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Proof step 85 from proof uint2bits-restsgn (previous step)

1 < 2 ^ (i1 + 1), 2 < 2 ^ (i1 + 1), 1 < 2 ^ i1, 0 < i0, 0 ≤ i0, i0 < 2 ^ (i1 + 1), 2 ^ (i1 + 1) < i0 * 2, i0 * 2 < 4 * 2 ^ (i1 + 1), (¬ uint2bits(2 * 2 ^ (i1 + 1) - i0).rest.first) ∈ uint2bits(2 * 2 ^ (i1 + 1) - i0).rest.rest, i0 ≤ 2 ^ i1, ~1 ≤ i1, 0 < i1, 0 < 2 ^ i1, 0 < 2 ^ (i1 + 1), 0 ≤ 2 ^ i1, 0 ≤ 2 ^ (i1 + 1), 1 < i0, ∀ j0, i. i→n(j0) < i→n(i0 * 2 + 0) → 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(2 * 2 ^ (i1 + 1) - i0).rest) = uint2bits(2 * 2 ^ (i1 + 1) - i0).rest, 4 * 2 ^ (i1 + 1) = 1 + i0 * 2, uint2bits(2 * 2 ^ (i1 + 1) - i0).rest = [], 0 = i1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j subst: [i, j] → [i1, 2] rotate: F spec: int-pot inst: name: succ

Additional information

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