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Proof step 2 from proof app-01 (previous step)

⊦ (x + y) -1l a = x + (y -1l a), a ∈ x

Heuristic structural induction applied rule structural induction

And obtained the following new goals

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

Rule argument

term: x

Additional information

Used simplifier rules: list freely generated by [], +;;%Nil: ⊦ [] + x = x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list