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Proof step 7 from proof keys-remove-leb (previous step)

ax.toSet = range ri | n, ri[key] = @(n, m0, m1), ri-cons(ri, fs), key ∈ ri ⊦ ∃ adr. adr ∈ ax ∧ fs[adr].key = key

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ key ∈ ri ↔ (∃ adr, ri0. ri = ri0[key, adr] ∧ ¬ key ∈ ri0)
Proof step 9:
ax.toSet = range ri | n, ri[key] = @(n, m0, m1), ri-cons(ri, fs), ∃ adr, ri0. ri = ri0[key, adr] ∧ ¬ key ∈ ri0 ⊦ ∃ adr. adr ∈ ax ∧ fs[adr].key = key

Rule argument

spec: store, inst: node-index name: exin seq: ⊦ key ∈ ri ↔ (∃ adr, ri0. ri = ri0[key, adr] ∧ ¬ key ∈ ri0) subst: [ri, key] → [ri, key] flags: <all paths>

Additional information

Used terms: ri, key