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Proof step 11 from proof uint2bits-pred (previous step)

j % 2 = 0, 1 < j, 0 < j, 0 ≤ j, ∀ j0. i→n(j0) < i→n(j) → 0 < j0 → uint2bits(j0 - 1) = sgn(bitsinvert(bitsinvert(uint2bits(j0)) +1)) ⊦ uint2bits(j / 2 - 1) + ((j - 1) % 2 = 1)' = sgn(bitsinvert(bitsinvert(uint2bits(j / 2)) +1) + true '), j = 2

User applied rule apply induction

And obtained the following new goals

Rule argument

subst: [j0] → [j / 2]

Additional information

Used simplifier rules: ⊦ 1 < i → ¬ i / 2 ≤ 0;% ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j);%j ≠ 0 ⊦ abs(i / j) = abs(i) / abs(j);% ⊦ 1 < i → abs(i) = i;% ⊦ 0 < j ∧ 0 ≤ i → (i / (* j) < j0 ↔ i < j * j0);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 0 < i → (i * j ≤ i ↔ j ≤ 1);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used terms: j / 2