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/Data/Fintype/Card.lean | Fintype.card_ulift | [] | [
369,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Mathlib/Algebra/Lie/Solvable.lean | LieAlgebra.derivedLength_zero | [
{
"state_after": "R : Type u\nL : Type v\nM : Type w\nL' : Type w₁\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\ninst✝¹ : LieRing L'\ninst✝ : LieAlgebra R L'\nI✝ J : LieIdeal R L\nf : L' →ₗ⁅R⁆ L\nI : LieIdeal R L\nhI : IsSolvable R { x // x ∈ ↑I }\ns : Set ℕ := {k | derivedSeriesOfIdeal R L... | [
362,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/Tactic/NormNum/Core.lean | Mathlib.Meta.NormNum.IsRat.nonneg_to_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DivisionRing α\nn d : ℕ\ninv✝ : Invertible ↑d\n⊢ ↑(Int.ofNat n) * ⅟↑d = ↑n / ↑d",
"tactic": "simp [div_eq_mul_inv]"
}
] | [
171,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.translationNumber_eq_int_iff | [
{
"state_after": "case mp\nf g : CircleDeg1Lift\nhf : Continuous ↑f\nm : ℤ\n⊢ τ f = ↑m → ∃ x, ↑f x = x + ↑m\n\ncase mpr\nf g : CircleDeg1Lift\nhf : Continuous ↑f\nm : ℤ\n⊢ (∃ x, ↑f x = x + ↑m) → τ f = ↑m",
"state_before": "f g : CircleDeg1Lift\nhf : Continuous ↑f\nm : ℤ\n⊢ τ f = ↑m ↔ ∃ x, ↑f x = x + ↑m",
... | [
948,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
941,
1
] |
Mathlib/Control/Bifunctor.lean | Bifunctor.comp_snd | [
{
"state_after": "no goals",
"state_before": "F : Type u₀ → Type u₁ → Type u₂\ninst✝¹ : Bifunctor F\ninst✝ : LawfulBifunctor F\nα : Type u₀\nβ₀ β₁ β₂ : Type u₁\ng : β₀ → β₁\ng' : β₁ → β₂\nx : F α β₀\n⊢ snd g' (snd g x) = snd (g' ∘ g) x",
"tactic": "simp [snd, bimap_bimap]"
}
] | [
111,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
src/lean/Init/Prelude.lean | Or.intro_left | [] | [
523,
11
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
522,
1
] |
Mathlib/RingTheory/FreeCommRing.lean | FreeRing.coe_zero | [] | [
329,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
11
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.foldl_eq_foldl_toList | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nα✝ : Type u_2\nf : α✝ → α → α✝\ninit : α✝\nt : RBNode α\n⊢ foldl f init t = List.foldl f init (toList t)",
"tactic": "induction t generalizing init <;> simp [*]"
}
] | [
347,
45
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
346,
1
] |
Std/Data/List/Lemmas.lean | List.get?_eq_some | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u_1\na : α✝\nl : List α✝\nn : Nat\ne : get? l n = some a\nhn : length l ≤ n\n⊢ False",
"tactic": "cases get?_len_le hn ▸ e"
},
{
"state_after": "no goals",
"state_before": "α✝ : Type u_1\na : α✝\nl : List α✝\nn : Nat\ne : get? l n = som... | [
517,
35
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
513,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.IsSt.map | [
{
"state_after": "case intro\nr : ℝ\nf : ℝ → ℝ\nhf : ContinuousAt f r\ng : ℕ → ℝ\nhxr : IsSt (ofSeq g) r\n⊢ IsSt (Germ.map f (ofSeq g)) (f r)",
"state_before": "x : ℝ*\nr : ℝ\nhxr : IsSt x r\nf : ℝ → ℝ\nhf : ContinuousAt f r\n⊢ IsSt (Germ.map f x) (f r)",
"tactic": "rcases ofSeq_surjective x with ⟨g, rf... | [
394,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.HasColimit.ofCoconesIso | [] | [
900,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
898,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.coe_one | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\ninst✝² : CommRing R\nS : Submonoid R\nP : Type u_1\ninst✝¹ : CommRing P\ninst✝ : Algebra R P\nloc : IsLocalization S P\n⊢ ↑1 = 1",
"tactic": "rw [coe_one_eq_coeSubmodule_top, coeSubmodule_top]"
}
] | [
377,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
] |
