snd := f } = x → u ∈ f '' univ",
"state_before": "F : Type u → Type u\ninst✝ : Functor F\nq : Qp... | [
623,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
612,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.one_imK | [] | [
877,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
877,
9
] |
Mathlib/NumberTheory/Padics/PadicNorm.lean | padicNorm.values_discrete | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nq : ℚ\nhq : q ≠ 0\n⊢ padicNorm p q = ↑p ^ (-padicValRat p q)",
"tactic": "simp [padicNorm, hq]"
}
] | [
125,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
11
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.union_mul_inter_subset | [] | [
872,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
871,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioo_subset_Ioo_iff | [
{
"state_after": "case intro.intro\nα : Type u_1\nβ : Type ?u.68154\ninst✝¹ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\ninst✝ : DenselyOrdered α\nh₁ : a₁ < b₁\nh : Ioo a₁ b₁ ⊆ Ioo a₂ b₂\nx : α\nxa : a₁ < x\nxb : x < b₁\n⊢ a₂ ≤ a₁ ∧ b₁ ≤ b₂",
"state_before": "α : Type u_1\nβ : Type ?u.68154\ninst✝¹ : LinearOrd... | [
1151,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1142,
1
] |
Mathlib/Algebra/Algebra/Tower.lean | AlgHom.comp_algebraMap_of_tower | [] | [
150,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Analysis/Calculus/FormalMultilinearSeries.lean | FormalMultilinearSeries.apply_order_ne_zero | [] | [
248,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Topology/UniformSpace/Completion.lean | UniformSpace.Completion.induction_on₂ | [] | [
506,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.closedUnder_univ | [] | [
71,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/RingTheory/Ideal/MinimalPrime.lean | Ideal.comap_minimalPrimes_eq_of_surjective | [
{
"state_after": "case h\nR : Type u_1\nS : Type u_2\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nI✝ J✝ : Ideal R\nf : R →+* S\nhf : Function.Surjective ↑f\nI : Ideal S\nJ : Ideal R\n⊢ J ∈ Ideal.minimalPrimes (comap f I) ↔ J ∈ comap f '' Ideal.minimalPrimes I",
"state_before": "R : Type u_1\nS : Type u_2\ninst... | [
190,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.le_one_iff | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.181428\nβ : Type ?u.181431\nγ : Type ?u.181434\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\na : Ordinal\n⊢ a ≤ 1 ↔ a = 0 ∨ a = 1",
"tactic": "simpa using @le_succ_bot_iff _ _ _ a _"
}
] | [
1097,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1096,
1
] |
Mathlib/Algebra/GroupPower/Basic.lean | pow_mul_pow_eq_one | [
{
"state_after": "case zero\nα : Type ?u.41048\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝¹ : Monoid M\ninst✝ : AddMonoid A\na b : M\nh : a * b = 1\n⊢ a ^ Nat.zero * b ^ Nat.zero = 1\n\ncase succ\nα : Type ?u.41048\nM : Type u\nN : Type v\nG : Type w\... | [
230,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/LinearAlgebra/Matrix/Circulant.lean | Matrix.Fin.transpose_circulant | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.8775\nm : Type ?u.8778\nn : Type ?u.8781\nR : Type ?u.8784\n⊢ ∀ (v : Fin 0 → α), (circulant v)ᵀ = circulant fun i => v (-i)",
"tactic": "simp [Injective]"
}
] | [
93,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Combinatorics/Composition.lean | CompositionAsSet.lt_length | [] | [
900,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
899,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_pi | [
{
