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Proof step 22 from proof int2bytes-byte-neg (previous step)

~256 < i, i < ~128, i < 0, # int2bits(i) ≤ 9 ⊦ i2b(bits2int(int2bits(i).rest)) = i2b(i)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ j < ~1 → bits2int(int2bits(j).rest) = j + 2 ^ (n→i(# int2bits(j)) - 1)
Proof step 24:
i < ~1, ~256 < i, i < ~128, i < 0, # int2bits(i) ≤ 9 ⊦ i2b(i + 2 ^ (n→i(# int2bits(i)) - 1)) = i2b(i)

Rule argument

seq: ⊦ j < ~1 → bits2int(int2bits(j).rest) = j + 2 ^ (n→i(# int2bits(j)) - 1) subst: [j] → [i] rotate: F spec: int2bits inst: name: int2int-rest-01

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < 0 → (~1 ≤ i ↔ i = ~1); Used terms: i