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Proof step 5 from proof int2bytes-len-le-neg-01 (previous step)

int2bytes(i).first = i2b(~1), ¬ b2i(int2bytes(i).rest.first) < 0 → bytes2int(i2b(~1) ' + int2bytes(i).rest.first ' + int2bytes(i).rest.rest) + 2 ^ (8 * (n→i(# int2bytes(i).rest.rest) + 1) - 1) < 0 ⊦ n ≤ # int2bytes(i) ↔ ¬ 0 ≤ i + 2 ^ (8 * (n→i(n) - 1) - 1)

User applied rule insert lemma

And obtained the following new goals

Proof step 6:
⊦ 0 ≤ b2i(by) → ~(2 ^ ((n→i(# bytes) + 1) * 8)) ≤ bytes2int(i2b(~1) ' + by ' + bytes)
Proof step 7:
0 ≤ b2i(int2bytes(i).rest.first) → ~(2 ^ ((n→i(# int2bytes(i).rest.rest) + 1) * 8)) ≤ bytes2int(i2b(~1) ' + int2bytes(i).rest.first ' + int2bytes(i).rest.rest), int2bytes(i).first = i2b(~1), ¬ b2i(int2bytes(i).rest.first) < 0 → bytes2int(i2b(~1) ' + int2bytes(i).rest.first ' + int2bytes(i).rest.rest) + 2 ^ (8 * (n→i(# int2bytes(i).rest.rest) + 1) - 1) < 0 ⊦ n ≤ # int2bytes(i) ↔ ¬ 0 ≤ i + 2 ^ (8 * (n→i(n) - 1) - 1)

Rule argument

name: bytes2int-size-05 subst: [by, bytes] → [int2bytes(i).rest.first, int2bytes(i).rest.rest]

Additional information

Used terms: int2bytes(i).rest.first, int2bytes(i).rest.rest