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Proof step 41 from proof abs-tree (previous step)

(((ino => mkdir(# entries, md, m0, m1, entries) * abs(sdt, entries)) * D0))(dirs), ((ino => mkdir(# entries, md, m0, m1, entries) * abs(sdt0, entries) * D1))(dirs), ∀ ino0. ⌜ino0⌝ ∈ sdt0.fids → ino0 ∈ files, ∀ tree1, ino, D1, dirs, tree0, D0, files. ((abs(tree1, ino) * D1))(dirs) ∧ ((abs(tree0, ino) * D0))(dirs) ∧ (∀ ino. ⌜ino⌝ ∈ tree1.fids → ino ∈ files) ∧ (∀ ino. ⌜ino⌝ ∈ tree0.fids → ino ∈ files) ∧ (∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs) → (p0 ∈ tree0 ↔ p0 ∈ tree1) ∧ (p0 ∈ tree0 → (tree0[p0].dir? ↔ tree1[p0].dir?) ∧ (tree0[p0].dir? ⊃ tree0[p0].meta = tree1[p0].meta;tree0[p0].fid = tree1[p0].fid)), ∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs, ∀ ino0. ⌜ino0⌝ ∈ sdt.fids → ino0 ∈ files ⊦ (str ∈ sdt ∧ p0 ∈ sdt[str] ↔ str ∈ sdt0 ∧ p0 ∈ sdt0[str]) ∧ ( str ∈ sdt ∧ p0 ∈ sdt[str] → (sdt[str][p0].dir? ↔ dnode(md, sdt0)[str ' + p0].dir?) ∧ (sdt[str][p0].dir? ⊃ sdt[str][p0].meta = dnode(md, sdt0)[str ' + p0].meta;sdt[str][p0].fid = dnode(md, sdt0)[str ' + p0].fid))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: entries-recdel seq: ⊦ str ∈ sdt → abs(sdt, sdi) = ( ⌜str ∈ sdi⌝ ∧ abs(sdt -- str, sdi -- str) * abs(sdt[str], sdi[str])) subst: [str, sdi, sdt] → [str, entries, sdt] flags: <all paths>

Additional information

Used simplifier rules: entries-dom2: ⊦ str ∈ sdt ∧ ((abs(sdt, sdi) * D))(dirs) → str ∈ sdi;%entries-dom1: ⊦ str ∈ sdi ∧ ((abs(sdt, sdi) * D))(dirs) → str ∈ sdt;%sep-ass: ⊦ (D * D0) * D1 = D * D0 * D1; from specification heap-sep[dir-heap]%sep-com: ⊦ D * D0 = D0 * D; from specification heap-sep[dir-heap] Used terms: str, entries, sdt