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Proof step 18 from proof add-eq2pot (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: pot-dist-pos seq: ⊦ 0 ≤ j ∧ 0 ≤ j0 → i ^ (j + j0) = i ^ j * i ^ j0 subst: [j0, j, i] → [i0, i1, 2] flags: <all paths>

Additional information

Used simplifier rules: neq-not-zero: ⊦ i * j ≠ i * j0 → i ≠ 0; (forward) from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; (s) Used terms: i0, i1, 2