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Proof step 4 from proof swap-init-setequal (previous step)

⊦ (∀ a1. a1 ∈ a ' + a0 ' → a1 ∈ a0 ' + a ' + x) ∧ a0 ' + a ' ⊆ a ' + a0 ' + x

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
⊦ a0 ' + a ' ⊆ a ' + a0 ' + x

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ a ∈ b ' ↔ a = b; (s)% ⊦ a ∈ x + y ↔ a ∈ x ∨ a ∈ y; (s)