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Proof step 6 from proof uint2bits-succ (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ 1 < i → uint2bits(i) = uint2bits(i / 2) + (i % 2 = 1)
Proof step 8:
1 < j + 1, 0 < j, 0 ≤ j, ∀ j0. i→n(j0) < i→n(j) → 0 ≤ j0 → uint2bits(j0 + 1) = sgn(false ' + uint2bits(j0) +1) ⊦ j = 1, uint2bits((j + 1) / 2) + ((j + 1) % 2 = 1) = sgn(false ' + (uint2bits(j / 2) + (j % 2 = 1)')+1)

Rule argument

name: uint2bits-rec rotate: F subst: [i] → [j + 1]

Additional information

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