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Proof step 30 from proof sis-pos-low (previous step)

int2bits(j) ≠ [] ∧ # int2bits(j) < 17, 16 = # (int2bits(j).first ' + fillsgn(17 -1, int2bits(j))).rest, 0 < i0, 0 ≤ i0, 0 ≤ j, 0 < 65536 * i0 + j, j ≤ 32767, 32767 < 65536 * i0 + j ⊦ s2i(i2s(bits2int((int2bits(j).first ' + fillsgn(17 -1, int2bits(j))).rest))) = j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
16 = # fillsgn(16, int2bits(j)), 32767 < 65536 * i0 + j, j ≤ 32767, 0 < 65536 * i0 + j, 0 ≤ j, 0 ≤ i0, 0 < i0, # int2bits(j) < 17 ⊦ s2i(i2s(j)) = j

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (forward)% ⊦ i + j = j + i;% ⊦ i * j = j * i;% ⊦ int2bits(j) ≠ [];% ⊦ bits2int(int2bits(i)) = i;% ⊦ bits ≠ [] → bits2int(fillsgn(n, bits)) = bits2int(bits);% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ (boolvar ' + bits).rest = bits;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ int2bits(j).first ↔ j < 0;