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Proof step 54 from proof inv-link (previous step)

dirs0[ino1] = mkdir(m4, md2, # links(ino1, dirs0), m8, entries), entries0[str] = entries[str], dirs0[m] = mkdir(m0, md1, # links(m, dirs0), m5, entries1), files0[entries[str]] = mkfile(m1, md4, # links(entries[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, entries[str]])], files = files0[entries[str], mkfile(m1, md4, # links(entries[str], dirs0) + 1, content0)], afs-cons (dirs0[m, mkdir(m0 + 1, md1, # links(m, dirs0), m5, entries1[str0, entries[str]])], files0[entries[str], mkfile(m1, md4, # links(entries[str], dirs0) + 1, content0)]), afs-cons(dirs0, files0), str ∈ entries, ino1 ∈ dirs0, ino0 ∈ dirs0, str ∈ entries0, m ∈ dirs0, entries[str] ∈ files0, ¬ str0 ∈ entries1, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino0, dirs0) ≠ ∅ ∨ ino0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_inode_sync#(mkinode(m, md, true, # links(m, dirs0), m5, m0); dirs, files)] ( afs-cons(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))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 55:
dirs0[ino0] = mkdir(m2, md3, # links(ino0, dirs0), m6, entries0), files0[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[ino1] = mkdir(m4, md2, # links(ino1, dirs0), m8, entries), dirs = dirs0[m, mkdir(m0 + 1, md1, # links(m, dirs0), m5, entries1[str0, entries[str]])], files = files0[entries[str], mkfile(m1, md4, # links(entries[str], dirs0) + 1, content0)], inode = mkinode(m, md, true, # links(m, dirs0), m5, m0), afs-cons(dirs0, files0), afs-cons (dirs0[m, mkdir(m0 + 1, md1, # links(m, dirs0), m5, entries1[str0, entries[str]])], files0[entries[str], mkfile(m1, md4, # links(entries[str], dirs0) + 1, content0)]), entries[str] ∈ files0, m ∈ dirs0, str ∈ entries0, ino0 ∈ dirs0, ino1 ∈ dirs0, str ∈ entries, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(ino0, dirs0) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [let ino = inode.ino in if ino ∈ files then {files[ino].size := inode.size; files[ino].meta := inode.meta} else if ino ∈ dirs then dirs[ino].meta := inode.meta] ( afs-cons(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

Rule argument

pos: right 1

Additional information

Used simplifier rules: internal-inode-sync: ⊦ ;