theorem Th21:
  deg (x-term) = 0
  proof set t = x-term;
    assume deg t <> 0;
    then t"[:the carrier' of S,{the carrier of S}:] is not empty;
    then consider a being object such that
A1: a in t"[:the carrier' of S,{the carrier of S}:] by XBOOLE_0:7;
    reconsider ta = t.a as set;
A4: ta in [:the carrier' of S,{the carrier of S}:] & a in dom t
    by A1,FUNCT_1:def 7;
    ta in rng t = {[x,s]} by A4,FUNCT_1:def 3,FUNCOP_1:8;
    then ta = [x,s] by TARSKI:def 1;
    then s in the carrier of S = s by A4,ZFMISC_1:106;
    hence contradiction;
  end;
