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Proof step 2 from proof refine-write_inode (previous step)

afs_asynced ↔ cache_asynced, afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = err0, 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), pre-write-inode(inode, afs_dirs, afs_files), synced(cache_dirs, cache_icache, cache_pcache), cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪cache_write_inode#(inode, cache_sync; err, cache_dirs, cache_files, cache_icache, cache_asynced)⟫ ⟨afs_write_inode#(inode; err0, afs_dirs, afs_files; afs_asynced)⟩ ((afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced)) ∧ err = err0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = err0, afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_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), cache_sync → synced(cache_files, cache_icache, cache_pcache), inode.ino ∈ cache_dirs ∧ inode.nlink = cache_dirs[inode.ino].nlink ∧ inode.size = cache_dirs[inode.ino].size ∧ inode.nsubdirs = cache_dirs[inode.ino].nsubdirs ∧ inode.directory ∨ inode.ino ∈ cache_files ∧ inode.nlink = ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory ⊦ ⟪cache_write_inode#(inode, cache_sync; err, cache_dirs, cache_files, cache_icache, cache_asynced)⟫ ⟨afs_write_inode#(inode; err0, afs_dirs, afs_files; afs_asynced)⟩ (afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced) ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ 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)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)%⊦ valid-dir-inode(inode, dirs, files) ↔ valid-dir-ino(inode.ino, dirs, files) ∧ inode.nlink = dirs[inode.ino].nlink ∧ inode.size = dirs[inode.ino].size ∧ inode.nsubdirs = dirs[inode.ino].nsubdirs ∧ inode.directory; (s)%⊦ valid-wb-inode(inode, dirs, files) ↔ valid-dir-inode(inode, dirs, files) ∨ valid-file-inode(inode, dirs, files); (s)%⊦ pre-write-inode(inode, dirs, files) ↔ valid-wb-inode(inode, dirs, files); (s)