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};