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;
reserve a,a1,a2,b,b1,b2,A,B,C,X,Y,Z,x,x1,x2,y,y1,y2,z for set,
U,U1,U2,U3 for non empty set, u,u1,u2 for Element of U,
P,Q,R for Relation, f,f1,f2,g,g1,g2 for Function,
k,m,n for Nat, kk,mm,nn for Element of NAT, m1, n1 for non zero Nat,
p, p1, p2 for FinSequence, q, q1, q2 for U-valued FinSequence;

theorem ::#Th77:
rng f1 /\ rng f2 = {} & b1<>b2 & rng f1 c= dom f2 & rng f2 c= dom f1
implies [:rng f1,{b2}:]\/[:rng f2,{b1}:] c=
((f1\/f2) >*> ([:rng f1,{b2}:]\/[:rng f2,{b1}:])) >*> ((b1,b2)-->(b2,b1))
by Lm68;
