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Proof step 24 from proof referenced-adrs-lookup-keys-nodups (previous step)

fs[adr0].key = fs[adr].key, referenced-adrs(ax, ri) = [], referenced-adrs(ax2, ri) = [], ri-cons(ri, fs), adr ∈ ri, adr0 ∈ ri ⊦ adr = adr0, dups(ax + ax2), dups(ax3 + ax + ax2), dups(ax2 + ax0), dups(ax3 + ax), dups(ax + ax2 + ax0), dups((ax3 + ax) + ax2 + ax0), dups((ax3 + ax) + ax2), dups(fs[referenced-adrs(ax3, ri)].keys), dups(fs[referenced-adrs(ax0, ri)].keys), dups(fs[referenced-adrs(ax3, ri)].keys + fs[referenced-adrs(ax0, ri)].keys), dups(ax3), dups(ax), dups(ax2), dups(ax0), adr ∈ ax2, adr ∈ ax, adr ∈ ax0, adr0 ∈ ax0, adr0 ∈ ax3, adr0 ∈ ax2, adr0 ∈ ax, adr ∈ ax3, fs[adr].key ∈ fs[referenced-adrs(ax0, ri)].keys, fs[adr].key ∈ fs[referenced-adrs(ax3, ri)].keys

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store+set, inst: node-index name: Data-in seq: ⊦ adr ∈ ri ↔ (∃ key. key ∈ ri ∧ ri[key] = adr) subst: [ri, adr] → [ri, adr] flags: <all paths>

Additional information

Used terms: ri, adr