feat(library/unifier): solved universe constraints of the form succ^k1 a = max k2 ?m (when k1 >= k2)
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3 changed files with 132 additions and 1 deletions
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@ -85,6 +85,9 @@ level mk_param_univ(name const & n);
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level mk_global_univ(name const & n);
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level mk_global_univ(name const & n);
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level mk_meta_univ(name const & n);
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level mk_meta_univ(name const & n);
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/** \brief Convert (succ^k l) into (l, k). If l is not a succ, then return (l, 0) */
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pair<level, unsigned> to_offset(level l);
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inline unsigned hash(level const & l) { return l.hash(); }
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inline unsigned hash(level const & l) { return l.hash(); }
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inline level_kind kind(level const & l) { return l.kind(); }
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inline level_kind kind(level const & l) { return l.kind(); }
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inline bool is_zero(level const & l) { return kind(l) == level_kind::Zero; }
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inline bool is_zero(level const & l) { return kind(l) == level_kind::Zero; }
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@ -8,6 +8,7 @@ Author: Leonardo de Moura
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#include <memory>
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#include <memory>
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#include <vector>
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#include <vector>
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#include <limits>
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#include <limits>
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#include <algorithm>
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#include "util/interrupt.h"
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#include "util/interrupt.h"
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#include "util/luaref.h"
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#include "util/luaref.h"
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#include "util/lazy_list_fn.h"
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#include "util/lazy_list_fn.h"
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@ -2043,7 +2044,7 @@ struct unifier_fn {
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}
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}
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}
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}
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/** \brief Return true iff \c is a constraint of the form
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/** \brief Return solved iff \c c is a constraint of the form
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lhs =?= max(rest, lhs)
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lhs =?= max(rest, lhs)
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and is successfully solved.
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and is successfully solved.
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*/
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*/
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@ -2060,6 +2061,43 @@ struct unifier_fn {
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return Continue;
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return Continue;
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}
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}
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/** Auxiliary method for process_succ_eq_max */
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status process_succ_eq_max_core(level const & lhs, level const & rhs, justification const & jst) {
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if (!is_succ(lhs) || !is_max(rhs))
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return Continue;
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level rhs_l = max_lhs(rhs);
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level rhs_r = max_rhs(rhs);
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if (is_meta(rhs_l))
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std::swap(rhs_l, rhs_r);
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if (!is_meta(rhs_r) || !is_explicit(rhs_l))
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return Continue;
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unsigned k_2 = to_explicit(rhs_l);
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pair<level, unsigned> lhs_k = to_offset(lhs);
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if (lhs_k.second < k_2)
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return Continue;
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if (assign(rhs_r, lhs, jst)) {
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return Solved;
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} else {
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set_conflict(jst);
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return Failed;
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}
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}
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/** \brief Return Solved iff \c c is a constraint of the form
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succ^k_1 a =?= max(k_2, ?m)
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where k_1 >= k_2
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and is successfully solved
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*/
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status process_succ_eq_max(constraint const & c) {
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lean_assert(is_level_eq_cnstr(c));
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level lhs = cnstr_lhs_level(c);
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level rhs = cnstr_rhs_level(c);
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justification jst = c.get_justification();
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status st = process_succ_eq_max_core(lhs, rhs, jst);
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if (st != Continue) return st;
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return process_succ_eq_max_core(rhs, lhs, jst);
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}
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/**
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/**
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\brief Process the following constraints
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\brief Process the following constraints
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1. (max l1 l2) =?= 0 OR
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1. (max l1 l2) =?= 0 OR
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@ -2152,6 +2190,8 @@ struct unifier_fn {
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}
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}
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status st = process_l_eq_max(c);
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status st = process_l_eq_max(c);
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if (st != Continue) return st == Solved;
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if (st != Continue) return st == Solved;
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st = process_succ_eq_max(c);
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if (st != Continue) return st == Solved;
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if (m_config.m_discard) {
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if (m_config.m_discard) {
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// we only try try_level_eq_zero and try_merge_max when we are discarding
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// we only try try_level_eq_zero and try_merge_max when we are discarding
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// constraints that canno be solved.
