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/Order/Synonym.lean | OrderDual.ofDual_lt_ofDual | [] | [
109,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Data/PNat/Basic.lean | PNat.pos_of_div_pos | [
{
"state_after": "n : ℕ+\na : ℕ\nh : a ∣ ↑n\n⊢ a ≠ 0",
"state_before": "n : ℕ+\na : ℕ\nh : a ∣ ↑n\n⊢ 0 < a",
"tactic": "apply pos_iff_ne_zero.2"
},
{
"state_after": "n : ℕ+\na : ℕ\nh : a ∣ ↑n\nhzero : a = 0\n⊢ False",
"state_before": "n : ℕ+\na : ℕ\nh : a ∣ ↑n\n⊢ a ≠ 0",
"tactic": "intro... | [
450,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.pred_lt_pred | [] | [
56,
41
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
54,
1
] |
Mathlib/Order/UpperLower/Basic.lean | isLowerSet_iUnion₂ | [] | [
144,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Order/Heyting/Basic.lean | compl_sup_compl_le | [] | [
926,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
925,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | exists_ratio_hasDerivAt_eq_ratio_slope | [
{
"state_after": "E : Type ?u.307798\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type ?u.307894\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf f' : ℝ → ℝ\na b : ℝ\nhab : a < b\nhfc : ContinuousOn f (Icc a b)\nhff' : ∀ (x : ℝ), x ∈ Ioo a b → HasDerivAt f (f' x) x\nhfd : Differentiab... | [
724,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
714,
1
] |
Mathlib/Topology/ContinuousFunction/Algebra.lean | ContinuousMap.coe_smul | [] | [
612,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
611,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.smul_testAgainstNN_apply | [
{
"state_after": "no goals",
"state_before": "Ω : Type u_1\ninst✝⁵ : MeasurableSpace Ω\nR : Type ?u.54872\ninst✝⁴ : SMul R ℝ≥0\ninst✝³ : SMul R ℝ≥0∞\ninst✝² : IsScalarTower R ℝ≥0 ℝ≥0∞\ninst✝¹ : IsScalarTower R ℝ≥0∞ ℝ≥0∞\ninst✝ : TopologicalSpace Ω\nc : ℝ≥0\nμ : FiniteMeasure Ω\nf : Ω →ᵇ ℝ≥0\n⊢ testAgainstNN... | [
378,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/Order/CompleteLattice.lean | sInf_sup_le_iInf_sup | [] | [
1932,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1931,
1
] |
Mathlib/Data/Nat/Choose/Basic.lean | Nat.choose_eq_factorial_div_factorial | [
{
"state_after": "n k : ℕ\nhk : k ≤ n\n⊢ choose n k = choose n k * (k ! * (n - k)!) / (k ! * (n - k)!)",
"state_before": "n k : ℕ\nhk : k ≤ n\n⊢ choose n k = n ! / (k ! * (n - k)!)",
"tactic": "rw [← choose_mul_factorial_mul_factorial hk, mul_assoc]"
},
{
"state_after": "no goals",
"state_be... | [
171,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Order/Filter/Pi.lean | Filter.pi_mem_pi_iff | [] | [
106,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.tr_respects | [] | [
1693,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1691,
1
] |
Mathlib/Algebra/Order/Pointwise.lean | sInf_inv | [
{
"state_after": "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 s : Set α\n⊢ (⨅ (a : α) (_ : a ∈ s), a⁻¹) = (sSup s)⁻¹",
"state_before": "α... | [
73,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.reClm_apply | [] | [
272,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.ext_iff | [] | [
362,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/Analysis/Convex/Quasiconvex.lean | QuasiconvexOn.convex | [] | [
96,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Data/List/Rotate.lean | List.nthLe_rotate' | [] | [
307,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.mem_sInf | [] | [
223,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/MeasureTheory/Measure/Regular.lean | MeasureTheory.Measure.InnerRegular.exists_subset_lt_add | [
{
