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Proof step 2 from proof int2bytes-len-eq-pos (previous step)

int2bytes(i).first = i2b(0), 0 ≤ i ⊦ # int2bytes(i) = n ↔ ¬ i < 2 ^ ((n→i(n) - 1) * 8 - 1) ∧ ¬ 2 ^ ((n→i(n) - 1) * 8) ≤ i ∧ n ≠ 0

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
⊦ b2i(by) < 0 → bytes2int(i2b(0) ' + by ' + bytes) < 2 ^ ((n→i(# bytes) + 1) * 8)
Proof step 4:
b2i(int2bytes(i).rest.first) < 0 → bytes2int(i2b(0) ' + int2bytes(i).rest.first ' + int2bytes(i).rest.rest) < 2 ^ ((n→i(# int2bytes(i).rest.rest) + 1) * 8), int2bytes(i).first = i2b(0), 0 ≤ i ⊦ # int2bytes(i) = n ↔ ¬ i < 2 ^ ((n→i(n) - 1) * 8 - 1) ∧ ¬ 2 ^ ((n→i(n) - 1) * 8) ≤ i ∧ n ≠ 0

Rule argument

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

Additional information

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