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Proof step 335 from proof refine-write_inode (previous step)

cache_icache[m3] = mkientry(boolvar, mkinode(m3, md2, false, # links(m3, cache_dirs), 0, m6)), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content), cache_files[m3] = mkfile(m1, md1, # links(m3, cache_dirs), content0), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m3 ∈ cache_files, m3 ∈ cache_icache, ino ∈ cache_files, ¬ boolvar → mkinode(m3, md2, false, # links(m3, cache_dirs), 0, m6) = mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m1) ⊦ (ino = m3 ⊃ mkfile(m2, md, # links(m3, cache_dirs), content);((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino]) = ((cache_files ⊕ cache_pcache) ⊕ cache_icache[m3, mkientry(true, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2))])[ino]

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 336:
⊦ 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 337:
cache_files[m3] = mkfile(m1, md1, # links(m3, cache_dirs), content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content), cache_icache[m3] = mkientry(boolvar, mkinode(m3, md2, false, # links(m3, cache_dirs), 0, m6)), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), ino ∈ cache_files, m3 ∈ cache_icache, m3 ∈ cache_files, ¬ boolvar → mkinode(m3, md2, false, # links(m3, cache_dirs), 0, m6) = mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m1) ⊦ (ino = m3 ⊃ mkfile(m2, md, # links(m3, cache_dirs), content);((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino]) = ((cache_files ⊕ cache_pcache) ⊕ cache_icache[m3, mkientry(true, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2))])[ino], ino ∈ cache_icache[m3, mkientry(true, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2))] ∧ ¬ cache_icache[m3, mkientry(true, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2))][ino].inode.directory
Proof step 348:
cache_files[m3] = mkfile(m1, md1, # links(m3, cache_dirs), content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content), cache_icache[m3] = mkientry(boolvar, mkinode(m3, md2, false, # links(m3, cache_dirs), 0, m6)), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), ino ∈ cache_files, m3 ∈ cache_icache, m3 ∈ cache_files, ino ∈ cache_icache[m3, mkientry(true, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2))], ¬ boolvar → mkinode(m3, md2, false, # links(m3, cache_dirs), 0, m6) = mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m1) ⊦ (ino = m3 ⊃ mkfile(m2, md, # links(m3, cache_dirs), content);((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino]) = mkfile (cache_icache[m3, mkientry(true, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2))][ino].inode.size, cache_icache[m3, mkientry(true, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2))][ino].inode.meta, cache_icache[m3, mkientry(true, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2))][ino].inode.nlink, (cache_files ⊕ cache_pcache)[ino].content), cache_icache[m3, mkientry(true, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2))][ino].inode.directory

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] → [ino, cache_icache [m3, mkientry (true, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2)) ], cache_files ⊕ cache_pcache] flags: <all paths>

Additional information

Used terms: ino, cache_icache [m3, mkientry (true, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2)) ], cache_files ⊕ cache_pcache