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/Algebra/BigOperators/Order.lean | Finset.prod_pos | [] | [
652,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
651,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Filter.Eventually.trans_isBigO | [] | [
531,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/Algebra/Module/LocalizedModule.lean | IsLocalizedModule.fromLocalizedModule.surj | [
{
"state_after": "R : Type u_1\ninst✝⁷ : CommRing R\nS : Submonoid R\nM : Type u_2\nM' : Type u_3\nM'' : Type ?u.663918\ninst✝⁶ : AddCommMonoid M\ninst✝⁵ : AddCommMonoid M'\ninst✝⁴ : AddCommMonoid M''\ninst✝³ : Module R M\ninst✝² : Module R M'\ninst✝¹ : Module R M''\nf : M →ₗ[R] M'\ng : M →ₗ[R] M''\ninst✝ : IsL... | [
796,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
792,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | summable_of_isBigO_nat | [] | [
2168,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2166,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Summable.const_smul | [] | [
1285,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1284,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.sigmaFinite_of_countable | [
{
"state_after": "α : Type u_1\nβ : Type ?u.758001\nγ : Type ?u.758004\nδ : Type ?u.758007\nι : Type ?u.758010\nR : Type ?u.758013\nR' : Type ?u.758016\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set α\nS : Set (Set α)\nhc : Set.Cou... | [
3771,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3767,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.eval_eq' | [] | [
1134,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1132,
1
] |
Mathlib/Topology/MetricSpace/IsometricSMul.lean | EMetric.preimage_mul_right_closedBall | [
{
"state_after": "M : Type u\nG : Type v\nX : Type w\ninst✝⁵ : PseudoEMetricSpace X\ninst✝⁴ : Group G\ninst✝³ : MulAction G X\ninst✝² : IsometricSMul G X\ninst✝¹ : PseudoEMetricSpace G\ninst✝ : IsometricSMul Gᵐᵒᵖ G\na b : G\nr : ℝ≥0∞\n⊢ (fun x => x * a) ⁻¹' closedBall b r = closedBall (b * a⁻¹) r",
"state_b... | [
328,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.apply_eq_of_dist_lt | [
{
"state_after": "case inl\nE : ℕ → Type u_1\nx : (n : ℕ) → E n\nn i : ℕ\nhi : i ≤ n\nh : dist x x < (1 / 2) ^ n\n⊢ x i = x i\n\ncase inr\nE : ℕ → Type u_1\nx y : (n : ℕ) → E n\nn : ℕ\nh : dist x y < (1 / 2) ^ n\ni : ℕ\nhi : i ≤ n\nhne : x ≠ y\n⊢ x i = y i",
"state_before": "E : ℕ → Type u_1\nx y : (n : ℕ) ... | [
336,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.equiv_symm | [
{
"state_after": "no goals",
"state_before": "ι : Type u_4\nι' : Type u_5\nR : Type u_3\nR₂ : Type ?u.553119\nK : Type ?u.553122\nM : Type u_1\nM' : Type u_2\nM'' : Type ?u.553131\nV : Type u\nV' : Type ?u.553136\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\ninst✝³ : AddCommMonoid M'\... | [
687,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
686,
1
] |
Mathlib/Analysis/Calculus/Monotone.lean | MonotoneOn.ae_differentiableWithinAt | [
{
"state_after": "f : ℝ → ℝ\ns : Set ℝ\nhf : MonotoneOn f s\nhs : MeasurableSet s\n⊢ ∀ᵐ (x : ℝ), x ∈ s → DifferentiableWithinAt ℝ f s x",
"state_before": "f : ℝ → ℝ\ns : Set ℝ\nhf : MonotoneOn f s\nhs : MeasurableSet s\n⊢ ∀ᵐ (x : ℝ) ∂Measure.restrict volume s, DifferentiableWithinAt ℝ f s x",
"tactic": ... | [
256,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.map_monotone | [
{
