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Proof step 5 from proof ushort-short (previous step)

¬(~32768 ≤ us2i(sho) ∧ us2i(sho) ≤ 32767) ⊦ s2i(i2s(us2i(sho))) = s2i(sho)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ 0 ≤ i ∧ 32767 < i % 65536 → s2i(i2s(i)) = i % 65536 - 65536
Proof step 7:
¬(0 ≤ us2i(sho) ∧ 32767 < us2i(sho) % 65536), ¬(~32768 ≤ us2i(sho) ∧ us2i(sho) ≤ 32767) ⊦ s2i(i2s(us2i(sho))) = s2i(sho)
Proof step 10:
0 ≤ us2i(sho) ∧ 32767 < us2i(sho) % 65536, ¬(~32768 ≤ us2i(sho) ∧ us2i(sho) ≤ 32767) ⊦ us2i(sho) % 65536 - 65536 = s2i(sho)

Rule argument

name: sis-pos-high rotate: F subst: [i] → [us2i(sho)]

Additional information

Used terms: us2i(sho)