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Proof step 3 from proof neq-03 (previous step)

n0 + 1 = n + m0, n0 < n + m, m < m0 ⊦ n + m = 0, m0 = 0

Heuristic structural induction applied rule structural induction

And closed the goal!

Rule argument

term: m0

Additional information

Used simplifier rules: gen: ⊦ ;%succ: ⊦ m +1 = m + 1;%a: ⊦ (m + n0) + n1 = m + n0 + n1;%eq-01: ⊦ m + n = m + n0 ↔ n = n0;%c: ⊦ m + n = n + m;%oz: ⊦ m + 1 ≠ 0;%s-04: ⊦ m < n + 1 ↔ ¬ n < m;%ls-04: ⊦ m < n ↔ ¬(m = n ∨ n < m);%l: ⊦ m + n < m + n0 ↔ n < n0;%ls-02: ⊦ m < n → ¬ n < m;