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Proof step 22 from proof shiftzero-pos (previous step)

# int2bits(i) < n, 0 ≤ i ⊦ bits2int(firstn(n, mklist(false, i→n(j)) + mklist(false, n - # int2bits(i)) + 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 23:
⊦ # bits ≤ n → firstn(n, bits + bits0) = bits + firstn(n - # bits, bits0)
Proof step 24:
¬ # mklist(false, i→n(j)) ≤ # int2bits(i), # int2bits(i) < n, 0 ≤ i ⊦ bits2int(firstn(n, mklist(false, i→n(j)) + mklist(false, n - # int2bits(i)) + int2bits(i))) = bits2int(firstn(# int2bits(i), mklist(false, i→n(j)) + int2bits(i)))
Proof step 42:
# mklist(false, i→n(j)) ≤ # int2bits(i), # int2bits(i) < n, 0 ≤ i ⊦ bits2int(firstn(n, mklist(false, i→n(j)) + mklist(false, n - # int2bits(i)) + int2bits(i))) = bits2int(mklist(false, i→n(j)) + firstn(# int2bits(i) - # mklist(false, i→n(j)), int2bits(i)))

Rule argument

seq: ⊦ # bits ≤ n → firstn(n, bits + bits0) = bits + firstn(n - # bits, bits0) subst: [bits0, bits, n] → [int2bits(i), mklist(false, i→n(j)), # int2bits(i)] rotate: F spec: list-del inst: bitlista name: firstn-app-01

Additional information

Used terms: int2bits(i), mklist(false, i→n(j)), # int2bits(i)