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Proof step 82 from proof int2bytes-len-ls-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 83:
n ≠ 0 ⊦ (n - 1) + 1 = n
Proof step 84:
i→n(8 * i0) ≠ 0, # int2bits(i) / 8 = i→n(i0), i→n(8 * i0) < # int2bits(i), i0 < n→i(n), 2 ^ (n→i(n) * 8 - 1) ≤ i, i→n(8 * i0) ≤ i→n(i0) * 8, 0 < i0, # int2bits(i) ≤ 1 + i→n(i0) * 8, 0 < i ⊦ n = 1, n = 0, i0 = 0, i = 0, # int2bits(i) % 8 = 0

Rule argument

seq: n ≠ 0 ⊦ (n - 1) + 1 = n subst: [n] → [i→n(8 * i0)] rotate: F spec: nat inst: name: num-02

Additional information

Used simplifier rules: ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ i * j = 0 ↔ i = 0 ∨ j = 0;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used terms: i→n(8 * i0)