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Proof step 51 from proof inv-link (previous step)

dent = negdentry(str), err = ESUCCESS, p ≠ ε, afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), px(user, dirs[ino0].meta), px-parent(user, q, ROOT_INO, dirs, files), ino0 ∈ dirs ⊦ ⟪afs_lookup#(ino0, dirs, files, asynced; dent, err); inode := (ino0 ∈ dirs ⊃ mkinode(ino0, dirs[ino0].meta, true, dirs[ino0].nlink, dirs[ino0].nsubdirs, dirs[ino0].size) ;mkinode(ino0, files[ino0].meta, false, files[ino0].nlink, 0, files[ino0].size) ); if err = ESUCCESS then afs_iget#(dent.ino, dirs, files, asynced; inode, err); if err = ESUCCESS ∧ inode.directory then err := EISDIR; c_inode := inode; old_dent := dent; if err = ESUCCESS then let ino = ROOT_INO, dent = negdentry(p.last), p0 = parent(p) in {vfs_walk#(p0, user, dirs, files, asynced; ino, err); if err = ESUCCESS then vfs_may_create#(ino, dent, user, dirs, files, asynced; inode, err); new_inode := inode, new_dent := dent}; if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then afs_link#(old_dent; new_inode, c_inode, new_dent, err, dirs, files; asynced)⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 52:
dirs[ino0] = mkdir(m, md, m0, m1, entries), dent = negdentry(str), err = ESUCCESS, afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), px(user, md), px-parent(user, q, ROOT_INO, dirs, files), ino0 ∈ dirs ⊦ ⟪afs_lookup#(ino0, dirs, files, asynced; dent, err); inode := (ino0 ∈ dirs ⊃ mkinode(ino0, md, true, m0, m1, m);mkinode(ino0, files[ino0].meta, false, files[ino0].nlink, 0, files[ino0].size)); if err = ESUCCESS then afs_iget#(dent.ino, dirs, files, asynced; inode, err); if err = ESUCCESS ∧ inode.directory then err := EISDIR; c_inode := inode; old_dent := dent; if err = ESUCCESS then let ino = ROOT_INO, dent = negdentry(p.last), p0 = parent(p) in {vfs_walk#(p0, user, dirs, files, asynced; ino, err); if err = ESUCCESS then vfs_may_create#(ino, dent, user, dirs, files, asynced; inode, err); new_inode := inode, new_dent := dent}; if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then afs_link#(old_dent; new_inode, c_inode, new_dent, err, dirs, files; asynced)⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files)), p = ε

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[ino0], m, md, m0, m1, entries]

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[ino0], m, md, m0, m1, entries