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Proof step 4 from proof mk-head (previous step)

mklist(a, n) + x = a0 + y ⊦ mklist(a, n) + x = [], a0 = a, n = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
mklist(a, n) + x = a0 ' + y, a0 ∈ x ⊦ a0 = a, n = 0, a0 ∈ mklist(a, n)

Rule argument

Additional information

Used simplifier rules: mk-elem: ⊦ a ∈ mklist(b, n) → a = b;% ⊦ a ∈ x + y ↔ a ∈ x ∨ a ∈ y; (s)% ⊦ a ' + x ≠ []; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list%in-14: ⊦ a ' + x = y → a ∈ y; (forward) from specification list% ⊦ a + x = a ' + x; (s)