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Proof step 33 from proof int2bytes-len-le (previous step)

i < 2 ^ (8 * n→i(# int2bytes(i)) - 1), 0 ≤ i, 2 ^ (8 * (n→i(# int2bytes(i)) - 1)) ≤ i, # int2bytes(i) < n, 2 ^ ((n→i(n) - 1) * 8) ≤ i, 1 + 8 * (n→i(# int2bytes(i)) - 1) < 8 * n→i(# int2bytes(i)), (n→i(n) - 1) * 8 + 1 < 8 * n→i(# int2bytes(i)), 1 ≤ # int2bytes(i) ⊦ int2bytes(i).first = i2b(0), n = 1

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 34:
j * i + j0 < j * i0, abs(j0) < j ⊦ i ≤ i0
Proof step 35:
n→i(n) - 1 ≤ n→i(# int2bytes(i)), i < 2 ^ (8 * n→i(# int2bytes(i)) - 1), 0 ≤ i, 2 ^ (8 * (n→i(# int2bytes(i)) - 1)) ≤ i, # int2bytes(i) < n, 2 ^ ((n→i(n) - 1) * 8) ≤ i, 1 + 8 * (n→i(# int2bytes(i)) - 1) < 8 * n→i(# int2bytes(i)), (n→i(n) - 1) * 8 + 1 < 8 * n→i(# int2bytes(i)), 1 ≤ # int2bytes(i) ⊦ int2bytes(i).first = i2b(0), n = 1

Rule argument

seq: j * i + j0 < j * i0, abs(j0) < j ⊦ i ≤ i0 subst: [j, i, j0, i0] → [8, n→i(n) - 1, 1, n→i(# int2bytes(i))] rotate: F spec: int-mult inst: name: modlsp-02

Additional information

Used simplifier rules: ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i * j = j * i;% ⊦ i + j < i0 ∧ ¬ j < j0 → i + j0 < i0; Used terms: 8, n→i(n) - 1, 1, n→i(# int2bytes(i))