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Proof step 12 from proof sis-neg-high (previous step)

# int2bits(j) ≤ 16, abs(j) < 2 ^ 16, ~32768 ≤ j, i0 * 2 ^ 16 + j < ~32768, j ≤ 0, i0 ≤ 0, i0 * 2 ^ 16 + j < 0 ⊦ s2i(i2s(bits2int(lastn(16, int2bits(i0 * 2 ^ 16 + j))))) = j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ j < 0 ∧ j0 < 0 ∧ abs(j0) < 2 ^ (i - 1) ∧ 0 < i → int2bits(j * 2 ^ i + j0) = int2bits(j - 1) + fillsgn(i→n(i), int2bits(j0))
Proof step 14:
¬(i0 < 0 ∧ j < 0 ∧ abs(j) < 2 ^ (16 - 1) ∧ 0 < 16), # int2bits(j) ≤ 16, abs(j) < 2 ^ 16, ~32768 ≤ j, i0 * 2 ^ 16 + j < ~32768, j ≤ 0, i0 ≤ 0, i0 * 2 ^ 16 + j < 0 ⊦ s2i(i2s(bits2int(lastn(16, int2bits(i0 * 2 ^ 16 + j))))) = j
Proof step 35:
i0 < 0 ∧ j < 0 ∧ abs(j) < 2 ^ (16 - 1) ∧ 0 < 16, # int2bits(j) ≤ 16, abs(j) < 2 ^ 16, ~32768 ≤ j, i0 * 2 ^ 16 + j < ~32768, j ≤ 0, i0 ≤ 0, i0 * 2 ^ 16 + j < 0 ⊦ s2i(i2s(bits2int(lastn(16, int2bits(i0 - 1) + fillsgn(i→n(16), int2bits(j)))))) = j

Rule argument

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

Additional information

Used terms: j, 16, i0