reserve i,j,k,n,m,l,s,t for Nat;
reserve a,b for Real;
reserve F for real-valued FinSequence;
reserve z for Complex;
reserve x,y for Complex;
reserve r,s,t for natural Number;
reserve p,q for natural Number;
reserve i0,i,i1,i2,i4 for Integer;
reserve x for set;
reserve p for Prime;

theorem
  SetPrimenumber m c= Seg m
proof
  let x be object;
  assume
A1: x in SetPrimenumber m;
  then reconsider x as Element of NAT;
  x is prime by A1,Def7;
  then
A2: 1 <= x by INT_2:def 4;
  x < m by A1,Def7;
  hence thesis by A2;
end;
