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Proof step 24 from proof bib-pos-high (previous step)

# int2bits(j) = 9, 127 < j, 64 ≤ j, j < 256, 0 < j ⊦ j = 256 + b2i(i2b(bits2int(int2bits(j).rest))), 0 = j, int2bits(j).rest.first

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ 0 < i → bits2int(int2bits(i).rest) = i - 2 ^ (n→i(# uint2bits(i)) - 1)
Proof step 26:
0 < j, # int2bits(j) = 9, 127 < j, 64 ≤ j, j < 256, 0 < j ⊦ j = 256 + b2i(i2b(j - 2 ^ (n→i(# uint2bits(j)) - 1))), 0 = 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