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Proof step 47 from proof bib-pos-high (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 48:
⊦ bits ≠ [] → # bits.rest = (# bits)-1
Proof step 49:
int2bits(j) ≠ [], 0 < j, 8 = (# int2bits(j))-1, 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: ⊦ bits ≠ [] → # bits.rest = (# bits)-1 subst: [bits] → [int2bits(j)] rotate: F spec: list-data inst: bitlista name: length-rest

Additional information

Used simplifier rules: ⊦ int2bits(j) ≠ []; Used terms: int2bits(j)