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Proof step 3 from proof lapp-04 (previous step)

a ' + x = y + b ', a ∈ y, b ∈ x ⊦ x.last = b, a = b

Heuristic structural induction applied rule structural induction

And closed the goal!

Rule argument

term: y

Additional information

Used simplifier rules: last-def: ⊦ (x + a ').last = a;%list freely generated by [], +;;% ⊦ a + x = a ' + x; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ a ' + x = b ' + y ↔ a = b ∧ x = y; (ws)% ⊦ a ∈ x + y ↔ a ∈ x ∨ a ∈ y; (s)% ⊦ a ∈ b ' ↔ a = b; (s)%in-15: ⊦ x + a ' = y → a ∈ y; (forward) from specification list% ⊦ [] + x = x; (s)% ⊦ a ' = b ' + x ↔ a = b ∧ x = []; (ws)