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Proof step 14 from proof bits2uint-inv-neg (previous step)

2 ^ n→i(# bits1) = bits2uint(bitsinvert(bits1)) + bits2uint(bits1) + 1, ∀ bits0. # bits0 < #(bits1 + true ') → true → bits0 = [] ∨ 2 ^ n→i(# bits0) = bits2uint(bitsinvert(bits0)) + bits2uint(bits0) + 1 ∨ bits0.first ⊦ 2 ^ (n→i(# bits1) + 1) = 2 * ((bits2uint(bitsinvert(bits1)) + bits2uint(bits1)) + 1), bits1 = [], bits1.first

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ 0 < i → j ^ i = j ^ i -1 * j

Rule argument

seq: ⊦ 0 < i → j ^ i = j ^ i -1 * j subst: [i, j] → [n→i(# bits1) + 1, 2] rotate: F spec: int-pot inst: name: Pot-pos

Additional information

Used simplifier rules: ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ (i + 1)-1 = i;% ⊦ 0 < i → (i * j = i * j0 ↔ j = j0);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ 0 ≤ n→i(n); Used terms: n→i(# bits1) + 1, 2