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Proof step 2 from proof fsync-pages-inv (previous step)

afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), valid-file-inode(inode, dirs, files) ⊦ ⟪cache_fsync-pages#(inode, dirs; err, files, pcache, asynced)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, icache, pcache) ∧ valid-file-inode(inode, 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), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), inode.ino ∈ files, ¬ inode.directory ⊦ ⟪cache_fsync-pages#(inode, dirs; err, files, pcache, asynced)⟫ ( 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)

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)