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Proof step 32 from proof bib-pos-high (previous step)

0 ≤ i0, 127 < j, 127 < i0 * 256 + j, 64 ≤ i0 * 256 + j, j < 256, 0 < j, 0 ≤ j, 0 < i0 * 256 + j, 0 < i0 ⊦ j = b2i(i2b(bits2int(lastn(8, int2bits(i0) + fillsgn(9, int2bits(j)).rest)))) + 256, 0 = i0 * 256 + j, lastn(8, int2bits(i0) + fillsgn(9, int2bits(j)).rest).first

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 33:
⊦ n ≤ # bits → fillsgn(n, bits) = bits
Proof step 34:
¬ 9 ≤ # int2bits(j), 0 ≤ i0, 127 < j, 127 < i0 * 256 + j, 64 ≤ i0 * 256 + j, j < 256, 0 < j, 0 ≤ j, 0 < i0 * 256 + j, 0 < i0 ⊦ j = b2i(i2b(bits2int(lastn(8, int2bits(i0) + fillsgn(9, int2bits(j)).rest)))) + 256, 0 = i0 * 256 + j, lastn(8, int2bits(i0) + fillsgn(9, int2bits(j)).rest).first
Proof step 37:
9 ≤ # int2bits(j), 0 ≤ i0, 127 < j, 127 < i0 * 256 + j, 64 ≤ i0 * 256 + j, j < 256, 0 < j, 0 ≤ j, 0 < i0 * 256 + j, 0 < i0 ⊦ j = b2i(i2b(bits2int(lastn(8, int2bits(i0) + int2bits(j).rest)))) + 256, 0 = i0 * 256 + j, lastn(8, int2bits(i0) + int2bits(j).rest).first

Rule argument

seq: ⊦ n ≤ # bits → fillsgn(n, bits) = bits subst: [bits, n] → [int2bits(j), 9] rotate: F spec: bitopsaux inst: name: fillsgn-longer

Additional information

Used terms: int2bits(j), 9