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// constraints that canno be solved.
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88
tests/lean/run/univ_problem.lean
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88
tests/lean/run/univ_problem.lean
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@ -0,0 +1,88 @@
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import logic data.nat.basic data.prod data.unit
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open nat prod
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inductive vector (A : Type) : nat → Type :=
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vnil {} : vector A zero,
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vcons : Π {n : nat}, A → vector A n → vector A (succ n)
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namespace vector
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print definition no_confusion
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infixr `::` := vcons
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section
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universe variables l₁ l₂
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variable {A : Type.{l₁}}
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variable {C : Π (n : nat), vector A n → Type.{l₂+1}}
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definition brec_on {n : nat} (v : vector A n) (H : Π (n : nat) (v : vector A n), @below A C n v → C n v) : C n v :=
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have general : C n v × @below A C n v, from
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rec_on v
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(pair (H zero vnil unit.star) unit.star)
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(λ (n₁ : nat) (a₁ : A) (v₁ : vector A n₁) (r₁ : C n₁ v₁ × @below A C n₁ v₁),
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have b : @below A C _ (vcons a₁ v₁), from
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r₁,
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have c : C (succ n₁) (vcons a₁ v₁), from
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H (succ n₁) (vcons a₁ v₁) b,
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pair c b),
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pr₁ general
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end
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print "====================="
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definition append {A : Type} {n m : nat} (w : vector A m) (v : vector A n) : vector A (n + m) :=
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brec_on w (λ (n : nat) (w : vector A n),
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cases_on w
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(λ (B : below vnil), v)
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(λ (n₁ : nat) (a₁ : A) (v₁ : vector A n₁) (B : below (vcons a₁ v₁)),
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vcons a₁ (pr₁ B)))
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exit
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check brec_on
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definition bw := @below
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definition sum {n : nat} (v : vector nat n) : nat :=
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brec_on v (λ (n : nat) (v : vector nat n),
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cases_on v
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(λ (B : bw vnil), zero)
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(λ (n₁ : nat) (a : nat) (v₁ : vector nat n₁) (B : bw (vcons a v₁)),
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a + pr₁ B))
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example : sum (10 :: 20 :: vnil) = 30 :=
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rfl
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definition addk {n : nat} (v : vector nat n) (k : nat) : vector nat n :=
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brec_on v (λ (n : nat) (v : vector nat n),
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cases_on v
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(λ (B : bw vnil), vnil)
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(λ (n₁ : nat) (a₁ : nat) (v₁ : vector nat n₁) (B : bw (vcons a₁ v₁)),
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vcons (a₁+k) (pr₁ B)))
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example : addk (1 :: 2 :: vnil) 3 = 4 :: 5 :: vnil :=
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rfl
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example : append (1 :: 2 :: vnil) (3 :: vnil) = 1 :: 2 :: 3 :: vnil :=
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rfl
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definition head {A : Type} {n : nat} (v : vector A (succ n)) : A :=
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cases_on v
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(λ H : succ n = 0, nat.no_confusion H)
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(λn' h t (H : succ n = succ n'), h)
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rfl
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definition tail {A : Type} {n : nat} (v : vector A (succ n)) : vector A n :=
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@cases_on A (λn' v, succ n = n' → vector A (pred n')) (succ n) v
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(λ H : succ n = 0, nat.no_confusion H)
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(λ (n' : nat) (h : A) (t : vector A n') (H : succ n = succ n'),
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t)
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rfl
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definition add {n : nat} (w v : vector nat n) : vector nat n :=
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@brec_on nat (λ (n : nat) (v : vector nat n), vector nat n → vector nat n) n w
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(λ (n : nat) (w : vector nat n),
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cases_on w
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(λ (B : bw vnil) (w : vector nat zero), vnil)
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(λ (n₁ : nat) (a₁ : nat) (v₁ : vector nat n₁) (B : bw (vcons a₁ v₁)) (v : vector nat (succ n₁)),
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vcons (a₁ + head v) (pr₁ B (tail v)))) v
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example : add (1 :: 2 :: vnil) (3 :: 5 :: vnil) = 4 :: 7 :: vnil :=
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rfl
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end vector
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