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Proof step 11 from proof uint2bits-add-low-01 (previous step)

0 < j, j0 < 0, 0 < i, 0 ≤ j0 + 2 ^ (i - 1), 2 ^ i + j0 < 0 ⊦ j = 1, uint2bits(2 ^ i * j + j0) = uint2bits(j - 1) + fillsgn(i→n(i), int2bits(j0))

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 12:
⊦ i < 0 ∧ 0 ≤ j → i ≤ j
Proof step 13:
2 ^ i + j0 < 0 ∧ 0 ≤ j0 + 2 ^ (i - 1) → 2 ^ i + j0 ≤ j0 + 2 ^ (i - 1), 0 < j, j0 < 0, 0 < i, 0 ≤ j0 + 2 ^ (i - 1), 2 ^ i + j0 < 0 ⊦ j = 1, uint2bits(2 ^ i * j + j0) = uint2bits(j - 1) + fillsgn(i→n(i), int2bits(j0))

Rule argument

seq: ⊦ i < 0 ∧ 0 ≤ j → i ≤ j subst: [i, j] → [2 ^ i + j0, j0 + 2 ^ (i - 1)] rotate: F spec: int-abs inst: name: zero-gels-03

Additional information

Used terms: 2 ^ i + j0, j0 + 2 ^ (i - 1)