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Proof step 25 from proof shiftzero-pos (previous step)

# int2bits(i) < i→n(j), 0 ≤ i, # int2bits(i) < n ⊦ 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))), j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ m ≤ # bits → firstn(m, bits + bits0) = firstn(m, bits)
Proof step 27:
# int2bits(i) ≤ # mklist(false, i→n(j)), # int2bits(i) < i→n(j), 0 ≤ i, # int2bits(i) < n ⊦ bits2int(firstn(n, mklist(false, i→n(j)) + mklist(false, n - # int2bits(i)) + int2bits(i))) = bits2int(firstn(# int2bits(i), mklist(false, i→n(j)))), j = 0

Rule argument

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

Additional information

Used simplifier rules: ⊦ # mklist(boolvar, n) = n;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n → ¬ n < m; Used terms: int2bits(i), mklist(false, i→n(j)), # int2bits(i)