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Proof step 34 from proof crash-neutral-link (previous step)

files[entries0[str]] = mkfile(m0, md4, # links(entries0[str], dirs), content0), dirs[m] = mkdir(m1, md2, # links(m, dirs), m5, entries1), dirs[ino1] = mkdir(m4, md3, # links(ino1, dirs), m6, entries0), entries0[str] = entries[str], dirs[ino0] = mkdir(m2, md1, m7, m8, entries), dirs1 = dirs[m, mkdir(m1 + 1, md2, # links(m, dirs), m5, entries1[str0, entries0[str]])], files0 = files, afs-cons(dirs, files), ino1 ∈ dirs, m ∈ dirs, entries0[str] ∈ files, ino0 ∈ dirs, str ∈ entries, str ∈ entries0, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO ⊦ ⟨afs_inc_nlink#(mkdentry(str, entries0[str]).ino; dirs1, files); new_dent := mkdentry(str0, mkdentry(str, entries0[str]).ino); afs_inode_sync#(mkinode(m, md, true, # links(m, dirs), m5, m1); dirs1, files); afs_inode_sync#(mkinode(entries0[str], md0, false, # links(entries0[str], dirs), 0, m3); dirs1, files); p_inode := (m ∈ dirs1 ⊃ mkinode(m, dirs1[m].meta, true, dirs1[m].nlink, dirs1[m].nsubdirs, dirs1[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := getinode(mkdentry(str, entries0[str]).ino, dirs1, files); err := ESUCCESS; asynced := ?⟩ (asynced ∧ dirs \ orphans(dirs, files0) = dirs1 \ orphans(dirs1, files) ∧ files0 \ orphans(dirs, files0) = files \ orphans(dirs1, files)), ⟨fail#(; ; err); asynced := ?⟩ asynced, str0 ∈ entries1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 35:
files[entries[str]] = mkfile(m0, md4, # links(entries[str], dirs), content0), dirs[m] = mkdir(m1, md2, # links(m, dirs), m5, entries1), dirs[ino1] = mkdir(m4, md3, # links(ino1, dirs), m6, entries0), entries0[str] = entries[str], dirs[ino0] = mkdir(m2, md1, # links(ino0, dirs), m8, entries), dirs1 = dirs[m, mkdir(m1 + 1, md2, # links(m, dirs), m5, entries1[str0, entries[str]])], files0 = files, afs-cons(dirs, files), ino1 ∈ dirs, m ∈ dirs, entries[str] ∈ files, ino0 ∈ dirs, str ∈ entries, str ∈ entries0, ¬ str0 ∈ entries1, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ asynced, ⟨afs_inc_nlink#(mkdentry(str, entries0[str]).ino; dirs1, files); new_dent := mkdentry(str0, mkdentry(str, entries0[str]).ino); afs_inode_sync#(mkinode(m, md, true, # links(m, dirs), m5, m1); dirs1, files); afs_inode_sync#(mkinode(entries0[str], md0, false, # links(entries0[str], dirs), 0, m3); dirs1, files); p_inode := (m ∈ dirs1 ⊃ mkinode(m, dirs1[m].meta, true, dirs1[m].nlink, dirs1[m].nsubdirs, dirs1[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := getinode(mkdentry(str, entries0[str]).ino, dirs1, files); err := ESUCCESS; asynced := ?⟩ (asynced ∧ dirs \ orphans(dirs, files0) = dirs1 \ orphans(dirs1, files) ∧ files0 \ orphans(dirs, files0) = files \ orphans(dirs1, files))

Rule argument

Additional information

Used simplifier rules: afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base