reserve A,B,C,Y,x,y,z for set, U, D for non empty set,
X for non empty Subset of D, d,d1,d2 for Element of D;
reserve P,Q,R for Relation, g for Function, p,q for FinSequence;
reserve f for BinOp of D, i,m,n for Nat;

theorem for d1,d2 be Element of (D*) holds D-multiCat.(<*d1,d2*>)=d1^d2
proof
let d1, d2 be Element of D*; set F=D-multiCat, f=D-concatenation, d =
<*d1,d2*>; reconsider dd = <*d1*>^<*d2*> as non empty Element of D**;
A1: F.dd=(MultPlace(f)).(dd) by Th14; thus F.d = f.((MultPlace(f)).<*d1*>,d2)
by Lm15, A1 .= f.(d1,d2) by Lm15 .= d1^d2 by Lm10;
end;
