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Proof step 70 from proof shiftzero-pos (previous step)

i→n(j) < # int2bits(i), 0 ≤ i, # int2bits(i) < n, i→n(j) < n, i→n(j) + 1 < n ⊦ # int2bits(i) = i→n(j), bits2int(firstn(n, mklist(false, i→n(j)) + mklist(false, n - # int2bits(i)) + int2bits(i))) = bits2int(firstn(# int2bits(i) - i→n(j), int2bits(i))), firstn(# int2bits(i) - i→n(j), int2bits(i)).first

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 71:
⊦ # bits ≤ n → firstn(n, bits + bits0) = bits + firstn(n - # bits, bits0)
Proof step 72:
# mklist(false, i→n(j)) ≤ n, i→n(j) < # int2bits(i), 0 ≤ i, # int2bits(i) < n, i→n(j) < n, i→n(j) + 1 < n ⊦ # int2bits(i) = i→n(j), bits2int(mklist(false, i→n(j)) + firstn(n - # mklist(false, i→n(j)), mklist(false, n - # int2bits(i)) + int2bits(i))) = bits2int(firstn(# int2bits(i) - i→n(j), int2bits(i))), firstn(# int2bits(i) - i→n(j), int2bits(i)).first

Rule argument

seq: ⊦ # bits ≤ n → firstn(n, bits + bits0) = bits + firstn(n - # bits, bits0) subst: [bits0, bits, n] → [mklist(false, n - # int2bits(i)) + int2bits(i), mklist(false, i→n(j)), n] rotate: F spec: list-del inst: bitlista name: firstn-app-01

Additional information

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