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Proof step 25 from proof int2bytes-len-le-neg (previous step)

0 ≤ 2 ^ (8 * n→i(# int2bytes(i)) - 1) + i, 8 * (n→i(n) - 1) + 1 < 8 * n→i(# int2bytes(i)), 8 * (n→i(# int2bytes(i)) - 1) + 1 < 8 * n→i(# int2bytes(i)), i + 2 ^ (8 * (n→i(n) - 1)) < 0, 2 ^ (8 * (n→i(# int2bytes(i)) - 1)) + i < 0, i < 0, 1 ≤ # int2bytes(i), # int2bytes(i) < n ⊦ n = 1, b2i(int2bytes(i).first) = ~1, int2bytes(i).first = i2b(~1)

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 26:
j * i + j0 < j * i0, abs(j0) < j ⊦ i ≤ i0
Proof step 27:
n→i(n) - 1 ≤ n→i(# int2bytes(i)), 0 ≤ 2 ^ (8 * n→i(# int2bytes(i)) - 1) + i, 8 * (n→i(n) - 1) + 1 < 8 * n→i(# int2bytes(i)), 8 * (n→i(# int2bytes(i)) - 1) + 1 < 8 * n→i(# int2bytes(i)), i + 2 ^ (8 * (n→i(n) - 1)) < 0, 2 ^ (8 * (n→i(# int2bytes(i)) - 1)) + i < 0, i < 0, 1 ≤ # int2bytes(i), # int2bytes(i) < n ⊦ n = 1, b2i(int2bytes(i).first) = ~1, int2bytes(i).first = i2b(~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; Used terms: 8, n→i(n) - 1, 1, n→i(# int2bytes(i))