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Proof step 1 from proof restrict-add (conclusion)

⊦ (as ++ @(m0, m1, m2)) | m0 = (as | m0) ++ @(m0, m1, m2)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ as = as0 ↔ (∀ adr. adr ∈ as ↔ adr ∈ as0)
Proof step 3:
⊦ ∀ adr. adr ∈ (as ++ @(m0, m1, m2)) | m0 ↔ adr ∈ (as | m0) ++ @(m0, m1, m2)

Rule argument

spec: set-basic, inst: address-store name: Extension seq: ⊦ as = as0 ↔ (∀ adr. adr ∈ as ↔ adr ∈ as0) subst: [as0, as] → [(as | m0) ++ @(m0, m1, m2), (as ++ @(m0, m1, m2)) | m0] flags: <all paths>

Additional information

Used terms: (as | m0) ++ @(m0, m1, m2), (as ++ @(m0, m1, m2)) | m0