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Proof step 67 from proof fsync-dirs (previous step)

icache[m] = mkientry(true, inode1), files0[m] = mkfile(m0, md0, m1, content), dirs = dirs0, err = ESUCCESS, err0 = ESUCCESS, inode = inode1, inode.directory, pre-write-inode(inode, dirs, files), m ∈ files0, m ∈ icache, m2 ≤ n * VFS_PAGE_SIZE ⊦ [icache_set_status#(m, false; err, icache); dirs[inode.ino].meta := inode.meta; if err = ESUCCESS then afs_fsync#(inode1, false, dirs, files; ; asynced2, err)] (dirs = dirs0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 68:
inode1.nlink = dirs0[inode1.ino].nlink, inode1.nsubdirs = dirs0[inode1.ino].nsubdirs, inode1.size = dirs0[inode1.ino].size, files0[m] = mkfile(m0, md0, m1, content), icache[m] = mkientry(true, inode1), err = ESUCCESS, inode1.directory, m ∈ icache, m ∈ files0, inode1.ino ∈ dirs0, m2 ≤ n * VFS_PAGE_SIZE ⊦ [icache_set_status#(m, false; err, icache); dirs := dirs0[inode1.ino, dirs0[inode1.ino].meta:= inode1.meta]; if err = ESUCCESS then afs_fsync#(inode1, 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)