theorem U1 c= U2 & Y c= U1* & p is Y-valued & p<>{} &
Y is with_non-empty_elements implies U1-multiCat.p=U2-multiCat.p
proof
assume U1 c= U2; then reconsider U11=U1 as non empty Subset of U2;
assume Y c= U1*; then reconsider Y1=Y as Subset of U11*;
reconsider Y2 = Y1 as Subset of U2* by XBOOLE_1:1; assume
p is Y-valued; then reconsider p1=p as Y1-valued
FinSequence; reconsider p2=p1 as Y2-valued FinSequence;
assume p <> {} & Y is with_non-empty_elements; then
U1-multiCat.p1 <> {} & U2-multiCat.p2 <> {} by Lm52; hence thesis by Th52;
end;
