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Proof step 4 from proof sis-on-bits (previous step)

~32768 ≤ i, i ≤ 32767 ⊦ i = bits2int(lastn(16, fillsgn(16, int2bits(i))))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ n = # bits → lastn(n, bits) = bits
Proof step 6:
16 ≠ # fillsgn(16, int2bits(i)), ~32768 ≤ i, i ≤ 32767 ⊦ i = bits2int(lastn(16, fillsgn(16, int2bits(i))))
Proof step 20:
16 = # fillsgn(16, int2bits(i)), ~32768 ≤ i, i ≤ 32767 ⊦ i = bits2int(fillsgn(16, int2bits(i)))

Rule argument

seq: ⊦ n = # bits → lastn(n, bits) = bits subst: [bits, n] → [fillsgn(16, int2bits(i)), 16] rotate: F spec: list-del inst: bitlista name: lastN-all

Additional information

Used terms: fillsgn(16, int2bits(i)), 16