"state_after": "case intro.intro.intro.intro\nι : Sort ?u.207467\n𝕜 : Type ?u.207470\nV : Type u\nW : Type v\nX : Type w\nG✝ : SimpleGraph V\nG'✝ : SimpleGraph W\na b c u✝ v✝ w : V\ne : Sym2 V\nf : V ↪ W\nG G' : SimpleGraph V\nh : G ≤ G'\nu v : V\nha : Adj G u v\n⊢ Adj (SimpleGraph.map f G') (↑f u) (↑f v)",
... | [
1249,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1247,
1
] |
Mathlib/Analysis/Convex/Side.lean | Wbtw.wSameSide₁₂ | [] | [
387,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/Algebra/Order/Monoid/WithTop.lean | WithBot.le_of_add_le_add_right | [] | [
681,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
679,
11
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | Complex.hasStrictFDerivAt_cpow' | [] | [
52,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieHom.surjective_rangeRestrict | [
{
"state_after": "case mk\nR : Type u\nL : Type v\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\nL₂ : Type w\ninst✝¹ : LieRing L₂\ninst✝ : LieAlgebra R L₂\nf : L →ₗ⁅R⁆ L₂\ny : L₂\nhy : y ∈ range f\n⊢ ∃ a, ↑(rangeRestrict f) a = { val := y, property := hy }",
"state_before": "R : Type u\n... | [
342,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/CategoryTheory/Adhesive.lean | CategoryTheory.Adhesive.mono_of_isPushout_of_mono_right | [] | [
256,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.not_mem_Ioc_of_gt | [] | [
727,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
727,
1
] |
Mathlib/Order/Heyting/Basic.lean | inf_sdiff_sup_right | [] | [
744,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
743,
1
] |
Mathlib/Data/Multiset/Lattice.lean | Multiset.inf_singleton | [] | [
137,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Std/Data/String/Lemmas.lean | String.str_eq | [] | [
22,
43
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
22,
9
] |
Mathlib/Logic/Function/Basic.lean | Function.Injective.ne_iff' | [] | [
119,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.mapDomain_support_of_injective | [] | [
577,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
575,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.disjoint_of_disjoint_of_mem | [] | [
718,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
716,
1
] |
Mathlib/Algebra/Group/Pi.lean | Pi.monoidHom_injective | [] | [
288,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/GroupTheory/Subgroup/ZPowers.lean | Subgroup.mem_zpowers_iff | [] | [
53,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | mul_lt_iff_lt_one_left' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.26156\ninst✝³ : MulOneClass α\ninst✝² : LT α\ninst✝¹ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x < x_1\ninst✝ : ContravariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x < x_1\na b : α\n⊢ a * b < a ↔ a * b < a * 1",
... | [
523,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
1
] |
Mathlib/Analysis/Convex/Function.lean | StrictConcaveOn.lt_on_open_segment' | [] | [
683,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
680,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Constructions.lean | Pmf.support_normalize | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.137804\nγ : Type ?u.137807\nf : α → ℝ≥0∞\nhf0 : tsum f ≠ 0\nhf : tsum f ≠ ⊤\na : α\n⊢ a ∈ support (normalize f hf0 hf) ↔ a ∈ Function.support f",
"tactic": "simp [hf, mem_support_iff]"
}
] | [
256,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/LinearAlgebra/Multilinear/FiniteDimensional.lean | MultilinearMap.free_and_finite_fin | [
{
