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Proof step 13 from proof shiftzero-pos (previous step)

0 ≤ i ⊦ bits2int(firstn(# fillsgn(n, int2bits(i)), mklist(false, i→n(j)) + fillsgn(n, int2bits(i)))) = bits2int(firstn(# int2bits(i), mklist(false, i→n(j)) + int2bits(i)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ n ≤ # bits → fillsgn(n, bits) = bits
Proof step 15:
¬ n ≤ # int2bits(i), 0 ≤ i ⊦ bits2int(firstn(# fillsgn(n, int2bits(i)), mklist(false, i→n(j)) + fillsgn(n, int2bits(i)))) = bits2int(firstn(# int2bits(i), mklist(false, i→n(j)) + int2bits(i)))

Rule argument

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

Additional information

Used terms: int2bits(i), n