theorem Th32:
  (a,x).W = p & m<=n implies (a,(x+*(m+1,x.m))).W = (p+*(m+1,p.m))
proof
  assume that
A1: (a,x).W = p and
A2: m<=n;
  W.(a,p) = x by A1,Th15;
  then W.(a,(p+*(m+1,p.m))) = (x+*(m+1,x.m)) by A2,Th31;
  hence thesis by Th15;
end;
