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/Order/Monoid/Lemmas.lean | Contravariant.MulLECancellable | [] | [
1589,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1586,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.ofReal_coe_nnreal | [] | [
209,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
9
] |
Mathlib/Algebra/Category/GroupCat/Biproducts.lean | AddCommGroupCat.biproductIsoPi_inv_comp_π | [] | [
147,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Topology/NoetherianSpace.lean | TopologicalSpace.NoetherianSpace.wellFounded_closeds | [] | [
114,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | le_inv_iff_mul_le_one_left | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : Group α\ninst✝¹ : LE α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b c d : α\n⊢ b * a ≤ b * b⁻¹ ↔ b * a ≤ 1",
"tactic": "rw [mul_inv_self]"
}
] | [
136,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isNat_zero | [] | [
27,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
26,
1
] |
Mathlib/Data/Nat/Squarefree.lean | Nat.minSqFac_has_prop | [
{
"state_after": "n : ℕ\n⊢ MinSqFacProp n (if 2 ∣ n then if 2 ∣ n / 2 then some 2 else minSqFacAux (n / 2) 3 else minSqFacAux n 3)",
"state_before": "n : ℕ\n⊢ MinSqFacProp n (minSqFac n)",
"tactic": "dsimp only [minSqFac]"
},
{
"state_after": "case inl.inl\nn : ℕ\nd2 : 2 ∣ n\nd4 : 2 ∣ n / 2\n⊢ M... | [
216,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPushout.of_isColimit' | [] | [
367,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Analysis/Convex/Function.lean | ConvexOn.convex_epigraph | [
{
"state_after": "case mk.intro.mk.intro\n𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.86134\nα : Type ?u.86137\nβ : Type u_3\nι : Type ?u.86143\ninst✝⁷ : OrderedSemiring 𝕜\ninst✝⁶ : AddCommMonoid E\ninst✝⁵ : AddCommMonoid F\ninst✝⁴ : OrderedAddCommMonoid α\ninst✝³ : OrderedAddCommMonoid β\ninst✝² : SMul 𝕜 E\nins... | [
254,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Data/Set/Sigma.lean | Set.image_sigmaMk_subset_sigma_right | [] | [
234,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Topology/Algebra/Order/LeftRight.lean | continuousAt_iff_continuous_left_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝² : TopologicalSpace α\ninst✝¹ : LinearOrder α\ninst✝ : TopologicalSpace β\na : α\nf : α → β\n⊢ ContinuousAt f a ↔ ContinuousWithinAt f (Iic a) a ∧ ContinuousWithinAt f (Ici a) a",
"tactic": "simp only [ContinuousWithinAt, Co... | [
79,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.boundedBy_top | [
{
"state_after": "α : Type u_1\nm : Set α → ℝ≥0∞\n⊢ ∀ (s : Set α), Set.Nonempty s → ↑⊤ s ≤ ⊤ s",
"state_before": "α : Type u_1\nm : Set α → ℝ≥0∞\n⊢ boundedBy ⊤ = ⊤",
"tactic": "rw [eq_top_iff, le_boundedBy']"
},
{
"state_after": "α : Type u_1\nm : Set α → ℝ≥0∞\ns : Set α\nhs : Set.Nonempty s\n⊢ ... | [
890,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
886,
1
] |
Mathlib/Data/Nat/Choose/Basic.lean | Nat.choose_symm_add | [] | [
207,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.BoundedFormula.realize_castLe_of_eq | [
{
"state_after": "L : Language\nL' : Language\nM : Type w\nN : Type ?u.70714\nP : Type ?u.70717\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nn l : ℕ\nφ✝ ψ : BoundedFormula L α l\nθ : BoundedFormula L α (Nat.succ l)\nv✝ : α → M\nxs✝ : Fin l → M\nm : ℕ\nφ : Bou... | [
362,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/LinearAlgebra/Ray.lean | SameRay.of_subsingleton | [
{
"state_after": "R : Type u_2\ninst✝⁶ : StrictOrderedCommSemiring R\nM : Type u_1\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\nN : Type ?u.5473\ninst✝³ : AddCommMonoid N\ninst✝² : Module R N\nι : Type ?u.5555\ninst✝¹ : DecidableEq ι\nx✝ y✝ z : M\ninst✝ : Subsingleton M\nx y : M\n⊢ SameRay R 0 y",
