reserve i for Nat,
  j for Element of NAT,
  X,Y,x,y,z for set;
reserve C for initialized ConstructorSignature,
  s for SortSymbol of C,
  o for OperSymbol of C,
  c for constructor OperSymbol of C;
reserve a,b for expression of C, an_Adj C;

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;
