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Proof step 120 from proof inv-link (previous step)

files[entries0[str]] = mkfile(m, md, # links(entries0[str], dirs), content), dirs[ino0] = mkdir(m0, md0, # links(ino0, dirs), m3, entries0), dent = negdentry(p.last), err = ESUCCESS, p ≠ ε, afs-cons(dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), ispath(parent(p), ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, dirs[ino1].meta), px(user, md0), px(user, dirs[ino1].meta), px-parent(user, q, ROOT_INO, dirs, files), px-parent(user, parent(p), ROOT_INO, dirs, files), str ∈ entries0, entries0[str] ∈ files, ino0 ∈ dirs, ino1 ∈ dirs, ¬ entries0[str] ∈ dirs, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO ⊦ ⟪afs_lookup#(ino1, dirs, files, asynced; dent, err); if err = ESUCCESS then err := EEXISTS else if err = ENOENT then err := ESUCCESS; new_inode := (ino1 ∈ dirs ⊃ mkinode(ino1, dirs[ino1].meta, true, dirs[ino1].nlink, dirs[ino1].nsubdirs, dirs[ino1].size) ;mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size) ), new_dent := negdentry(p.last); err0 := err; 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))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 121:
dirs[ino0] = mkdir(m0, md0, # links(ino0, dirs), m3, entries0), files[entries0[str]] = mkfile(m, md, # links(entries0[str], dirs), content), dirs[ino1] = mkdir(m1, md1, m2, m4, entries), dent = negdentry(p.last), err = ESUCCESS, afs-cons(dirs, files), ispath(parent(p), ROOT_INO, ino1, dirs, files), ispath(q, ROOT_INO, ino0, dirs, files), of-cons(of, dirs, files), pw(user, md1), px(user, md1), px(user, md0), px-parent(user, parent(p), ROOT_INO, dirs, files), px-parent(user, q, ROOT_INO, dirs, files), ino1 ∈ dirs, ino0 ∈ dirs, entries0[str] ∈ files, str ∈ entries0, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO ⊦ ⟪afs_lookup#(ino1, dirs, files, asynced; dent, err); if err = ESUCCESS then err := EEXISTS else if err = ENOENT then err := ESUCCESS; new_inode := (ino1 ∈ dirs ⊃ mkinode(ino1, md1, true, m2, m4, m1);mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size)), new_dent := negdentry(p.last); err0 := err; 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

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], m2, md1, m3, m4, 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], m2, md1, m3, m4, entries0