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Proof step 37 from proof bib-pos-high (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 38:
⊦ n = # bits → lastn(n, bits0 + bits) = bits
Proof step 39:
8 ≠ # int2bits(j).rest, 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
Proof step 45:
8 = # int2bits(j).rest, 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(int2bits(j).rest))) + 256, 0 = i0 * 256 + j, int2bits(j).rest.first

Rule argument

seq: ⊦ n = # bits → lastn(n, bits0 + bits) = bits subst: [bits, bits0, n] → [int2bits(j).rest, int2bits(i0), 8] rotate: F spec: list-del inst: bitlista name: lastN-append

Additional information

Used terms: int2bits(j).rest, int2bits(i0), 8