IF-THEN Proof

 { PRE: x > 3 }

    if ( x < 25 ) then x := 2 * x

 { POST: x >= 8 }



 1) show { PRE and x < 25 } x := 2*x { POST }
 2) show PRE and ~(x < 25) ==> POST
 3) conclude  

    { PRE } if ( x < 25 ) then x := 2*x { POST }

    by IF-THEN rule of inference 

 QED