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Proof step 15 from proof band-65535-pos (previous step)

16 < # bytes * 8 - 1, 0 ≤ 2 ^ n→i(# bytes * 8 - 1) + bytes2int(bytes), bytes2int(bytes) < 2 ^ n→i(# bytes * 8 - 1), # bytes ≤ 2, 0 ≤ bytes2int(bytes), 65536 ≤ bytes2int(bytes), 0 < bytes2int(bytes) ⊦ bytes = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
n < n0 ⊦ m + n < n0 ↔ m < n0 - n
Proof step 17:
1 < # bytes * 8, 16 + 1 < # bytes * 8, 0 ≤ 2 ^ n→i(# bytes * 8 - 1) + bytes2int(bytes), bytes2int(bytes) < 2 ^ n→i(# bytes * 8 - 1), # bytes ≤ 2, 0 ≤ bytes2int(bytes), 65536 ≤ bytes2int(bytes), 0 < bytes2int(bytes) ⊦ bytes = []

Rule argument

seq: n < n0 ⊦ m + (* n) < (* n0) ↔ m < n0 - n subst: [n, n0, m] → [1, # bytes * 8, 16] rotate: T spec: nat inst: name: l-num-05

Additional information

Used simplifier rules: ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1);% ⊦ m0 * m = 1 ↔ m0 = 1 ∧ m = 1;% ⊦ m0 * m * n = (m0 * m) * n;% ⊦ m * n = n * m;% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ m < n → n ≠ 0; (forward) Used terms: 1, # bytes * 8, 16