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Proof step 7 from proof sis-on-bits (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ # bits ≤ n → # fillsgn(n, bits) = n
Proof step 9:
¬ # int2bits(i) ≤ 16, i ≤ 32767, ~32768 ≤ i ⊦ 16 = # fillsgn(16, int2bits(i)), i = bits2int(lastn(16, fillsgn(16, int2bits(i))))

Rule argument

seq: ⊦ # bits ≤ n → # fillsgn(n, bits) = n subst: [bits, n] → [int2bits(i), 16] rotate: F spec: bitopsaux inst: name: fill-length

Additional information

Used terms: int2bits(i), 16