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Proof step 37 from proof crash-neutral-unlink (previous step)

dirs0[m] = mkdir(m1 + 1, md1, # links(m, dirs0), m2, entries0), files1[entries0[str]] = mkfile(m3, md2, m4, content), dirs = dirs0[m, mkdir(m1, md1, # links(m, dirs0), m2, entries0 -- str)], files = files1[entries0[str], files1[entries0[str]].nlink:= m0], m4 = m0 + 1, afs-cons(dirs0, files1), m ∈ dirs0, entries0[str] ∈ files1, str ∈ entries0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_inode_sync#(mkinode(m, md, true, # links(m, dirs0), m2, m1 + 1); dirs, files); afs_inode_sync#(mkinode(entries0[str], md0, false, m4, 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)), ⟨fail#(; ; err); asynced := ?⟩ asynced

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 38:
# 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, md1, # links(m, dirs0), m2, entries0 -- str)], files = files1[entries0[str], mkfile(m3, md2, m0, content)], afs-cons(dirs0, files1), m ∈ dirs0, entries0[str] ∈ files1, str ∈ entries0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ asynced, ⟨afs_inode_sync#(mkinode(m, md, true, # links(m, dirs0), m2, m1 + 1); dirs, files); 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))

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).nlink:= m2 = mkfile(m, md, m2, content); (s)%afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base