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Proof step 4 from proof bytes2int-range (previous step)

⊦ bytes = [], ¬ 2 ^ n→i(# bytes * 8 - 1) + bits2int(bytes2bits(bytes)) < 0 ∧ ¬ 2 ^ n→i(# bytes * 8 - 1) ≤ bits2int(bytes2bits(bytes))

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 5:
bits ≠ [] ⊦ ~(2 ^ n→i(# bits - 1)) ≤ bits2int(bits) ∧ bits2int(bits) < 2 ^ n→i(# bits - 1)

Rule argument

seq: bits ≠ [] ⊦ ~(2 ^ n→i(# bits - 1)) ≤ bits2int(bits) ∧ bits2int(bits) < 2 ^ n→i(# bits - 1) subst: [bits] → [bytes2bits(bytes)] rotate: F spec: int2bits inst: name: bits2int-range

Additional information

Used simplifier rules: bytes2bits-empty-01: ⊦ bytes2bits(bytes) = [] ↔ bytes = [];%bytes2bits-length: ⊦ # bytes2bits(bytes) = i→n(8) * # bytes;% ⊦ ~ i ≤ j ↔ 0 ≤ i + j;% ⊦ m * n = n * m;% ⊦ i + j = j + i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: bytes2bits(bytes)