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Proof step 24 from proof int2bytes-len-le-neg-01 (previous step)

int2bytes(i).first = i2b(~1), # int2bytes(i) < 2, 0 ≤ b2i(int2bytes(i).rest.first), 0 ≤ 2 ^ (8 * (1 + n→i(# int2bytes(i) - 1 - 1))) + i, 2 ^ (8 * (1 + n→i(# int2bytes(i) - 1 - 1)) - 1) + i < 0 ⊦ int2bytes(i).rest = [], 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 25:
⊦ n ≠ 1 → (n < 2 ↔ n = 0)
Proof step 26:
¬ # int2bytes(i) ≠ 1, int2bytes(i).first = i2b(~1), # int2bytes(i) < 2, 0 ≤ b2i(int2bytes(i).rest.first), 0 ≤ 2 ^ (8 * (1 + n→i(# int2bytes(i) - 1 - 1))) + i, 2 ^ (8 * (1 + n→i(# int2bytes(i) - 1 - 1)) - 1) + i < 0 ⊦ int2bytes(i).rest = [], n ≤ # int2bytes(i) ↔ ¬ 0 ≤ i + 2 ^ (8 * (n→i(n) - 1) - 1)

Rule argument

seq: ⊦ n ≠ 1 → (n < 2 ↔ n = 0) subst: [n] → [# int2bytes(i)] rotate: F spec: nat-basic1 inst: name: lstwo

Additional information

Used simplifier rules: int2bytes-empty: ⊦ int2bytes(i) ≠ [];% ⊦ # bytes = 0 ↔ bytes = []; Used terms: # int2bytes(i)