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Proof step 2 from proof crash-neutral-fsync (previous step)

asynced, dirs0 = dirs \ orphans(dirs, files), files0 = files \ orphans(dirs, files), afs-cons(dirs, files), valid-file-inode(inode, dirs, files) ⊦ ⟨afs_fsync#(inode, asynced0, dirs, files; ; asynced, err)⟩ (asynced ∧ dirs0 = dirs \ orphans(dirs, files) ∧ files0 = files \ orphans(dirs, files))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
inode.nlink = files[inode.ino].nlink, inode.nsubdirs = 0, afs-cons(dirs, files), inode.ino ∈ files, ¬ inode.directory ⊦ ⟨afs_fsync#(inode, asynced0, dirs, files; ; asynced, err)⟩ asynced

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)