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Proof step 2 from proof ls-trans (previous step)

n∞ < n∞1, n∞1 < n∞2, n∞2 < n∞1, n∞1 < n∞ ⊦ n∞ < n∞2

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 3:
n∞ < ⌜m⌝ , ⌜m⌝ < n∞2, n∞2 < ⌜m⌝ , ⌜m⌝ < n∞ ⊦ n∞ < n∞2

Rule argument

term: n∞1

Additional information

Used simplifier rules: inf-less: ⊦ n∞ < ∞ ↔ n∞ ≠ ∞;%less-inf1: ⊦ ¬ ∞ < n∞;%natinf freely generated by ∞, ⌜ ⌝;;