
theorem
for A be non empty closed_interval Subset of REAL, n be Nat st
 vol A > 0 & len EqDiv(A,2|^n) = 1 holds n = 0
proof
    let A be non empty closed_interval Subset of REAL, n be Nat;
    assume that
A1:  vol A > 0 and
A2:  len EqDiv(A,2|^n) = 1;

    2|^n > 0 by NEWTON:83; then
    EqDiv(A,2|^n) divide_into_equal 2|^n by A1,Def1; then
    len EqDiv(A,2|^n) = 2|^n by INTEGRA4:def 1;
    hence n = 0 by A2,NAT_1:14,NEWTON:86;
end;
