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Proof step 24 from proof int2bytes-len-le (previous step)

bytes2int(int2bytes(i).first ' + int2bytes(i).rest) < 2 ^ ((n→i(# int2bytes(i).rest) + 1) * 8 - 1), 2 ^ ((n→i(n) - 1) * 8) ≤ i, # int2bytes(i) < n, 2 ^ (8 * n→i(# int2bytes(i) - 1)) ≤ i, 0 ≤ i ⊦ int2bytes(i).first = i2b(0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ bytes ≠ [] → bytes.first ' + bytes.rest = bytes
Proof step 26:
int2bytes(i) ≠ [], bytes2int(int2bytes(i)) < 2 ^ ((n→i(# int2bytes(i).rest) + 1) * 8 - 1), 2 ^ ((n→i(n) - 1) * 8) ≤ i, # int2bytes(i) < n, 2 ^ (8 * n→i(# int2bytes(i) - 1)) ≤ i, 0 ≤ i ⊦ int2bytes(i).first = i2b(0)

Rule argument

seq: ⊦ bytes ≠ [] → bytes.first ' + bytes.rest = bytes subst: [bytes] → [int2bytes(i)] rotate: F spec: list inst: bytelist name: fr

Additional information

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