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Proof step 51 from proof int2bytes-len-ls-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 52:
⊦ 0 ≤ i ∧ 0 ≤ j → i→n(i * j) = i→n(i) * i→n(j)
Proof step 53:
0 ≤ 8 ∧ 0 ≤ i0, # int2bits(i) / 8 = i→n(i0), 1 + (i→n(8) * i→n(i0) - 1) < # int2bits(i), i < 2 ^ (n→i(n) * 8 - 1), n→i(n) ≤ i0, i→n(8) * i→n(i0) ≤ i→n(i0) * 8, 0 < i0, # int2bits(i) ≤ 1 + i→n(i0) * 8, 0 < i ⊦ n = 0, i0 = 0, i = 0, # int2bits(i) % 8 = 0

Rule argument

seq: ⊦ 0 ≤ i ∧ 0 ≤ j → i→n(i * j) = i→n(i) * i→n(j) subst: [j, i] → [i0, 8] rotate: F spec: intnat inst: name: i2n-mult

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i; Used terms: i0, 8