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Proof step 23 from proof sis-neg-low (previous step)

j0 < 0 ∧ 0 < 16 ∧ 2 ^ (16 - 1) < abs(j0) ∧ abs(j0) < 2 ^ 16 ∧ i0 < 0, # int2bits(j0) = 17, j0 < ~32768, i0 * 2 ^ 16 + j0 < ~32768, ~65536 < j0, i0 ≤ 0, i0 * 2 ^ 16 + j0 < 0, j0 < 0 ⊦ s2i(i2s(bits2int(lastn(16, int2bits(i0 - 1) + fillsgn(i→n(16), int2bits(j0).rest))))) = j0 + 2 ^ 16, j0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%zero-gels-03: ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%numlelsdel-01: i0 ≠ 0, i0 ≤ i ⊦ (* i) < j → (* i0) < j; from specification int-abs%numls-02: ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; from specification int-abs%neg-13: ⊦ ~ i < j ↔ 0 < j + i; from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%numlelsdel: j0 ≠ 0, j ≤ j0 ⊦ i < (* j) → i < (* j0); from specification int-abs%numls-03: ⊦ i + (* j) < (* j0) ↔ i < j0 - j; from specification int-abs%neg-07: ⊦ i < ~ j ↔ i + j < 0; from specification int-abs%abs-08: ⊦ i < 0 → abs(i) = ~ i; from specification int-abs