"state_after": "α : Type u_3\nβ : Type ?u.696195\nE : Type ?u.696198\nF : Type ?u.696201\nG : Type ?u.696204\nE'✝ : Type ?u.696207\nF' : Type u_4\nG' : Type ?u.696213\nE'' : Type ?u.696216\nF'' : Type ?u.696219\nG'' : Type ?u.696222\nR : Type ?u.696225\nR' : Type ?u.696228\n𝕜 : Type ?u.696231\n𝕜' : Type ?u.... | [
2152,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2149,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pushoutCoconeOfLeftIso_ι_app_left | [] | [
1800,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1799,
1
] |
Mathlib/RingTheory/Filtration.lean | Ideal.iInf_pow_smul_eq_bot_of_localRing | [
{
"state_after": "R M : Type u\ninst✝⁵ : CommRing R\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\nI : Ideal R\nF F' : Filtration I M\ninst✝² : IsNoetherianRing R\ninst✝¹ : LocalRing R\ninst✝ : Module.Finite R M\nh : I ≠ ⊤\n⊢ (⨅ (i : ℕ), I ^ i • ⊤) ≤ ⊥",
"state_before": "R M : Type u\ninst✝⁵ : CommRing R\ni... | [
469,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.Lp.simpleFunc.toLp_smul | [] | [
581,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
] |
Mathlib/RingTheory/Filtration.lean | Ideal.Filtration.antitone | [] | [
80,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
11
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.lift.principalSeg_coe | [] | [
1300,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1298,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.coe_min' | [] | [
1520,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1519,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.mk_succ_pos | [
{
"state_after": "n m i : ℕ\nh : i < n\n⊢ 0 < ↑{ val := Nat.succ i, isLt := (_ : i + 1 < n + 1) }",
"state_before": "n m i : ℕ\nh : i < n\n⊢ 0 < { val := Nat.succ i, isLt := (_ : i + 1 < n + 1) }",
"tactic": "rw [lt_iff_val_lt_val, val_zero]"
},
{
"state_after": "no goals",
"state_before": "... | [
943,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
941,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Submodule.mem_of_span_top_of_smul_mem | [
{
"state_after": "R : Type u\nM : Type v\nF : Type ?u.105735\nG : Type ?u.105738\ninst✝² : CommSemiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nI J : Ideal R\nN P : Submodule R M\nS : Set R\nT : Set M\nM' : Submodule R M\ns : Set R\nhs : Ideal.span s = ⊤\nx : M\nH : ∀ (r : ↑s), ↑r • x ∈ M'\n⊢ ⊤ • span ... | [
258,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.ofReal_ofNat | [] | [
687,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
9
] |
Mathlib/Topology/Constructions.lean | Continuous.prod_mk | [] | [
402,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | GroupTopology.toTopologicalSpace_sInf | [] | [
1964,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1963,
1
] |
Std/Data/Option/Lemmas.lean | Option.not_isSome | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u_1\na : Option α✝\n⊢ isSome a = false ↔ isNone a = true",
"tactic": "cases a <;> simp"
}
] | [
62,
19
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
61,
9
] |
Mathlib/Data/Nat/Factorial/Basic.lean | Nat.pow_sub_le_descFactorial | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ (n + 1 - 0) ^ 0 ≤ descFactorial n 0",
"tactic": "rw [descFactorial_zero, pow_zero]"
},
{
"state_after": "n k : ℕ\n⊢ (n - k) * (n - k) ^ k ≤ (n - k) * descFactorial n k",
"state_before": "n k : ℕ\n⊢ (n + 1 - (k + 1)) ^ (k + 1) ≤ descFacto... | [
441,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
1
] |
Mathlib/Deprecated/Subring.lean | Ring.closure_mono | [] | [
205,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Tactic/NormNum/Prime.lean | Mathlib.Meta.NormNum.isNat_minFac_3 | [