"state_after": "case zero\nι : Type ?u.2153\nR : Type u_2\nM₂ : Type u_3\nM₁ : ι → Type ?u.2164\ninst✝¹³ : Finite ι\ninst✝¹² : CommRing R\ninst✝¹¹ : AddCommGroup M₂\ninst✝¹⁰ : Module R M₂\ninst✝⁹ : Module.Finite R M₂\ninst✝⁸ : Module.Free R M₂\nn : ℕ\nN✝ : Fin n → Type u_1\ninst✝⁷ : (i : Fin n) → AddCommGroup... | [
54,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
9
] |
Mathlib/Order/Minimal.lean | IsGreatest.maximals_eq | [] | [
230,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Data/MvPolynomial/PDeriv.lean | MvPolynomial.pderiv_def | [
{
"state_after": "R : Type u\nσ : Type v\na a' a₁ a₂ : R\ns : σ →₀ ℕ\ninst✝¹ : CommSemiring R\ninst✝ : DecidableEq σ\ni : σ\n⊢ mkDerivation R (Pi.single i 1) = mkDerivation R (Pi.single i 1)",
"state_before": "R : Type u\nσ : Type v\na a' a₁ a₂ : R\ns : σ →₀ ℕ\ninst✝¹ : CommSemiring R\ninst✝ : DecidableEq σ... | [
70,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.abs_arg_le_pi | [] | [
160,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_lt_top | [] | [
289,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
9
] |
Mathlib/Analysis/InnerProductSpace/Adjoint.lean | LinearMap.isSelfAdjoint_iff' | [] | [
477,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
1
] |
Mathlib/Data/Int/Cast/Basic.lean | Int.ofNat_bit1 | [] | [
139,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Data/Finset/Sym.lean | Finset.mk'_mem_sym2_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\na b : α\nm : Sym2 α\n⊢ Quotient.mk (Sym2.Rel.setoid α) (a, b) ∈ Finset.sym2 s ↔ a ∈ s ∧ b ∈ s",
"tactic": "rw [mem_sym2_iff, Sym2.ball]"
}
] | [
67,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/CategoryTheory/Types.lean | CategoryTheory.FunctorToTypes.map_comp_apply | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nF G H : C ⥤ Type w\nX Y Z : C\nσ : F ⟶ G\nτ : G ⟶ H\nf : X ⟶ Y\ng : Y ⟶ Z\na : F.obj X\n⊢ F.map (f ≫ g) a = F.map g (F.map f a)",
"tactic": "simp [types_comp]"
}
] | [
146,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Analysis/SumIntegralComparisons.lean | MonotoneOn.sum_le_integral_Ico | [
{
"state_after": "x₀ : ℝ\na b : ℕ\nf : ℝ → ℝ\nhab : a ≤ b\nhf : MonotoneOn f (Icc ↑a ↑b)\n⊢ (∫ (x : ℝ) in ↑a..↑b, -f x) ≤ ∑ x in Finset.Ico a b, -f ↑x",
"state_before": "x₀ : ℝ\na b : ℕ\nf : ℝ → ℝ\nhab : a ≤ b\nhf : MonotoneOn f (Icc ↑a ↑b)\n⊢ ∑ x in Finset.Ico a b, f ↑x ≤ ∫ (x : ℝ) in ↑a..↑b, f x",
"ta... | [
165,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.updateColumn_self | [] | [
2757,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2755,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.SummableFamily.zero_apply | [] | [
1477,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1476,
1
] |
Mathlib/Data/List/Perm.lean | List.nodup_permutations'Aux_of_not_mem | [
{
"state_after": "case nil\nα : Type uu\nβ : Type vv\nl₁ l₂ s : List α\nx : α\nhx✝ : ¬x ∈ s\nhx : ¬x ∈ []\n⊢ Nodup (permutations'Aux x [])\n\ncase cons\nα : Type uu\nβ : Type vv\nl₁ l₂ s✝ : List α\nx : α\nhx✝ : ¬x ∈ s✝\ny : α\ns : List α\nIH : ¬x ∈ s → Nodup (permutations'Aux x s)\nhx : ¬x ∈ y :: s\n⊢ Nodup (pe... | [
1411,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1402,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.funLeft_injective_of_surjective | [
{
"state_after": "case intro\nR : Type u_4\nR₁ : Type ?u.2323244\nR₂ : Type ?u.2323247\nR₃ : Type ?u.2323250\nR₄ : Type ?u.2323253\nS : Type ?u.2323256\nK : Type ?u.2323259\nK₂ : Type ?u.2323262\nM : Type u_3\nM' : Type ?u.2323268\nM₁ : Type ?u.2323271\nM₂ : Type ?u.2323274\nM₃ : Type ?u.2323277\nM₄ : Type ?u.2... | [
2637,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2632,
