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Proof step 48 from proof int2bytes-len-ls-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: j ≤ i, 0 ≤ j ⊦ i→n(i - j) = i→n(i) - i→n(j) subst: [j, i] → [1, 8 * i0] rotate: F spec: intnat inst: name: sub

Additional information

Used simplifier rules: ⊦ 1 ≤ i ↔ 0 < i;% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i < j → ¬ j < i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used terms: 1, 8 * i0