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Proof step 11 from proof int2bytes-rec-neg-05 (previous step)

# int2bytes(j) = i→n(i) + 1, 0 < i, j + 2 ^ (i * 8 - 1) < 0, 0 < j + 2 ^ (i * 8), 0 < 2 ^ (i * 8) + j, j < 0 ⊦ j = 0, bits2bytes(int2bits(j)) = i2b(~1) ' + fix(i→n(i) + 1, int2bytes(j)).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ # bytes ≥ n → fix(n, bytes) = lastn(n, bytes)
Proof step 13:
# int2bytes(j) ≥ i→n(i) + 1, # int2bytes(j) = i→n(i) + 1, 0 < i, j + 2 ^ (i * 8 - 1) < 0, 0 < j + 2 ^ (i * 8), 0 < 2 ^ (i * 8) + j, j < 0 ⊦ j = 0, bits2bytes(int2bits(j)) = i2b(~1) ' + lastn(i→n(i) + 1, int2bytes(j)).rest

Rule argument

name: fix-longer rotate: F subst: [bytes, n] → [int2bytes(j), i→n(i) + 1]

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ n ≥ m ↔ m ≤ n;% ⊦ m + 1 ≤ n ↔ m < n;% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ m = n + 1 → ¬ m ≤ n; Used terms: int2bytes(j), i→n(i) + 1