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Proof step 31 from proof abs-acyclic (previous step)

entries[str] = ROOT_INO, tree[p] = dnode(md0, sdt), (( ino => mkdir(# entries, md0, # links(ino, dirs), m2, entries) * (abs(sdt -- str, entries -- str) * abs(sdt[str], ROOT_INO)) * abs|(tree, ROOT_INO, p, ino)) )(dirs), abs(tree, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(tree, abs-files(files), ofh), ispath(p, ROOT_INO, ino, dirs, files), str ∈ entries, str ∈ sdt ⊦ sdt[str].dir?, (∀ ino. ¬ ino ∈ files ∨ ¬ ino ∈ dirs) ∧ (∀ ino. ⌜ino⌝ ∈ tree.fids → ino ∈ files) ∧ ((abs(tree, ROOT_INO) * emp))(dirs) ∧ ispath(p + str, ROOT_INO, entries[str], dirs, files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
tree[p] = dnode(md0, sdt), entries[str] = ROOT_INO, (( ino => mkdir(# entries, md0, # links(ino, dirs), m2, entries) * (abs(sdt -- str, entries -- str) * abs(sdt[str], ROOT_INO)) * abs|(tree, ROOT_INO, p, ino)) )(dirs), abs(tree, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(tree, abs-files(files), ofh), ispath(p, ROOT_INO, ino, dirs, files), str ∈ sdt, str ∈ entries ⊦ sdt[str].dir?, (⌜ino0⌝ ∈ tree.fids → ino0 ∈ files) ∧ ispath(p + str ', ROOT_INO, ROOT_INO, dirs, files)

Rule argument

Additional information

Used simplifier rules: ⊦ p + str = p + str '; (s)%sep-com: ⊦ D * D0 = D0 * D; from specification heap-sep[dir-heap]%sep-ass: ⊦ (D * D0) * D1 = D * D0 * D1; from specification heap-sep[dir-heap]% ⊦ emp * D = D; (s)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)