"state_after": "case inl\nα : Type u_1\nm : MeasurableSpace α\nμ : Measure α\np q : Set α → Prop\nU : Set α\nε : ℝ≥0∞\nH : InnerRegular μ p q\nh0 : p ∅\nhU : q U\nhμU : ↑↑μ U ≠ ⊤\nhε : ε ≠ 0\nh₀ : ↑↑μ U = 0\n⊢ ∃ K, K ⊆ U ∧ p K ∧ ↑↑μ U < ↑↑μ K + ε\n\ncase inr\nα : Type u_1\nm : MeasurableSpace α\nμ : Measure α... | [
169,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | HasStrictFDerivAt.of_local_left_inverse | [
{
"state_after": "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.375202\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.375297\... | [
382,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/Logic/Equiv/Fin.lean | finRotate_of_lt | [
{
"state_after": "case h\nm n k : ℕ\nh : k < n\n⊢ ↑(↑(finRotate (n + 1)) { val := k, isLt := (_ : k < n + 1) }) =\n ↑{ val := k + 1, isLt := (_ : Nat.succ k < Nat.succ n) }",
"state_before": "m n k : ℕ\nh : k < n\n⊢ ↑(finRotate (n + 1)) { val := k, isLt := (_ : k < n + 1) } = { val := k + 1, isLt := (_ :... | [
403,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/RingTheory/TensorProduct.lean | Module.endTensorEndAlgHom_apply | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nM : Type u_2\nN : Type u_3\ninst✝⁴ : CommSemiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid N\ninst✝¹ : Module R M\ninst✝ : Module R N\nf : End R M\ng : End R N\n⊢ ↑endTensorEndAlgHom (f ⊗ₜ[R] g) = map f g",
"tactic": "simp only [endT... | [
1102,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1099,
1
] |
Mathlib/LinearAlgebra/FreeModule/Rank.lean | rank_finsupp_self' | [
{
"state_after": "no goals",
"state_before": "R : Type u\nM : Type v\nN : Type w\ninst✝⁷ : Ring R\ninst✝⁶ : StrongRankCondition R\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\ninst✝³ : Module.Free R M\ninst✝² : AddCommGroup N\ninst✝¹ : Module R N\ninst✝ : Module.Free R N\nι : Type u\n⊢ Module.rank R (ι →₀ ... | [
60,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Algebra/Order/CompleteField.lean | LinearOrderedField.inducedMap_one | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.19004\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.19013\ninst✝³ : LinearOrderedField α\ninst✝² : ConditionallyCompleteLinearOrderedField β\ninst✝¹ : ConditionallyCompleteLinearOrderedField γ\ninst✝ : Archimedean α\n⊢ inducedMap α β 1 = 1",
"tactic":... | [
209,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.deleteEdges_deleteEdges | [
{
"state_after": "case Adj.h.h.a\nι : Sort ?u.155613\n𝕜 : Type ?u.155616\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\ns s' : Set (Sym2 V)\nx✝¹ x✝ : V\n⊢ Adj (deleteEdges (deleteEdges G s) s') x✝¹ x✝ ↔ Adj (deleteEdges G (s ∪ s')) x✝¹ x✝",
"state_b... | [
1135,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1132,
1
] |
Mathlib/LinearAlgebra/Isomorphisms.lean | LinearMap.quotKerEquivRange_apply_mk | [] | [
57,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Analysis/SpecialFunctions/Exp.lean | Complex.continuous_exp | [
{
"state_after": "case h'.h.e'_4\nz y✝ x✝ : ℝ\nx y : ℂ\na✝ : ‖y - x‖ < 1\n⊢ 2 * ‖exp x‖ * dist y x = (1 + 1) * ‖exp x‖ * ‖y - x‖",
"state_before": "z y✝ x✝ : ℝ\nx y : ℂ\n⊢ dist y x < 1 → dist (exp y) (exp x) ≤ 2 * ‖exp x‖ * dist y x",
"tactic": "convert locally_lipschitz_exp zero_le_one le_rfl x y using... | [
77,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Data/Set/Intervals/OrdConnected.lean | Set.ordConnected_dual | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.3064\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ns✝ t s : Set α\nh : OrdConnected (↑ofDual ⁻¹' s)\n⊢ OrdConnected s",
"tactic": "simpa only [ordConnected_def] using h.dual"
}
] | [
100,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.add_congr | [] | [
1773,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1771,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.coe_add | [] | [
