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Proof step 82 from proof refine-iget (previous step)

cache_dirs[ino] = mkdir(m, md, # links(ino, cache_dirs), m1, entries), 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), ino ∈ cache_dirs, ino0 ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino0] = ((cache_files ⊕ cache_pcache) ⊕ cache_icache[ino, mkientry(false, mkinode(ino, md, true, # links(ino, cache_dirs), m1, m))])[ino0], ino ∈ cache_icache

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 83:
⊦ ino ∈ icache ∧ ¬ icache[ino].inode.directory → (files ⊕ icache)[ino] = mkfile(icache[ino].inode.size, icache[ino].inode.meta, icache[ino].inode.nlink, files[ino].content)
Proof step 84:
cache_dirs[ino] = mkdir(m, md, # links(ino, cache_dirs), m1, entries), 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), ino0 ∈ cache_files, ino ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino0] = ((cache_files ⊕ cache_pcache) ⊕ cache_icache[ino, mkientry(false, mkinode(ino, md, true, # links(ino, cache_dirs), m1, m))])[ino0], ino ∈ cache_icache, ino0 ∈ cache_icache[ino, mkientry(false, mkinode(ino, md, true, # links(ino, cache_dirs), m1, m))] ∧ ¬ cache_icache[ino, mkientry(false, mkinode(ino, md, true, # links(ino, cache_dirs), m1, m))][ino0].inode.directory
Proof step 101:
cache_dirs[ino] = mkdir(m, md, # links(ino, cache_dirs), m1, entries), 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), ino0 ∈ cache_files, ino ∈ cache_dirs, ino0 ∈ cache_icache[ino, mkientry(false, mkinode(ino, md, true, # links(ino, cache_dirs), m1, m))], cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino0] = mkfile (cache_icache[ino, mkientry(false, mkinode(ino, md, true, # links(ino, cache_dirs), m1, m))][ino0].inode.size, cache_icache[ino, mkientry(false, mkinode(ino, md, true, # links(ino, cache_dirs), m1, m))][ino0].inode.meta, cache_icache[ino, mkientry(false, mkinode(ino, md, true, # links(ino, cache_dirs), m1, m))][ino0].inode.nlink, (cache_files ⊕ cache_pcache)[ino0].content), cache_icache[ino, mkientry(false, mkinode(ino, md, true, # links(ino, cache_dirs), m1, m))][ino0].inode.directory, ino ∈ cache_icache

Rule argument

spec: cache-base name: at-icache-overwrite seq: ⊦ ino ∈ icache ∧ ¬ icache[ino].inode.directory → (files ⊕ icache)[ino] = mkfile (icache[ino].inode.size, icache[ino].inode.meta, icache[ino].inode.nlink, files[ino].content) subst: [ino, icache, files] → [ino0, cache_icache [ino, mkientry (false, mkinode (ino, md, true, # links(ino, cache_dirs), m1, m)) ], cache_files ⊕ cache_pcache] flags: <all paths>

Additional information

Used terms: ino0, cache_icache [ino, mkientry (false, mkinode(ino, md, true, # links(ino, cache_dirs), m1, m)) ], cache_files ⊕ cache_pcache