"state... | [
69,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.productMap_range | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nA : Type u_3\nB : Type u_4\nS : Type u_1\ninst✝⁶ : CommSemiring R\ninst✝⁵ : Semiring A\ninst✝⁴ : Semiring B\ninst✝³ : CommSemiring S\ninst✝² : Algebra R A\ninst✝¹ : Algebra R B\ninst✝ : Algebra R S\nf : A →ₐ[R] S\ng : B →ₐ[R] S\n⊢ AlgHom.range (pro... | [
989,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
986,
1
] |
Mathlib/Algebra/Hom/Group.lean | OneHom.coe_copy | [] | [
817,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
815,
1
] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieHom.range_eq_map | [
{
"state_after": "case h\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\nK K' : LieSubalgebra R L\nK₂ : LieSubalgebra R L₂\nx✝ : L₂\n⊢ x✝ ∈ LieHom.range f ↔ x✝ ∈ map f ⊤",
"state_before": "R... | [
470,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
1
] |
Mathlib/Algebra/Hom/Units.lean | IsUnit.mul_div_mul_right | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.60370\nG : Type ?u.60373\nα : Type u_1\nM : Type ?u.60379\nN : Type ?u.60382\ninst✝ : DivisionMonoid α\na✝ b✝ c : α\nh : IsUnit c\na b : α\n⊢ a * c / (b * c) = a / b",
"tactic": "simp only [div_eq_mul_inv, mul_inv_rev, mul_assoc, h.mul_inv_cancel... | [
449,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
11
] |
Mathlib/Data/List/Cycle.lean | Cycle.nil_toMultiset | [] | [
699,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
698,
1
] |
Mathlib/Analysis/NormedSpace/IndicatorFunction.lean | nnnorm_indicator_eq_indicator_nnnorm | [] | [
34,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | union_support_maximal_linearIndependent_eq_range_basis | [
{
"state_after": "K : Type u\nV V₁ V₂ V₃ : Type v\nV' V'₁ : Type v'\nV'' : Type v''\nι✝ : Type w\nι' : Type w'\nη : Type u₁'\nφ : η → Type ?u.160592\nR : Type u\ninst✝⁷ : Ring R\nM : Type v\ninst✝⁶ : AddCommGroup M\ninst✝⁵ : Module R M\nM' : Type v'\ninst✝⁴ : AddCommGroup M'\ninst✝³ : Module R M'\nM₁ : Type v\n... | [
423,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/CategoryTheory/Limits/ExactFunctor.lean | CategoryTheory.LeftExactFunctor.of_fst | [] | [
226,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | linearIndependent_le_span_finset | [
{
"state_after": "no goals",
"state_before": "K : Type u\nV V₁ V₂ V₃ : Type v\nV' V'₁ : Type v'\nV'' : Type v''\nι✝ : Type w\nι' : Type w'\nη : Type u₁'\nφ : η → Type ?u.355098\nR : Type u\ninst✝³ : Ring R\ninst✝² : StrongRankCondition R\nM : Type v\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nι : Type u_1... | [
718,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
716,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.coe_smul_finset | [] | [
1603,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1602,
1
] |
Mathlib/GroupTheory/Index.lean | Subgroup.finiteIndex_of_finite_quotient | [] | [
561,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
560,
1
] |
Std/Data/HashMap/Basic.lean | Std.HashMap.Imp.WF.empty | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nn : Nat\ninst✝¹ : BEq α\ninst✝ : Hashable α\n⊢ WF\n (let nbuckets := numBucketsForCapacity n;\n let n_1 :=\n if h : nbuckets = 0 then { val := 8, property := empty.proof_1 }\n else { val := nbuckets, property := (_ : 0 < nbuckets) };\n Imp.empty' ... | [
240,
96
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
240,
1
] |
Mathlib/Order/CompactlyGenerated.lean | CompleteLattice.isSupClosedCompact_iff_wellFounded | [] | [
