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Proof step 12 from proof int2unit-inv-rest (previous step)

int2bits(i).rest ≠ [] ∧ int2bits(i).rest.first, 0 < i ⊦ 2 ^ (n→i(# uint2bits(i)) - 1) = (~ bits2int(int2bits(i).rest) - 1) + i + 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ 0 < i → bits2int(int2bits(i).rest) = i - 2 ^ (n→i(# uint2bits(i)) - 1)

Rule argument

name: int2int-rest rotate: F subst: [i] → [i]

Additional information

Used simplifier rules: ⊦ ~ i - j = ~(i + j);% ⊦ i + (j - i0) = i + j - i0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i + ~ j = i - j;% ⊦ i - j = i0 ↔ i = i0 + j;% ⊦ i + (j - i) = j;% ⊦ i + j = i + i0 ↔ j = i0; Used terms: i