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Proof step 6 from proof shiftzero-rec-neg-longer (previous step)

0 < j, 1 < j, i < 0, n < # int2bits(i), i < ~1 ⊦ bits2int(sublist(0, # fillsgn(n, int2bits(i)), mklist(false, i→n(j)) + fillsgn(n, int2bits(i)))) = bits2int(sublist(0, # fillsgn(n, int2bits((i - 1) / 2)), mklist(false, i→n(j - 1)) + fillsgn(n, int2bits((i - 1) / 2))))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ j < 0 ∧ j ≠ ~1 → int2bits(j) = int2bits((j - 1) / 2) + (~1 = j % 2)'
Proof step 8:
i < 0 ∧ i ≠ ~1, 0 < j, 1 < j, i < 0, n < #(int2bits((i - 1) / 2) + (~1 = i % 2)'), i < ~1 ⊦ bits2int (sublist(0, # fillsgn(n, int2bits((i - 1) / 2) + (~1 = i % 2)'), mklist(false, i→n(j)) + fillsgn(n, int2bits((i - 1) / 2) + (~1 = i % 2)'))) = bits2int(sublist(0, # fillsgn(n, int2bits((i - 1) / 2)), mklist(false, i→n(j - 1)) + fillsgn(n, int2bits((i - 1) / 2))))

Rule argument

seq: ⊦ j < 0 ∧ j ≠ ~1 → int2bits(j) = int2bits((j - 1) / 2) + (~1 = j % 2)' subst: [j] → [i] rotate: F spec: int2bits inst: name: int2bits-rec-neg

Additional information

Used simplifier rules: ⊦ 1 < i → i→n(i - 1) = i→n(i) -1;% ⊦ n -1 = n - 1;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: i