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Proof step 2 from proof swap-init-setequal (previous step)

⊦ a ' + a0 ' ⊆ a0 ' + a ' + x ∧ a0 ' + a ' ⊆ a ' + a0 ' + x

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ x ⊆ y ↔ (∀ a. a ∈ x → a ∈ y)
Proof step 4:
⊦ (∀ a1. a1 ∈ a ' + a0 ' → a1 ∈ a0 ' + a ' + x) ∧ a0 ' + a ' ⊆ a ' + a0 ' + x

Rule argument

spec: list-set inst: name: subset seq: ⊦ x ⊆ y ↔ (∀ a. a ∈ x → a ∈ y) subst: [y, x] → [a0 ' + a ' + x, a ' + a0 '] flags: rewrite

Additional information

Used terms: a0 ' + a ' + x, a ' + a0 '