reserve f for Function;
reserve p,q for FinSequence;
reserve A,B,C for set,x,x1,x2,y,z for object;
reserve k,l,m,n for Nat;
reserve a for Nat;
reserve D for non empty set;
reserve d,d1,d2,d3 for Element of D;
reserve L,M for Element of NAT;
reserve f for Function of A,B;
reserve f for Function;
reserve x1,x2,x3,x4,x5 for object;

theorem Th75:
  <*x1,x2,x3,x4,x5*>=<*x1,x2,x3*>^<*x4,x5*> & <*x1,x2,x3,x4,x5*>=
<*x1,x2,x3,x4*>^<*x5*> & <*x1,x2,x3,x4,x5*>=<*x1*>^<*x2*>^<*x3*>^<*x4*>^<*x5*>
& <*x1,x2,x3,x4,x5*>=<*x1,x2*>^<*x3,x4,x5*> & <*x1,x2,x3,x4,x5*>=<*x1*>^<*x2,x3
  ,x4,x5*>
proof
  thus <*x1,x2,x3,x4,x5*>=<*x1,x2,x3*>^<*x4,x5*>;
  thus
A1: <*x1,x2,x3,x4,x5*>=<*x1,x2,x3,x4*>^<*x5*> by FINSEQ_1:32;
  thus <*x1,x2,x3,x4,x5*>=<*x1*>^<*x2*>^<*x3*>^<*x4*>^<*x5*> by FINSEQ_1:32;
  thus <*x1,x2,x3,x4,x5*>=<*x1,x2*>^(<*x3*>^<*x4*>)^<*x5*> by A1,FINSEQ_1:32
    .=<*x1,x2*>^<*x3,x4,x5*> by FINSEQ_1:32;
  hence <*x1,x2,x3,x4,x5*>=<*x1*>^(<*x2*>^<*x3,x4,x5*>) by FINSEQ_1:32
    .=<*x1*>^<*x2,x3,x4,x5*> by Th74;
end;
