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Proof step 15 from proof int2bytes-len-ls-01 (previous step)

n→i(# int2bits(i)) % 8 = 1, 0 < i ⊦ # int2bits(i) % 8 = 0, i = 0, n ≤ # int2bits(i) / 8 ↔ ¬ i < 2 ^ (n→i(n) * 8 - 1)

User applied rule insert elim lemma

And obtained the following new goals

Proof step 16:
n→i(# int2bits(i)) = i0 * 8 + j ∧ 0 ≤ j ∧ j < 8 ∧ 0 ≤ i0 ∧ 0 < 8 ∧ 0 ≤ n→i(# int2bits(i)), j = 1, 0 < i ⊦ # int2bits(i) % 8 = 0, i = 0, n ≤ # int2bits(i) / 8 ↔ ¬ i < 2 ^ (n→i(n) * 8 - 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] → [n→i(# int2bits(i)), 8, i0, j] rotate: T spec: int-div inst: name: div-elim-pospos

Additional information

Used simplifier rules: ⊦ 0 ≤ n→i(n);%⊦ 0 < j ∧ 0 ≤ i → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j ∧ 0 ≤ i0); (elim) Used terms: n→i(# int2bits(i)), 8, i0, j