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

# int2bits(j0) = 17, j0 < ~32768, i0 * 2 ^ 16 + j0 < ~32768, ~65536 < j0, i0 ≤ 0, i0 * 2 ^ 16 + j0 < 0, j0 < 0 ⊦ s2i(i2s(bits2int(lastn(16, int2bits(i0 * 2 ^ 16 + j0))))) = j0 + 2 ^ 16, j0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ j0 < 0 ∧ 0 < i ∧ 2 ^ (i - 1) < abs(j0) ∧ abs(j0) < 2 ^ i ∧ j < 0 → int2bits(j * 2 ^ i + j0) = int2bits(j - 1) + fillsgn(i→n(i), int2bits(j0).rest)
Proof step 14:
¬(j0 < 0 ∧ 0 < 16 ∧ 2 ^ (16 - 1) < abs(j0) ∧ abs(j0) < 2 ^ 16 ∧ i0 < 0), # int2bits(j0) = 17, j0 < ~32768, i0 * 2 ^ 16 + j0 < ~32768, ~65536 < j0, i0 ≤ 0, i0 * 2 ^ 16 + j0 < 0, j0 < 0 ⊦ s2i(i2s(bits2int(lastn(16, int2bits(i0 * 2 ^ 16 + j0))))) = j0 + 2 ^ 16, j0 = 0
Proof step 23:
j0 < 0 ∧ 0 < 16 ∧ 2 ^ (16 - 1) < abs(j0) ∧ abs(j0) < 2 ^ 16 ∧ i0 < 0, # int2bits(j0) = 17, j0 < ~32768, i0 * 2 ^ 16 + j0 < ~32768, ~65536 < j0, i0 ≤ 0, i0 * 2 ^ 16 + j0 < 0, j0 < 0 ⊦ s2i(i2s(bits2int(lastn(16, int2bits(i0 - 1) + fillsgn(i→n(16), int2bits(j0).rest))))) = j0 + 2 ^ 16, j0 = 0

Rule argument

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

Additional information

Used terms: j0, 16, i0