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Proof step 2 from proof mk-in (previous step)

⊦ m = 0, a ∈ mklist(a, m)

Heuristic structural induction applied rule structural induction

And closed the goal!

Rule argument

term: m

Additional information

Used simplifier rules: mk-succ: ⊦ mklist(a, n + 1) = a ' + mklist(a, n);%nat freely generated by 0, +1;;%succ: ⊦ m +1 = m + 1; from specification nat-basic2%oz: ⊦ m + 1 ≠ 0; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%in-06: ⊦ ¬ a ∈ b ' + x ↔ a ≠ b ∧ ¬ a ∈ x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list