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Proof step 141 from proof refine-create (previous step)

# entries = dirs[ino1].size, # links(ino1, dirs) = dirs[ino1].nlink, dirs[ino1] = mkdir(# entries, md0, dirs[ino1].nlink, dirs[ino1].nsubdirs, entries), dent = negdentry(str), err = ESUCCESS, fs = abs-files(files), inode = mkinode(ino1, md0, true, dirs[ino1].nlink, dirs[ino1].nsubdirs, # entries), ino ≠ 0, root.dir?, root[q].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), ino1 ∈ dirs, ¬ str ∈ dirs[ino1].entries, ¬ str ∈ entries, ¬ ino ∈ files, ¬ ino ∈ dirs, psynced → asynced0, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [afs_create_ino#(ino1, md, ino; dent, err, dirs, files); afs_inode_sync#(inode; dirs, files); inode := (inode.ino ∈ dirs ⊃ mkinode(inode.ino, dirs[inode.ino].meta, true, dirs[inode.ino].nlink, dirs[inode.ino].nsubdirs, dirs[inode.ino].size) ;mkinode(inode.ino, files[inode.ino].meta, false, files[inode.ino].nlink, 0, files[inode.ino].size) ); c_inode := getinode(dent.ino, dirs, files); asynced := ?] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_create#(q + str ', md, user, abs-of(of); err2, root, fs; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err2))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 142:
# links(ino1, dirs) = m0, # entries = m, dirs[ino1] = mkdir(# entries, md0, m0, m1, entries), dirs[ino1] = mkdir(m, md1, m0, m1, entries0), dent = negdentry(str), err = ESUCCESS, fs = abs-files(files), inode = mkinode(ino1, md0, true, m0, m1, # entries), root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), ino1 ∈ dirs, psynced → asynced0, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [afs_create_ino#(ino1, md, ino; dent, err, dirs, files); afs_inode_sync#(inode; dirs, files); inode := (inode.ino ∈ dirs ⊃ mkinode(inode.ino, dirs[inode.ino].meta, true, dirs[inode.ino].nlink, dirs[inode.ino].nsubdirs, dirs[inode.ino].size) ;mkinode(inode.ino, files[inode.ino].meta, false, files[inode.ino].nlink, 0, files[inode.ino].size) ); c_inode := getinode(dent.ino, dirs, files); asynced := ?] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_create#(q + str ', md, user, abs-of(of); err2, root, fs; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err2)), ino = 0, str ∈ entries0, str ∈ entries, ino ∈ files, ino ∈ dirs

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [dirs[ino1], m, md1, m0, m1, entries0]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: dirs[ino1], m, md1, m0, m1, entries0