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Proof step 2 from proof int2bits-rec-2pot-neg-02 (previous step)

0 < i, j + 2 ^ i ≤ 0, j + 2 ^ i < i ⊦ j % 2 ^ i = 0, int2bits(j) = int2bits(j / 2 ^ i - 1) + fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ i < 0 → int2bits(i) = sgn(bitsinvert(uint2bits(abs(i))) +1)
Proof step 4:
j < 0, 0 < i, j + 2 ^ i ≤ 0, j + 2 ^ i < i ⊦ j % 2 ^ i = 0, sgn(bitsinvert(uint2bits(abs(j))) +1) = int2bits(j / 2 ^ i - 1) + fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest

Rule argument

name: int2bits-neg rotate: F subst: [i] → [j]

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward)% ⊦ i + j ≤ i ↔ j ≤ 0;% ⊦ 2 ^ i ≤ 0 ↔ i < 0;% ⊦ i < j → ¬ j < i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: j