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Proof step 17 from proof add-eq2pot (previous step)

2 ^ i1 = i2 + 1, j = 2 ^ i0 * i2, 0 ≤ i0, 0 ≤ j, 0 ≤ i1 + i0, 0 ≤ i1 ⊦ 2 ^ (i1 + i0) = 2 ^ i0 + j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
2 ^ i1 = i2 + 1, 0 ≤ i1 + i0, 0 ≤ i0, 0 ≤ i1, 0 ≤ 2 ^ i0 * i2 ⊦ 2 ^ (i1 + i0) = 2 ^ i0 * (i2 + 1)

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult% ⊦ i * j + i = i * (j + 1); (s)