reserve a,b,c,h for Integer;
reserve k,m,n for Nat;
reserve i,j,z for Integer;
reserve p for Prime;

theorem Th74:
  seq(m,n) misses { m+n+1,m+n+2 }
  proof
    assume seq(m,n) meets { m+n+1,m+n+2 };
    then consider x being object such that
A1: x in seq(m,n) and
A2: x in { m+n+1,m+n+2 } by XBOOLE_0:3;
    consider k being Element of NAT such that
A3: x = k and
    1+m <= k and
A4: k <= m+n by A1;
    per cases by A2,TARSKI:def 2;
    suppose x = m+n+1;
      then m+n+1 <= m+n+0 by A3,A4;
      hence contradiction by XREAL_1:6;
    end;
    suppose x = m+n+2;
      then m+n+2 <= m+n+0 by A3,A4;
      hence contradiction by XREAL_1:6;
    end;
  end;