Mathlib/Topology/Semicontinuous.lean | LowerSemicontinuousWithinAt.add | [] | [
487,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Mathlib/Order/FixedPoints.lean | OrderHom.map_gfp_comp | [] | [
165,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Order/Bounds/Basic.lean | not_bddAbove_iff' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ns t : Set α\na b : α\n⊢ ¬BddAbove s ↔ ∀ (x : α), ∃ y, y ∈ s ∧ ¬y ≤ x",
"tactic": "simp [BddAbove, upperBounds, Set.Nonempty]"
}
] | [
122,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.le_findGreatest | [] | [
644,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
643,
1
] |
Mathlib/Analysis/Calculus/Series.lean | continuous_tsum | [
{
"state_after": "α : Type u_3\nβ : Type u_1\n𝕜 : Type ?u.14249\nE : Type ?u.14252\nF : Type u_2\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : CompleteSpace F\nu : α → ℝ\ninst✝ : TopologicalSpace β\nf : α → β → F\nhu : Summable u\nhfu : ∀... | [
97,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | DifferentiableAt.clm_comp | [] | [
90,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.erase_ssubset_insert | [] | [
1969,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1967,
1
] |
Mathlib/Data/Fintype/Card.lean | Finite.injective_iff_surjective_of_equiv | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.27313\ninst✝ : Finite α\nf : α → β\ne : α ≃ β\nthis : Injective (↑e.symm ∘ f) ↔ Surjective (↑e.symm ∘ f)\nhinj : Injective f\n⊢ Surjective f",
"tactic": "simpa [Function.comp] using e.surjective.comp (this.1 (e.symm.in... | [
646,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
641,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Basic.lean | MeasureTheory.Measure.toPmf_toMeasure | [
{
"state_after": "α : Type u_1\nβ : Type ?u.141584\nγ : Type ?u.141587\ninst✝³ : Countable α\ninst✝² : MeasurableSpace α\ninst✝¹ : MeasurableSingletonClass α\nμ : Measure α\ninst✝ : IsProbabilityMeasure μ\ns : Set α\nhs : MeasurableSet s\n⊢ (∑' (x : α), Set.indicator s (↑(toPmf μ)) x) = ∑' (x : α), Set.indicato... | [
363,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/Order/LocallyFinite.lean | Finset.coe_Ioo | [] | [
363,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/Init/Algebra/Order.lean | Decidable.eq_or_lt_of_le | [] | [
221,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Data/Polynomial/Monic.lean | Polynomial.Monic.mul_right_ne_zero | [
{
"state_after": "case pos\nR : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝ : Semiring R\np : R[X]\nhp : Monic p\nq : R[X]\nhq : q ≠ 0\nh : p = 1\n⊢ p * q ≠ 0\n\ncase neg\nR : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝ : Semiring R\np : R[X]\nhp : Monic p\nq : R[X]\nhq : q ≠ 0\nh : ¬p =... | [
455,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Std/Data/List/Basic.lean | List.dropSlice_zero₂ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nn : Nat\nx : α\nxs : List α\n⊢ dropSlice (n + 1) 0 (x :: xs) = x :: xs",
"tactic": "simp [dropSlice, dropSlice_zero₂]"
}
] | [
1261,
55
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1259,
1
] |
Mathlib/LinearAlgebra/Prod.lean | LinearMap.tailing_disjoint_tunnel_succ | [
{
"state_after": "R : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nM₅ : Type ?u.543558\nM₆ : Type ?u.543561\ninst✝⁴ : Ring R\nN : Type u_1\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : AddCommGroup N\ninst✝ : Module R N\nf... | [
947,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
941,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.monomial_eq_zero_iff | [] | [
470,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
