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Proof step 5 from proof ushort-neg (previous step)
| s2i(sho) < 0 ⊦ bits2uint(fillsgn(16, int2bits(s2i(sho)))) = s2i(sho) + 65536 |
User applied rule insert rewrite lemma
And obtained the following new goals
- Proof step 6:
⊦ bits ≠ [] ∧ bits.first → bits2uint(bits) = bits2int(bits) + 2 ^ n→i(# bits)
- Proof step 7:
fillsgn(16, int2bits(s2i(sho))) ≠ [] ∧ fillsgn(16, int2bits(s2i(sho))).first, s2i(sho) < 0
⊦ bits2int(fillsgn(16, int2bits(s2i(sho)))) + 2 ^ n→i(# fillsgn(16, int2bits(s2i(sho)))) = s2i(sho) + 65536
Rule argument
seq: ⊦ bits ≠ [] ∧ bits.first
→ bits2uint(bits) = bits2int(bits) + 2 ^ n→i(# bits)
subst: [bits] → [fillsgn(16, int2bits(s2i(sho)))]
rotate: F
spec: int2bits
inst:
name: ubits2bitsAdditional information
Used simplifier rules:
⊦ fillsgn(n, bits) = [] ↔ bits = [] ∧ n = 0;% ⊦ int2bits(j) ≠ [];% ⊦ fillsgn(n, int2bits(j)).first ↔ int2bits(j).first;% ⊦ j < 0 → int2bits(j).first;
Used terms: fillsgn(16, int2bits(s2i(sho)))