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Proof step 164 from proof uint2bits-restsgn (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

seq: j * i + j0 < j * i0, abs(j0) < j ⊦ i ≤ i0 subst: [j, i, j0, i0] → [2, i0, 1, 2 ^ i] rotate: F spec: int-mult inst: name: modlsp-02

Additional information

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