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Proof step 136 from proof refine-iget (previous step)

cache_icache[ino0] = mkientry(boolvar1, mkinode(m5, md2, boolvar0, m6, m7, m8)), cache_icache[ino, mkientry(false, mkinode(ino, md, false, # links(ino, cache_dirs), 0, m))][ino0] = mkientry(boolvar, mkinode(m0, md0, false, m1, m2, m3)), cache_files[ino] = mkfile(m, md, # links(ino, cache_dirs), content), cache_files[ino0] = mkfile(m4, md1, # links(ino0, cache_dirs), content0), 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), ino ∈ cache_files, ino0 ∈ cache_files, ino0 ∈ cache_icache[ino, mkientry(false, mkinode(ino, md, false, # links(ino, cache_dirs), 0, m))], cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino0] = mkfile(m3, md0, m1, content0 ⊕ mkcontent(ino0, cache_pcache)), ino ∈ cache_icache, ino ∈ cache_dirs, ino0 ∈ cache_icache ∧ ¬ boolvar0

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 137:
⊦ ino ∈ icache ∧ icache[ino].inode.directory → (files ⊕ icache)[ino] = files[ino]
Proof step 138:
cache_files[ino0] = mkfile(m4, md1, # links(ino0, cache_dirs), content0), cache_files[ino] = mkfile(m, md, # links(ino, cache_dirs), content), cache_icache[ino, mkientry(false, mkinode(ino, md, false, # links(ino, cache_dirs), 0, m))][ino0] = mkientry(boolvar, mkinode(m0, md0, false, m1, m2, m3)), cache_icache[ino0] = mkientry(boolvar1, mkinode(m5, md2, boolvar0, m6, m7, m8)), 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), ino0 ∈ cache_icache[ino, mkientry(false, mkinode(ino, md, false, # links(ino, cache_dirs), 0, m))], ino0 ∈ cache_files, ino ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino0] = mkfile(m3, md0, m1, content0 ⊕ mkcontent(ino0, cache_pcache)), ino ∈ cache_dirs, ino ∈ cache_icache, ino0 ∈ cache_icache ∧ ¬ boolvar0, ino0 ∈ cache_icache ∧ cache_icache[ino0].inode.directory

Rule argument

spec: cache-base name: at-icache-overwrite-no-file seq: ⊦ ino ∈ icache ∧ icache[ino].inode.directory → (files ⊕ icache)[ino] = files[ino] subst: [ino, icache, files] → [ino0, cache_icache, cache_files ⊕ cache_pcache] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ino ∈ icache ∧ ¬ ino0 ∈ icache → icache[ino0, ie][ino] = icache[ino]; (s)%⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)); (s)%⊦ mkientry(boolvar, inode) = mkientry(boolvar0, inode0) ↔ (boolvar ↔ boolvar0) ∧ inode = inode0; (ws)%⊦ mkinode(m, md, boolvar, m0, m1, m2) = mkinode(m3, md0, boolvar0, m4, m5, m6) ↔ m = m3 ∧ md = md0 ∧ (boolvar ↔ boolvar0) ∧ m0 = m4 ∧ m1 = m5 ∧ m2 = m6; (ws) Used terms: ino0, cache_icache, cache_files ⊕ cache_pcache