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Proof step 1 from proof lapp-04 (conclusion)

⊦ a ' + x = y + b ' ∧ a ≠ b → x.last = b

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
a ' + x = y + b ', a ∈ y, b ∈ x ⊦ a = b, x.last = b

Rule argument

Additional information

Used simplifier rules: in-01: ⊦ a ≠ b → (a ∈ b ' + x ↔ a ∈ x); from specification list%in-11: ⊦ a ∈ x → a ∈ x + y; from specification list%in-15: ⊦ x + a ' = y → a ∈ y; (forward) from specification list%in-14: ⊦ a ' + x = y → a ∈ y; (forward) from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%inapp-10: ⊦ a ' + x = y + b ' ∧ a ≠ b → a ∈ y ∧ b ∈ x; (forward) from specification list