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Proof step 7 from proof blast-head (previous step)

a0 ' + y = y0 + a1 ', a ∈ y0, a = a0 ∨ a ∈ y ⊦ a0 ' + y = [], y0.head = a0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
a0 ' + y = y0 + a1 ', a ∈ y0, a = a0 ∨ a ∈ y, a0 ∈ y0 ∨ a0 = a1, a1 = a0 ∨ a1 ∈ y ⊦ y0.head = a0

Rule argument

Additional information

Used simplifier rules: ⊦ a ∈ b ' ↔ a = b; (s)% ⊦ a ∈ x + y ↔ a ∈ x ∨ a ∈ y; (s)%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% ⊦ a ' + x ≠ []; (s)