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Proof step 27 from proof inv-gc (previous step)

# kx = # ax, as ∩ ax.toSet = ∅, as ∩ log0.toSet = ∅, ax.toSet ∩ log0.toSet = ∅, as ∩ range ri0[kx, ax] = ∅, fo.inodes?, ro.inodes?, log-cons(log0, fs0), new(ax, fs0), node-cons(fs0[adr].key, fs0[adr]), ri-cons(ri0, fs0), ri-cons(ri0[kx, ax], fs0[ax, fs0[ri0[kx]]]), ri-inj(fi), ri-inj(ri0), adr ∈ as, adr ∈ fs0, adr ∈ log0, kx.toSet ⊆ dom ri0 ⊦ # as = 0, as = ∅, dups(ax), dups(kx)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: set-basic, inst: node-store name: Extension seq: ⊦ as = as0 ↔ (∀ adr. adr ∈ as ↔ adr ∈ as0) subst: [as0, as] → [∅, as ∩ log0.toSet] flags: <all paths>

Additional information

Used terms: ∅, as ∩ log0.toSet