theorem Th32: U-multiCat.x=(MultPlace(U-concatenation)).x
proof
set D=U*, f=U-concatenation, F=MultPlace f, G=U-multiCat;
set g = {} .--> {};
reconsider g as {{}}-valued Function;
dom f=[:D,D:] & dom F=D*\{{}} & dom G=D* by FUNCT_2:def 1; then
reconsider dF=dom F as Subset of dom G;
per cases;
suppose x in dom F; hence G.x=F.x by FUNCT_4:13; end;
suppose A1: not x in dom F; hence G.x = g.x by FUNCT_4:11 .=
F.x by FUNCT_1:def 2, A1; end;
end;
