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Proof step 7 from proof sis-pos-low (previous step)

32767 < i, 0 < i, i % 65536 < i, 32767 < i, 0 ≤ i, i % 65536 ≤ 32767 ⊦ 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 ∧ 0 ≤ j ∧ j < 65536 ∧ 0 ≤ i0 ∧ 0 < 65536, 32767 < i, 0 < i, j < i, 32767 < i, 0 ≤ i, j ≤ 32767 ⊦ s2i(i2s(bits2int(lastn(16, int2bits(i))))) = j

Rule argument

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] rotate: T spec: int-div inst: name: div-elim-pospos

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i;%⊦ 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