theorem Th35:
  L is_Finseq_for v & 1<= k & k<len(L) implies CastNode(L.(k+1),v)
  is_succ_of CastNode(L.k,v)
proof
  assume L is_Finseq_for v & 1<= k & k<len(L);
  then consider N,M such that
A1: N = L.k and
A2: M=L.(k+1) & M is_succ_of N;
  CastNode(L.k,v) = N by A1,Def16;
  hence thesis by A2,Def16;
end;
