Comments (3)
The third one of these theorems is closely related to float_infinities in binary_ieeeScript.sml. The critical difference is that it uses float_equal rather than =.
(testing for x = float_minus_infinity is equivalent to testing for float_equal x float_minus_infinity, but you need to prove that)
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We might also need:
! x y . (float_is_infinite x) ==> ((float_equal x y) <=> (x = y))
float_equal is not the same as = for zeros and nans, but is is for infinities, normal numbers and submormal numbers.
P.S. I had a try at proving this, but it turned out to be difficult:
Basic plan:
Case split on float_value x
simp[float_is_infinite_def] deals with cases where x is not an infinity
in remaining case, simp[float_equal_def,float_compare_def]
Case split on float value y
... which gets us down to the tricky case where x and y are both infinities
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First in the list now done (by 02db589)
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