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Proof step 50 from proof int2bits-add-low (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 51:
⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1
Proof step 52:
2 ^ i + j0 ≤ 0 ∧ 0 ≤ j0 + 2 ^ (i - 1) → 2 ^ i + j0 ≤ j0 + 2 ^ (i - 1), 0 < 2 ^ (i - 1) + j0, j0 < 0, j < 0, 0 < i, i < n→i(# int2bits(~(j * 2 ^ i + j0))), j * 2 ^ i + j0 < 0, 0 < j + 2 ^ (n→i(# int2bits(~(j * 2 ^ i + j0))) - i), 0 ≤ (j + 2 ^ (n→i(# int2bits(~(j * 2 ^ i + j0))) - i)) * 2 ^ i + j0, 0 ≤ j0 + 2 ^ (i - 1), 2 ^ i + j0 ≤ 0 ⊦ sgn(uint2bits(j + 2 ^ (n→i(# int2bits(~(j * 2 ^ i + j0))) - i) - 1).rest + fillsgn(i→n(i), int2bits(j0))) = int2bits(j - 1) + fillsgn(i→n(i), int2bits(j0)), j * 2 ^ i + j0 = 0

Rule argument

seq: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1 subst: [j, j0, j1] → [2 ^ i + j0, 0, j0 + 2 ^ (i - 1)] rotate: F spec: int-abs inst: name: fle-02

Additional information

Used terms: 2 ^ i + j0, 0, j0 + 2 ^ (i - 1)