reserve X for set;
reserve a,b,c,k,m,n for Nat;
reserve i,j for Integer;
reserve r,s for Real;
reserve p,p1,p2,p3 for Prime;

theorem Th103:
  m < n implies 3|^m - 3 to_power(1-m) < 3|^n - 3 to_power(1-n)
  proof
    assume
A1: m < n;
A2: 3|^m < 3|^n by A1,Lm57,NAT_6:2;
    1-n < 1-m by A1,XREAL_1:15;
    then 3 to_power(1-n) < 3 to_power(1-m) by POWER:39;
    hence thesis by A2,XREAL_1:14;
  end;
