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Proof step 9 from proof eq-01 (previous step)

b ' + y + c ' + z = y0 + a ' + c ' + z0, x0 = a + y0, b ∈ y0 ⊦ a = c, a = b, b = c, x0 = [], dups(z), c ∈ z, a ∈ z, a ∈ y

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
b ' + y + c ' + z = y0 + a ' + c ' + z0, b ∈ y0 ⊦ a = c, a = b, b = c, dups(z), c ∈ z, a ∈ z, a ∈ y

Rule argument

Additional information

Used simplifier rules: ⊦ a ∈ x → a ∈ x + y; (s)%in-14: ⊦ a ' + x = y → a ∈ y; (forward) from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ a ' + x ≠ []; (s)% ⊦ a + x = a ' + x; (s)