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Proof step 56 from proof keys-same-fs (previous step)

fs0[adr0] = fs1[adr0], adr0 ∈ fs0, adr0 ∈ ax, adr0 ∈ fs1 ⊦ fs1[adr0] = (fs1 | ax.toSet)[adr0], fs0[adr].key = fs1[adr].key ∧ keys(fs0, ax) = keys(fs1, ax)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store+set, inst: node-store name: restrict-at seq: ⊦ adr ∈ fs ∧ adr ∈ as → (fs | as)[adr] = fs[adr] subst: [adr, as, fs] → [adr0, ax.toSet, fs1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ adr ∈ ax.toSet ↔ adr ∈ ax; (s) Used terms: adr0, ax.toSet, fs1