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Proof step 6 from proof keys-nodes-in-ri (previous step)

ax.toSet = range ri | n, ri-cons(ri, fs), key ∈ keys(fs, ax) ⊦ key ∈ ri

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ key ∈ keys(fs, ax) ↔ (∃ adr. adr ∈ ax ∧ fs[adr].key = key)
Proof step 8:
ax.toSet = range ri | n, ri-cons(ri, fs), ∃ adr. adr ∈ ax ∧ fs[adr].key = key ⊦ key ∈ ri

Rule argument

spec: aubifs-base name: keys-in-elim seq: ⊦ key ∈ keys(fs, ax) ↔ (∃ adr. adr ∈ ax ∧ fs[adr].key = key) subst: [ax, fs, key] → [ax, fs, key] flags: <all paths>

Additional information

Used terms: ax, fs, key