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Proof step 1 from proof int2int-rest (conclusion)

⊦ 0 < i → bits2int(int2bits(i).rest) = i - 2 ^ (n→i(# uint2bits(i)) - 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ 0 ≤ i → int2bits(i) = uint2bits(i)
Proof step 3:
0 ≤ i ⊦ 0 < i → bits2int(uint2bits(i).rest) = i - 2 ^ (n→i(# uint2bits(i)) - 1)

Rule argument

name: int2bits-pos rotate: F subst: [i] → [i]

Additional information

Used simplifier rules: ⊦ i - j = i0 ↔ i = i0 + j;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i; Used terms: i