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Proof step 88 from proof fsync-dirs (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 89:
inode1.nlink = files[inode1.ino].nlink, inode1.nsubdirs = 0, icache[m] = mkientry(true, inode1), files0[m] = mkfile(m0, md0, m1, content), err = ESUCCESS, m ∈ files0, m ∈ icache, inode1.ino ∈ files, m2 ≤ n * VFS_PAGE_SIZE, ¬ inode1.directory ⊦ [icache_set_status#(m, false; err, icache); dirs := dirs0; if err = ESUCCESS then afs_fsync# (inode1, false, dirs, files[inode1.ino, (inode1.ino ∈ files ⊃ files[inode1.ino].meta:= inode1.meta;files[inode1.ino]).size:= inode1.size] ; ; asynced2, err)] (dirs = dirs0)

Rule argument

Additional information

Used simplifier rules: ⊦ files[ino, af][ino, af0] = files[ino, af0]; (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (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)% ⊦ 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)