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Proof step 25 from proof ushort-plus (previous step)

s2i(sho) + s2i(sho0) < 0, 0 ≤ s2i(sho0), s2i(sho) < 0 ⊦ us2i(i2s(s2i(sho) + s2i(sho0))) = 65536 + s2i(sho) + s2i(sho0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ s2i(sho) < 0 → us2i(sho) = 2 ^ 16 + s2i(sho)
Proof step 27:
¬ s2i(i2s(s2i(sho) + s2i(sho0))) < 0, s2i(sho) + s2i(sho0) < 0, 0 ≤ s2i(sho0), s2i(sho) < 0 ⊦ us2i(i2s(s2i(sho) + s2i(sho0))) = 65536 + s2i(sho) + s2i(sho0)
Proof step 30:
s2i(i2s(s2i(sho) + s2i(sho0))) < 0, s2i(sho) + s2i(sho0) < 0, 0 ≤ s2i(sho0), s2i(sho) < 0 ⊦ 2 ^ 16 + s2i(i2s(s2i(sho) + s2i(sho0))) = 65536 + s2i(sho) + s2i(sho0)

Rule argument

name: ushort-neg rotate: F subst: [sho] → [i2s(s2i(sho) + s2i(sho0))]

Additional information

Used terms: i2s(s2i(sho) + s2i(sho0))