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Proof step 18 from proof in-ri-update-in-ri (previous step)

# ax1 = # ax0, adr ∈ ri, ax1.toSet ⊆ range ri, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ fs[adr].key ∈ keys(fs, ax1), fs[adr].key ∈ ri

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ adr ∈ ri ↔ (∃ key. key ∈ ri ∧ ri[key] = adr)
Proof step 20:
# ax1 = # ax0, ax1.toSet ⊆ range ri, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]), ∃ key. key ∈ ri ∧ ri[key] = adr ⊦ fs[adr].key ∈ ri, fs[adr].key ∈ keys(fs, ax1)

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