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Proof step 57 from proof int2bytes-len-eq-pos (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 58:
⊦ bytes ≠ [] → # bytes.rest = (# bytes)-1
Proof step 59:
int2bytes(i) ≠ [], int2bytes(i).first = i2b(0), 1 + ((# int2bytes(i))-1 - 1) < n, n→i(n) ≤ 1 + n→i(# int2bytes(i) - 1), 2 ^ (8 * (1 + n→i((# int2bytes(i))-1 - 1)) - 1) ≤ i, 0 ≤ i, 2 ≤ # int2bytes(i), i < 2 ^ (8 * n→i(# int2bytes(i) - 1)), i < 2 ^ ((n→i(n) - 1) * 8), 2 ^ ((n→i(n) - 1) * 8 - 1) ≤ i ⊦ # int2bytes(i) = n, int2bytes(i).rest = []

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)