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Proof step 5 from proof sis-pos-high (previous step)

0 < i, 32767 < i, 32767 < i % 65536, 0 ≤ i, 0 < i % 65536 ⊦ i % 65536 = s2i(i2s(i)) + 65536

User applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
i = i0 * 65536 + j0 ∧ 0 ≤ j0 ∧ j0 < 65536 ∧ 0 ≤ i0 ∧ 0 < 65536, 0 < i, 32767 < i, 32767 < j0, 0 ≤ i, 0 < j0 ⊦ j0 = s2i(i2s(i)) + 65536

Rule argument

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

Additional information

Used simplifier rules: zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%⊦ 0 < j ∧ 0 ≤ i → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j ∧ 0 ≤ i0); (elim) Used terms: i, 65536, i0, j