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Proof step 2 from proof in-append0-not-left (previous step)

a ' + x = x0 + x1, a ∈ x1 ⊦ x0 = [], a ∈ x0

Heuristic structural induction applied rule structural induction

And closed the goal!

Rule argument

term: x0

Additional information

Used simplifier rules: c: ⊦ a + x = a ' + x;%a: ⊦ (x + y) + z = x + y + z;%c-06: ⊦ a ' + x = b ' + y ↔ a = b ∧ x = y;%e-01: ⊦ a ' + x ≠ [];%in-06: ⊦ ¬ a ∈ b ' + x ↔ a ≠ b ∧ ¬ a ∈ x;%list freely generated by [], +;;