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Proof step 37 from proof shiftzero-pos (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: ⊦ mklist(boolvar, m + n) = mklist(boolvar, m) + mklist(boolvar, n);% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # mklist(boolvar, n) = n;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m ≤ n → (n < m ↔ false); Used terms: i→n(j) + (n - # int2bits(i)), false, n