theorem Th20:
  1 <= n <= len prg & PrgLocalOverlapSeq(A,loc,d1,prg,pos).m in dom(prg.n)
  implies
  prg.n.(PrgLocalOverlapSeq(A,loc,d1,prg,pos).m)
    is TypeSCNominativeData of V,A
  proof
    set F = PrgLocalOverlapSeq(A,loc,d1,prg,pos);
    set P = prg.n;
    assume that
A1: 1 <= n and
A2: n <= len prg and
A3: F.m in dom(P);
    n in dom prg by A1,A2,FINSEQ_3:25;
    then P in rng prg by FUNCT_1:def 3;
    then
A4: rng(P) c= ND(V,A) by RELAT_1:def 19;
    P.(F.m) in rng P by A3,FUNCT_1:def 3;
    hence thesis by A4,NOMIN_1:39;
  end;
