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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward)% ⊦ i < (* j) ∧ j < 0 → i < 0; (forward)% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;