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;
reserve X for set, f for Function;
reserve U1,U2 for non empty set;
reserve f for BinOp of D;

theorem Th31:
(MultPlace(f)).(<*d*>) = d & for x being D-valued FinSequence st
x is non empty holds (MultPlace(f)).(x^<*d*>) = f.((MultPlace(f)).x, d)
proof
set F=MultPlace f; thus F.<*d*>=d by Lm15;
let x be D-valued FinSequence; assume x is non empty; then
reconsider xx=x as non empty FinSequence of D by Lm1;
F.(xx^<*d*>)=f.(F.xx,d) by Lm15; hence thesis;
end;
