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Proof step 49 from proof refine-fsync (previous step)

asynced0 ↔ asynced, cache_files[m] = mkfile(m3, md1, # links(m, cache_dirs), content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, # links(m, cache_dirs), content), dirs = cache_dirs, files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, inode = mkinode(m, md, false, # links(m, cache_dirs), 0, m2), (cache_files0 ⊕ cache_pcache0) ⊕ cache_icache0 = (cache_files ⊕ cache_pcache) ⊕ cache_icache, afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, cache_files0), dcache-cons(cache_dcache, cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files0), icache-cons(cache_icache, cache_dirs, cache_files), icache-cons(cache_icache0, cache_dirs, cache_files0), pcache-cons(cache_pcache, cache_dirs, cache_files), pcache-cons(cache_pcache0, cache_dirs, cache_files0), synced(cache_dirs, cache_icache, cache_pcache), synced(cache_dirs, cache_icache0, cache_pcache0), m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), cache_sync → synced(cache_files0, cache_icache0, cache_pcache0), err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ valid-file-inode(inode, dirs, files)

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ ino ∈ files ⊕ pcache ↔ ino ∈ files; (s)% ⊦ ino ∈ files ⊕ icache ↔ ino ∈ files; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (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)