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Proof step 81 from proof bits2int-pos (previous step)

0 < bits2uint(bits0), b2i(i2b(bits2uint(bits0))) < 0, 127 < bits2uint(bits0), # bits0 ≤ 7 ⊦

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 82:
⊦ # bits ≤ n → bits2uint(bits) < 2 ^ n→i(n)

Rule argument

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

Additional information

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