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Proof step 7 from proof eq-01 (previous step)

b ' + y + c ' + z = x0.tail + a ' + c ' + z0, a = x0.head ⊦ a = b, a = c, b = c, x0 = [], dups(z), a ∈ y, a ∈ z, c ∈ z

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
b ' + y + c ' + z = x0.tail + x0.head ' + c ' + z0, b ∈ x0.tail ⊦ x0.head = b, x0.head = c, b = c, x0 = [], dups(z), x0.head ∈ y, x0.head ∈ z, c ∈ z

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ a ∈ y → (y + c ' + z = a ' + z0 ↔ y = [] ∧ c = a ∧ z = z0); (ws)% ⊦ a ≠ b → (a ∈ b ' + x ↔ a ∈ x); (s)% ⊦ a ∈ x + y ↔ a ∈ x ∨ a ∈ y; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list%in-14: ⊦ a ' + x = y → a ∈ y; (forward) from specification list