reserve D for non empty set,
  i,j,k,l for Nat,
  n for Nat,
  x for set,
  a,b,c,r,r1,r2 for Real,
  p,q for FinSequence of REAL,
  MR,MR1 for Matrix of REAL;

theorem Th4:
  a>1 & b>1 implies log(a,b) > 0
proof
  assume that
A1: a>1 and
A2: b>1;
A3: a to_power log(a,b) > 1 by A1,A2,POWER:def 3;
  assume
A4: log(a,b) <=0;
  per cases by A4;
  suppose
    log(a,b) =0;
    hence contradiction by A3,POWER:24;
  end;
  suppose
    log(a,b) <0;
    hence contradiction by A1,A3,POWER:36;
  end;
end;
