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Proof step 30 from proof inv-link (previous step)

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, md1, # links(m, dirs0), m5, entries1), entries0[str] = entries[str], dirs0[ino] = mkdir(m4, md2, m7, m8, entries), dirs = dirs0[m, mkdir(m0 + 1, md1, # links(m, dirs0), m5, entries1[str0, entries0[str]])], afs-cons(dirs0, files), entries0[str] ∈ files, m ∈ dirs0, str ∈ entries0, ino0 ∈ dirs0, ino ∈ dirs0, str ∈ 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, # 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), str0 ∈ entries1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
dirs0[ino0] = mkdir(m2, md3, # links(ino0, dirs0), m6, entries0), files[entries[str]] = mkfile(m1, md4, # links(entries[str], dirs0), content0), dirs0[m] = mkdir(m0, md1, # links(m, dirs0), m5, entries1), entries0[str] = entries[str], dirs0[ino] = mkdir(m4, md2, # links(ino, dirs0), m8, entries), dirs = dirs0[m, mkdir(m0 + 1, md1, # links(m, dirs0), m5, entries1[str0, entries[str]])], afs-cons(dirs0, files), entries[str] ∈ files, m ∈ dirs0, str ∈ entries0, ino0 ∈ dirs0, ino ∈ dirs0, str ∈ entries, ¬ str0 ∈ entries1, 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, # 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: afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base