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Proof step 53 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), afs-cons(dirs0, files1), m ∈ dirs0, str ∈ entries0, entries0[str] ∈ files1, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⌊EFAIL⌋ ∧ ⟨err := EFAIL; asynced := ?⟩ asynced, ⟨let ino = entries0[str] in {files := files1[entries0[str], mkfile(m3, md2, m0, content)]; dirs := dirs0[m, mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)]; if ino ∈ files then {files[ino].size := m8; files[ino].meta := md3} else if ino ∈ dirs then dirs[ino].meta := md3}; 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))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 54:
# 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), afs-cons(dirs0, files1), entries0[str] ∈ files1, str ∈ entries0, m ∈ dirs0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨let ino = entries0[str] in {files := files1[entries0[str], mkfile(m3, md2, m0, content)]; dirs := dirs0[m, mkdir(m1, md, # links(m, dirs0), m2, entries0 -- str)]; if ino ∈ files then {files[ino].size := m8; files[ino].meta := md3} else if ino ∈ dirs then dirs[ino].meta := md3}; 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)), ⟨err := EFAIL; asynced := ?⟩ asynced

Rule argument

Additional information

Used simplifier rules: ⊦ ⌊EFAIL⌋ ; (s)