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Proof step 8 from proof uint2bits-2pot (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
0 < 2 ^ (i1 + 1), ~1 ≤ i1, ∀ i0. i→n(i0) < i→n(i1 + 1) → 0 ≤ i0 → uint2bits(2 ^ i0) = false ' + true ' + mklist(false, i→n(i0)) ⊦ 2 ^ (i1 + 1) = 1, uint2bits(2 ^ i1) + (2 ^ (i1 + 1) % 2 = 1)' = false ' + true ' + mklist(false, i→n(i1 + 1))

Rule argument

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;