469,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.ratCast_im | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nE : Type ?u.6542975\ninst✝ : IsROrC K\nq : ℚ\n⊢ ↑im ↑q = 0",
"tactic": "rw [← ofReal_ratCast, ofReal_im]"
}
] | [
686,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
686,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.single_neg | [] | [
919,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
917,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.smul_inter_subset | [] | [
1401,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1400,
1
] |
Mathlib/RingTheory/Polynomial/ScaleRoots.lean | Polynomial.map_scaleRoots | [
{
"state_after": "case a\nA : Type ?u.488366\nK : Type ?u.488369\nR : Type u_1\nS : Type u_2\ninst✝⁴ : CommRing A\ninst✝³ : IsDomain A\ninst✝² : Field K\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nM : Submonoid A\np : R[X]\nx : R\nf : R →+* S\nh : ↑f (leadingCoeff p) ≠ 0\nn✝ : ℕ\n⊢ coeff (map f (scaleRoots p x)) ... | [
146,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.exp_bound | [
{
"state_after": "x : ℂ\nhx : ↑abs x ≤ 1\nn : ℕ\nhn : 0 < n\n⊢ CauSeq.lim (cauSeqAbs (exp' x + -const (↑abs) (∑ m in range n, x ^ m / ↑(Nat.factorial m)))) ≤\n ↑abs x ^ n * (↑(Nat.succ n) * (↑(Nat.factorial n) * ↑n)⁻¹)",
"state_before": "x : ℂ\nhx : ↑abs x ≤ 1\nn : ℕ\nhn : 0 < n\n⊢ ↑abs (exp x - ∑ m in r... | [
1640,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1611,
1
] |
Mathlib/Combinatorics/SetFamily/Compression/UV.lean | UV.compress_sdiff_sdiff | [
{
"state_after": "α : Type u_1\ninst✝² : GeneralizedBooleanAlgebra α\ninst✝¹ : DecidableRel Disjoint\ninst✝ : DecidableRel fun x x_1 => x ≤ x_1\ns : Finset α\nu v a✝ b✝ a b : α\n⊢ (b ⊔ a \\ b) \\ (b \\ a) = a",
"state_before": "α : Type u_1\ninst✝² : GeneralizedBooleanAlgebra α\ninst✝¹ : DecidableRel Disjoi... | [
158,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.int_add | [
{
"state_after": "q : ℚ\nx y : ℝ\nh : Irrational x\nm : ℤ\n⊢ Irrational (↑↑m + x)",
"state_before": "q : ℚ\nx y : ℝ\nh : Irrational x\nm : ℤ\n⊢ Irrational (↑m + x)",
"tactic": "rw [← cast_coe_int]"
},
{
"state_after": "no goals",
"state_before": "q : ℚ\nx y : ℝ\nh : Irrational x\nm : ℤ\n⊢ Ir... | [
239,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Data/Finset/Prod.lean | Finset.filter_product_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.28906\ns s' : Finset α\nt t' : Finset β\na : α\nb : β\np : α → Prop\ninst✝ : DecidablePred p\n⊢ filter (fun x => p x.fst) (s ×ˢ t) = filter p s ×ˢ t",
"tactic": "simpa using filter_product p fun _ => true"
}
] | [
154,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf_exists | [] | [
1315,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1314,
1
] |
Mathlib/Data/PNat/Interval.lean | PNat.card_fintype_Ioc | [
{
"state_after": "no goals",
"state_before": "a b : ℕ+\n⊢ Fintype.card ↑(Set.Ioc a b) = ↑b - ↑a",
"tactic": "rw [← card_Ioc, Fintype.card_ofFinset]"
}
] | [
107,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Data/Set/Basic.lean | Set.coe_setOf | [] | [
182,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Data/Part.lean | Part.Mem.left_unique | [] | [
151,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Data/PNat/Xgcd.lean | PNat.XgcdType.reduce_a | [
{
"state_after": "u✝ u : XgcdType\nh : r u = 0\n⊢ (if x : r u = 0 then finish u else flip (reduce (step u))) = finish u",
"state_before": "u✝ u : XgcdType\nh : r u = 0\n⊢ reduce u = finish u",
"tactic": "rw [reduce]"
},
{
"state_after": "no goals",
"state_before": "u✝ u : XgcdType\nh : r u =... | [
353,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Mathlib/Tactic/PushNeg.lean | Mathlib.Tactic.PushNeg.not_or_eq | [] | [
