reserve i for Nat, x,y for set;
reserve S for non empty non void ManySortedSign;
reserve X for non-empty ManySortedSet of S;

theorem Th51:
  for B being non empty BoolSignature
  for C being non empty ConnectivesSignature holds
  the carrier of B+*C = (the carrier of B)\/the carrier of C &
  the carrier' of B+*C = (the carrier' of B)\/the carrier' of C &
  the Arity of B+*C = (the Arity of B)+*the Arity of C &
  the ResultSort of B+*C = (the ResultSort of B)+*the ResultSort of C
  proof
    let B be non empty BoolSignature;
    let C be non empty ConnectivesSignature;
    the ManySortedSign of B+*C = (B qua non empty ManySortedSign)+*C by Def52;
    hence thesis by CIRCCOMB:def 2;
  end;
