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Proof step 36 from proof int2bytes-len-le-neg-03 (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 37:
int2bytes(i) = by + bytes ∧ int2bytes(i) ≠ [], by = i2b(~1), bytes2int(i2b(~1) ' + bytes.first ' + bytes.rest) + 2 ^ (8 * (n→i(# bytes.rest) + 1) - 1) < 0, 0 ≤ 2 ^ ((n→i(# bytes.rest) + 1) * 8) + bytes2int(i2b(~1) ' + bytes.first ' + bytes.rest), 0 ≤ b2i(bytes.first) ⊦ i2b(~1) ' + bytes.first ' + bytes.rest = int2bytes(i), # int2bytes(i) ≤ n ↔ ¬ 2 ^ (8 * n→i(n) - 1) + i < 0

Rule argument

seq: ⊦ bytes ≠ [] → (by = bytes.first ∧ bytes0 = bytes.rest ↔ bytes = by + bytes0) subst: [bytes, by, bytes0] → [int2bytes(i), by, bytes] rotate: T spec: list-data inst: bytelist name: elim-1

Additional information

Used simplifier rules: int2bytes-empty: ⊦ int2bytes(i) ≠ [];%⊦ bytes ≠ [] → (by = bytes.first ∧ bytes0 = bytes.rest ↔ bytes = by + bytes0); (elim) Used terms: int2bytes(i), by, bytes