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Proof step 40 from proof fsync-inode-inv (previous step)

icache[m] = mkientry(true, inode1), files[m] = mkfile(m0, md0, # links(m, dirs), content), err = ESUCCESS, inode0 = inode1, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), pre-write-inode(inode1, dirs, files), synced(dirs, icache, pcache), m ∈ icache, m ∈ files ⊦ [afs_write_inode#(inode1; err, dirs, files; asynced1)] ( afs-cons(dirs, files) → ⟪inode := inode1; if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, icache, pcache) ∧ inode.ino ∈ files ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 41:
files[m] = mkfile(m0, md0, # links(m, dirs), content), icache[m] = mkientry(true, inode1), err = ESUCCESS, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ files, m ∈ icache, inode1.ino ∈ dirs ∧ inode1.nlink = dirs[inode1.ino].nlink ∧ inode1.size = dirs[inode1.ino].size ∧ inode1.nsubdirs = dirs[inode1.ino].nsubdirs ∧ inode1.directory ∨ inode1.ino ∈ files ∧ inode1.nlink = files[inode1.ino].nlink ∧ inode1.nsubdirs = 0 ∧ ¬ inode1.directory ⊦ [afs_write_inode#(inode1; err, dirs, files; asynced1)] ( afs-cons(dirs, files) → ⟪inode := inode1; if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ inode.ino ∈ files ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory))

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)