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Proof step 20 from proof int2bytes-len-ls-01 (previous step)

# int2bits(i) = i→n(i0 * 8 + 1), 0 < i, 0 ≤ i0 ⊦ # int2bits(i) % 8 = 0, i = 0, n ≤ # int2bits(i) / 8 ↔ ¬ i < 2 ^ (n→i(n) * 8 - 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 < i → i→n(i) = i→n(i - 1) + 1 subst: [i] → [i0 * 8 + 1] rotate: F spec: intnat inst: name: Int2nat-pos

Additional information

Used simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ ¬ i < j ↔ j ≤ i; Used terms: i0 * 8 + 1