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Proof step 51 from proof shiftzero-pos (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 52:
⊦ m ≠ 0 → bits2int(mklist(false, m)) = 0
Proof step 53:
i→n(j) ≠ 0, # int2bits(i) = i→n(j), 0 ≤ i, i→n(j) < n ⊦ bits2int(firstn(n, mklist(false, i→n(j)) + mklist(false, n - i→n(j)) + int2bits(i))) = 0

Rule argument

seq: ⊦ m ≠ 0 → bits2int(mklist(false, m)) = 0 subst: [m] → [i→n(j)] rotate: F spec: int2bits inst: name: bits2int-zeros-03

Additional information

Used simplifier rules: ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ # bits = 0 ↔ bits = [];% ⊦ int2bits(j) ≠ []; Used terms: i→n(j)