Well, that seems to fix that simple example.  How does one work in general?  I have a routine which generates linear equalites and inequalities and I want to see if there are any solutions.  The following should give no solutions

  solve([0 < 2*f[1], 5 < f[1]+f[2], 8 < f[1]+f[3], f[1]+f[4] = 7, 0 < 2*f[2], f[2]+f[3] = 6, 
    6 < f[2]+f[4], 0 < 2*f[3], 11/2 < f[3]+f[4], 0 < 2*f[4]],{f[1],f[2],f[3],f[4]});

But gives

{f[1] = 7-f[4], f[2] = 6-f[3], f[3] = f[3], f[4] = f[4]}

Rewriting as you suggest

  solve([ 5 < f[1]+f[2], 8 < f[1]+f[3], f[1]+f[4] = 7, f[2]+f[3] = 6, 
               6 < f[2]+f[4],11/2 < f[3]+f[4]])  
      assuming And(f[1]>0,f[2]>0,f[3]>0,f[4]>0);

gives the same wrong answer.