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Proof step 15 from proof sis-pos-high (previous step)

# int2bits(j0) = 17, 0 < j0, 0 < i0 * 2 ^ 16 + j0, 0 ≤ i0, 0 ≤ j0, 32767 < j0, 32767 < i0 * 2 ^ 16 + j0, j0 < 2 ^ 16 ⊦ j0 = s2i(i2s(bits2int(lastn(16, int2bits(i0 * 2 ^ 16 + j0))))) + 2 ^ 16

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ 0 < j ∧ 0 ≤ j0 ∧ j0 < 2 ^ i ∧ 0 ≤ i → int2bits(j * 2 ^ i + j0) = int2bits(j) + fillsgn(i→n(i + 1), int2bits(j0)).rest
Proof step 17:
¬(0 < i0 ∧ 0 ≤ j0 ∧ j0 < 2 ^ 16 ∧ 0 ≤ 16), # int2bits(j0) = 17, 0 < j0, 0 < i0 * 2 ^ 16 + j0, 0 ≤ i0, 0 ≤ j0, 32767 < j0, 32767 < i0 * 2 ^ 16 + j0, j0 < 2 ^ 16 ⊦ j0 = s2i(i2s(bits2int(lastn(16, int2bits(i0 * 2 ^ 16 + j0))))) + 2 ^ 16
Proof step 28:
0 < i0 ∧ 0 ≤ j0 ∧ j0 < 2 ^ 16 ∧ 0 ≤ 16, # int2bits(j0) = 17, 0 < j0, 0 < i0 * 2 ^ 16 + j0, 0 ≤ i0, 0 ≤ j0, 32767 < j0, 32767 < i0 * 2 ^ 16 + j0, j0 < 2 ^ 16 ⊦ j0 = s2i(i2s(bits2int(lastn(16, int2bits(i0) + fillsgn(i→n(16 + 1), int2bits(j0)).rest)))) + 2 ^ 16

Rule argument

spec: int2bits inst: name: int2bits-mod2pot 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] → [j0, 16, i0] flags: rewrite

Additional information

Used terms: j0, 16, i0