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Proof step 7 from proof uint2uint-inv (previous step)

2 ^ n→i(# uint2bits(i / 2)) = bits2uint(bitsinvert(uint2bits(i / 2))) + i / 2 + 1, 0 < i, ∀ i0. i→n(i0) < i→n(i) → 0 < i0 → 2 ^ n→i(# uint2bits(i0)) = bits2uint(bitsinvert(uint2bits(i0))) + i0 + 1 ⊦ i = 1, 2 ^ (n→i(# uint2bits(i / 2)) + 1) = 1 + bits2uint(bitsinvert(uint2bits(i / 2)) + (i % 2 ≠ 1)') + i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j
Proof step 9:
0 ≤ n→i(# uint2bits(i / 2)), 2 ^ n→i(# uint2bits(i / 2)) = bits2uint(bitsinvert(uint2bits(i / 2))) + i / 2 + 1, 0 < i, ∀ i0. i→n(i0) < i→n(i) → 0 < i0 → 2 ^ n→i(# uint2bits(i0)) = bits2uint(bitsinvert(uint2bits(i0))) + i0 + 1 ⊦ i = 1, 2 ^ n→i(# uint2bits(i / 2)) * 2 = 1 + bits2uint(bitsinvert(uint2bits(i / 2)) + (i % 2 ≠ 1)') + i

Rule argument

seq: ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j subst: [i, j] → [n→i(# uint2bits(i / 2)), 2] rotate: F spec: int-pot inst: name: succ

Additional information

Used simplifier rules: ⊦ 0 ≤ n→i(n); Used terms: n→i(# uint2bits(i / 2)), 2