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

j % 2 = 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) +1 + false ')

User applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
j = i * 2 + j1 ∧ 0 ≤ j1 ∧ j1 < 2 ∧ 0 < 2, j1 = 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(i) +1 + false ')

Rule argument

seq: ⊦ 0 < j ∧ 0 ≤ i → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j) subst: [i, j, i0, j0] → [j, 2, i, j1] rotate: T spec: int-div inst: name: div-elim-pos

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i;%⊦ 0 < j ∧ 0 ≤ i → (i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j); (elim) Used terms: j, 2, i, j1