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Proof step 8 from proof crash-neutral-write_inode (previous step)

dirs0 = dirs \ orphans(dirs, files), files0 = files \ orphans(dirs, files), inode = mkinode(m, md, boolvar, m0, m1, m2), afs-cons(dirs, files), pre-write-inode(inode, dirs, files), m ∈ dirs ∧ m0 = dirs[m].nlink ∧ m2 = dirs[m].size ∧ m1 = dirs[m].nsubdirs ∧ boolvar ∨ m ∈ files ∧ m0 = files[m].nlink ∧ m1 = 0 ∧ ¬ boolvar ⊦ ⟨fail#(; ; err); asynced := ?⟩ (asynced ∧ dirs0 = dirs \ orphans(dirs, files) ∧ files0 = files \ orphans(dirs, files)), ⟨if inode.directory then dirs[inode.ino].meta := inode.meta else {files[inode.ino].meta := inode.meta; files[inode.ino].size := inode.size}; err := ESUCCESS; asynced := ?⟩ (asynced ∧ dirs0 = dirs \ orphans(dirs, files) ∧ files0 = files \ orphans(dirs, files))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
dirs0 = dirs \ orphans(dirs, files), files0 = files \ orphans(dirs, files), afs-cons(dirs, files), m ∈ dirs ∧ m0 = dirs[m].nlink ∧ m2 = dirs[m].size ∧ m1 = dirs[m].nsubdirs ∧ boolvar ∨ m ∈ files ∧ m0 = files[m].nlink ∧ m1 = 0 ∧ ¬ boolvar ⊦ ⟨fail#(; ; err); asynced := ?⟩ asynced, ⟨if boolvar then dirs[m].meta := md else {files[m].meta := md; files[m].size := m2}; err := ESUCCESS; asynced := ?⟩ (asynced ∧ dirs0 = dirs \ orphans(dirs, files) ∧ files0 = files \ orphans(dirs, files))

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ valid-dir-inode(inode, dirs, files) ↔ valid-dir-ino(inode.ino, dirs, files) ∧ inode.nlink = dirs[inode.ino].nlink ∧ inode.size = dirs[inode.ino].size ∧ inode.nsubdirs = dirs[inode.ino].nsubdirs ∧ inode.directory; (s)%⊦ valid-wb-inode(inode, dirs, files) ↔ valid-dir-inode(inode, dirs, files) ∨ valid-file-inode(inode, dirs, files); (s)%⊦ pre-write-inode(inode, dirs, files) ↔ valid-wb-inode(inode, dirs, files); (s)