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Proof step 9 from proof restrict-2 (previous step)

adr ∈ as1, adr ∈ as0, adr ∈ iast ⊦ # as0 = 0, # as1 = 0, iast[adr] = (iast | (as0 ∩ as1))[adr], as0 = ∅, as1 = ∅

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store+set, inst: index-store-address-store name: restrict-at seq: ⊦ adr ∈ iast ∧ adr ∈ as → (iast | as)[adr] = iast[adr] subst: [adr, as, iast] → [adr, as0 ∩ as1, iast] flags: <all paths>

Additional information

Used simplifier rules: ⊦ adr ∈ as ∩ as0 ↔ adr ∈ as ∧ adr ∈ as0; (ws)%int-a: ⊦ (as ∩ as0) ∩ as1 = as ∩ as0 ∩ as1; from specification set-union[node-store]%int-c: ⊦ as ∩ as0 = as0 ∩ as; from specification set-union[node-store] Used terms: adr, as0 ∩ as1, iast