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Proof step 5 from proof keys-remove-leb (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ key ∈ keys(fs, ax) ↔ (∃ adr. adr ∈ ax ∧ fs[adr].key = key)
Proof step 7:
ax.toSet = range ri | n, ri[key] = @(n, m0, m1), ri-cons(ri, fs), key ∈ ri ⊦ ∃ adr. adr ∈ ax ∧ fs[adr].key = key

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