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Proof step 4 from proof bits2uint-nle-01 (previous step)

bits2uint(bits) < 2 ^ n→i(# bits), # bits ≤ n, 2 ^ n→i(n) ≤ bits2uint(bits), 2 ^ n→i(n) < 2 ^ n→i(# bits) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 0 ≤ j → (2 ^ j < 2 ^ j0 ↔ j < j0)

Rule argument

seq: ⊦ 0 ≤ j → (2 ^ j < 2 ^ j0 ↔ j < j0) subst: [j0, j] → [n→i(# bits), n→i(n)] rotate: F spec: int-pot inst: name: ls-pos-2pot

Additional information

Used simplifier rules: ⊦ 0 ≤ n→i(n);% ⊦ n→i(m) < n→i(n) ↔ m < n;% ⊦ m < n ∧ n ≤ n0 → m < n0; (forward)% ⊦ m < n → n ≠ 0; (forward)% ⊦ m ≤ n ∧ n < n0 → m < n0; (forward)% ⊦ # bits = 0 ↔ bits = [];% ⊦ ¬ n < n; Used terms: n→i(# bits), n→i(n)