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Proof step 58 from proof shiftzero-pos (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 59:
⊦ m ≤ n → firstn(m, mklist(boolvar, n)) = mklist(boolvar, m)
Proof step 60:
n ≤ n, n ≤ # mklist(false, n), # int2bits(i) = i→n(j), 0 ≤ i, i→n(j) < n ⊦ bits2int(mklist(false, n)) = 0, j = 0

Rule argument

seq: ⊦ m ≤ n → firstn(m, mklist(boolvar, n)) = mklist(boolvar, m) subst: [n, boolvar, m] → [n, false, n] rotate: F spec: list-del inst: bitlista name: first-mklist

Additional information

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