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Proof step 2 from proof inv-truncate-buff-none-uncached (previous step)

pageno = inode.size / VFS_PAGE_SIZE, buf-opt.none?, 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), asynced → synced(files, icache, pcache) ⊦ ⟪cache_truncate#(n, pageno; buf-opt, inode, asynced0, err, dirs, files, asynced1, icache, pcache)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache))), datakey(inode.ino, pageno) ∈ pcache

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
inode.nlink = files[inode.ino].nlink, inode.nsubdirs = 0, buf-opt = none, 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, ¬ datakey(inode.ino, inode.size / VFS_PAGE_SIZE) ∈ pcache, asynced → synced(files, icache, pcache) ⊦ ⟪cache_truncate#(n, inode.size / VFS_PAGE_SIZE; buf-opt, inode, asynced0, err, dirs, files, asynced1, icache, pcache)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)))

Rule argument

Additional information

Used simplifier rules: ⊦ buf-opt.none? ↔ buf-opt = none; (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)