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Proof step 7 from proof sis-neg-high (previous step)

i < ~32768, ~32768 ≤ i % 65536, i < 0, i < ~32768 ⊦ s2i(i2s(bits2int(lastn(16, int2bits(i))))) = i % 65536

User applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
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

Rule argument

seq: ⊦ 0 < j ∧ i < 0 → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ j0 ≤ 0 ∧ abs(j0) < j ∧ i0 ≤ 0) subst: [i, j, i0, j0] → [i, 65536, i0, j] rotate: T spec: int-div inst: name: div-elim-negpos

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);%⊦ 0 < j ∧ i < 0 → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ j0 ≤ 0 ∧ abs(j0) < j ∧ i0 ≤ 0); (elim) Used terms: i, 65536, i0, j