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Proof step 5 from proof lsle-trans (previous step)

n∞ < ⌜m⌝ , m ≤ m0 ⊦ n∞ < ⌜m0⌝

User applied rule structural induction

And closed the goal!

Rule argument

indvar: n∞

Additional information

Used simplifier rules: less-inf1: ⊦ ¬ ∞ < n∞;%less-fin: ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n;%natinf freely generated by ∞, ⌜ ⌝;;%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%le-ls-simp: ⊦ m ≤ n → (n < m ↔ false); from specification nat