1
] |
Mathlib/Algebra/CharP/Two.lean | CharTwo.neg_eq | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nι : Type ?u.6385\ninst✝¹ : Ring R\ninst✝ : CharP R 2\nx : R\n⊢ -x = x",
"tactic": "rw [neg_eq_iff_add_eq_zero, ← two_smul R x, two_eq_zero, zero_smul]"
}
] | [
68,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Analysis/Calculus/Deriv/Pow.lean | derivWithin_pow | [] | [
101,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Order/Bounds/Basic.lean | IsGreatest.image2 | [] | [
1392,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1390,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.bddAbove_image | [
{
"state_after": "α β : Type u\nf : Cardinal → Cardinal\ns : Set Cardinal\nhs : Small ↑s\n⊢ Small ↑(f '' s)",
"state_before": "α β : Type u\nf : Cardinal → Cardinal\ns : Set Cardinal\nhs : BddAbove s\n⊢ BddAbove (f '' s)",
"tactic": "rw [bddAbove_iff_small] at hs ⊢"
},
{
"state_after": "no goals... | [
977,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
973,
1
] |
Mathlib/Data/Set/Image.lean | Subtype.range_coe_subtype | [] | [
1408,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1407,
1
] |
Mathlib/Logic/Function/Conjugate.lean | Function.Commute.option_map | [] | [
131,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/LinearAlgebra/Matrix/MvPolynomial.lean | Matrix.mvPolynomialX_mapMatrix_eval | [] | [
63,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/LinearAlgebra/Vandermonde.lean | Matrix.vandermonde_cons | [
{
"state_after": "case a.h\nR : Type u_1\ninst✝ : CommRing R\nn : ℕ\nv0 : R\nv : Fin n → R\ni j : Fin (n + 1)\n⊢ vandermonde (Fin.cons v0 v) i j =\n Fin.cons (fun j => v0 ^ ↑j) (fun i => Fin.cons 1 fun j => v i * vandermonde v i j) i j",
"state_before": "R : Type u_1\ninst✝ : CommRing R\nn : ℕ\nv0 : R\nv... | [
58,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_of_subsingleton | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝¹ : Semiring R\np q r : R[X]\ninst✝ : Subsingleton R\n⊢ degree p = ⊥",
"tactic": "rw [Subsingleton.elim p 0, degree_zero]"
}
] | [
121,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.ceil_natCast | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.50519\nα : Type u_1\nβ : Type ?u.50525\ninst✝¹ : LinearOrderedSemiring α\ninst✝ : FloorSemiring α\na✝ : α\nn✝ n a : ℕ\n⊢ ⌈↑n⌉₊ ≤ a ↔ n ≤ a",
"tactic": "rw [ceil_le, cast_le]"
}
] | [
316,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | differentiableAt_const_sub_iff | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.553278\ninst✝³ : NormedAddCommGroup G\ninst✝² : Normed... | [
636,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
635,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.Measure.pi_eval_preimage_null | [
{
"state_after": "case intro.intro.intro\nι : Type u_2\nι' : Type ?u.3165675\nα : ι → Type u_1\ninst✝² : Fintype ι\nm : (i : ι) → OuterMeasure (α i)\ninst✝¹ : (i : ι) → MeasurableSpace (α i)\nμ : (i : ι) → Measure (α i)\ninst✝ : ∀ (i : ι), SigmaFinite (μ i)\ni : ι\ns : Set (α i)\nhs : ↑↑(μ i) s = 0\nt : Set (α ... | [
441,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.sum_zero | [] | [
348,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
1
] |
Mathlib/Order/SuccPred/Relation.lean | transGen_of_succ_of_gt | [] | [
62,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Data/Finmap.lean | Finmap.ext | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : α → Type v\nl₁ : Multiset (Sigma β)\nh₁ : Multiset.NodupKeys l₁\nl₂ : Multiset (Sigma β)\nnodupKeys✝ : Multiset.NodupKeys l₂\nH : { entries := l₁, nodupKeys := h₁ }.entries = { entries := l₂, nodupKeys := nodupKeys✝ }.entries\n⊢ { entries := l₁, ... | [
