theorem Th33: p is U*-valued implies
(U-multiCat).(p^<*q*>) = (U-multiCat.p)^q
proof
set C=U-multiCat, g=U-concatenation, G=MultPlace g;
reconsider qq=q as FinSequence of U by Lm1;
per cases;
suppose p is empty; then reconsider e=p as empty set;
A1: (C.e)^q=q & C.(e^<*q*>) = C.(<*q*>);
C.(e^<*q*>)=G.(<*qq*>) by Th32 .= qq by Th31; hence thesis
by A1; end;
suppose A2: not p is empty; assume p is U*-valued; then reconsider
pp=p as non empty U*-valued FinSequence by A2;
reconsider ppp=pp as non empty FinSequence of U* by Lm1;
C.(pp^<*q*>)= G.(pp^<*qq*>) by Th32 .= g.(G.pp, qq) by Th31 .=
g.(C.ppp, q) by Th32 .= (C.p) ^ q by Th4; hence thesis;
end;
end;
