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Proof step 97 from proof fsync-dirs (previous step)

files0[m] = mkfile(m0, md0, m1, content), icache[m] = mkientry(true, inode1), dirs = dirs0, err = ESUCCESS, inode = inode1, pre-write-inode(inode, dirs, files), m ∈ icache, m ∈ files0, m2 ≤ n * VFS_PAGE_SIZE ⊦ [fail#(; ; err); asynced := ?; inode := inode1; if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache)}; if err = ESUCCESS then afs_fsync#(inode, false, dirs, files; ; asynced2, err)] (dirs = dirs0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 98:
icache[m] = mkientry(true, inode1), files0[m] = mkfile(m0, md0, m1, content), m ∈ files0, m ∈ icache, m2 ≤ n * VFS_PAGE_SIZE, inode1.ino ∈ dirs0 ∧ inode1.nlink = dirs0[inode1.ino].nlink ∧ inode1.size = dirs0[inode1.ino].size ∧ inode1.nsubdirs = dirs0[inode1.ino].nsubdirs ∧ inode1.directory ∨ inode1.ino ∈ files ∧ inode1.nlink = files[inode1.ino].nlink ∧ inode1.nsubdirs = 0 ∧ ¬ inode1.directory ⊦ [fail#(; ; err); asynced := ?; inode := inode1; if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache)}; dirs := dirs0; if err = ESUCCESS then afs_fsync#(inode, false, dirs, files; ; asynced2, err)] (dirs = dirs0)

Rule argument

Additional information

Used simplifier rules: ⊦ 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)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (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)