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Proof step 178 from proof refine-readmeta (previous step)

dirs[lookup(parent(p), ROOT_INO, dirs, files)] = mkdir(m2, md, m3, m4, entries), files[entries0[str]] = mkfile(m0, md1, # links(entries0[str], dirs), content), dirs[m1] = mkdir(# entries0, md0, # links(m1, dirs), m7, entries0), root.dir?, root[p0].dir?, dom of < ino6, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(p0, ROOT_INO, m1, dirs, files), ispath(path, ROOT_INO, entries0[str], dirs, files), of-cons(of, dirs, files), pr(user, md1), px-parent(user, path, ROOT_INO, dirs, files), entries0[str] ∈ files, ROOT_INO ∈ dirs, str ∈ entries0, m1 ∈ dirs, psynced → asynced ⊦ # links(entries0[str], dirs) = count(⌜entries0[str]⌝ , root.fids), root[path].dir?, entries0[str] ∈ dirs, p0 + str ' ∈ root ∧ root[p0 + str '] = fnode(⌜entries0[str]⌝ )

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 179:
⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p + str ' ∈ tree ↔ m ∈ dirs ∧ str ∈ dirs[m].entries)
Proof step 180:
dirs[lookup(parent(p), ROOT_INO, dirs, files)] = mkdir(m2, md, m3, m4, entries), files[entries0[str]] = mkfile(m0, md1, # links(entries0[str], dirs), content), dirs[m1] = mkdir(# entries0, md0, # links(m1, dirs), m7, entries0), root.dir?, root[p0].dir?, dom of < ino6, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(p0, ROOT_INO, m1, dirs, files), ispath(path, ROOT_INO, entries0[str], dirs, files), of-cons(of, dirs, files), pr(user, md1), px-parent(user, path, ROOT_INO, dirs, files), entries0[str] ∈ files, ROOT_INO ∈ dirs, str ∈ entries0, m1 ∈ dirs, psynced → asynced ⊦ # links(entries0[str], dirs) = count(⌜entries0[str]⌝ , root.fids), root[p0 + str '] = fnode(⌜entries0[str]⌝ ), root[path].dir?, entries0[str] ∈ dirs

Rule argument

Additional information

Used simplifier rules: path-in-last: ⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p + str ' ∈ tree ↔ m ∈ dirs ∧ str ∈ dirs[m].entries);% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]