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Proof step 5 from proof fsync-dirs (previous step)

asynced0 ↔ bv0, asynced1 ↔ bv, ¬ asynced0, dirs = dirs0, err = ESUCCESS, valid-file-inode(inode, dirs, files) ⊦ [cache_fsync-pages#(inode, dirs; err, files, pcache, asynced); if err = ESUCCESS ∧ ¬ asynced1 then cache_fsync-inode#(; inode, err, dirs, files, icache, asynced); if err = ESUCCESS then afs_fsync#(inode, asynced1, dirs, files; ; asynced, err)] (dirs = dirs0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
inode.nlink = files[inode.ino].nlink, inode.nsubdirs = 0, err = ESUCCESS, inode.ino ∈ files, ¬ inode.directory ⊦ [cache_fsync-pages#(inode, dirs0; err, files, pcache, asynced); dirs := dirs0; if err = ESUCCESS ∧ ¬ asynced1 then cache_fsync-inode#(; inode, err, dirs, files, icache, asynced); if err = ESUCCESS then afs_fsync#(inode, asynced1, dirs, files; ; asynced, 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)