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Proof step 7 from proof bits2int-nle (previous step)

# bits = m + 1, 2 ^ n→i(n) + bits2int(bits) ≤ 0, 0 ≤ 2 ^ n→i(m) + bits2int(bits), 2 ^ n→i(n) ≤ 2 ^ n→i(m), bits2int(bits) < 2 ^ n→i(m), m < n ⊦ bits = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ 0 ≤ i → (2 ^ i ≤ 2 ^ j ↔ i ≤ j)

Rule argument

seq: ⊦ 0 ≤ i → (2 ^ i ≤ 2 ^ j ↔ i ≤ j) subst: [j, i] → [n→i(m), n→i(n)] rotate: F spec: int-pot inst: name: two-le

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 ≤ n0 → m < n0; (forward)% ⊦ ¬ n < n; Used terms: n→i(m), n→i(n)