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Proof step 48 from proof afs-cons-rename-dir-dentry (previous step)

# links(m, dirs0) = m8, dirs0[entries2[str0]] = mkdir(m4, md3, # links(entries2[str0], dirs0), m7, entries1), dirs0[entries[str]] = mkdir(m3, md6, # links(entries[str], dirs0), m5, ∅), dirs0[m] = mkdir(m6, md4, m8, m9, entries), dirs0[m0] = mkdir(m1 + 1, md0, # links(m0, dirs0), m2 + 1, entries2), entries[str] = entries0[str], dirs0[m] = mkdir(m6, md5, m8, m9, entries0), dirs = dirs0[m0, mkdir(m1, md0, # links(m0, dirs0), m2, entries2 -- str0)] [m, (m = m0 ⊃ mkdir(m1, md0, # links(m0, dirs0), m2, entries2 -- str0);dirs0[m]) .entries:= (m = m0 ⊃ mkdir(m1, md0, # links(m0, dirs0), m2, entries2 -- str0);dirs0[m]).entries[str, entries2[str0]] ], afs-cons(dirs0, files), str ∈ entries, str0 ∈ entries2, entries[str] ∈ dirs0, entries2[str0] ∈ dirs0, m ∈ dirs0, m0 ∈ dirs0, str ∈ entries0, m = m0 → md1 = md2, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪afs_drop_nlink#(mkdentry(str, entries[str]).ino; dirs, files); old_dent := mkdentry(str0, entries2[str0]); asynced1 := true; if ¬ asynced1 then {dirs[m].size := dirs[m].size + 1; if old_dent.ino ∈ dirs then dirs[m].nsubdirs := dirs[m].nsubdirs + 1}; new_dent := mkdentry(mkdentry(str, entries[str]).name, old_dent.ino); old_dent := negdentry(old_dent.name); afs_inode_sync#(mkinode(m0, md2, true, # links(m0, dirs0), m2 + 1, m1 + 1); dirs, files); afs_inode_sync#(mkinode(m, md1, true, # links(m, dirs0), m9, m6); dirs, files); if asynced1 then {afs_inode_sync#(mkinode(entries[str], md, true, # links(entries[str], dirs0), m5, m3); dirs, files); new_child_inode := getinode(entries[str], dirs, files)}; old_parent_inode := (m0 ∈ dirs ⊃ mkinode(m0, dirs[m0].meta, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size) ;mkinode(m0, files[m0].meta, false, files[m0].nlink, 0, files[m0].size) ); new_parent_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) ); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files), entries[str] = ROOT_INO, m0 = m ∧ mkdentry(str, entries[str]) = mkdentry(str0, entries2[str0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 49:
dirs0[m0] = mkdir(m1 + 1, md0, # links(m0, dirs0), m2 + 1, entries2), dirs0[m] = mkdir(m6, md5, # links(m, dirs0), m9, entries0), dirs0[entries0[str]] = mkdir(m3, md6, # links(entries0[str], dirs0), m5, ∅), dirs0[entries2[str0]] = mkdir(m4, md3, # links(entries2[str0], dirs0), m7, entries1), dirs = dirs0[m0, mkdir(m1, md0, # links(m0, dirs0), m2, entries2 -- str0)] [m, (m = m0 ⊃ mkdir(m1, md0, # links(m0, dirs0), m2, entries2 -- str0);mkdir(m6, md5, # links(m, dirs0), m9, entries0)) .entries:= (m = m0 ⊃ mkdir(m1, md0, # links(m0, dirs0), m2, entries2 -- str0);mkdir(m6, md5, # links(m, dirs0), m9, entries0)).entries [str, entries2[str0] ] ], entries0[str] ≠ ROOT_INO, afs-cons(dirs0, files), m0 ∈ dirs0, m ∈ dirs0, entries2[str0] ∈ dirs0, entries0[str] ∈ dirs0, str0 ∈ entries2, str ∈ entries0, m = m0 → md1 = md2, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪afs_drop_nlink#(mkdentry(str, entries0[str]).ino; dirs, files); old_dent := mkdentry(str0, entries2[str0]); asynced1 := true; if ¬ asynced1 then {dirs[m].size := dirs[m].size + 1; if old_dent.ino ∈ dirs then dirs[m].nsubdirs := dirs[m].nsubdirs + 1}; new_dent := mkdentry(mkdentry(str, entries0[str]).name, old_dent.ino); old_dent := negdentry(old_dent.name); afs_inode_sync#(mkinode(m0, md2, true, # links(m0, dirs0), m2 + 1, m1 + 1); dirs, files); afs_inode_sync#(mkinode(m, md1, true, # links(m, dirs0), m9, m6); dirs, files); if asynced1 then {afs_inode_sync#(mkinode(entries0[str], md, true, # links(entries0[str], dirs0), m5, m3); dirs, files); new_child_inode := getinode(entries0[str], dirs, files)}; old_parent_inode := (m0 ∈ dirs ⊃ mkinode(m0, dirs[m0].meta, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size) ;mkinode(m0, files[m0].meta, false, files[m0].nlink, 0, files[m0].size) ); new_parent_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) ); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files), m0 = m ∧ mkdentry(str, entries0[str]) = mkdentry(str0, entries2[str0])

Rule argument

Additional information

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