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Proof step 9 from proof uint2bits-2pot-neg-mone (previous step)

0 < 2 * 2 ^ (i - 1) * j - 1 ∧ 2 * 2 ^ (i - 1) * j - 1 ≠ 1, 0 < i, 0 < j, ∀ j, i0. i→n(i0) < i→n(i) → 0 < j ∧ 0 < i0 → uint2bits(j * 2 ^ i0 - 1) = uint2bits(j - 1) + mklist(true, i→n(i0)) ⊦ uint2bits((2 * 2 ^ (i - 1) * j - 1) / 2) + ((2 * 2 ^ (i - 1) * j - 1) % 2 = 1) = uint2bits(j - 1) + mklist(true, i→n(i))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
0 < j, 0 < i, ∀ j, i0. i→n(i0) < i→n(i) → 0 < j ∧ 0 < i0 → uint2bits(j * 2 ^ i0 - 1) = uint2bits(j - 1) + mklist(true, i→n(i0)) ⊦ uint2bits((2 * 2 ^ (i - 1) * j - 1) / 2) + ((2 * 2 ^ (i - 1) * j - 1) % 2 ≠ 0)' = uint2bits(j - 1) + mklist(true, i→n(i)), 2 ^ (i - 1) * j = 1

Rule argument

Additional information

Used simplifier rules: ⊦ 1 ≤ i ↔ 0 < i;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ 0 < i ∧ 0 ≤ j → ((* j) < (* i) * i0 ↔ j / i < i0);% ⊦ i < j - i0 ↔ i + i0 < j;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = i ↔ i = 0 ∨ j = 1;% ⊦ i - j = i0 ↔ i = i0 + j;% ⊦ bits + boolvar = bits + boolvar ';% ⊦ 0 < i → (i % 2 ≠ 1 ↔ i % 2 = 0);