290,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.frequently_ae_mem_iff | [] | [
390,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.add_one_lt_iff | [
{
"state_after": "n✝ m n : ℕ\nk : Fin (n + 2)\n⊢ (↑k + ↑1) % (n + 2) < ↑k ↔ ↑k = n + 1",
"state_before": "n✝ m n : ℕ\nk : Fin (n + 2)\n⊢ k + 1 < k ↔ k = last (n + 1)",
"tactic": "simp only [lt_iff_val_lt_val, val_add, val_last, ext_iff]"
},
{
"state_after": "case mk\nn✝ m n k : ℕ\nhk : k < n + 2... | [
959,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
954,
1
] |
Std/Logic.lean | congrArg₂ | [
{
"state_after": "α : Sort u_1\nβ : Sort u_2\nγ : Sort u_3\nf : α → β → γ\nx : α\ny : β\n⊢ f x y = f x y",
"state_before": "α : Sort u_1\nβ : Sort u_2\nγ : Sort u_3\nf : α → β → γ\nx x' : α\ny y' : β\nhx : x = x'\nhy : y = y'\n⊢ f x y = f x' y'",
"tactic": "subst hx hy"
},
{
"state_after": "no g... | [
670,
73
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
669,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.einfsep_pair_eq_inf | [] | [
167,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/CategoryTheory/Opposites.lean | CategoryTheory.op_inv | [
{
"state_after": "case hom_inv_id\nC : Type u₁\ninst : Category C\nX Y : C\nf : X ⟶ Y\ninst_1 : IsIso f\n⊢ f.op ≫ (inv f).op = 𝟙 (op Y)",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nX Y : C\nf : X ⟶ Y\ninst✝ : IsIso f\n⊢ (inv f).op = inv f.op",
"tactic": "aesop_cat_nonterminal"
},
{
"sta... | [
165,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Analysis/NormedSpace/AddTorsor.lean | nndist_left_midpoint | [] | [
177,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Data/List/ToFinsupp.lean | List.toFinsupp_cons_eq_single_add_embDomain | [
{
"state_after": "case h.e'_3.h.e'_5\nM : Type ?u.15101\ninst✝⁴ : Zero M\nl : List M\ninst✝³ : DecidablePred fun x => getD l x 0 ≠ 0\nn : ℕ\nR : Type u_1\ninst✝² : AddZeroClass R\nx : R\nxs : List R\ninst✝¹ : DecidablePred fun x_1 => getD (x :: xs) x_1 0 ≠ 0\ninst✝ : DecidablePred fun x => getD xs x 0 ≠ 0\n⊢ Fi... | [
139,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.compContinuousLinearMapEquivL_apply | [] | [
1242,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1238,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.codeSupp'_self | [
{
"state_after": "no goals",
"state_before": "c : Code\nk : Cont'\n⊢ trStmts₁ (trNormal c k) ⊆ codeSupp' c k",
"tactic": "cases c <;> first |rfl|exact Finset.subset_union_left _ _"
},
{
"state_after": "case fix\nk : Cont'\na✝ : Code\n⊢ trStmts₁ (trNormal (Code.fix a✝) k) ⊆ codeSupp' (Code.fix a✝... | [
1786,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1785,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiff.of_le | [] | [
1460,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1459,
1
] |
Mathlib/Algebra/Order/Pointwise.lean | sSup_div | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝³ : CompleteLattice α\ninst✝² : Group α\ninst✝¹ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\ninst✝ : CovariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\ns t : Set α\n⊢ sSup (s / t) = sSup s / sInf t",
... | [
92,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Order/BoundedOrder.lean | Subtype.coe_eq_top_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.39622\nδ : Type ?u.39625\np : α → Prop\ninst✝² : PartialOrder α\ninst✝¹ : OrderTop α\ninst✝ : OrderTop (Subtype p)\nhtop : p ⊤\nx : { x // p x }\n⊢ ↑x = ⊤ ↔ x = ⊤",
"tactic": "rw [← coe_top htop, ext_iff]"
}
] | [
788,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
786,
1
] |
Mathlib/Order/Minimal.lean | minimals_antichain | [] | [
