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Proof step 16 from proof uint2bits-falsein-01 (previous step)

false ∈ uint2bits(j / 2).rest ↔ (∀ i. 2 ^ i ≠ j / 2 + 1), 0 < j, ∀ j0. i→n(j0) < i→n(j) → 0 < j0 → (false ∈ uint2bits(j0).rest ↔ (∀ i. 2 ^ i ≠ j0 + 1)) ⊦ j % 2 = 0, j = 1, j % 2 ≠ 1 ∨ false ∈ uint2bits(j / 2).rest ↔ (∀ i. 2 ^ i ≠ j + 1)

User applied rule insert elim lemma

And obtained the following new goals

Proof step 17:
j = i0 * 2 + j1 ∧ 0 ≤ j1 ∧ j1 < 2 ∧ 0 ≤ i0 ∧ 0 < 2 ∧ 0 ≤ j, false ∈ uint2bits(i0).rest ↔ (∀ i. 2 ^ i ≠ i0 + 1), 0 < j, ∀ j0. i→n(j0) < i→n(j) → 0 < j0 → (false ∈ uint2bits(j0).rest ↔ (∀ i. 2 ^ i ≠ j0 + 1)) ⊦ j1 = 0, j = 1, j1 ≠ 1 ∨ false ∈ uint2bits(i0).rest ↔ (∀ i. 2 ^ i ≠ j + 1)

Rule argument

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

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 ∧ 0 ≤ i0); (elim) Used terms: j, 2, i0, j1