reserve G for non empty DTConstrStr,
  s for Symbol of G,
  n,m for String of G;
reserve n1,n2,n3 for String of G;

theorem Th7:
  n ==> m implies m is_derivable_from n
proof
  assume
A1: n ==> m;
  take p = <*n,m*>;
A2: len p = 2 by FINSEQ_1:44;
  hence len p >= 1 & p.1 = n & p.(len p) = m;
  let i be Element of NAT;
  assume that
A3: i >= 1 and
A4: i < len p;
  take a = n, b = m;
  2 = 1 + 1;
  then i <= 1 by A2,A4,NAT_1:13;
  then
A5: i = 1 by A3,XXREAL_0:1;
  hence p.i = a;
  thus p.(i+1) = b by A5;
  thus thesis by A1;
end;