104,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.isometry_id | [] | [
859,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
858,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.invOfUnit_eq' | [
{
"state_after": "σ : Type u_1\nR : Type ?u.1782406\nk : Type u_2\ninst✝ : Field k\nφ : MvPowerSeries σ k\nu : kˣ\nh : ↑(constantCoeff σ k) φ = ↑u\n⊢ invOfUnit φ u = invOfUnit φ (Units.mk0 (↑(constantCoeff σ k) φ) (_ : ↑(constantCoeff σ k) φ ≠ 0))",
"state_before": "σ : Type u_1\nR : Type ?u.1782406\nk : Ty... | [
981,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
976,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.map_cons | [
{
"state_after": "α : Type u\nβ : Type v\nδ : Type w\nf : α → β\na : α\ns : Stream' α\n⊢ head (f (head (a :: s)) :: map f (tail (a :: s))) :: tail (f (head (a :: s)) :: map f (tail (a :: s))) =\n f a :: map f s",
"state_before": "α : Type u\nβ : Type v\nδ : Type w\nf : α → β\na : α\ns : Stream' α\n⊢ map ... | [
169,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Order/Bounded.lean | Set.bounded_ge_of_bounded_gt | [] | [
128,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/AlgebraicGeometry/Stalks.lean | AlgebraicGeometry.PresheafedSpace.restrictStalkIso_hom_eq_germ | [] | [
88,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.relIso_enum | [
{
"state_after": "case h.e'_4\nα✝ : Type ?u.98043\nβ✝ : Type ?u.98046\nγ : Type ?u.98049\nr✝ : α✝ → α✝ → Prop\ns✝ : β✝ → β✝ → Prop\nt : γ → γ → Prop\nα β : Type u\nr : α → α → Prop\ns : β → β → Prop\ninst✝¹ : IsWellOrder α r\ninst✝ : IsWellOrder β s\nf : r ≃r s\no : Ordinal\nhr : o < type r\n⊢ type s = type r",... | [
557,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
549,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.one_toReal | [] | [
227,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
9
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | CommGroupWithZero.coe_normUnit | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.350228\nG₀ : Type u_1\ninst✝¹ : CommGroupWithZero G₀\ninst✝ : DecidableEq G₀\na : G₀\nh0 : a ≠ 0\n⊢ ↑(normUnit a) = a⁻¹",
"tactic": "simp [normUnit, h0]"
}
] | [
1420,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1420,
1
] |
Mathlib/Data/List/Perm.lean | List.Perm.product_left | [] | [
1113,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1111,
1
] |
Mathlib/Control/Functor.lean | Functor.ext | [
{
"state_after": "case refl\nF✝ : Type u → Type v\nα β γ : Type u\ninst✝¹ : Functor F✝\ninst✝ : LawfulFunctor F✝\nF : Type u_1 → Type u_2\nm : {α β : Type u_1} → (α → β) → F α → F β\nmc mc' : {α β : Type u_1} → α → F β → F α\nH1 : LawfulFunctor F\nH2 : LawfulFunctor F\nH : ∀ (α β : Type u_1) (f : α → β) (x : F ... | [
65,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Data/Fintype/Basic.lean | Set.toFinset_setOf | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.93002\nγ : Type ?u.93005\ns t : Set α\ninst✝² : Fintype α\np : α → Prop\ninst✝¹ : DecidablePred p\ninst✝ : Fintype ↑{x | p x}\na✝ : α\n⊢ a✝ ∈ toFinset {x | p x} ↔ a✝ ∈ filter p Finset.univ",
"state_before": "α : Type u_1\nβ : Type ?u.93002\nγ : Type ?u.930... | [
760,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
757,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.image₂_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nα' : Type ?u.33328\nβ : Type u_3\nβ' : Type ?u.33334\nγ : Type u_1\nγ' : Type ?u.33340\nδ : Type ?u.33343\nδ' : Type ?u.33346\nε : Type ?u.33349\nε' : Type ?u.33352\nζ : Type ?u.33355\nζ' : Type ?u.33358\nν : Type ?u.33361\ninst✝⁷ : DecidableEq α'\... | [
167,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.BinaryCofan.isColimit_iff_isIso_inl | [