22,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
22,
1
] |
Mathlib/CategoryTheory/Functor/Basic.lean | CategoryTheory.Functor.id_obj | [] | [
98,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/LinearAlgebra/FreeModule/PID.lean | Submodule.basis_of_pid_aux | [
{
"state_after": "ι : Type u_1\nR : Type u_3\ninst✝⁷ : CommRing R\ninst✝⁶ : IsDomain R\ninst✝⁵ : IsPrincipalIdealRing R\nM✝ : Type ?u.43078\ninst✝⁴ : AddCommGroup M✝\ninst✝³ : Module R M✝\nb : ι → M✝\ninst✝² : Finite ι\nO : Type u_2\ninst✝¹ : AddCommGroup O\ninst✝ : Module R O\nM N : Submodule R O\nb'M : Basis ... | [
289,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/LinearAlgebra/Matrix/SpecialLinearGroup.lean | Matrix.SpecialLinearGroup.coe_pow | [] | [
161,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderIso.apply_symm_apply | [] | [
857,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
856,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.cardDistinctFactors_eq_cardFactors_iff_squarefree | [
{
"state_after": "R : Type ?u.569435\nn : ℕ\nh0 : n ≠ 0\n⊢ List.length (List.dedup (factors n)) = ↑Ω n ↔ List.Nodup (factors n)",
"state_before": "R : Type ?u.569435\nn : ℕ\nh0 : n ≠ 0\n⊢ ↑ω n = ↑Ω n ↔ Squarefree n",
"tactic": "rw [squarefree_iff_nodup_factors h0, cardDistinctFactors_apply]"
},
{
... | [
928,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
921,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.min'_lt_max'_of_card | [
{
"state_after": "case intro.intro.intro.intro\nF : Type ?u.344901\nα : Type u_1\nβ : Type ?u.344907\nγ : Type ?u.344910\nι : Type ?u.344913\nκ : Type ?u.344916\ninst✝ : LinearOrder α\ns : Finset α\nH : Finset.Nonempty s\nx : α\nh₂ : 1 < card s\na : α\nha : a ∈ s\nb : α\nhb : b ∈ s\nhab : a ≠ b\n⊢ min' s (_ : F... | [
1406,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1402,
1
] |
Mathlib/Order/Filter/Cofinite.lean | Filter.coprodᵢ_cofinite | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\nα✝ : Type ?u.3999\nβ : Type ?u.4002\nl : Filter α✝\nα : ι → Type u_1\ninst✝ : Finite ι\ns : Set ((i : ι) → α i)\n⊢ (sᶜ ∈ Filter.coprodᵢ fun i => cofinite) ↔ sᶜ ∈ cofinite",
"tactic": "simp only [compl_mem_coprodᵢ, mem_cofinite, compl_compl, for... | [
126,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/LinearAlgebra/Determinant.lean | LinearMap.det_comp | [] | [
252,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.coeToSubmodule_ne_bot | [] | [
337,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/Data/Set/Intervals/Instances.lean | Set.Ico.coe_lt_one | [] | [
216,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Order/JordanHolder.lean | CompositionSeries.length_pos_of_mem_ne | [] | [
374,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.coe_funUnique | [] | [
2441,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2440,
1
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.toNonUnitalRingHom_eq_coe | [] | [
614,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
613,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.coe_mono | [] | [
382,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
11
] |
Mathlib/Topology/Instances/Int.lean | Int.pairwise_one_le_dist | [
{
"state_after": "m n : ℤ\nhne : m ≠ n\n⊢ 1 ≤ dist m n",
"state_before": "⊢ Pairwise fun m n => 1 ≤ dist m n",
"tactic": "intro m n hne"
},
{
"state_after": "m n : ℤ\nhne : m ≠ n\n⊢ 1 ≤ abs (↑m - ↑n)",
"state_before": "m n : ℤ\nhne : m ≠ n\n⊢ 1 ≤ dist m n",
"tactic": "rw [dist_eq]"
},
... | [
43,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Control/Basic.lean | fish_assoc | [] | [
127,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/LinearAlgebra/Matrix/Charpoly/Basic.lean | Matrix.charpoly_reindex | [
