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Proof step 8 from proof sis-neg-low (previous step)

i = i0 * 65536 + j0 ∧ j0 ≤ 0 ∧ abs(j0) < 65536 ∧ i0 ≤ 0 ∧ 0 < 65536, i < ~32768, i < 0, j0 < ~32768, i < ~32768 ⊦ s2i(i2s(bits2int(lastn(16, int2bits(i))))) = j0 + 65536, j0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
j0 < ~32768, i0 * 65536 + j0 < ~32768, ~65536 < j0, i0 ≤ 0, i0 * 65536 + j0 < 0, j0 < 0 ⊦ s2i(i2s(bits2int(lastn(16, int2bits(i0 * 65536 + j0))))) = j0 + 65536, j0 = 0

Rule argument

Additional information

Used simplifier rules: forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%numlsf: ⊦ i < (* j) ∧ j < 0 → i < 0; (forward) from specification int-basic1%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) 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%numls-02: ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; from specification int-abs%neg-13: ⊦ ~ i < j ↔ 0 < j + i; from specification int-abs%abs-08: ⊦ i < 0 → abs(i) = ~ i; from specification int-abs%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs