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Proof step 32 from proof bits2bytes-mklist-02 (previous step)

bits2bytes(mklist(true, n0 * 8 - 8)) = mklist(i2b(~1), (n0 * 8 - 8) / 8), 8 < n0 * 8, ∀ n1. n1 < n0 * 8 → n1 % 8 = 0 → n1 = 0 ∨ bits2bytes(mklist(true, n1)) = mklist(i2b(~1), n1 / 8) ⊦ n0 = 0, i2b(~1) ' + mklist(i2b(~1), (n0 * 8 - 8) / 8) = mklist(i2b(~1), n0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 33:
⊦ m ≠ 0 → m * n - n = (m - 1) * n
Proof step 34:
n0 ≠ 0, bits2bytes(mklist(true, (n0 - 1) * 8)) = mklist(i2b(~1), ((n0 - 1) * 8) / 8), 8 < n0 * 8, ∀ n1. n1 < n0 * 8 → n1 % 8 = 0 → n1 = 0 ∨ bits2bytes(mklist(true, n1)) = mklist(i2b(~1), n1 / 8) ⊦ n0 = 0, i2b(~1) ' + mklist(i2b(~1), ((n0 - 1) * 8) / 8) = mklist(i2b(~1), n0)

Rule argument

seq: ⊦ m ≠ 0 → m * n - n = (m - 1) * n subst: [n, m] → [8, n0] rotate: F spec: nat-mult inst: name: dist-sub-01

Additional information

Used terms: 8, n0