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

0 < i0 * 256 + j, 0 ≤ j, 0 < j, j < 256, 64 ≤ i0 * 256 + j, 127 < i0 * 256 + j, 127 < j, 0 ≤ i0 ⊦ 0 = i0 * 256 + j, j = b2i(i2b(bits2int(lastn(8, int2bits(i0 * 256 + j))))) + 256, lastn(8, int2bits(i0 * 256 + j)).first

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ 0 < j ∧ 0 ≤ j0 ∧ j0 < 256 → int2bits(j * 256 + j0) = int2bits(j) + fillsgn(9, int2bits(j0)).rest
Proof step 17:
¬(0 < i0 ∧ 0 ≤ j ∧ j < 256), 0 < i0 * 256 + j, 0 ≤ j, 0 < j, j < 256, 64 ≤ i0 * 256 + j, 127 < i0 * 256 + j, 127 < j, 0 ≤ i0 ⊦ 0 = i0 * 256 + j, j = b2i(i2b(bits2int(lastn(8, int2bits(i0 * 256 + j))))) + 256, lastn(8, int2bits(i0 * 256 + j)).first
Proof step 31:
0 < i0 ∧ 0 ≤ j ∧ j < 256, 0 < i0 * 256 + j, 0 ≤ j, 0 < j, j < 256, 64 ≤ i0 * 256 + j, 127 < i0 * 256 + j, 127 < j, 0 ≤ i0 ⊦ 0 = i0 * 256 + j, j = b2i(i2b(bits2int(lastn(8, int2bits(i0) + fillsgn(9, int2bits(j)).rest)))) + 256, lastn(8, int2bits(i0) + fillsgn(9, int2bits(j)).rest).first

Rule argument

seq: ⊦ 0 < j ∧ 0 ≤ j0 ∧ j0 < 256 → int2bits(j * 256 + j0) = int2bits(j) + fillsgn(9, int2bits(j0)).rest subst: [j0, j] → [j, i0] rotate: F spec: int2bits inst: name: int2bits-mod256

Additional information

Used terms: j, i0