{
"state_after": "R : Type u\ninst✝⁴ : CommRing R\nn : Type w\ninst✝³ : DecidableEq n\ninst✝² : Fintype n\nm : Type v\ninst✝¹ : DecidableEq m\ninst✝ : Fintype m\ne : n ≃ m\nM : Matrix n n R\n⊢ det (charmatrix (↑(reindex e e) M)) = det (charmatrix M)",
"state_before": "R : Type u\ninst✝⁴ : CommRing R\nn : Ty... | [
101,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Algebra/Ring/Idempotents.lean | IsIdempotentElem.coe_compl | [] | [
126,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.prod_eq_pow_single | [
{
"state_after": "case h\nι : Type ?u.29694\nα : Type u_1\nβ : Type ?u.29700\nγ : Type ?u.29703\ninst✝¹ : CommMonoid α\ns t : Multiset α\na✝ : α\nm : Multiset ι\nf g : ι → α\ninst✝ : DecidableEq α\na : α\nh✝ : ∀ (a' : α), a' ≠ a → a' ∈ s → a' = 1\nl : List α\nh : ∀ (a' : α), a' ≠ a → a' ∈ Quotient.mk (List.isSe... | [
148,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Data/Set/Basic.lean | Set.inclusion_inclusion | [
{
"state_after": "case mk\nα : Type u_1\ns t u : Set α\nhst : s ⊆ t\nhtu : t ⊆ u\nval✝ : α\nproperty✝ : val✝ ∈ s\n⊢ inclusion htu (inclusion hst { val := val✝, property := property✝ }) =\n inclusion (_ : s ⊆ u) { val := val✝, property := property✝ }",
"state_before": "α : Type u_1\ns t u : Set α\nhst : s... | [
2794,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2791,
1
] |
Mathlib/Order/Filter/Extr.lean | isMaxFilter_dual_iff | [] | [
214,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/CategoryTheory/Groupoid.lean | CategoryTheory.Groupoid.reverse_eq_inv | [] | [
99,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lift_mk_shrink'' | [
{
"state_after": "no goals",
"state_before": "α✝ β : Type u\nα : Type (max u v)\ninst✝ : Small α\n⊢ lift (#Shrink α) = (#α)",
"tactic": "rw [← lift_umax', lift_mk_shrink.{max u v, v, 0} α, ← lift_umax, lift_id]"
}
] | [
1032,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1030,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.restrict_nonzero_iff | [
{
"state_after": "no goals",
"state_before": "Ω : Type u_1\ninst✝⁴ : MeasurableSpace Ω\nR : Type ?u.41322\ninst✝³ : SMul R ℝ≥0\ninst✝² : SMul R ℝ≥0∞\ninst✝¹ : IsScalarTower R ℝ≥0 ℝ≥0∞\ninst✝ : IsScalarTower R ℝ≥0∞ ℝ≥0∞\nμ : FiniteMeasure Ω\nA : Set Ω\n⊢ restrict μ A ≠ 0 ↔ (fun s => ENNReal.toNNReal (↑↑↑μ s)... | [
305,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.power_nat_le | [] | [
958,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
957,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.succ_cast_eq | [
{
"state_after": "no goals",
"state_before": "n m n' : ℕ\ni : Fin n\nh : n = n'\n⊢ Nat.succ n = Nat.succ n'",
"tactic": "rw [h]"
},
{
"state_after": "no goals",
"state_before": "n m n' : ℕ\ni : Fin n\nh : n = n'\n⊢ ↑(succ (↑(cast h) i)) = ↑(↑(cast (_ : Nat.succ n = Nat.succ n')) (succ i))",
... | [
1198,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1196,
1
] |
Mathlib/Topology/Category/TopCat/Limits/Products.lean | TopCat.piIsoPi_inv_π | [
{
"state_after": "no goals",
"state_before": "J : Type v\ninst✝ : SmallCategory J\nι : Type v\nα : ι → TopCatMax\ni : ι\n⊢ (piIsoPi α).inv ≫ Pi.π α i = piπ α i",
"tactic": "simp [piIsoPi]"
}
] | [
71,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | ciSup_mono' | [] | [
1093,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1091,
1
] |
Mathlib/Algebra/Category/GroupCat/EpiMono.lean | GroupCat.SurjectiveOfEpiAuxs.h_apply_fromCoset_nin_range | [
{
"state_after": "A B : GroupCat\nf : A ⟶ B\nx : ↑B\nhx : x ∈ MonoidHom.range f\nb : ↑B\nhb : ¬b ∈ MonoidHom.range f\n⊢ ↑((τ.symm.trans (↑g x)).trans τ)\n (fromCoset\n { val := b *l (MonoidHom.range f).toSubmonoid.toSubsemigroup.carrier,\n property :=\n (_ :\n ∃ y,\n... | [
