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Proof step 65 from proof uint2bits-restsgn (previous step)

0 ≤ i0 ∧ 0 ≤ n→i(# bits0), 2 ^ i0 = i + 1, 2 ^ n→i(# bits0) * (i + 1) = 2 ^ i0 * 2 ^ n→i(# bits0), i * 2 ^ n→i(# bits0) < 2 * (i * 2 ^ n→i(# bits0) * 2 + 1), 0 ≤ 2 ^ i0 * 2 ^ n→i(# bits0), 0 < i * 2 ^ n→i(# bits0), 1 < i0 + n→i(# bits0), 0 ≤ i * 2 ^ n→i(# bits0), 0 ≤ 2 ^ n→i(# bits0) * i, i * 2 ^ n→i(# bits0) * 2 + 1 < 2 ^ i0 * 2 ^ n→i(# bits0), 2 ^ i0 * 2 ^ n→i(# bits0) < 2 * (i * 2 ^ n→i(# bits0) * 2 + 1), 2 ^ n→i(# bits0) * i < 2 ^ i0 * 2 ^ n→i(# bits0), i * 2 ^ n→i(# bits0) < 2 ^ i0 * 2 ^ n→i(# bits0), i * 2 ^ n→i(# bits0) + 1 < 2 * (i * 2 ^ n→i(# bits0) * 2 + 1), 0 ≤ i0, 1 < 2 ^ i0 * 2 ^ n→i(# bits0), 0 < i0 + n→i(# bits0), 0 ≤ i0 + n→i(# bits0), 0 < 2 ^ i0 * 2 ^ n→i(# bits0), ∀ j0, i1. i→n(j0) < i→n(2 * (i * 2 ^ n→i(# bits0) * 2 + 1) + 0) → 0 < i1 ∧ 0 ≤ j0 ∧ 2 ^ i1 < j0 ∧ j0 < 2 * 2 ^ i1 → sgn(uint2bits(2 ^ (i1 + 2) - j0).rest) = uint2bits(2 ^ (i1 + 2) - j0).rest ⊦ 4 * 2 ^ i0 * 2 ^ n→i(# bits0) = 1 + 2 * (i * 2 ^ n→i(# bits0) * 2 + 1), bits0 = [], false ∈ bits0

User applied rule insert equation

And obtained the following new goals

Rule argument

pos: left 2 flags:

Additional information