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Proof step 33 from proof shiftzero-pos (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 34:
⊦ m ≤ # bits → firstn(m, bits + bits0) = firstn(m, bits)
Proof step 35:
¬ n ≤ # mklist(false, i→n(j) + (n - # int2bits(i))), # int2bits(i) < i→n(j), 0 ≤ i, # int2bits(i) < n ⊦ j = 0, bits2int(firstn(n, mklist(false, i→n(j) + (n - # int2bits(i))) + int2bits(i))) = 0
Proof step 37:
n ≤ # mklist(false, i→n(j) + (n - # int2bits(i))), # int2bits(i) < i→n(j), 0 ≤ i, # int2bits(i) < n ⊦ j = 0, bits2int(firstn(n, mklist(false, i→n(j) + (n - # int2bits(i))))) = 0

Rule argument

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

Additional information

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