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Proof step 11 from proof shiftzero-by-one-01 (previous step)

i < ~1, i < 0 ⊦ fillsgn(n - 1, int2bits((i - 1) / 2)) = [], n = 0, 2 ^ n→i(# fillsgn(n - 1, int2bits((i - 1) / 2))) = 2 ^ n→i(# fillsgn(n, int2bits(i)) - 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ j < 0 ∧ j ≠ ~1 → int2bits(j) = int2bits((j - 1) / 2) + (~1 = j % 2)'
Proof step 13:
i < 0 ∧ i ≠ ~1, i < ~1, i < 0 ⊦ fillsgn(n - 1, int2bits((i - 1) / 2)) = [], n = 0, 2 ^ n→i(# fillsgn(n - 1, int2bits((i - 1) / 2))) = 2 ^ n→i(# fillsgn(n, int2bits((i - 1) / 2) + (~1 = i % 2)') - 1)

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