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Proof step 8 from proof sis-pos-low (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: i0 ≠ 0, i0 < i ⊦ (* i) < j → (* i0) < j;% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward)% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ 0 ≤ j ∧ 0 ≤ j0 ∧ 0 ≤ i0 → 0 ≤ i0 * j + j0;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ i < i + j ↔ 0 < j;%j0 ≠ 0, j < j0 ⊦ i ≤ (* j) → i < (* j0);