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Proof step 22 from proof int2bytes-len-le-neg (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ bytes ≠ [] → # bytes.rest = (# bytes)-1
Proof step 24:
int2bytes(i) ≠ [], # int2bytes(i) < n, 1 ≤ # int2bytes(i), i < 0, 2 ^ (8 * (n→i(# int2bytes(i)) - 1)) + i < 0, i + 2 ^ (8 * (n→i(n) - 1)) < 0, 0 ≤ i + 2 ^ ((n→i((# int2bytes(i))-1) + 1) * 8 - 1), 8 * (n→i(# int2bytes(i)) - 1) + 1 < (n→i((# int2bytes(i))-1) + 1) * 8, 8 * (n→i(n) - 1) + 1 < (n→i((# int2bytes(i))-1) + 1) * 8 ⊦ int2bytes(i).first = i2b(~1), b2i(int2bytes(i).first) = ~1, n = 1

Rule argument

seq: ⊦ bytes ≠ [] → # bytes.rest = (# bytes)-1 subst: [bytes] → [int2bytes(i)] rotate: F spec: list-data inst: bytelist name: length-rest

Additional information

Used simplifier rules: int2bytes-empty: ⊦ int2bytes(i) ≠ []; Used terms: int2bytes(i)