anchor.diff:                                   GSYM REAL_MUL_LNEG])
   
   let RAT_LEMMA4 = 
  +#if BUGGY
       prove
           ((parse_term @"&0 < y1 /\ &0 < y2 ==> (x1 / y1 <= x2 / y2 <=> x1 * y2 <= x2 * y1)"), 
            let lemma = 
  
positive.code:                    GSYM REAL_OF_NUM_ADD; GSYM REAL_OF_NUM_MUL] |>THEN<|
         ONCE_REWRITE_TAC[GSYM REAL_SUB_0] |>THEN<|
         REWRITE_TAC[GSYM REAL_ENTIRE] |>THEN<| REAL_ARITH_TAC)
     let REAL_RABINOWITSCH = 
        prove ((parse_term @"!x y:real. ~(x = y) <=> ?z. (x - y) * z = &1"),
          REPEAT GEN_TAC |>THEN<|
  
negative.code: // real_ideal_cofactors: Produces cofactors proving that one real polynomial is in the ideal generated by others.
  let REAL_RING,real_ideal_cofactors =
     let REAL_INTEGRAL = 
     #if BUGGY
       prove ((parse_term @"(!x. &0 * x = &0) /\
         (!x y z. (x + y = x + z) <=> (y = z)) /\
         (!w x y z. (w * y + x * z = w * z + x * y) <=> (w = x) \/ (y = z))"),
  