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Proof step 10 from proof refine-evict (previous step)

asynced ↔ cache_asynced, afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dirs = cache_dirs, err = err0, files = cache_files, inode = mkinode(m, md, boolvar, m0, m1, m2), 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), cache_sync → synced(cache_files, cache_icache, cache_pcache), m ∈ cache_dirs ∧ m0 = cache_dirs[m].nlink ∧ m2 = cache_dirs[m].size ∧ m1 = cache_dirs[m].nsubdirs ∧ boolvar ∨ m ∈ cache_files ∧ m0 = cache_files[m].nlink ∧ m1 = 0 ∧ ¬ boolvar, m ∈ cache_dirs ∧ m0 = cache_dirs[m].nlink ∧ m2 = cache_dirs[m].size ∧ m1 = cache_dirs[m].nsubdirs ∧ boolvar ∨ m ∈ cache_files ∧ m0 = ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m].nlink ∧ m1 = 0 ∧ ¬ boolvar ⊦ ⟪if pre-evict(inode, dirs, files) then {err := ESUCCESS; let ino = inode.ino in if ino ∈ dirs then if dirs[ino].nlink = 0 then dirs := dirs -- ino else if files[ino].nlink = 0 then files := files -- ino} else abort; if err = ESUCCESS ∧ m0 = 0 then {icache_delete#(m; err, cache_icache); if ¬ boolvar then pcache_evict#(m; err, cache_pcache)}⟫ ⟨afs_evict#(mkinode(m, md, boolvar, m0, m1, m2), cache_asynced; err0, afs_dirs, afs_files)⟩ (afs_dirs = dirs ∧ afs_files = (files ⊕ cache_pcache) ⊕ cache_icache ∧ err = err0), m = ROOT_INO

Heuristic symbolic execution applied rule if positive right

And obtained the following new goals

Proof step 11:
asynced ↔ cache_asynced, afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dirs = cache_dirs, err = err0, files = cache_files, inode = mkinode(m, md, boolvar, m0, m1, m2), 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), m ∈ cache_dirs ∧ m0 = cache_dirs[m].nlink ∧ m2 = cache_dirs[m].size ∧ m1 = cache_dirs[m].nsubdirs ∧ boolvar ∨ m ∈ cache_files ∧ m0 = ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m].nlink ∧ m1 = 0 ∧ ¬ boolvar, m ∈ cache_dirs ∧ m0 = cache_dirs[m].nlink ∧ m2 = cache_dirs[m].size ∧ m1 = cache_dirs[m].nsubdirs ∧ boolvar ∨ m ∈ cache_files ∧ m0 = cache_files[m].nlink ∧ m1 = 0 ∧ ¬ boolvar ⊦ ⟪err := ESUCCESS; let ino = inode.ino in if ino ∈ dirs then if dirs[ino].nlink = 0 then dirs := dirs -- ino else if files[ino].nlink = 0 then files := files -- ino; if err = ESUCCESS ∧ m0 = 0 then {icache_delete#(m; err, cache_icache); if ¬ boolvar then pcache_evict#(m; err, cache_pcache)}⟫ ⟨afs_evict#(mkinode(m, md, boolvar, m0, m1, m2), cache_asynced; err0, afs_dirs, afs_files)⟩ (afs_dirs = dirs ∧ afs_files = (files ⊕ cache_pcache) ⊕ cache_icache ∧ err = err0), m = ROOT_INO

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ pre-evict(inode, dirs, files) ↔ valid-wb-inode(inode, dirs, files) ∧ inode.ino ≠ ROOT_INO; (s)%⊦ valid-wb-inode(inode, dirs, files) ↔ valid-dir-inode(inode, dirs, files) ∨ valid-file-inode(inode, dirs, files); (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)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (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-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)