Article REAL, MML version 4.99.1005
:: REAL:th 1
theorem
for b1, b2 being real set
st b1 <= b2 & b1 is positive
holds b2 is positive;
:: REAL:th 2
theorem
for b1, b2 being real set
st b1 <= b2 & b2 is negative
holds b1 is negative;
:: REAL:th 3
theorem
for b1, b2 being real set
st b1 <= b2 & b1 is not negative
holds b2 is not negative;
:: REAL:th 4
theorem
for b1, b2 being real set
st b1 <= b2 & b2 is not positive
holds b1 is not positive;
:: REAL:th 5
theorem
for b1, b2 being real set
st b1 <= b2 & b2 is not empty & b1 is not negative
holds b2 is positive;
:: REAL:th 6
theorem
for b1, b2 being real set
st b1 <= b2 & b1 is not empty & b2 is not positive
holds b1 is negative;
:: REAL:th 7
theorem
for b1, b2 being real set
st b2 < b1 & b1 is not positive
holds b2 is negative;
:: REAL:th 8
theorem
for b1, b2 being real set
st b2 < b1 & b2 is not negative
holds b1 is positive;