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Proof step 48 from proof abs-acyclic (previous step)

tree[p] = dnode(md0, sdt), entries[str] = ROOT_INO, sdt[str] = dnode(md, sdt0), (( ( ( (ROOT_INO => mkdir(# entries0, md, m0, m1, entries0) * abs(sdt0, entries0)) * ino => mkdir(# entries, md0, # links(ino, dirs), m2, entries)) * abs(sdt -- str, entries -- str)) * 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 ⊦

User applied rule constructor cut

And obtained the following new goals

Proof step 49:
sdt[str] = dnode(md, sdt0), entries[str] = ROOT_INO, tree[p] = dnode(md0, sdt), tree = dnode(md1, sdt1), (( ( ( (ROOT_INO => mkdir(# entries0, md, m0, m1, entries0) * abs(sdt0, entries0)) * ino => mkdir(# entries, md0, # links(ino, dirs), m2, entries)) * abs(sdt -- str, entries -- str)) * 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 ⊦

Rule argument

var: tree

Additional information

Used simplifier rules: directory-tree, entries-tree generated by ∅, dnode, fnode, [ ];;% ⊦ abs(fnode(fid), ino) = (emp ∧ ⌜ino = fid.ino⌝ ); (s)% ⊦ ((D ∧ D0))(dirs) ↔ D(dirs) ∧ D0(dirs); (s)% ⊦ emp(dirs) ↔ dirs = ∅; (s)% ⊦ ⌜bv⌝ (dirs) ↔ bv; (s)%and-ass: ⊦ ((D ∧ D0) ∧ D1) = (D ∧ D0 ∧ D1); from specification heap-sep[dir-heap]%and-com: ⊦ (D ∧ D0) = (D0 ∧ D); from specification heap-sep[dir-heap]% ⊦ tree[ε] = tree; (s)% ⊦ fnode(fid) ≠ dnode(md, sdt); (s)%path-in-dirs: p ≠ ε ⊦ ispath(p, n, m, dirs, files) → n ∈ dirs; (forward) from specification afs-base% ⊦ ¬ ino ∈ ∅; (s)