790,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
789,
1
] |
Mathlib/Data/Num/Lemmas.lean | ZNum.cast_lt | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedRing α\nm n : ZNum\n⊢ ↑m < ↑n ↔ m < n",
"tactic": "rw [← cast_to_int m, ← cast_to_int n, Int.cast_lt, lt_to_int]"
}
] | [
1407,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1406,
1
] |
Mathlib/RingTheory/GradedAlgebra/Basic.lean | DirectSum.coe_decompose_mul_of_right_mem_of_le | [
{
"state_after": "case intro\nι : Type u_3\nR : Type ?u.367118\nA : Type u_1\nσ : Type u_2\ninst✝⁸ : Semiring A\ninst✝⁷ : DecidableEq ι\ninst✝⁶ : CanonicallyOrderedAddMonoid ι\ninst✝⁵ : SetLike σ A\ninst✝⁴ : AddSubmonoidClass σ A\n𝒜 : ι → σ\ninst✝³ : GradedRing 𝒜\na : A\nn i : ι\ninst✝² : Sub ι\ninst✝¹ : Orde... | [
324,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.TM2to1.addBottom_map | [
{
"state_after": "no goals",
"state_before": "K : Type ?u.595576\ninst✝² : DecidableEq K\nΓ : K → Type ?u.595590\nΛ : Type ?u.595593\ninst✝¹ : Inhabited Λ\nσ : Type ?u.595599\ninst✝ : Inhabited σ\nL : ListBlank ((k : K) → Option (Γ k))\n⊢ default.snd = default",
"tactic": "rfl"
},
{
"state_after... | [
2378,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2373,
1
] |
Mathlib/CategoryTheory/Over.lean | CategoryTheory.Over.iteratedSliceBackward_forget_forget | [] | [
287,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/Data/Sigma/Basic.lean | Sigma.subtype_ext_iff | [] | [
87,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Data/PFun.lean | PFun.id_apply | [] | [
574,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
573,
1
] |
Mathlib/Data/Sym/Sym2.lean | Sym2.other_spec' | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.101059\nγ : Type ?u.101062\ninst✝ : DecidableEq α\na x✝ y✝ : α\nh : a ∈ Quotient.mk (Rel.setoid α) (x✝, y✝)\n⊢ Quotient.mk (Rel.setoid α) (a, Mem.other' h) = Quotient.mk (Rel.setoid α) (x✝, y✝)",
"state_before": "α : Type u_1\nβ : Type ?u.101059\nγ : Type ... | [
706,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.cos_sq' | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ cos x ^ 2 = 1 - sin x ^ 2",
"tactic": "rw [← sin_sq_add_cos_sq x, add_sub_cancel']"
}
] | [
1298,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1298,
1
] |
Mathlib/CategoryTheory/Sites/Grothendieck.lean | CategoryTheory.GrothendieckTopology.transitive | [] | [
136,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Algebra/Group/Basic.lean | mul_left_eq_self | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.14402\nβ : Type ?u.14405\nG : Type ?u.14408\nM : Type u\ninst✝ : RightCancelMonoid M\na b : M\n⊢ a * b = b ↔ a * b = 1 * b",
"tactic": "rw [one_mul]"
}
] | [
213,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Order/Filter/Extr.lean | IsMinOn.sub | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type x\ninst✝ : OrderedAddCommGroup β\nf g : α → β\na : α\ns : Set α\nl : Filter α\nhf : IsMinOn f s a\nhg : IsMaxOn g s a\n⊢ IsMinOn (fun x => f x - g x) s a",
"tactic": "simpa only [sub_eq_add_neg] using hf.add hg.ne... | [
515,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
514,
1
] |
Mathlib/Order/Monotone/Monovary.lean | Antivary.dual | [] | [
204,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Computability/Ackermann.lean | exists_lt_ack_of_nat_primrec | [
{
"state_after": "case zero\nf : ℕ → ℕ\n⊢ ∃ m, ∀ (n : ℕ), (fun x => 0) n < ack m n\n\ncase succ\nf : ℕ → ℕ\n⊢ ∃ m, ∀ (n : ℕ), succ n < ack m n\n\ncase left\nf : ℕ → ℕ\n⊢ ∃ m, ∀ (n : ℕ), (fun n => (unpair n).fst) n < ack m n\n\ncase right\nf : ℕ → ℕ\n⊢ ∃ m, ∀ (n : ℕ), (fun n => (unpair n).snd) n < ack m n\n\ncas... | [