{
"state_after": "case mp\nC : Type u\ninst✝ : Category C\nX✝ Y✝ X Y : C\nh : IsInitial Y\nc : BinaryCofan X Y\n⊢ Nonempty (IsColimit c) → IsIso (inl c)\n\ncase mpr\nC : Type u\ninst✝ : Category C\nX✝ Y✝ X Y : C\nh : IsInitial Y\nc : BinaryCofan X Y\n⊢ IsIso (inl c) → Nonempty (IsColimit c)",
"state_before"... | [
483,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/Topology/Sequences.lean | isSeqClosed_of_seqClosure_eq | [] | [
108,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_div_coe_angle | [
{
"state_after": "no goals",
"state_before": "x y : ℂ\nhx : x ≠ 0\nhy : y ≠ 0\n⊢ ↑(arg (x / y)) = ↑(arg x) - ↑(arg y)",
"tactic": "rw [div_eq_mul_inv, arg_mul_coe_angle hx (inv_ne_zero hy), arg_inv_coe_angle, sub_eq_add_neg]"
}
] | [
488,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroObjects.lean | CategoryTheory.Iso.isZero_iff | [] | [
148,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Order/UpperLower/Basic.lean | isLowerSet_sInter | [] | [
152,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Data/Polynomial/Expand.lean | Polynomial.contract_expand | [
{
"state_after": "case a\nR : Type u\ninst✝¹ : CommSemiring R\nS : Type v\ninst✝ : CommSemiring S\np q : ℕ\nf : R[X]\nhp : p ≠ 0\nn✝ : ℕ\n⊢ coeff (contract p (↑(expand R p) f)) n✝ = coeff f n✝",
"state_before": "R : Type u\ninst✝¹ : CommSemiring R\nS : Type v\ninst✝ : CommSemiring S\np q : ℕ\nf : R[X]\nhp :... | [
222,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.coe_subtype | [] | [
158,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | MonoidHom.map_finprod_mem' | [
{
"state_after": "α : Type u_3\nβ : Type ?u.282817\nι : Type ?u.282820\nG : Type ?u.282823\nM : Type u_1\nN : Type u_2\ninst✝¹ : CommMonoid M\ninst✝ : CommMonoid N\nf✝ g✝ : α → M\na b : α\ns t : Set α\nf : α → M\ng : M →* N\nh₀ : Set.Finite (s ∩ mulSupport f)\n⊢ (∏ᶠ (i : α), ↑g (∏ᶠ (_ : i ∈ s), f i)) = ∏ᶠ (i : ... | [
702,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
698,
1
] |
Mathlib/Logic/Basic.lean | forall_or_right | [] | [
857,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
856,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.comp_tendsto | [] | [
422,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
] |
Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean | List.Nat.antidiagonalTuple_two | [
{
"state_after": "n : ℕ\n⊢ (List.bind (antidiagonal n) fun ni => map (fun x => Fin.cons ni.fst x) (antidiagonalTuple 1 ni.snd)) =\n map (fun i => ![i.fst, i.snd]) (antidiagonal n)",
"state_before": "n : ℕ\n⊢ antidiagonalTuple 2 n = map (fun i => ![i.fst, i.snd]) (antidiagonal n)",
"tactic": "rw [anti... | [
152,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | Commute.orderOf_dvd_lcm_mul | [
{
"state_after": "case pos\nG : Type u\nA : Type v\nx y : G\na b : A\nn m : ℕ\ninst✝¹ : Monoid G\ninst✝ : AddMonoid A\nh : _root_.Commute x y\nh0 : orderOf x = 0\n⊢ orderOf y ∣ lcm (orderOf x) (orderOf (x * y))\n\ncase neg\nG : Type u\nA : Type v\nx y : G\na b : A\nn m : ℕ\ninst✝¹ : Monoid G\ninst✝ : AddMonoid ... | [
398,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
] |
Mathlib/Algebra/DirectSum/Decomposition.lean | DirectSum.decompose_sum | [] | [
169,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Order/OrdContinuous.lean | RightOrdContinuous.map_inf | [] | [
205,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Sized.eq_node' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns : ℕ\nl : Ordnode α\nx : α\nr : Ordnode α\nh : Sized (node s l x r)\n⊢ node s l x r = Ordnode.node' l x r",
"tactic": "rw [h.1]"
}
] | [
