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Proof step 2 from proof refine-truncate-buff-none-cached (previous step)

asynced ↔ asynced0, afs_asynced ↔ cache_asynced, afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, buf-opt = buf-opt0, err = err0, inode = inode0, pageno = inode.size / VFS_PAGE_SIZE, buf-opt.none?, afs-cons(cache_dirs, cache_files), afs-cons(afs_dirs, afs_files), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), valid-file-inode(inode, afs_dirs, afs_files), datakey(inode.ino, pageno) ∈ cache_pcache, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪cache_truncate#(n, pageno; buf-opt, inode, asynced, err, cache_dirs, cache_files, cache_asynced, cache_icache, cache_pcache)⟫ ⟨afs_truncate#(n, pageno; buf-opt0, inode0, asynced0, err0, afs_dirs, afs_files, afs_asynced)⟩ ( (afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced)) ∧ buf-opt = buf-opt0 ∧ inode = inode0 ∧ (asynced ↔ asynced0) ∧ err = err0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
inode0.nlink = ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[inode0.ino].nlink, inode0.nsubdirs = 0, asynced ↔ asynced0, afs_asynced ↔ cache_asynced, afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, buf-opt = none, err = err0, inode = inode0, afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), inode0.ino ∈ cache_files, datakey(inode0.ino, inode0.size / VFS_PAGE_SIZE) ∈ cache_pcache, ¬ inode0.directory, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪cache_truncate# (n, inode0.size / VFS_PAGE_SIZE; buf-opt, inode, asynced, err, cache_dirs, cache_files, cache_asynced, cache_icache, cache_pcache)⟫ ⟨buf-opt0 := none; afs_truncate#(n, inode0.size / VFS_PAGE_SIZE; buf-opt0, inode0, asynced0, err0, afs_dirs, afs_files, afs_asynced)⟩ ( afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced) ∧ buf-opt = buf-opt0 ∧ inode = inode0 ∧ (asynced ↔ asynced0) ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ buf-opt.none? ↔ buf-opt = none; (s)% ⊦ ino ∈ files ⊕ pcache ↔ ino ∈ files; (s)% ⊦ ino ∈ files ⊕ icache ↔ ino ∈ files; (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)