380,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/GroupTheory/GroupAction/Defs.lean | smul_ite | [
{
"state_after": "no goals",
"state_before": "M : Type u_2\nN : Type ?u.14217\nG : Type ?u.14220\nA : Type ?u.14223\nB : Type ?u.14226\nα : Type u_1\nβ : Type ?u.14232\nγ : Type ?u.14235\nδ : Type ?u.14238\ninst✝¹ : SMul M α\np : Prop\ninst✝ : Decidable p\na : M\nb₁ b₂ : α\n⊢ (a • if p then b₁ else b₂) = if... | [
462,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | HomogeneousIdeal.toIdeal_iSup₂ | [
{
"state_after": "no goals",
"state_before": "ι : Type u_3\nσ : Type u_4\nR : Type ?u.163506\nA : Type u_5\ninst✝⁵ : Semiring A\ninst✝⁴ : DecidableEq ι\ninst✝³ : AddMonoid ι\ninst✝² : SetLike σ A\ninst✝¹ : AddSubmonoidClass σ A\n𝒜 : ι → σ\ninst✝ : GradedRing 𝒜\nκ : Sort u_1\nκ' : κ → Sort u_2\ns : (i : κ)... | [
408,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.infsep_pair_eq_toReal | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.57659\ninst✝ : PseudoEMetricSpace α\nx y : α\ns : Set α\nhxy : x = y\n⊢ infsep {x, y} = ENNReal.toReal (edist x y)\n\ncase neg\nα : Type u_1\nβ : Type ?u.57659\ninst✝ : PseudoEMetricSpace α\nx y : α\ns : Set α\nhxy : ¬x = y\n⊢ infsep {x, y} = ENNReal.toReal ... | [
389,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/Order/WithBot.lean | WithTop.ofDual_apply_coe | [] | [
690,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
689,
1
] |
Mathlib/Analysis/Normed/Group/AddTorsor.lean | Filter.Tendsto.lineMap | [] | [
312,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Order/Bounds/Basic.lean | mem_lowerBounds_image2_of_mem_upperBounds | [] | [
1464,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1462,
1
] |
Mathlib/Data/Fintype/Pi.lean | Fintype.piFinset_subsingleton | [] | [
72,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Data/List/Infix.lean | List.isPrefix.map | [
{
"state_after": "case nil\nα : Type u_1\nβ : Type u_2\nl l₁ l₂✝ l₃ : List α\na b : α\nm n : ℕ\nh✝ : l₁ <+: l₂✝\nf : α → β\nl₂ : List α\nh : [] <+: l₂\n⊢ List.map f [] <+: List.map f l₂\n\ncase cons\nα : Type u_1\nβ : Type u_2\nl l₁ l₂✝ l₃ : List α\na b : α\nm n : ℕ\nh✝ : l₁ <+: l₂✝\nf : α → β\nhd : α\ntl : Lis... | [
290,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
src/lean/Init/SimpLemmas.lean | Bool.and_self | [
{
"state_after": "no goals",
"state_before": "b : Bool\n⊢ (b && b) = b",
"tactic": "cases b <;> rfl"
}
] | [
114,
87
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
114,
9
] |
Mathlib/Algebra/Ring/Defs.lean | ite_mul | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u\nβ : Type v\nγ : Type w\nR : Type x\nα : Type u_1\ninst✝¹ : Mul α\nP : Prop\ninst✝ : Decidable P\na b c : α\n⊢ (if P then a else b) * c = if P then a * c else b * c",
"tactic": "split_ifs <;> rfl"
}
] | [
205,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Logic/Relation.lean | Relation.TransGen.lift' | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.23283\nδ : Type ?u.23286\nr : α → α → Prop\na✝ b✝ c d : α\np : β → β → Prop\na b : α\nf : α → β\nh : ∀ (a b : α), r a b → TransGen p (f a) (f b)\nhab : TransGen r a b\n⊢ TransGen p (f a) (f b)",
"tactic": "simpa [trans... | [
484,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.preimage_symm_preimage | [] | [
2133,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2131,
11
] |
Mathlib/NumberTheory/LegendreSymbol/ZModChar.lean | ZMod.neg_one_pow_div_two_of_one_mod_four | [
{
"state_after": "n : ℕ\nhn : n % 4 = 1\n⊢ ↑χ₄ ↑1 = 1",
"state_before": "n : ℕ\nhn : n % 4 = 1\n⊢ (-1) ^ (n / 2) = 1",
"tactic": "rw [← χ₄_eq_neg_one_pow (Nat.odd_of_mod_four_eq_one hn), ← nat_cast_mod, hn]"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\nhn : n % 4 = 1\n⊢ ↑χ₄ ↑1 = 1... | [
