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Proof step 28 from proof inv-link (previous step)

# links(m, dirs0) = m4, dirs0[ino0] = mkdir(m2, md3, # links(ino0, dirs0), m6, entries0), files[entries0[str]] = mkfile(m1, md4, # links(entries0[str], dirs0), content0), dirs0[m] = mkdir(m0, md2, m4, m5, entries), entries0[str] = dirs0[ino].entries[str], dirs0[m] = mkdir(m0, md1, m4, m5, entries1), dirs = dirs0[m, (dirs0[m].entries:= entries1[str0, entries0[str]]).size:= (m0 + 1)], afs-cons(dirs0, files), entries0[str] ∈ files, m ∈ dirs0, str ∈ entries0, ino0 ∈ dirs0, ino ∈ dirs0, str ∈ dirs0[ino].entries, links(m, dirs0) ≠ ∅ ∨ m = 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(str0, mkdentry(str, entries0[str]).ino); afs_inode_sync#(mkinode(m, md, true, m4, m5, m0); dirs, files); afs_inode_sync#(mkinode(entries0[str], md0, false, # links(entries0[str], dirs0), 0, m3); dirs, files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files), str0 ∈ entries, str0 ∈ entries1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
entries0[str] = dirs0[ino].entries[str], dirs0[m] = mkdir(m0, md1, # links(m, dirs0), m5, entries1), files[entries0[str]] = mkfile(m1, md4, # links(entries0[str], dirs0), content0), dirs0[ino0] = mkdir(m2, md3, # links(ino0, dirs0), m6, entries0), dirs = dirs0[m, mkdir(m0 + 1, md1, # links(m, dirs0), m5, entries1[str0, entries0[str]])], afs-cons(dirs0, files), str ∈ dirs0[ino].entries, ino ∈ dirs0, ino0 ∈ dirs0, str ∈ entries0, m ∈ dirs0, entries0[str] ∈ files, ¬ str0 ∈ entries1, links(ino, dirs0) ≠ ∅ ∨ ino = ROOT_INO, links(ino0, dirs0) ≠ ∅ ∨ ino0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪afs_inc_nlink#(mkdentry(str, entries0[str]).ino; dirs, files); new_dent := mkdentry(str0, mkdentry(str, entries0[str]).ino); afs_inode_sync#(mkinode(m, md, true, # links(m, dirs0), m5, m0); dirs, files); afs_inode_sync#(mkinode(entries0[str], md0, false, # links(entries0[str], dirs0), 0, m3); dirs, files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files)

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).size:= m2 = mkdir(m2, md, m0, m1, entries); (s)%⊦ mkdir(m, md, m0, m1, entries).entries:= entries0 = mkdir(m, md, m0, m1, entries0); (s)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)