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Proof step 3 from proof mk-one (previous step)

mklist(a, m) + x = a ' ⊦ m = 0, m = 1 ∧ x = []

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);%mk-empty: ⊦ mklist(a, m) = [] ↔ m = 0;%nat freely generated by 0, +1;;% ⊦ m +1 = m + 1; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ a ' = b ' + x ↔ a = b ∧ x = []; (ws)% ⊦ x + y = [] ↔ x = [] ∧ y = []; (as)% ⊦ m + 1 ≠ 0; (s)% ⊦ m + n = 1 ↔ m = 0 ∧ n = 1 ∨ n = 0 ∧ m = 1; (ws)