124,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Topology/ContinuousOn.lean | frequently_nhdsWithin_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.711\nγ : Type ?u.714\nδ : Type ?u.717\ninst✝ : TopologicalSpace α\nz : α\ns : Set α\np : α → Prop\n⊢ (∃ᶠ (x : α) in 𝓝[s] z, p x) ↔ ∃ᶠ (x : α) in 𝓝 z, p x ∧ x ∈ s",
"tactic": "simp only [Filter.Frequently, eventually_nhdsWithin_iff... | [
59,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.mono_of_isLimit_fork | [] | [
838,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
837,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.mod_two_eq_zero_or_one | [
{
"state_after": "no goals",
"state_before": "n : Nat\n⊢ 2 > 0",
"tactic": "simp"
}
] | [
244,
21
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
241,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_neg_Ioc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\n⊢ -Ioc a b = Ico (-b) (-a)",
"tactic": "simp [← Ioi_inter_Iic, ← Ici_inter_Iio, inter_comm]"
}
] | [
163,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Analysis/SpecialFunctions/Exponential.lean | hasFDerivAt_exp_smul_const' | [] | [
391,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Order/LocallyFinite.lean | Finset.coe_Iio | [] | [
435,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.rev_involutive | [] | [
455,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/RingTheory/GradedAlgebra/Basic.lean | DirectSum.coe_decompose_mul_of_right_mem_of_not_le | [
{
"state_after": "case intro\nι : Type u_3\nR : Type ?u.348167\nA : Type u_1\nσ : Type u_2\ninst✝⁵ : Semiring A\ninst✝⁴ : DecidableEq ι\ninst✝³ : CanonicallyOrderedAddMonoid ι\ninst✝² : SetLike σ A\ninst✝¹ : AddSubmonoidClass σ A\n𝒜 : ι → σ\ninst✝ : GradedRing 𝒜\na : A\nn i : ι\nh : ¬i ≤ n\nb : { x // x ∈ 𝒜 ... | [
310,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/Deprecated/Group.lean | IsGroupHom.map_one | [] | [
295,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Data/PEquiv.lean | PEquiv.ofSet_eq_some_iff | [] | [
239,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Data/Finset/Sort.lean | Finset.orderEmbOfCardLe_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.61043\ninst✝ : LinearOrder α\ns : Finset α\nk : ℕ\nh : k ≤ card s\na : Fin k\n⊢ ↑(orderEmbOfCardLe s h) a ∈ s",
"tactic": "simp only [orderEmbOfCardLe, RelEmbedding.coe_trans, Finset.orderEmbOfFin_mem,\n Function.comp_apply]"
}
] | [
254,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Topology/Sheaves/SheafCondition/EqualizerProducts.lean | TopCat.Presheaf.SheafConditionEqualizerProducts.fork_π_app_walkingParallelPair_one | [] | [
139,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Data/Fintype/Basic.lean | Fintype.univ_bool | [] | [
903,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
902,
1
] |
Mathlib/Data/Multiset/Powerset.lean | Multiset.powersetLen_zero_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns : Multiset α\nl : List α\n⊢ powersetLen 0 (Quotient.mk (isSetoid α) l) = {0}",
"tactic": "simp [powersetLen_coe']"
}
] | [
247,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.rel_eq_refl | [] | [
2680,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2679,
1
] |
Mathlib/RingTheory/FinitePresentation.lean | Algebra.FinitePresentation.quotient | [
{
"state_after": "case intro.intro\nR : Type w₁\nA : Type w₂\nB : Type w₃\ninst✝⁴ : CommRing R\ninst✝³ : CommRing A\ninst✝² : Algebra R A\ninst✝¹ : CommRing B\ninst✝ : Algebra R B\nI : Ideal A\nh : Ideal.FG I\nn : ℕ\nf : MvPolynomial (Fin n) R →ₐ[R] A\nhf : Surjective ↑f ∧ Ideal.FG (RingHom.ker ↑f)\n⊢ FinitePre... | [
137,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
11
] |
Mathlib/CategoryTheory/Limits/Shapes/WidePullbacks.lean | CategoryTheory.Limits.WidePushout.ι_desc | [
