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Proof step 48 from proof crash-neutral-unlink (previous step)

# links(entries0[str], dirs0) = m0 + 1, files1[entries0[str]] = mkfile(m3, md2, m0 + 1, content), dirs0[m] = mkdir(m1 + 1, md1, # links(m, dirs0), m2, entries0), dirs = dirs1[ino, dirs1[ino].meta:= inode.meta], dirs1 = dirs0[m, mkdir(m1, md1, # links(m, dirs0), m2, entries0 -- str)], files = files1[entries0[str], mkfile(m3, md2, m0, content)], ino = inode.ino, inode = mkinode(m, md, true, # links(m, dirs0), m2, m1 + 1), afs-cons(dirs0, files1), str ∈ entries0, entries0[str] ∈ files1, m ∈ dirs0, ino ∈ dirs1, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_inode_sync#(mkinode(entries0[str], md0, false, m0 + 1, 0, m5); 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 := (entries0[str] ∈ dirs ⊃ mkinode(entries0[str], dirs[entries0[str]].meta, true, dirs[entries0[str]].nlink, dirs[entries0[str]].nsubdirs, dirs[entries0[str]].size) ;mkinode(entries0[str], files[entries0[str]].meta, false, files[entries0[str]].nlink, 0, files[entries0[str]].size) ); err := ESUCCESS; asynced := ?⟩ (asynced ∧ dirs0 \ orphans(dirs0, files1) = dirs \ orphans(dirs, files) ∧ files1 \ orphans(dirs0, files1) = files \ orphans(dirs, files)), ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; asynced := ?⟩ asynced, ino ∈ files

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 49:
# links(entries0[str], dirs0) = m0 + 1, dirs0[m] = mkdir(m1 + 1, md1, # links(m, dirs0), m2, entries0), files1[entries0[str]] = mkfile(m3, md2, m0 + 1, content), dirs = dirs0[m, mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)], files = files1[entries0[str], mkfile(m3, md2, m0, content)], afs-cons(dirs0, files1), entries0[str] ∈ files1, str ∈ entries0, m ∈ dirs0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_inode_sync#(mkinode(entries0[str], md0, false, m0 + 1, 0, m5); 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 := (entries0[str] ∈ dirs ⊃ mkinode(entries0[str], dirs[entries0[str]].meta, true, dirs[entries0[str]].nlink, dirs[entries0[str]].nsubdirs, dirs[entries0[str]].size) ;mkinode(entries0[str], files[entries0[str]].meta, false, files[entries0[str]].nlink, 0, files[entries0[str]].size) ); err := ESUCCESS; asynced := ?⟩ (asynced ∧ dirs0 \ orphans(dirs0, files1) = dirs \ orphans(dirs, files) ∧ files1 \ orphans(dirs0, files1) = files \ orphans(dirs, files)), ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; asynced := ?⟩ asynced

Rule argument

Additional information

Used simplifier rules: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ dirs[ino, ad][ino, ad0] = dirs[ino, ad0]; (s)%⊦ mkdir(m, md, m0, m1, entries).meta:= md0 = mkdir(m, md0, m0, m1, entries); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)