theorem Th44:
  (non_op C)term a = (non_op C)term b implies a = b
proof
  assume (non_op C)term a = (non_op C)term b;
  then [non_op, the carrier of C]-tree <*a*> = (non_op C)term b by Th43
    .= [non_op, the carrier of C]-tree <*b*> by Th43;
  then <*a*> = <*b*> by TREES_4:15;
  hence thesis by FINSEQ_1:76;
end;
