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Proof step 29 from proof sis-on-bits (previous step)

# int2bits(i) < 16, i ≤ 0 ⊦ s2i(i2s(bits2int(lastn(16, int2bits(i))))) = bits2int(lastn(16, fillsgn(16, int2bits(i)))), i ∈short

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
⊦ i < ~1 → (# int2bits(i) < m ↔ 0 ≤ i + 2 ^ (n→i(m) - 2))
Proof step 31:
¬ i < ~1, # int2bits(i) < 16, i ≤ 0 ⊦ s2i(i2s(bits2int(lastn(16, int2bits(i))))) = bits2int(lastn(16, fillsgn(16, int2bits(i)))), i ∈short
Proof step 33:
i < ~1, 0 ≤ i + 2 ^ (n→i(16) - 2), i ≤ 0 ⊦ s2i(i2s(bits2int(lastn(16, int2bits(i))))) = bits2int(lastn(16, fillsgn(16, int2bits(i)))), i ∈short

Rule argument

seq: ⊦ i < ~1 → (# int2bits(i) < m ↔ 0 ≤ i + 2 ^ (n→i(m) - 2)) subst: [m, i] → [16, i] rotate: F spec: int2bits inst: name: int2bits-lslen-03

Additional information

Used terms: 16, i