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Proof step 2 from proof int2bits-len-pos-02 (previous step)

0 < j, 0 ≤ i ⊦ # int2bits(j * 2 ^ i) = # int2bits(j) + i→n(i)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 0 ≤ i → int2bits(i) = uint2bits(i)
Proof step 4:
0 ≤ j * 2 ^ i, 0 < j, 0 ≤ i ⊦ # uint2bits(j * 2 ^ i) = # int2bits(j) + i→n(i)

Rule argument

name: int2bits-pos rotate: F subst: [i] → [j * 2 ^ i]

Additional information

Used simplifier rules: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ ¬ 2 ^ i < 0;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used terms: j * 2 ^ i