117,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.cos_add_two_pi | [] | [
1212,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1211,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_pow | [] | [
689,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
688,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.isBasis_basic_opens | [
{
"state_after": "R : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\n⊢ TopologicalSpace.IsTopologicalBasis (SetLike.coe '' Set.range basicOpen)",
"state_before": "R : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\n⊢ TopologicalSpace.Opens.IsBasis (Set.range basicOpen)",
"tact... | [
839,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
835,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.image_id' | [] | [
418,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | DifferentiableAt.congr_of_eventuallyEq | [] | [
933,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
931,
1
] |
Mathlib/AlgebraicGeometry/SheafedSpace.lean | AlgebraicGeometry.SheafedSpace.congr_app | [
{
"state_after": "C : Type u\ninst✝ : Category C\nX Y : SheafedSpace C\nα : X ⟶ Y\nU : (Opens ↑↑Y.toPresheafedSpace)ᵒᵖ\n⊢ (Functor.op (Opens.map α.base)).obj U = (Functor.op (Opens.map α.base)).obj U",
"state_before": "C : Type u\ninst✝ : Category C\nX Y : SheafedSpace C\nα β : X ⟶ Y\nh : α = β\nU : (Opens ... | [
159,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Analysis/LocallyConvex/Polar.lean | LinearMap.polar_empty | [] | [
106,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.set_biInter_biUnion | [] | [
2084,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2082,
1
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | ConvexCone.map_id | [] | [
277,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/GroupTheory/Perm/Option.lean | Equiv.optionCongr_one | [] | [
24,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
23,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | linearIndependent_option | [
{
"state_after": "no goals",
"state_before": "ι : Type u'\nι' : Type ?u.1220994\nR : Type ?u.1220997\nK : Type u_1\nM : Type ?u.1221003\nM' : Type ?u.1221006\nM'' : Type ?u.1221009\nV : Type u\nV' : Type ?u.1221014\ninst✝⁴ : DivisionRing K\ninst✝³ : AddCommGroup V\ninst✝² : AddCommGroup V'\ninst✝¹ : Module ... | [
1204,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1201,
1
] |
Mathlib/Order/Monotone/Monovary.lean | monovaryOn_self | [] | [
112,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Data/Nat/Cast/Basic.lean | Nat.strictMono_cast | [] | [
121,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Deprecated/Subgroup.lean | Group.normalClosure.is_normal | [
{
"state_after": "case basic\nG : Type u_1\nH : Type ?u.144028\nA : Type ?u.144031\na a₁ a₂ b c : G\ns : Set G\ninst✝ : Group G\nsrc✝ : IsSubgroup (normalClosure s) := isSubgroup s\nn g x : G\nhx : x ∈ conjugatesOfSet s\n⊢ g * x * g⁻¹ ∈ normalClosure s\n\ncase one\nG : Type u_1\nH : Type ?u.144028\nA : Type ?u.... | [
726,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
717,
1
] |
Mathlib/GroupTheory/DoubleCoset.lean | Doset.doset_eq_of_mem | [
{
"state_after": "case intro.intro.intro.intro.intro.intro.intro.intro\nG : Type u_1\ninst✝¹ : Group G\nα : Type ?u.4114\ninst✝ : Mul α\nJ : Subgroup G\ng : G\nH K : Subgroup G\nk h a : G\nhh : h ∈ ↑H\nhk : k ∈ ↑K\n⊢ doset ((fun x x_1 => x * x_1) ((fun x x_1 => x * x_1) h a) k) ↑H ↑K = doset a ↑H ↑K",
"stat... | [
58,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid'.node3R | [] | [
1139,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1136,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_emptyCollection_iff | [