{
"state_after": "no goals",
"state_before": "J : Type w\nC : Type u\ninst✝² : Category C\nD : Type u_1\ninst✝¹ : Category D\nB : D\nobjs : J → D\narrows : (j : J) → B ⟶ objs j\ninst✝ : HasWidePushout B objs arrows\nX : D\nf : B ⟶ X\nfs : (j : J) → objs j ⟶ X\nw : ∀ (j : J), arrows j ≫ fs j = f\nj : J\n⊢ ι ... | [
422,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/Data/Fintype/Basic.lean | exists_seq_of_forall_finset_exists | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.153481\nβ : Type ?u.153484\nγ : Type ?u.153487\nα : Type u_1\nP : α → Prop\nr : α → α → Prop\nh : ∀ (s : Finset α), (∀ (x : α), x ∈ s → P x) → ∃ y, P y ∧ ∀ (x : α), x ∈ s → r x y\n⊢ ∃ f, (∀ (n : ℕ), P (f n)) ∧ ∀ (m n : ℕ), m < n → r (f m) (f n)",
... | [
1242,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1217,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.integrableOn_zero | [] | [
118,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.norm_const_smul_le | [
{
"state_after": "case inl\nα : Type u_1\nE : α → Type u_2\nq : ℝ≥0∞\ninst✝⁶ : (i : α) → NormedAddCommGroup (E i)\n𝕜 : Type u_3\n𝕜' : Type ?u.424487\ninst✝⁵ : NormedRing 𝕜\ninst✝⁴ : NormedRing 𝕜'\ninst✝³ : (i : α) → Module 𝕜 (E i)\ninst✝² : (i : α) → Module 𝕜' (E i)\ninst✝¹ : ∀ (i : α), BoundedSMul 𝕜 (E ... | [
689,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
660,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | Commute.cast_nat_mul_self | [] | [
1120,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1119,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | HasStrictFDerivAt.snd | [] | [
245,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
11
] |
Mathlib/Algebra/Group/Basic.lean | div_mul_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.41688\nG : Type ?u.41691\ninst✝ : DivisionCommMonoid α\na b c d : α\n⊢ a / b * c = c / b * a",
"tactic": "simp"
}
] | [
575,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
575,
1
] |
Mathlib/Tactic/IntervalCases.lean | Mathlib.Tactic.IntervalCases.of_not_le_left | [] | [
134,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.Primes.coe_nat_injective | [] | [
779,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
778,
1
] |
Mathlib/Probability/Integration.lean | ProbabilityTheory.lintegral_mul_eq_lintegral_mul_lintegral_of_indepFun | [] | [
116,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Algebra/RingQuot.lean | RingQuot.one_quot | [
{
"state_after": "no goals",
"state_before": "R : Type u₁\ninst✝³ : Semiring R\nS : Type u₂\ninst✝² : CommSemiring S\nA : Type u₃\ninst✝¹ : Semiring A\ninst✝ : Algebra S A\nr : R → R → Prop\n⊢ { toQuot := Quot.mk (Rel r) 1 } = RingQuot.one r",
"tactic": "rw [one_def]"
}
] | [
233,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_apply | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1047\nι : Type ?u.1050\nM : Type u_2\nN : Type ?u.1056\ninst✝² : One M\ninst✝¹ : One N\ns✝ t : Set α\nf✝ g : α → M\na✝ : α\ns : Set α\nf : α → M\na : α\ninst✝ : Decidable (a ∈ s)\n⊢ (let x := a;\n if x ∈ s then f x else 1) =\n if a ∈ s then f a else 1",
"sta... | [
74,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | one_lt_div | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.76204\nα : Type u_1\nβ : Type ?u.76210\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nhb : 0 < b\n⊢ 1 < a / b ↔ b < a",
"tactic": "rw [lt_div_iff hb, one_mul]"
}
] | [
430,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/Data/Polynomial/Splits.lean | Polynomial.splits_of_degree_eq_one | [] | [
103,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Data/List/Perm.lean | List.subperm_singleton_iff | [
{
"state_after": "no goals",