291,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.ofVectorSpaceIndex.linearIndependent | [
{
"state_after": "case h.e'_4\nι : Type ?u.1148087\nι' : Type ?u.1148090\nR : Type ?u.1148093\nR₂ : Type ?u.1148096\nK : Type u_1\nM : Type ?u.1148102\nM' : Type ?u.1148105\nM'' : Type ?u.1148108\nV : Type u\nV' : Type ?u.1148113\ninst✝⁴ : DivisionRing K\ninst✝³ : AddCommGroup V\ninst✝² : AddCommGroup V'\ninst✝... | [
1489,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1485,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.lt_of_succ_le | [] | [
311,
4
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
310,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.sumAssoc_symm_apply_inl | [] | [
372,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_neg_Iio | [] | [
149,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Topology/Order.lean | TopologicalSpace.le_generateFrom_iff_subset_isOpen | [] | [
170,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Algebra/Module/PointwisePi.lean | smul_pi | [] | [
54,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_comm' | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.324815\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf✝ g : α → β\ninst✝ : CommMonoid β\ns : Finset γ\nt : γ → Finset α\nt' : Finset α\ns' : α → Finset γ\nh : ∀ (x : γ) (y : α), x ∈ s ∧ y ∈ t x ↔ x ∈ s' y ∧ y ∈ t'\nf : γ → α → β\n⊢... | [
710,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
699,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.pow_bit0 | [
{
"state_after": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na : R\nk : ℕ\n⊢ a ^ Nat.mul 2 k = a ^ k * a ^ k",
"state_before": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na : R\nk : ℕ\nb c : R\nx✝¹ : a ... | [
662,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
661,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.einfsep_insert | [
{
"state_after": "α : Type u_1\nβ : Type ?u.44124\ninst✝ : PseudoEMetricSpace α\nx y z : α\ns t : Set α\n⊢ (⨅ (y : α) (_ : y ∈ s) (_ : x ≠ y), edist x y) ⊓ einfsep s ≤ einfsep (insert x s)",
"state_before": "α : Type u_1\nβ : Type ?u.44124\ninst✝ : PseudoEMetricSpace α\nx y z : α\ns t : Set α\n⊢ einfsep (in... | [
232,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Analysis/Complex/RealDeriv.lean | HasStrictDerivAt.complexToReal_fderiv | [
{
"state_after": "no goals",
"state_before": "e : ℂ → ℂ\ne' : ℂ\nz : ℝ\nE : Type ?u.117471\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nf : ℂ → ℂ\nf' x : ℂ\nh : HasStrictDerivAt f f' x\n⊢ HasStrictFDerivAt f (f' • 1) x",
"tactic": "simpa only [Complex.restrictScalars_one_smulRight] using h.h... | [
123,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.one_half_lt_one | [] | [
1748,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1747,
11
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.mem_comap | [] | [
524,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
] |
Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.LocalInvariantProp.liftPropWithinAt_mono_of_mem | [
{
"state_after": "H : Type u_1\nM : Type u_2\nH' : Type u_3\nM' : Type u_4\nX : Type ?u.47928\ninst✝⁶ : TopologicalSpace H\ninst✝⁵ : TopologicalSpace M\ninst✝⁴ : ChartedSpace H M\ninst✝³ : TopologicalSpace H'\ninst✝² : TopologicalSpace M'\ninst✝¹ : ChartedSpace H' M'\ninst✝ : TopologicalSpace X\nG : StructureGr... | [
452,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Order/Monotone/Basic.lean | StrictAnti.compares | [] | [
842,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
840,
11
] |
Mathlib/SetTheory/ZFC/Basic.lean | Class.mem_sInter | [
{