{
"state_after": "case mp\nα✝ β α : Type u\ns : Set α\n⊢ (#↑s) = 0 → s = ∅\n\ncase mpr\nα✝ β α : Type u\ns : Set α\n⊢ s = ∅ → (#↑s) = 0",
"state_before": "α✝ β α : Type u\ns : Set α\n⊢ (#↑s) = 0 ↔ s = ∅",
"tactic": "constructor"
},
{
"state_after": "case mp\nα✝ β α : Type u\ns : Set α\nh : (#↑s)... | [
1990,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1984,
1
] |
Mathlib/Order/Filter/Pi.lean | Filter.pi_mem_pi | [
{
"state_after": "ι : Type u_1\nα : ι → Type u_2\nf f₁ f₂ : (i : ι) → Filter (α i)\ns : (i : ι) → Set (α i)\nI : Set ι\nhI : Set.Finite I\nh : ∀ (i : ι), i ∈ I → s i ∈ f i\n⊢ (⋂ (x : ↑I), eval ↑x ⁻¹' s ↑x) ∈ pi f",
"state_before": "ι : Type u_1\nα : ι → Type u_2\nf f₁ f₂ : (i : ι) → Filter (α i)\ns : (i : ι... | [
73,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/NumberTheory/Padics/PadicNorm.lean | padicNorm.triangle_ineq | [] | [
220,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.normSq_nonneg | [] | [
626,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
625,
1
] |
Mathlib/Data/Part.lean | Part.get_eq_get_of_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.6349\nγ : Type ?u.6352\na : Part α\nha : a.Dom\nb : Part α\nh : a = b\n⊢ get a ha = get b (_ : b.Dom)",
"tactic": "congr"
}
] | [
236,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Data/Set/Basic.lean | Set.ite_inter_inter | [
{
"state_after": "case h\nα : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns s₁✝ s₂✝ t✝ t₁ t₂ u t s₁ s₂ s₁' s₂' : Set α\nx : α\n⊢ x ∈ Set.ite t (s₁ ∩ s₂) (s₁' ∩ s₂') ↔ x ∈ Set.ite t s₁ s₁' ∩ Set.ite t s₂ s₂'",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns s₁✝ s₂✝ t✝ t₁ ... | [
2311,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2307,
1
] |
Mathlib/Analysis/MeanInequalities.lean | Real.young_inequality | [] | [
269,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/Data/Finset/Basic.lean | Multiset.toFinset_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.445536\nγ : Type ?u.445539\ninst✝ : DecidableEq α\ns t : Multiset α\na : α\n⊢ toFinset {a} = {a}",
"tactic": "rw [← cons_zero, toFinset_cons, toFinset_zero, IsLawfulSingleton.insert_emptyc_eq]"
}
] | [
3153,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3152,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | ContDiffAt.cosh | [] | [
1107,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1105,
1
] |
Std/Data/List/Init/Lemmas.lean | List.foldr_self_append | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl' l : List α\n⊢ foldr cons l' l = l ++ l'",
"tactic": "induction l <;> simp [*]"
}
] | [
203,
27
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
202,
9
] |
Std/Data/Int/DivMod.lean | Int.fmod_one | [
{
"state_after": "no goals",
"state_before": "a : Int\n⊢ fmod a 1 = 0",
"tactic": "simp [fmod_def, Int.one_mul, Int.sub_self]"
}
] | [
353,
45
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
352,
9
] |
Mathlib/Topology/MetricSpace/Kuratowski.lean | KuratowskiEmbedding.embeddingOfSubset_coe | [] | [
54,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Order/Bounds/Basic.lean | AntitoneOn.map_isGreatest | [] | [
1250,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1249,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.ceil_le | [] | [
1096,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1095,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | CompleteLatticeHom.comp_assoc | [] | [
757,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
755,
1
] |
Mathlib/Analysis/NormedSpace/CompactOperator.lean | IsCompactOperator.isCompact_closure_image_ball | [] | [
159,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.