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Proof step 41 from proof afs-cons-rename-dir-negdentry (previous step)

asynced0 ↔ old_ino = new_ino ∧ new_dent = old_dent, asynced1 ↔ new_dent.dentry?, dirs0[m] = mkdir(m4, md4, # links(m, dirs0), m7, entries1), dirs0[m0] = mkdir(m1, md2, # links(m0, dirs0), m3, entries), dirs0[entries1[str]] = mkdir(m2, md3, # links(entries1[str], dirs0), m5, entries0), ¬ asynced0, ¬ asynced1, dirs = dirs4[new_ino, dirs4[new_ino].nsubdirs:= (dirs4[new_ino].nsubdirs + 1)], dirs1 = dirs0[old_ino, dirs0[old_ino].entries:= (dirs0[old_ino].entries -- old_dent.name)], dirs2 = dirs1[old_ino, dirs1[old_ino].size:= (dirs1[old_ino].size - 1)], dirs3 = dirs2[old_ino, dirs2[old_ino].nsubdirs:= (dirs2[old_ino].nsubdirs - 1)] [new_ino, dirs2[old_ino, dirs2[old_ino].nsubdirs:= (dirs2[old_ino].nsubdirs - 1)][new_ino] .entries:= dirs2[old_ino, dirs2[old_ino].nsubdirs:= (dirs2[old_ino].nsubdirs - 1)][new_ino].entries[new_dent.name, old_dent.ino] ], dirs4 = dirs3[new_ino, dirs3[new_ino].size:= (dirs3[new_ino].size + 1)], new_dent = negdentry(str0), new_ino = new_parent_inode.ino, new_parent_inode = mkinode(m0, md1, true, # links(m0, dirs0), m3, m1), old_child_inode = mkinode(entries1[str], md, true, # links(entries1[str], dirs0), m5, m2), old_dent = mkdentry(str, entries1[str]), old_ino = old_parent_inode.ino, old_parent_inode = mkinode(m, md0, true, # links(m, dirs0), m7, m4), old_dent.dentry?, afs-cons(dirs0, files), pre-rename(old_parent_inode, old_dent, old_child_inode, new_parent_inode, new_dent, new_child_inode, dirs0, files), old_dent.ino ∈ dirs2, str ∈ entries1, entries1[str] ∈ dirs0, m ∈ dirs0, m0 ∈ dirs0, old_dent.ino ∈ dirs4, dirs1[old_ino].size ≥ 1, dirs2[old_ino].nsubdirs ≥ 1, m0 = m → md1 = md0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪afs_inode_sync#(old_parent_inode; dirs, files); afs_inode_sync#(new_parent_inode; dirs, files); if asynced1 then {afs_inode_sync#(new_child_inode; dirs, files); new_child_inode := getinode(new_child_inode.ino, dirs, files)}; old_parent_inode := getinode(old_parent_inode.ino, dirs, files); new_parent_inode := getinode(new_parent_inode.ino, dirs, files); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files), str0 ∈ entries, asynced1 ∧ ¬ asynced0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
# links(entries1[str], dirs0) = dirs0[entries1[str]].nlink, # links(m0, dirs0) = dirs0[m0].nlink, # links(m, dirs0) = dirs0[m].nlink, entries1[str] = dirs0[m].entries[str], dirs0[m] = mkdir(dirs0[m].size, md4, dirs0[m].nlink, dirs0[m].nsubdirs, entries1), dirs0[m0] = mkdir(dirs0[m0].size, md2, dirs0[m0].nlink, dirs0[m0].nsubdirs, entries), dirs0[entries1[str]] = mkdir(dirs0[entries1[str]].size, md3, dirs0[entries1[str]].nlink, dirs0[entries1[str]].nsubdirs, entries0), dirs = dirs0[m, ((dirs0[m].entries:= (dirs0[m].entries -- str)).size:= (dirs0[m].size - 1)).nsubdirs:= (dirs0[m].nsubdirs - 1)] [m0, ( ( (m0 = m ⊃ ((dirs0[m].entries:= (dirs0[m].entries -- str)).size:= (dirs0[m].size - 1)).nsubdirs:= (dirs0[m].nsubdirs - 1) ;dirs0[m0] ) .entries:= (m0 = m ⊃ ((dirs0[m].entries:= (dirs0[m].entries -- str)).size:= (dirs0[m].size - 1)).nsubdirs:= (dirs0[m].nsubdirs - 1) ;dirs0[m0] ) .entries [str0, entries1[str] ]) .size:= ( (m0 = m ⊃ ((dirs0[m].entries:= (dirs0[m].entries -- str)).size:= (dirs0[m].size - 1)).nsubdirs:= (dirs0[m].nsubdirs - 1) ;dirs0[m0] ) .size + 1)) .nsubdirs:= ( (m0 = m ⊃ ((dirs0[m].entries:= (dirs0[m].entries -- str)).size:= (dirs0[m].size - 1)).nsubdirs:= (dirs0[m].nsubdirs - 1);dirs0[m0]) .nsubdirs + 1) ], afs-cons(dirs0, files), str ∈ dirs0[m].entries, str ∈ entries1, m ∈ dirs0, m0 ∈ dirs0, entries1[str] ∈ dirs0, 1 ≤ dirs0[m].size, 1 ≤ dirs0[m].nsubdirs, ¬ str0 ∈ dirs0[m0].entries, ¬ str0 ∈ entries, m0 = m → md1 = md0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪afs_inode_sync#(mkinode(m, md0, true, dirs0[m].nlink, dirs0[m].nsubdirs, dirs0[m].size); dirs, files); afs_inode_sync#(mkinode(m0, md1, true, # links(m0, dirs0), dirs0[m0].nsubdirs, dirs0[m0].size); dirs, files); skip; old_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) ); new_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) ); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files)

Rule argument

Additional information

Used simplifier rules: ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ mkdentry(str, m) ≠ negdentry(str0); (s)% ⊦ ¬ negdentry(str).dentry?; (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ mkdentry(str, m).ino = m; (s)% ⊦ negdentry(str).name = str; (s)% ⊦ (ad.entries:= entries).nsubdirs = ad.nsubdirs; (s)% ⊦ (ad.size:= m).nsubdirs = ad.nsubdirs; (s)% ⊦ dirs[ino, ad][ino, ad0] = dirs[ino, ad0]; (s)% ⊦ (ad.entries:= entries).size = ad.size; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)