"state_before": "α✝ : Type uu\nβ : Type vv\nl₁ l₂ : List α✝\ninst✝ : DecidableEq α✝\nα : Type u_1\nl : List α\na : α\nx✝ : [a] <+~ l\ns : List α\nhla : s ~ [a]\nh : s <+ l\n⊢ a ∈ l",
"tactic": "rwa [perm_singleton.mp hla, singleton_sublist] at h"
}
] | [
933,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
931,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Icc_eq_empty_of_lt | [] | [
104,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Order/Heyting/Basic.lean | fst_sdiff | [] | [
133,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/Deprecated/Submonoid.lean | IsSubmonoid.iInter | [] | [
102,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Formula.realize_rel | [
{
"state_after": "no goals",
"state_before": "L : Language\nL' : Language\nM : Type w\nN : Type ?u.235577\nP : Type ?u.235580\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nn : ℕ\nφ ψ : Formula L α\nv : α → M\nk : ℕ\nR : Relations L k\nts : Fin k → Term L α... | [
643,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
641,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.continuous_infDist_pt | [] | [
575,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
574,
1
] |
Mathlib/CategoryTheory/Monoidal/End.lean | CategoryTheory.ε_inv_app_obj | [
{
"state_after": "C : Type u\ninst✝² : Category C\nM : Type u_2\ninst✝¹ : Category M\ninst✝ : MonoidalCategory M\nF : MonoidalFunctor M (C ⥤ C)\nn : M\nX : C\n⊢ 𝟙 ((F.obj (𝟙_ M)).obj ((F.obj n).obj X)) =\n ((LaxMonoidalFunctor.μ F.toLaxMonoidalFunctor n (𝟙_ M)).app X ≫ (F.map (ρ_ n).hom).app X) ≫\n F... | [
235,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.sin_sub | [
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ sin (x - y) = sin x * cos y - cos x * sin y",
"tactic": "simp [sub_eq_add_neg, sin_add, sin_neg, cos_neg]"
}
] | [
869,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
868,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.results_bind | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ns : Computation α\nf : α → Computation β\na : α\nb : β\nm n : ℕ\nh1 : Results s a m\nh2 : Results (f a) b n\nthis : a ∈ s\n⊢ Results (bind s f) b (n + m)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : Computation α\nf : α → Computation β\na :... | [
805,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
792,
1
] |
Mathlib/Analysis/Normed/Group/AddTorsor.lean | nndist_vadd_cancel_left | [] | [
104,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Analysis/NormedSpace/AddTorsor.lean | nndist_midpoint_midpoint_le | [] | [
276,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/CategoryTheory/Abelian/RightDerived.lean | CategoryTheory.Abelian.Functor.preserves_exact_of_preservesFiniteLimits_of_mono | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝⁶ : Category C\nD : Type u\ninst✝⁵ : Category D\nF : C ⥤ D\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\ninst✝⁴ : Abelian C\ninst✝³ : Abelian D\ninst✝² : Functor.Additive F\ninst✝¹ : PreservesFiniteLimits F\ninst✝ : Mono f\nex : Exact f g\n⊢ F.map f ≫ F.map... | [
198,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.one_lt_rpow_of_pos_of_lt_one_of_neg | [
{
"state_after": "case intro\nz : ℝ\nhz : z < 0\nx : ℝ≥0\nhx1 : 0 < ↑x\nhx2 : ↑x < 1\n⊢ 1 < ↑x ^ z",
"state_before": "x : ℝ≥0∞\nz : ℝ\nhx1 : 0 < x\nhx2 : x < 1\nhz : z < 0\n⊢ 1 < x ^ z",
"tactic": "lift x to ℝ≥0 using ne_of_lt (lt_of_lt_of_le hx2 le_top)"
},
{
"state_after": "case intro\nz : ℝ\n... | [
711,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
707,
1
] |
Mathlib/Order/Hom/Bounded.lean | BoundedOrderHom.coe_comp_orderHom | [] | [
659,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
657,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.