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Proof step 159 from proof uint2bits-restsgn (previous step)

~1 ≤ i0, false ∈ uint2bits(2 * 2 ^ i - i0 + 1).rest, i0 < 2 * 2 ^ i, 0 < i0, 0 ≤ i0, 0 ≤ i, i0 * 2 + 1 < 4 * 2 ^ i, 2 ^ i ≤ i0 * 2, i0 < 2 ^ i, 1 < 2 ^ i, 0 < 2 ^ i, 0 ≤ 2 ^ i, 0 < i, ∀ j0, i. i→n(j0) < i→n(i0 * 2 + 1) → 0 < i ∧ 0 ≤ j0 ∧ 2 ^ i < j0 ∧ j0 < 2 * 2 ^ i → sgn(uint2bits(2 ^ (i + 2) - j0).rest) = uint2bits(2 ^ (i + 2) - j0).rest ⊦ i0 = 1, sgn(uint2bits(2 * 2 ^ i - i0 + 1).rest) = uint2bits(2 * 2 ^ i - i0 + 1).rest, 4 * 2 ^ i = 2 * (i0 + 1), i = 1, 2 ^ i ≠ i0 + 1 ∧ ¬ i0 < 2 ^ (i - 1)

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

seq: j * i ≤ j * i0 + j0, 0 ≤ j0, j0 < j ⊦ i ≤ i0 subst: [j, i, i0, j0] → [2, 2 ^ (i - 1), i0, 1] rotate: F spec: int-mult inst: name: modlep

Additional information

Used terms: 2, 2 ^ (i - 1), i0, 1