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Proof step 12 from proof int2bytes-len-ls-01 (previous step)

n→i(# int2bits(i)) % 8 = 1, # int2bits(i) % 8 = 0, 0 < i ⊦ n < # int2bytes(i) ↔ ¬ i < 2 ^ (n→i(n) * 8 - 1), i = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ n ≠ 0 → (m % n = 0 ↔ (∃ n0. m = n0 * n))

Rule argument

seq: ⊦ n ≠ 0 → (m % n = 0 ↔ (∃ n0. m = n0 * n)) subst: [n, m] → [8, # int2bits(i)] rotate: F spec: nat-div inst: name: modex

Additional information

Used simplifier rules: ⊦ n→i(m * n) = n→i(m) * n→i(n);% ⊦ m0 * m * n = (m0 * m) * n;% ⊦ m * n = n * m;%i0 % j = 0, j ≠ 0 ⊦ (i * (* i0)) % (* j) = 0;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used terms: 8, # int2bits(i)