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Proof step 8 from proof ushort-neg (previous step)

s2i(sho) < 0 ⊦ bits2int(fillsgn(16, int2bits(s2i(sho)))) + 2 ^ n→i(# fillsgn(16, int2bits(s2i(sho)))) = s2i(sho) + 65536, fillsgn(16, int2bits(s2i(sho))) = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ bits ≠ [] → bits2int(fillsgn(n, bits)) = bits2int(bits)
Proof step 10:
int2bits(s2i(sho)) ≠ [], s2i(sho) < 0 ⊦ bits2int(int2bits(s2i(sho))) + 2 ^ n→i(# fillsgn(16, int2bits(s2i(sho)))) = s2i(sho) + 65536, fillsgn(16, int2bits(s2i(sho))) = []

Rule argument

seq: ⊦ bits ≠ [] → bits2int(fillsgn(n, bits)) = bits2int(bits) subst: [bits, n] → [int2bits(s2i(sho)), 16] rotate: F spec: int2bits inst: name: bits2int-fill

Additional information

Used simplifier rules: ⊦ int2bits(j) ≠ []; Used terms: int2bits(s2i(sho)), 16