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Proof step 45 from proof bib-pos-high (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 46:
⊦ 0 < i → bits2int(int2bits(i).rest) = i - 2 ^ (n→i(# uint2bits(i)) - 1)
Proof step 47:
0 < j, 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(j - 2 ^ (n→i(# uint2bits(j)) - 1))) + 256, 0 = i0 * 256 + j, int2bits(j).rest.first

Rule argument

seq: ⊦ 0 < i → bits2int(int2bits(i).rest) = i - 2 ^ (n→i(# uint2bits(i)) - 1) subst: [i] → [j] rotate: F spec: int2bits inst: name: int2uint-rest

Additional information

Used terms: j