Article AXIOMS, MML version 4.99.1005

:: AXIOMS:th 19
theorem
for b1 being real set holds
   ex b2 being real set st
      b1 + b2 = 0;

:: AXIOMS:th 20
theorem
for b1 being real set
      st b1 <> 0
   holds ex b2 being real set st
      b1 * b2 = 1;

:: AXIOMS:th 26
theorem
for b1, b2 being Element of bool REAL
      st for b3, b4 being real set
              st b3 in b1 & b4 in b2
           holds b3 <= b4
   holds ex b3 being real set st
      for b4, b5 being real set
            st b4 in b1 & b5 in b2
         holds b4 <= b3 & b3 <= b5;

:: AXIOMS:th 28
theorem
for b1, b2 being real set
      st b1 in NAT & b2 in NAT
   holds b1 + b2 in NAT;

:: AXIOMS:th 29
theorem
for b1 being Element of bool REAL
      st 0 in b1 &
         (for b2 being real set
               st b2 in b1
            holds b2 + 1 in b1)
   holds NAT c= b1;

:: AXIOMS:th 30
theorem
for b1 being natural set holds
   b1 = {b2 where b2 is Element of NAT: b2 < b1};