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Proof step 179 from proof inv-link (previous step)

entries[str] = dirs0[ino].entries[str], dirs0[ino1] = mkdir(m1, md2, # links(ino1, dirs0), m5, entries2), files[entries[str]] = mkfile(m, md3, # links(entries[str], dirs0), content), dirs0[ino0] = mkdir(m0, md0, # links(ino0, dirs0), m3, entries0), entries0[str] = entries[str], dirs0[ino2] = mkdir(m2, md1, # links(ino2, dirs0), m6, entries), dirs = dirs0[ino1, mkdir(m1 + 1, md2, # links(ino1, dirs0), m5, entries2[p.last, entries[str]])], p ≠ ε, afs-cons(dirs0, files), ispath(q, ROOT_INO, ino0, dirs0, files), ispath(parent(p), ROOT_INO, ino1, dirs0, files), of-cons(of, dirs0, files), pw(user, md2), px(user, md0), px(user, md2), px-parent(user, q, ROOT_INO, dirs0, files), px-parent(user, parent(p), ROOT_INO, dirs0, files), str ∈ dirs0[ino].entries, ino ∈ dirs0, str ∈ entries0, entries[str] ∈ files, ino0 ∈ dirs0, ino1 ∈ dirs0, ino2 ∈ dirs0, str ∈ entries, ¬ p.last ∈ entries2, ¬ entries[str] ∈ dirs0, links(ino, dirs0) ≠ ∅ ∨ ino = ROOT_INO, links(ino0, dirs0) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino2, dirs0) ≠ ∅ ∨ ino2 = ROOT_INO ⊦ [afs_inc_nlink#(mkdentry(str, entries0[str]).ino; dirs, files); new_dent := mkdentry(p.last, mkdentry(str, entries0[str]).ino); afs_inode_sync#(mkinode(ino1, md2, true, # links(ino1, dirs0), m5, m1); dirs, files); afs_inode_sync#(mkinode(entries[str], md3, false, # links(entries[str], dirs0), 0, m); dirs, files); 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) ); c_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); err := ESUCCESS; asynced := ?] (afs-cons(dirs, files) → of-cons(of, dirs, files))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 180:
dirs0[ino2] = mkdir(m2, md1, # links(ino2, dirs0), m6, entries), entries0[str] = entries[str], dirs0[ino0] = mkdir(m0, md0, # links(ino0, dirs0), m3, entries0), files[entries[str]] = mkfile(m, md3, # links(entries[str], dirs0), content), dirs0[ino1] = mkdir(m1, md2, # links(ino1, dirs0), m5, entries2), entries[str] = entries1[str], dirs0[ino] = mkdir(m4, md, m7, m8, entries1), dirs = dirs0[ino1, mkdir(m1 + 1, md2, # links(ino1, dirs0), m5, entries2[p.last, entries[str]])], afs-cons(dirs0, files), ispath(parent(p), ROOT_INO, ino1, dirs0, files), ispath(q, ROOT_INO, ino0, dirs0, files), of-cons(of, dirs0, files), pw(user, md2), px(user, md2), px(user, md0), px-parent(user, parent(p), ROOT_INO, dirs0, files), px-parent(user, q, ROOT_INO, dirs0, files), str ∈ entries, ino2 ∈ dirs0, ino1 ∈ dirs0, ino0 ∈ dirs0, entries[str] ∈ files, str ∈ entries0, ino ∈ dirs0, str ∈ entries1, links(ino2, dirs0) ≠ ∅ ∨ ino2 = ROOT_INO, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino0, dirs0) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino, dirs0) ≠ ∅ ∨ ino = ROOT_INO ⊦ [afs_inc_nlink#(mkdentry(str, entries0[str]).ino; dirs, files); new_dent := mkdentry(p.last, mkdentry(str, entries0[str]).ino); afs_inode_sync#(mkinode(ino1, md2, true, # links(ino1, dirs0), m5, m1); dirs, files); afs_inode_sync#(mkinode(entries[str], md3, false, # links(entries[str], dirs0), 0, m); dirs, files); 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) ); c_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); err := ESUCCESS; asynced := ?] (afs-cons(dirs, files) → of-cons(of, dirs, files)), p = ε, p.last ∈ entries2, entries[str] ∈ dirs0

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] → [dirs0[ino], m4, md, m7, m8, entries1]

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: dirs0[ino], m4, md, m7, m8, entries1