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

dirs0[m] = mkdir(m0, md3, # links(m, dirs0), m2, entries0), dirs0[entries0[str]] = mkdir(m1, md2, # links(entries0[str], dirs0), m4, ∅), dirs = dirs0[m, mkdir(m3, md3, # links(m, dirs0), m2 - 1, entries0 -- str)], ino = mkdentry(str, entries0[str]).ino, m0 = m3 + 1, mkdentry(str, entries0[str]).dentry?, afs-cons(dirs0, files), m ∈ dirs0, str ∈ entries0, entries0[str] ∈ dirs0, 1 ≤ m2, 1 ≤ m0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪if ino ∈ dirs then dirs[ino].nlink := dirs[ino].nlink - 1; if ino ∈ files then files[ino].nlink := files[ino].nlink - 1; dent := negdentry(mkdentry(str, entries0[str]).name); afs_inode_sync#(mkinode(m, md0, true, # links(m, dirs0), m2, m0); dirs, files); afs_inode_sync#(mkinode(entries0[str], md, true, # links(entries0[str], dirs0), m4, m1); 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(entries0[str], dirs, files); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files), entries0[str] = ROOT_INO, m0 = 0, m2 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
dirs0[entries0[str]] = mkdir(m1, md2, # links(entries0[str], dirs0), m4, ∅), dirs0[m] = mkdir(m3 + 1, md3, # links(m, dirs0), m2, entries0), dirs = dirs0[m, mkdir(m3, md3, # links(m, dirs0), m2 - 1, entries0 -- str)], ino = entries0[str], entries0[str] ≠ ROOT_INO, m2 ≠ 0, afs-cons(dirs0, files), entries0[str] ∈ dirs0, str ∈ entries0, m ∈ dirs0, 1 ≤ m2, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪if ino ∈ dirs then dirs[ino].nlink := dirs[ino].nlink - 1; if ino ∈ files then files[ino].nlink := files[ino].nlink - 1; dent := negdentry(mkdentry(str, entries0[str]).name); afs_inode_sync#(mkinode(m, md0, true, # links(m, dirs0), m2, m3 + 1); dirs, files); afs_inode_sync#(mkinode(entries0[str], md, true, # links(entries0[str], dirs0), m4, m1); 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(entries0[str], dirs, files); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files)

Rule argument

Additional information

Used simplifier rules: ⊦ mkdentry(str, m).dentry?; (s)% ⊦ m ≤ m + n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)% ⊦ mkdentry(str, m).ino = m; (s)