Prove or disprove: For all rounding modes, rounding to single precision can be performed in two steps: a) round to double precision, then b) round the double precision result to single precision...

Prove or disprove: For all rounding modes, rounding to single precision can be performed in two steps:

a) round to double precision, then

b) round the double precision result to single precision

Complete the following proofs:

1. the proof of lemma 7.3

2. the proof of theorem 7.4 for rounding mode rne

3. the proof of lemma 7.9 part