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Proof step 75 from proof refine-writemeta (previous step)

dirs0[m] = mkdir(# entries, md0, # links(m, dirs0), m2, entries), root[path] = dnode(md0, sdt), ((m => mkdir(# entries, md, # links(m, dirs0), m2, entries) * abs|(root, ROOT_INO, path, m) * abs(sdt, entries)))(dirs), root.dir?, dom of < ino0, afs-cons(dirs0, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, m, dirs0, files), of-cons(of, dirs0, files), pw(user, md0), px-parent(user, path, ROOT_INO, dirs0, files), m ∈ dirs0, path ∈ root, dirs ≡ dirs0[m, mkdir(# entries, md, # links(m, dirs0), m2, entries)], psynced0 → asynced0 ⊦ mkdir(# entries, md, # links(m, dirs0), m2, entries).meta = md ∧ mkdir(# entries, md, # links(m, dirs0), m2, entries).size = # mkdir(# entries, md, # links(m, dirs0), m2, entries).entries ∧ (( ( m => mkdir(# entries, md, # links(m, dirs0), m2, entries) * abs(sdt, mkdir(# entries, md, # links(m, dirs0), m2, entries).entries)) * abs|(root[path, dnode(mkdir(# entries, md, # links(m, dirs0), m2, entries).meta, sdt)], ROOT_INO, path, m)) )(dirs)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 76:
root[path] = dnode(md0, sdt), dirs0[m] = mkdir(# entries, md0, # links(m, dirs0), m2, entries), ((m => mkdir(# entries, md, # links(m, dirs0), m2, entries) * abs|(root, ROOT_INO, path, m) * abs(sdt, entries)))(dirs), root.dir?, dom of < ino0, afs-cons(dirs0, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, m, dirs0, files), of-cons(of, dirs0, files), pw(user, md0), px-parent(user, path, ROOT_INO, dirs0, files), path ∈ root, m ∈ dirs0, dirs ≡ dirs0[m, mkdir(# entries, md, # links(m, dirs0), m2, entries)], psynced0 → asynced0 ⊦ (((m => mkdir(# entries, md, # links(m, dirs0), m2, entries) * abs(sdt, entries)) * abs|(root[path, dnode(md, sdt)], ROOT_INO, path, m)) )(dirs)

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)% ⊦ mkdir(m, md, m0, m1, entries).meta = md; (s)