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Proof step 58 from proof bits2int-pos (previous step)

0 < bits2uint(firstn(# bits0 % 8, bits0)), ~128 ≤ bits2uint(firstn(# bits0 % 8, bits0)), 127 < bits2uint(firstn(# bits0 % 8, bits0)), bits2int(fillsgn(8, int2bits(b2i(i2b(bits2uint(firstn(# bits0 % 8, bits0)))))) + bytes2bits(bits2bytes(restn(# bits0 % 8, bits0)))) < 0, # bits0 % 8 < # bits0, # bits0 % 8 ≤ 7, 7 < # bits0 ⊦ (# bits0 + 1) % 8 = 0, bits0 = []

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

seq: ⊦ # bits ≤ n → bits2uint(bits) < 2 ^ n→i(n) subst: [bits, n] → [firstn(# bits0 % 8, bits0), 7] rotate: F spec: int2bits inst: name: bits2uint-ls

Additional information

Used simplifier rules: ⊦ # firstn(n, bits) = n;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m ≤ n → (n < m ↔ false);%i + 1 = i0 ⊦ j < (* i0) → ¬ (* i) < j; Used terms: firstn(# bits0 % 8, bits0), 7