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Proof step 48 from proof shiftzero-pos (previous step)

firstn(# int2bits(i) - i→n(j), int2bits(i)).first, 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(mklist(false, i→n(j)) + firstn(# int2bits(i) - i→n(j), int2bits(i)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 49:
⊦ n ≠ 0 ∧ bits ≠ [] → (firstn(n, bits).first ↔ bits.first)

Rule argument

seq: ⊦ n ≠ 0 ∧ bits ≠ [] → (firstn(n, bits).first ↔ bits.first) subst: [bits, n] → [int2bits(i), # int2bits(i) - i→n(j)] rotate: F spec: list-del inst: bitlista name: firstn-first

Additional information

Used simplifier rules: ⊦ int2bits(j) ≠ [];% ⊦ n < m → m - n ≠ 0;% ⊦ int2bits(j).first ↔ j < 0;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: int2bits(i), # int2bits(i) - i→n(j)