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Proof step 2 from proof lapp-05 (previous step)

a ' + b ' + x = y + a ' ⊦ (b ' + x).last = a

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 [], +;;%c: ⊦ a + x = a ' + x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%c-06: ⊦ a ' + x = b ' + y ↔ a = b ∧ x = y; from specification list%in-14: ⊦ a ' + x = y → a ∈ y; (forward) from specification list%in-15: ⊦ x + a ' = y → a ∈ y; (forward) from specification list%Nil: ⊦ [] + x = x; from specification list%c-03: ⊦ a ' = b ' + x ↔ a = b ∧ x = []; from specification list%e-01: ⊦ a ' + x ≠ []; from specification list