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Proof step 7 from proof int2bits-len-range (previous step)

0 < 2 ^ i0, i→n(i + 1) < # int2bits(j), 0 ≤ 2 ^ i + j, j < 2 ^ i, 0 ≤ i0, 2 ^ i0 ≤ abs(j), abs(j) < 2 ^ i0 * 2 ⊦ j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ j < 0 → abs(j) = 0 - j
Proof step 9:
¬ j < 0, 0 < 2 ^ i0, i→n(i + 1) < # int2bits(j), 0 ≤ 2 ^ i + j, j < 2 ^ i, 0 ≤ i0, 2 ^ i0 ≤ abs(j), abs(j) < 2 ^ i0 * 2 ⊦ j = 0
Proof step 15:
j < 0, 0 < 2 ^ i0, i→n(i + 1) < # int2bits(j), 0 ≤ 2 ^ i + j, j < 2 ^ i, 0 ≤ i0, 2 ^ i0 ≤ 0 - j, 0 - j < 2 ^ i0 * 2 ⊦ j = 0

Rule argument

seq: ⊦ j < 0 → abs(j) = 0 - j subst: [j] → [j] rotate: F spec: int-abs inst: name: Abs-neg

Additional information

Used terms: j