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Proof step 30 from proof int2bits-2pot-04 (previous step)

0 ≤ j * 2 ^ i, 0 ≤ i ⊦ j = 0, uint2bits(j * 2 ^ i) = int2bits(j) + mklist(false, i→n(i))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
0 ≤ i, 0 < j ⊦ uint2bits(j * 2 ^ i) = uint2bits(j) + mklist(false, i→n(i))
Proof step 32:
0 ≤ i ∧ 0 < j, 0 ≤ j * 2 ^ i, 0 ≤ i ⊦ j = 0, uint2bits(j) + mklist(false, i→n(i)) = int2bits(j) + mklist(false, i→n(i))

Rule argument

name: uint2bits-2pot-01 rotate: F subst: [i, j] → [i, j]

Additional information

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