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Proof step 26 from proof bib-pos-high (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
⊦ 0 ≤ i → int2bits(i) = uint2bits(i)
Proof step 28:
0 ≤ j, 0 < j, # int2bits(j) = 9, 127 < j, 64 ≤ j, j < 256, 0 < j ⊦ j = 256 + b2i(i2b(j - 2 ^ (n→i(# int2bits(j)) - 1))), 0 = j, int2bits(j).rest.first

Rule argument

seq: ⊦ 0 ≤ i → int2bits(i) = uint2bits(i) subst: [i] → [j] rotate: T spec: int2bits inst: name: int2bits-pos

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i; Used terms: j