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Proof step 2 from proof app (previous step)

a ∈ x ⊦ (x + y) -1l a = (x -1l a) + y

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ a, y. a ∈ x0 → (x0 + y) -1l a = (x0 -1l a) + y, a ∈ a0 + x0 ⊦ ((a0 + x0) + y) -1l a = ((a0 + x0) -1l a) + y

Rule argument

term: x

Additional information

Used simplifier rules: del1-e: ⊦ [] -1l a = [];%list freely generated by [], +;;%Nil: ⊦ [] + x = x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%in-empty: ⊦ ¬ a ∈ []; from specification list