{
"state_after": "n k : ℕ\nh1 : MinFacHelper n k\nh2 : k ∣ n\n⊢ IsNat (minFac n) k",
"state_before": "n k : ℕ\nh1 : MinFacHelper n k\nh2 : 0 = n % k\n⊢ IsNat (minFac n) k",
"tactic": "rw [eq_comm, ← Nat.dvd_iff_mod_eq_zero] at h2"
},
{
"state_after": "no goals",
"state_before": "n k : ℕ\nh1 ... | [
112,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Data/Finset/Slice.lean | Set.sized_iUnion₂ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nι : Sort u_2\nκ : ι → Sort u_3\nA B : Set (Finset α)\nr : ℕ\nf : (i : ι) → κ i → Set (Finset α)\n⊢ Sized r (⋃ (i : ι) (j : κ i), f i j) ↔ ∀ (i : ι) (j : κ i), Sized r (f i j)",
"tactic": "simp only [Set.sized_iUnion]"
}
] | [
74,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.mem_symmDiff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.285746\nγ : Type ?u.285749\ninst✝ : DecidableEq α\ns t : Finset α\na b : α\n⊢ a ∈ s ∆ t ↔ a ∈ s ∧ ¬a ∈ t ∨ a ∈ t ∧ ¬a ∈ s",
"tactic": "simp_rw [symmDiff, sup_eq_union, mem_union, mem_sdiff]"
}
] | [
2377,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2376,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.mapsTo_sin | [] | [
635,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
635,
1
] |
Mathlib/Order/Disjoint.lean | codisjoint_assoc | [] | [
325,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Std/Data/Rat/Lemmas.lean | Rat.normalize_num_den' | [
{
"state_after": "num : Int\nden : Nat\nnz : den ≠ 0\n⊢ num = (normalize num den).num * ↑(Nat.gcd (Int.natAbs num) den) ∧\n den = (normalize num den).den * Nat.gcd (Int.natAbs num) den",
"state_before": "num : Int\nden : Nat\nnz : den ≠ 0\n⊢ ∃ d, d ≠ 0 ∧ num = (normalize num den).num * ↑d ∧ den = (normal... | [
76,
47
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
72,
1
] |
Std/Data/Int/Lemmas.lean | Int.mul_sub | [
{
"state_after": "no goals",
"state_before": "a b c : Int\n⊢ a * (b - c) = a * b - a * c",
"tactic": "simp [Int.sub_eq_add_neg, Int.mul_add]"
}
] | [
478,
41
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
477,
11
] |
Mathlib/Algebra/Hom/GroupAction.lean | DistribMulActionHom.zero_apply | [] | [
355,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/Order/Filter/CountableInter.lean | Filter.mem_countableGenerate_iff | [
{
"state_after": "case mp\nι : Sort ?u.18419\nα : Type u_1\nβ : Type ?u.18425\nl : Filter α\ninst✝ : CountableInterFilter l\ng : Set (Set α)\ns : Set α\nh : s ∈ countableGenerate g\n⊢ ∃ S, S ⊆ g ∧ Set.Countable S ∧ ⋂₀ S ⊆ s\n\ncase mpr\nι : Sort ?u.18419\nα : Type u_1\nβ : Type ?u.18425\nl : Filter α\ninst✝ : C... | [
249,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/MeasureTheory/Function/Jacobian.lean | MeasureTheory.measurable_image_of_fderivWithin | [] | [
784,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
781,
1
] |
Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.Homotopic.equivalence | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.285748\nX : Type u\nY : Type v\nZ : Type w\nZ' : Type x\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace Y\ninst✝¹ : TopologicalSpace Z\ninst✝ : TopologicalSpace Z'\n⊢ ∀ {x y : C(X, Y)}, Homotopic x y → Homotopic y x",
"tactic": "apply sym... | [
380,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/Data/Nat/Periodic.lean | Nat.periodic_coprime | [
{
"state_after": "no goals",
"state_before": "a : ℕ\n⊢ Periodic (coprime a) a",
"tactic": "simp only [coprime_add_self_right, forall_const, iff_self_iff, eq_iff_iff, Periodic]"
}
] | [