165,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | linearIndependent_of_ne_zero_of_inner_eq_zero | [
{
"state_after": "𝕜 : Type u_3\nE : Type u_2\nF : Type ?u.1881979\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nι : Type u_1\nv : ι → E\nhz : ∀ (i : ι), v i ≠ 0\nho : ∀ (i j : ι), i ≠ j →... | [
739,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
727,
1
] |
Mathlib/Order/BoundedOrder.lean | StrictMono.minimal_preimage_bot | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type ?u.24778\nδ : Type ?u.24781\ninst✝² : LinearOrder α\ninst✝¹ : PartialOrder β\ninst✝ : OrderBot β\nf : α → β\nH : StrictMono f\na : α\nh_bot : f a = ⊥\nx : α\np : β\n⊢ ⊥ ≤ p",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.24778\nδ : Type ?u.24781\nins... | [
431,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/Algebra/Category/ModuleCat/Kernels.lean | ModuleCat.hasKernels_moduleCat | [] | [
77,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.mul_const | [] | [
145,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Analysis/NormedSpace/FiniteDimension.lean | Basis.exists_op_norm_le | [
{
"state_after": "case intro.intro\n𝕜 : Type u\ninst✝¹¹ : NontriviallyNormedField 𝕜\nE : Type v\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace 𝕜 E\nF : Type w\ninst✝⁸ : NormedAddCommGroup F\ninst✝⁷ : NormedSpace 𝕜 F\nF' : Type x\ninst✝⁶ : AddCommGroup F'\ninst✝⁵ : Module 𝕜 F'\ninst✝⁴ : TopologicalSp... | [
316,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/CategoryTheory/Monoidal/Rigid/Basic.lean | CategoryTheory.tensorRightHomEquiv_naturality | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\ninst✝¹ : MonoidalCategory C\nX Y Y' Z Z' : C\ninst✝ : ExactPairing Y Y'\nf : X ⊗ Y ⟶ Z\ng : Z ⟶ Z'\n⊢ (ρ_ X).inv ≫ (𝟙 X ⊗ η_ Y Y') ≫ (α_ X Y Y').inv ≫ (f ≫ g ⊗ 𝟙 Y') =\n ((ρ_ X).inv ≫ (𝟙 X ⊗ η_ Y Y') ≫ (α_ X Y Y').inv ≫ (f ⊗ 𝟙 Y')) ≫ (g ⊗ 𝟙 Y')",
"... | [
397,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | LinearMap.isClosed_range_coe | [] | [
374,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.im_sq | [
{
"state_after": "no goals",
"state_before": "S : Type ?u.771397\nT : Type ?u.771400\nR : Type u_1\ninst✝ : CommRing R\nr x y z : R\na b c : ℍ[R]\n⊢ im a ^ 2 = -↑(↑normSq (im a))",
"tactic": "simp_rw [sq, ← star_mul_self, im_star, neg_mul, neg_neg]"
}
] | [
1235,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1234,
1
] |
Mathlib/Order/BooleanAlgebra.lean | sup_inf_sdiff | [] | [
101,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Data/Set/Sigma.lean | Set.sigma_union | [] | [
141,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Topology/VectorBundle/Basic.lean | Trivialization.apply_eq_prod_continuousLinearEquivAt | [
{
"state_after": "case h₁\nR : Type u_4\nB : Type u_1\nF : Type u_2\nE : B → Type u_3\ninst✝⁹ : NontriviallyNormedField R\ninst✝⁸ : (x : B) → AddCommMonoid (E x)\ninst✝⁷ : (x : B) → Module R (E x)\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace R F\ninst✝⁴ : TopologicalSpace B\ninst✝³ : TopologicalSpace (T... | [
513,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion_image_left | [
{
"state_after": "case h\nα : Type u_2\nβ : Type u_3\nγ : Type u_1\nι : Sort ?u.244602\nι' : Sort ?u.244605\nι₂ : Sort ?u.244608\nκ : ι → Sort ?u.244613\nκ₁ : ι → Sort ?u.244618\nκ₂ : ι → Sort ?u.244623\nκ' : ι' → Sort ?u.244628\nf : α → β → γ\ns : Set α\nt : Set β\ny : γ\n⊢ (y ∈ ⋃ (a : α) (_ : a ∈ s), f a '' t... | [
