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Proof step 11 from proof sis-pos-low (previous step)

0 < i0, 0 ≤ i0, 0 ≤ j, 0 < i0 * 2 ^ 16 + j, j ≤ 32767, 32767 < i0 * 2 ^ 16 + j ⊦ s2i(i2s(bits2int(lastn(16, int2bits(i0 * 2 ^ 16 + j))))) = j

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 < j ∧ 0 ≤ j0 ∧ j0 < 2 ^ i ∧ 0 ≤ i → int2bits(j * 2 ^ i + j0) = int2bits(j) + fillsgn(i→n(i + 1), int2bits(j0)).rest subst: [j0, i, j] → [j, 16, i0] rotate: F spec: int2bits inst: name: int2bits-mod2pot

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ i + j = j + i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);%j0 ≠ 0, j < j0 ⊦ i ≤ (* j) → i < (* j0);% ⊦ i + 0 = i;% ⊦ i + j + i0 = (i + j) + i0; Used terms: j, 16, i0