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;

theorem for p,q being FinSequence st p is non empty holds (p^q).1=p.1
proof
let p,q be FinSequence; assume p is non empty; then reconsider
p as non empty FinSequence; set n=len p;
1<=1 & 1<=n by NAT_1:14; then 1 in Seg n; then
1 in dom p by FINSEQ_1:def 3; hence thesis by FINSEQ_1:def 7;
end;
