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Proof step 13 from proof uint2bits-2pot-01 (previous step)

i = i1 + 1, 0 ≤ j, 0 < i, 0 < j, 0 ≤ i, 0 < 2 ^ i, ∀ i0, j. i→n(i0) < i→n(i) → 0 ≤ i0 ∧ 0 < j → uint2bits(j * 2 ^ i0) = uint2bits(j) + mklist(false, i→n(i0)) ⊦ j * 2 ^ i = 1, uint2bits(j * 2 ^ i1) + false ' = uint2bits(j) + mklist(false, i→n(i))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
0 < 2 ^ (i1 + 1), 0 ≤ j, 0 ≤ i1, 0 < j, ~1 ≤ i1, ∀ i0, j. i→n(i0) < i→n(i1 + 1) → 0 ≤ i0 ∧ 0 < j → uint2bits(j * 2 ^ i0) = uint2bits(j) + mklist(false, i→n(i0)) ⊦ j * 2 ^ (i1 + 1) = 1, uint2bits(j * 2 ^ i1) + false ' = uint2bits(j) + false ' + mklist(false, i→n(i1))

Rule argument

Additional information

Used simplifier rules: ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ mklist(boolvar, n) + boolvar ' = boolvar ' + mklist(boolvar, n);% ⊦ mklist(boolvar, 1) = boolvar ';% ⊦ mklist(boolvar, m + n) = mklist(boolvar, m) + mklist(boolvar, n);% ⊦ 0 < i + 1 → i→n(i + 1) = i→n(i) + 1;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;