reserve i,j,k,n,m for Nat,
  x,y,z,y1,y2 for object, X,Y,D for set,
  p,q for XFinSequence;
reserve k1,k2 for Nat;
reserve D for non empty set,
  F,G for XFinSequence of D,
  b for BinOp of D,
  d,d1,d2 for Element of D;
reserve F for XFinSequence,
        rF,rF1,rF2 for real-valued XFinSequence,
        r for Real,
        cF,cF1,cF2 for complex-valued XFinSequence,
        c,c1,c2 for Complex;

theorem Th77:
  p c= q implies p ^ (q /^ len p) = q
 proof assume
A1: p c= q;
A2: len p + len (q /^ len p)
       = len p + (len q -' len p) by Def2
      .= len q + len p -' len p by A1,NAT_1:43,NAT_D:38
      .= dom q by NAT_D:34;
A3: for k st k in dom p holds q.k=p.k by A1,GRFUNC_1:2;
   for k st k in dom(q /^ len p) holds q.(len p + k) = (q /^ len p).k
                by Def2;
  hence p ^ (q /^ len p) = q by A2,A3,AFINSQ_1:def 3;
 end;
