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Proof step 14 from proof uint2bits-mod2pot (previous step)

0 < j, 2 ^ i < j, 0 < i, ∀ j0, i. i→n(j0) < i→n(j) → 0 ≤ i ∧ 2 ^ i < j0 → uint2bits(j0 % 2 ^ i) = sgn(false ' + lastn(i→n(i), uint2bits(j0).rest)) ⊦ 0 ≤ i - 1 ∧ 2 ^ (i - 1) < j / 2, j = 1, uint2bits(j % 2 ^ i) = sgn(false ' + lastn(i→n(i) - 1, uint2bits(j / 2).rest) + (j % 2 = 1)'), i = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
0 < j, 2 ^ i < j, 0 < i, j / 2 ≤ 2 ^ (i - 1), ∀ j0, i. i→n(j0) < i→n(j) → 0 ≤ i ∧ 2 ^ i < j0 → uint2bits(j0 % 2 ^ i) = sgn(false ' + lastn(i→n(i), uint2bits(j0).rest)) ⊦ j = 1, uint2bits(j % 2 ^ i) = sgn(false ' + lastn(i→n(i) - 1, uint2bits(j / 2).rest) + (j % 2 = 1)'), i = 0

Rule argument

Additional information

Used simplifier rules: ⊦ i < j → ¬ j < i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;