32,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
31,
1
] |
Mathlib/CategoryTheory/Monoidal/Types/Symmetric.lean | CategoryTheory.braiding_inv_apply | [] | [
40,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.tr_pred | [] | [
1132,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1127,
1
] |
Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.det_adjugate | [
{
"state_after": "case inl\nm : Type u\nn : Type v\nα : Type w\ninst✝⁴ : DecidableEq n\ninst✝³ : Fintype n\ninst✝² : DecidableEq m\ninst✝¹ : Fintype m\ninst✝ : CommRing α\nA : Matrix n n α\nh_card : Fintype.card n = 0\n⊢ det (adjugate A) = det A ^ (Fintype.card n - 1)\n\ncase inr\nm : Type u\nn : Type v\nα : Ty... | [
393,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Std/Data/Int/Lemmas.lean | Int.min_le_left | [] | [
697,
97
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
697,
11
] |
Mathlib/Data/Fin/Basic.lean | Fin.castAdd_natAdd | [
{
"state_after": "case h\nn✝ m✝ p m n : ℕ\ni : Fin n\n⊢ ↑(↑(castAdd p) (↑(natAdd m) i)) = ↑(↑(cast (_ : m + (n + p) = m + n + p)) (↑(natAdd m) (↑(castAdd p) i)))",
"state_before": "n✝ m✝ p m n : ℕ\ni : Fin n\n⊢ ↑(castAdd p) (↑(natAdd m) i) = ↑(cast (_ : m + (n + p) = m + n + p)) (↑(natAdd m) (↑(castAdd p) i... | [
1437,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1434,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.val_mul | [
{
"state_after": "case zero\na b : ZMod Nat.zero\n⊢ val (a * b) = val a * val b % Nat.zero\n\ncase succ\nn✝ : ℕ\na b : ZMod (Nat.succ n✝)\n⊢ val (a * b) = val a * val b % Nat.succ n✝",
"state_before": "n : ℕ\na b : ZMod n\n⊢ val (a * b) = val a * val b % n",
"tactic": "cases n"
},
{
"state_after... | [
607,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
1
] |
Mathlib/Data/PEquiv.lean | PEquiv.trans_single_of_mem | [] | [
377,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | Valuation.map_one | [] | [
163,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Combinatorics/SimpleGraph/Regularity/Equitabilise.lean | Finpartition.exists_equipartition_card_eq | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\nm n a b : ℕ\nP : Finpartition s\nh : a * m + b * (m + 1) = card s\nhn : 0 < n\nhs : n ≤ card s\n⊢ ∃ P, IsEquipartition P ∧ card P.parts = n",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\nm n a b : ℕ\nP : Finparti... | [
216,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Analysis/InnerProductSpace/l2Space.lean | HilbertBasis.summable_inner_mul_inner | [] | [
502,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
500,
11
] |
Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.lower_le_upper | [] | [
91,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Order/Concept.lean | Concept.sSup_snd | [] | [
358,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/Tactic/Ring/RingNF.lean | Mathlib.Tactic.RingNF.int_rawCast_2 | [
{
"state_after": "no goals",
"state_before": "R✝ : Type ?u.78183\ninst✝² : CommSemiring R✝\nn : ℕ\nR : Type u_1\ninst✝¹ : Ring R\ninst✝ : Nat.AtLeastTwo n\n⊢ Int.rawCast (Int.negOfNat n) = -OfNat.ofNat n",
"tactic": "simp [Int.negOfNat_eq, OfNat.ofNat]"
}
] | [
121,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Std/Data/Int/DivMod.lean | Int.fmod_eq_of_lt | [
{
"state_after": "no goals",
"state_before": "a b : Int\nH1 : 0 ≤ a\nH2 : a < b\n⊢ fmod a b = a",
"tactic": "rw [fmod_eq_emod _ (Int.le_trans H1 (Int.le_of_lt H2)), emod_eq_of_lt H1 H2]"
}
] | [
364,
79
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
363,
1
] |
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