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Proof step 13 from proof int2bytes-len-le-neg-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ bytes ≠ [] → # bytes.rest = (# bytes)-1
Proof step 15:
¬ int2bytes(i).rest ≠ [], int2bytes(i).first = i2b(~1), 2 ^ (8 * (n→i(# int2bytes(i).rest.rest) + 1) - 1) + i < 0, 0 ≤ i + 2 ^ ((n→i(# int2bytes(i).rest.rest) + 1) * 8), 0 ≤ b2i(int2bytes(i).rest.first) ⊦ n ≤ # int2bytes(i) ↔ ¬ 0 ≤ i + 2 ^ (8 * (n→i(n) - 1) - 1)
Proof step 17:
int2bytes(i).rest ≠ [], int2bytes(i).first = i2b(~1), 2 ^ (8 * (n→i((# int2bytes(i).rest)-1) + 1) - 1) + i < 0, 0 ≤ i + 2 ^ ((n→i((# int2bytes(i).rest)-1) + 1) * 8), 0 ≤ b2i(int2bytes(i).rest.first) ⊦ n ≤ # int2bytes(i) ↔ ¬ 0 ≤ i + 2 ^ (8 * (n→i(n) - 1) - 1)

Rule argument

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

Additional information

Used terms: int2bytes(i).rest