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Proof step 16 from proof int2uint-neg (previous step)

j + 2 ^ n→i(# bits) = 0, j < 2 ^ n→i(# bits), 0 < 2 ^ n→i(# bits), j ≤ 0, j < 0, j + 1 < 2 ^ n→i(# bits) ⊦ 2 ^ n→i(# bits) = 2 ^ (1 + n→i(# bits)) + j, true ∈ bits

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j

Rule argument

seq: ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j subst: [i, j] → [n→i(# bits), 2] rotate: F spec: int-pot inst: name: succ

Additional information

Used simplifier rules: ⊦ 0 < i → (0 < i ^ j ↔ i = 1 ∨ 0 ≤ j);% ⊦ i = (* i1) * i + j0 ↔ 0 = (i1 - 1) * i + j0;% ⊦ 1 * i = i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ 0 ≤ n→i(n);% ⊦ i + j = j + i; Used terms: n→i(# bits), 2