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Proof step 2 from proof int2bits-2pot-neg-mone (previous step)

0 < j, 0 < i ⊦ int2bits(j * 2 ^ i - 1) = int2bits(j - 1) + mklist(true, 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 - 1, 0 < j, 0 < i ⊦ uint2bits(j * 2 ^ i - 1) = int2bits(j - 1) + mklist(true, i→n(i))

Rule argument

name: int2bits-pos-num rotate: F subst: [i] → [j * 2 ^ i - 1]

Additional information

Used simplifier rules: ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used terms: j * 2 ^ i - 1