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Proof step 94 from proof inv-link (previous step)

dirs[ino0] = mkdir(m0, md0, # links(ino0, dirs), m3, entries0), files[entries0[str]] = mkfile(m, md, m1, content), err0 = ESUCCESS, inode = mkinode(entries0[str], md, false, m1, 0, m), afs-cons(dirs, files), ispath(parent(p), ROOT_INO, ino1, dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), px(user, md0), px-parent(user, parent(p), ROOT_INO, dirs, files), px-parent(user, q, ROOT_INO, dirs, files), ino0 ∈ dirs, entries0[str] ∈ files, str ∈ entries0, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO ⊦ ⟪vfs_may_create#(ino1, negdentry(p.last), user, dirs, files, asynced; inode, err0); new_inode := inode, new_dent := negdentry(p.last); if err0 = ESUCCESS then afs_check_commit#(dirs, files; err0; asynced); if err0 = ESUCCESS then {c_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); afs_link#(mkdentry(str, entries0[str]); new_inode, c_inode, new_dent, err0, dirs, files; asynced)}⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files)), p = ε, entries0[str] ∈ dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 95:
dirs[ino0] = mkdir(m0, md0, # links(ino0, dirs), m3, entries0), files[entries0[str]] = mkfile(m, md, # links(entries0[str], dirs), content), err0 = ESUCCESS, inode = mkinode(entries0[str], md, false, # links(entries0[str], dirs), 0, m), p ≠ ε, afs-cons(dirs, files), ispath(parent(p), ROOT_INO, ino1, dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), px(user, md0), px-parent(user, parent(p), ROOT_INO, dirs, files), px-parent(user, q, ROOT_INO, dirs, files), ino0 ∈ dirs, entries0[str] ∈ files, str ∈ entries0, ¬ entries0[str] ∈ dirs, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO ⊦ ⟪vfs_may_create#(ino1, negdentry(p.last), user, dirs, files, asynced; inode, err0); new_inode := inode, new_dent := negdentry(p.last); if err0 = ESUCCESS then afs_check_commit#(dirs, files; err0; asynced); if err0 = ESUCCESS then {c_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); afs_link#(mkdentry(str, entries0[str]); new_inode, c_inode, new_dent, err0, dirs, files; asynced)}⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files))

Rule argument

Additional information

Used simplifier rules: afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base