"state_after": "x y : Class\nh : Set.Nonempty x\nH : ∀ (z : Class), z ∈ x → y ∈ z\n⊢ y ∈ ⋂₀ x",
"state_before": "x y : Class\nh : Set.Nonempty x\n⊢ y ∈ ⋂₀ x ↔ ∀ (z : Class), z ∈ x → y ∈ z",
"tactic": "refine' ⟨fun hy z => mem_of_mem_sInter hy, fun H => _⟩"
},
{
"state_after": "x y : Class\nh :... | [
1722,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1716,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.withTopEquiv_zero | [
{
"state_after": "no goals",
"state_before": "⊢ ↑withTopEquiv 0 = 0",
"tactic": "simpa only [Nat.cast_zero] using withTopEquiv_natCast 0"
}
] | [
701,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
1
] |
Mathlib/Data/Finmap.lean | Finmap.keys_empty | [] | [
234,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.image_vsub_prod | [] | [
605,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
604,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.compl_Iic | [] | [
1061,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1060,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.max_eq_bot | [
{
"state_after": "case intro\nF : Type ?u.314269\nα : Type u_1\nβ : Type ?u.314275\nγ : Type ?u.314278\nι : Type ?u.314281\nκ : Type ?u.314284\ninst✝ : LinearOrder α\ns : Finset α\nh : Finset.max s = ⊥\nH : Finset.Nonempty s\na : α\nha : Finset.max s = ↑a\n⊢ s = ∅",
"state_before": "F : Type ?u.314269\nα : ... | [
1194,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1190,
1
] |
Mathlib/Data/Set/Intervals/Monoid.lean | Set.image_const_add_Ioc | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\ninst✝¹ : OrderedCancelAddCommMonoid M\ninst✝ : ExistsAddOfLE M\na b c d : M\n⊢ (fun x => a + x) '' Ioc b c = Ioc (a + b) (a + c)",
"tactic": "simp only [add_comm a, image_add_const_Ioc]"
}
] | [
137,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.map_one | [
{
"state_after": "case a.h\nl : Type ?u.76780\nm : Type ?u.76783\nn : Type u_1\no : Type ?u.76789\nm' : o → Type ?u.76794\nn' : o → Type ?u.76799\nR : Type ?u.76802\nS : Type ?u.76805\nα : Type v\nβ : Type w\nγ : Type ?u.76812\ninst✝⁴ : DecidableEq n\ninst✝³ : Zero α\ninst✝² : One α\ninst✝¹ : Zero β\ninst✝ : On... | [
558,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/LogDeriv.lean | DifferentiableOn.clog | [] | [
145,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.mem_supported | [] | [
201,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_X | [] | [
518,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
] |
Mathlib/CategoryTheory/Category/Pointed.lean | Pointed.coe_of | [] | [
56,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/LinearAlgebra/Pi.lean | Submodule.pi_top | [] | [
293,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/FieldTheory/Separable.lean | Polynomial.Separable.map | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝¹ : CommSemiring R\nS : Type v\ninst✝ : CommSemiring S\np : R[X]\nh : Separable p\nf : R →+* S\na b : R[X]\nH : a * p + b * ↑derivative p = 1\n⊢ Polynomial.map f a * Polynomial.map f p + Polynomial.map f b * ↑derivative (Polynomial.map f p) = 1"... | [
133,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/CategoryTheory/Subobject/Limits.lean | CategoryTheory.Limits.kernelSubobjectIso_comp_kernel_map | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝³ : Category C\nX Y Z : C\ninst✝² : HasZeroMorphisms C\nf : X ⟶ Y\ninst✝¹ : HasKernel f\nX' Y' : C\nf' : X' ⟶ Y'\ninst✝ : HasKernel f'\nsq : Arrow.mk f ⟶ Arrow.mk f'\n⊢ (kernelSubobjectIso f).hom ≫\n kernel.map f f' sq.left sq.right\n ... | [
187,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | contDiffAt_id | [] | [
182,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
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