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Proof step 3 from proof tot (previous step)

∀ m. n0 = m ∨ n0 < m ∨ m < n0 ⊦ n0 +1 = m, n0 +1 < m, m < n0 +1

User applied rule structural induction

And obtained the following new goals

Proof step 4:
∀ n0. (∀ m. n0 = m ∨ n0 < m ∨ m < n0) → n0 +1 = m0 ∨ n0 +1 < m0 ∨ m0 < n0 +1, ∀ m. n0 = m ∨ n0 < m ∨ m < n0 ⊦ n0 +1 = m0 +1, n0 +1 < m0 +1, m0 +1 < n0 +1

Rule argument

term: m

Additional information

Used simplifier rules: gen: ⊦ ;%disj-1: ⊦ 0 ≠ n +1;%zero-01: ⊦ ¬ m < 0;%zero: ⊦ 0 < m ↔ m ≠ 0;