
theorem Th7:
for m,n,k be non zero Nat, X be non-empty m-element FinSequence
 st k <= n & n <= m holds SubFin(X,k) = SubFin(SubFin(X,n),k)
proof
    let m,n,k be non zero Nat, X be non-empty m-element FinSequence;
    assume that
A1:  k <= n and
A2:  n <= m;

A3: SubFin(X,n) = X|n by A2,Def5;
A4: SubFin(SubFin(X,n),k) = (X|n)|k by A1,A3,Def5;

    SubFin(X,k) = X|k by A2,A1,XXREAL_0:2,Def5;
    hence SubFin(X,k) = SubFin(SubFin(X,n),k) by A4,A1,FINSEQ_1:82;
end;
