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Proof step 26 from proof shiftzero-rec-neg-shorter (previous step)

i→n(j) = m0 + 1, # int2bits((i - 1) / 2) ≤ m, i < ~1, # int2bits(i) ≤ m + 1, i < 0, 1 < j, 0 < j ⊦ j = 0, bits2uint(firstn(m, mklist(false, m0) + fillsgn(m + 1, int2bits(i)))) = bits2int(firstn(m, mklist(false, m0) + fillsgn(m, int2bits((i - 1) / 2))))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
⊦ j < 0 ∧ j ≠ ~1 → int2bits(j) = int2bits((j - 1) / 2) + (~1 = j % 2)'
Proof step 28:
i < 0 ∧ i ≠ ~1, i→n(j) = m0 + 1, # int2bits((i - 1) / 2) ≤ m, i < ~1, #(int2bits((i - 1) / 2) + (~1 = i % 2)') ≤ m + 1, i < 0, 1 < j, 0 < j ⊦ j = 0, bits2uint(firstn(m, mklist(false, m0) + fillsgn(m + 1, int2bits((i - 1) / 2) + (~1 = i % 2)'))) = bits2int(firstn(m, mklist(false, m0) + fillsgn(m, 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: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: i