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Proof step 201 from proof fix-bits2bytes-01 (previous step)

# bits = n0 + m * 8, n - 1 - m = 0, m < n, # bits2bytes(bits) < n, bits.first, n0 < 8 ⊦ n0 = 0, n * 8 = # bits, bits = [], mklist(i2b(~1), n - # bits2bytes(bits)) + bits2bytes(bits) = bits2bytes(mklist(true, 8 - n0) + bits)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 202:
⊦ m ≤ n → (n - m = 0 ↔ n = m)
Proof step 203:
m ≤ n - 1, # bits = n0 + m * 8, n - 1 = m, m < n, # bits2bytes(bits) < n, bits.first, n0 < 8 ⊦ n0 = 0, n * 8 = # bits, bits = [], mklist(i2b(~1), n - # bits2bytes(bits)) + bits2bytes(bits) = bits2bytes(mklist(true, 8 - n0) + bits)

Rule argument

seq: ⊦ m ≤ n → (n - m = 0 ↔ n = m) subst: [m, n] → [m, n - 1] rotate: F spec: nat inst: name: zero-02

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0;% ⊦ m < 1 ↔ m = 0;% ⊦ ¬ m ≤ n ↔ n < m;%n0 ≤ n ⊦ m ≤ n - n0 ↔ m + n0 ≤ n;% ⊦ m + 1 ≤ n ↔ m < n;% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ m < n → (n ≤ m ↔ false);% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: m, n - 1