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Proof step 153 from proof uint2bits-restsgn (previous step)

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

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] → [i - 1, 2] rotate: T spec: int-pot inst: name: succ

Additional information

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