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Proof step 2 from proof potmonleq (previous step)

⊦ 2^ m ≤ 2^ n ↔ m ≤ n, 2^ m < 2^ n

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
n < m, 2^ m ≤ 2^ n ⊦ n = m

Rule argument

Additional information

Used simplifier rules: potmon: ⊦ 2^ m < 2^ n ↔ m < n;% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)% ⊦ m ≤ m; (s)% ⊦ m ≤ n → (n ≤ m ↔ m = n); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)