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Proof step 21 from proof keys-same-fs (previous step)

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

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] → [adr, ax.toSet ++ adr, fs0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ adr ∈ fs ∧ adr ∈ as → (fs | as)[adr] = fs[adr]; (s)% ⊦ adr ∈ as ++ adr0 ↔ adr = adr0 ∨ adr ∈ as; (s)% ⊦ ¬ adr ∈ fs → fs[adr] = (∅)[adr]; (s) Used terms: adr, ax.toSet ++ adr, fs0