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Proof step 7 from proof l (previous step)

m + n1 + 1 < m + n, n < n1 + 1, n1 + m < m + n, ∀ m, n. m + n < m + n1 ↔ n < n1 ⊦ m + n = 0, n = n1 + 1, n = n1

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 4 terms: m, n

Additional information

Used simplifier rules: c: ⊦ m + n = n + m;%ls-02: ⊦ m < n → ¬ n < m;%neq-01: ⊦ m ≠ n → (m < n ↔ ¬ n < m);%f: ⊦ m < n → n ≠ 0;%trans-01: ⊦ n < n0 ∧ n0 < n1 → n +1 < n1;%trans: ⊦ n < n0 ∧ n0 < n1 → n < n1;%succ: ⊦ m +1 = m + 1;%ref: ⊦ ¬ n < n; Used terms: m, n