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Proof step 12 from proof plinks-fids (previous step)

∀ str. str ∈ sdt → (∀ fid1. # links(fid1, sdt[str]) = count(fid1, sdt[str].fids)), ∀ sdt0, fid1, md. # sdt0 < # sdt → (∀ str. str ∈ sdt0 → (∀ fid1. # links(fid1, sdt0[str]) = count(fid1, sdt0[str].fids))) → # links(fid1, dnode(md, sdt0)) = count(fid1, sdt0.fids) ⊦ # links(fid1, dnode(md, sdt)) = count(fid1, sdt.fids), sdt = ∅

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store, inst: directory-tree-inst name: exnotempty seq: ⊦ sdt = ∅ ↔ ¬(∃ str, tree, sdt0. sdt = sdt0[str, tree] ∧ ¬ str ∈ sdt0) subst: [sdt] → [sdt] flags: <all paths>

Additional information

Used terms: sdt