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Proof step 41 from proof sis-neg-low (previous step)

¬(~32768 ≤ j0 + 65536 ∧ j0 + 65536 ≤ 32767), 16 = # int2bits(j0).rest, # int2bits(j0) = 17, i0 < 0, i0 * 65536 + j0 < 0, ~65536 < j0, i0 * 65536 + j0 < ~32768, j0 < ~32768, j0 < 0, j0 < ~1 ⊦ j0 = 0, int2bits(j0).rest = [], s2i(i2s(j0 + 65536)) = j0 + 65536

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%numlslsdel-01: i0 ≠ 0, i0 < i ⊦ (* i) < j → (* i0) < j; from specification int-basic1%lst: ⊦ i < j ∧ ¬ i0 < j → ¬ i0 < i; from specification int-basic1%numle-03: ⊦ i + (* j) ≤ (* j0) ↔ i ≤ j0 - j; from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%numle-02: ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0; 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%commutativity: ⊦ i * j = j * i; from specification int-mult