1864,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1862,
1
] |
Mathlib/Analysis/SpecialFunctions/Exp.lean | Real.range_exp | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.52919\nx y z : ℝ\nl : Filter α\n⊢ Set.range exp = Set.Ioi 0",
"tactic": "rw [← coe_comp_expOrderIso, range_comp, expOrderIso.range_eq, image_univ, Subtype.range_coe]"
}
] | [
297,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/GroupTheory/Coset.lean | Subgroup.card_quotient_dvd_card | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝² : Group α\ns✝ t : Subgroup α\ninst✝¹ : Fintype α\ns : Subgroup α\ninst✝ : DecidablePred fun x => x ∈ s\n⊢ Fintype.card (α ⧸ s) ∣ Fintype.card α",
"tactic": "simp [card_eq_card_quotient_mul_card_subgroup s, @dvd_mul_right ℕ]"
}
] | [
801,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
799,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.castSucc_pos | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\ninst✝ : NeZero n\ni : Fin n\nh : 0 < i\n⊢ 0 < ↑castSucc i",
"tactic": "simpa [lt_iff_val_lt_val] using h"
}
] | [
1286,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1285,
1
] |
Mathlib/Data/Subtype.lean | Subtype.forall | [] | [
47,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
11
] |
Mathlib/Tactic/Linarith/Lemmas.lean | Linarith.lt_irrefl | [] | [
25,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
25,
1
] |
Std/Logic.lean | Decidable.or_congr_left' | [
{
"state_after": "c a b : Prop\ninst✝ : Decidable c\nh : ¬c → (a ↔ b)\n⊢ ¬c → a ↔ ¬c → b",
"state_before": "c a b : Prop\ninst✝ : Decidable c\nh : ¬c → (a ↔ b)\n⊢ a ∨ c ↔ b ∨ c",
"tactic": "rw [or_iff_not_imp_right, or_iff_not_imp_right]"
},
{
"state_after": "no goals",
"state_before": "c a ... | [
620,
75
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
619,
1
] |
Mathlib/Topology/Connected.lean | isTotallyDisconnected_empty | [] | [
1225,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1224,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csSup_image2_eq_csInf_csInf | [] | [
1406,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1403,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.coe_subtype | [] | [
788,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
787,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.iSup_lt_lift | [
{
"state_after": "α : Type ?u.30918\nr : α → α → Prop\nι : Type u\nf : ι → Cardinal\nc : Cardinal\nhι : Cardinal.lift (#ι) < cof (ord c)\nhf : ∀ (i : ι), f i < c\n⊢ (⨆ (i : ι), ord (f i)) < ord c",
"state_before": "α : Type ?u.30918\nr : α → α → Prop\nι : Type u\nf : ι → Cardinal\nc : Cardinal\nhι : Cardina... | [
372,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieModuleHom.coe_linear_mk | [
{
"state_after": "no goals",
"state_before": "R : Type u\nL : Type v\nM : Type w\nN : Type w₁\nP : Type w₂\ninst✝¹⁴ : CommRing R\ninst✝¹³ : LieRing L\ninst✝¹² : LieAlgebra R L\ninst✝¹¹ : AddCommGroup M\ninst✝¹⁰ : AddCommGroup N\ninst✝⁹ : AddCommGroup P\ninst✝⁸ : Module R M\ninst✝⁷ : Module R N\ninst✝⁶ : Mod... | [
829,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
828,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.val_eq_val | [] | [
191,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Data/Sym/Sym2.lean | Sym2.mem_mk''_left | [] | [
330,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
] |
Mathlib/RingTheory/Coprime/Basic.lean | isCoprime_zero_right | [] | [
69,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Topology/Algebra/Module/LinearPMap.lean | LinearPMap.IsClosable.closure_isClosed | [
{
"state_after": "R : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝¹¹ : CommRing R\ninst✝¹⁰ : AddCommGroup E\ninst✝⁹ : AddCommGroup F\ninst✝⁸ : Module R E\ninst✝⁷ : Module R F\ninst✝⁶ : TopologicalSpace E\ninst✝⁵ : TopologicalSpace F\ninst✝⁴ : ContinuousAdd E\ninst✝³ : ContinuousAdd F\ninst✝² : TopologicalSpace R... | [
147,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Combinatorics/Colex.lean | Colex.forall_lt_of_colex_lt_of_forall_lt | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrder α\nA B : Finset α\nt : α\nh₁ : ∃ k, (∀ {x : α}, k < x → (x ∈ A ↔ x ∈ B)) ∧ ¬k ∈ A ∧ k ∈ B\nh₂ : ∀ (x : α), x ∈ B → x < t\n⊢ ∀ (x : α), x ∈ A → x < t",
"state_before": "α : Type u_1\ninst✝ : LinearOrder α\nA B : Finset α\nt : α\nh₁ : toColex A < toColex B\n... | [
271,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.foldl_add | [] | [
1373,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1372,
1
] |
Mathlib/Logic/Basic.lean | exists_swap | [] | [
667,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
666,
1
] |
Mathlib/Data/Set/Basic.lean | Set.inclusion_comp_inclusion | [] | [
2800,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2798,
1
] |
Mathlib/Algebra/Hom/Aut.lean | AddAut.smul_def | [] | [
257,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
11
] |
Mathlib/Order/Closure.lean | LowerAdjoint.closure_iSup_closure | [] | [
465,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | uniformity_comap | [] | [
1268,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1266,
1
] |
Mathlib/Data/Nat/Choose/Basic.lean | Nat.triangle_succ | [
{
"state_after": "n : ℕ\n⊢ n * (n + 1) / 2 = n * (n - 1 + 2) / 2\n\ncase H\nn : ℕ\n⊢ 0 < 2",
"state_before": "n : ℕ\n⊢ (n + 1) * (n + 1 - 1) / 2 = n * (n - 1) / 2 + n",
"tactic": "rw [← add_mul_div_left, mul_comm 2 n, ← mul_add, add_tsub_cancel_right, mul_comm]"
},
{
"state_after": "case H\nn : ... | [
97,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Analysis/Convex/Basic.lean | Antitone.convex_ge | [] | [
405,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Order/RelIso/Basic.lean | RelEmbedding.ofMapRelIff_coe | [] | [
510,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | pow_eq | [] | [
1279,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1279,
9
] |
Mathlib/Algebra/Order/Invertible.lean | pos_invOf_of_invertible_cast | [] | [
48,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Fin.nndist_insertNth_insertNth | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u\nβ : Type v\nX : Type ?u.407920\nι : Type ?u.407923\ninst✝³ : PseudoMetricSpace α✝\nπ : β → Type ?u.407931\ninst✝² : Fintype β\ninst✝¹ : (b : β) → PseudoMetricSpace (π b)\nn : ℕ\nα : Fin (n + 1) → Type u_1\ninst✝ : (i : Fin (n + 1)) → PseudoMetricSpa... | [
2081,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2078,
1
] |
Mathlib/Combinatorics/Colex.lean | Colex.sdiff_lt_sdiff_iff_lt | [
{
"state_after": "α : Type u_1\ninst✝¹ : LT α\ninst✝ : DecidableEq α\nA B : Finset α\n⊢ (∃ k, (∀ {x : α}, k < x → (x ∈ A \\ B ↔ x ∈ B \\ A)) ∧ ¬k ∈ A \\ B ∧ k ∈ B \\ A) ↔\n ∃ k, (∀ {x : α}, k < x → (x ∈ A ↔ x ∈ B)) ∧ ¬k ∈ A ∧ k ∈ B",
"state_before": "α : Type u_1\ninst✝¹ : LT α\ninst✝ : DecidableEq α\nA ... | [
327,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.coe_copy | [] | [
218,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.