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Proof step 102 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), ino0 ∈ cache_icache[ino, mkientry(false, mkinode(ino, md, true, # links(ino, cache_dirs), m1, m))], ino ∈ cache_dirs, ino0 ∈ cache_files, 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[ino0].content ⊕ mkcontent(ino0, cache_pcache)), cache_icache[ino, mkientry(false, mkinode(ino, md, true, # links(ino, cache_dirs), m1, m))][ino0].inode.directory, ino ∈ cache_icache

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 103:
cache_icache[ino, mkientry(false, mkinode(ino, md, true, # links(ino, cache_dirs), m1, m))][ino0].inode = mkinode(m0, md0, boolvar, m2, m3, m4), cache_dirs[ino] = mkdir(m, md, # links(ino, cache_dirs), m1, entries), ¬ boolvar, 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(m4, md0, m2, cache_files[ino0].content ⊕ mkcontent(ino0, cache_pcache)), ino ∈ cache_icache

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [cache_icache [ino, mkientry (false, mkinode (ino, md, true, # links(ino, cache_dirs), m1, m)) ] [ino0 ] .inode, m0, md0, boolvar, m2, m3, m4]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: cache_icache [ino, mkientry (false, mkinode(ino, md, true, # links(ino, cache_dirs), m1, m)) ] [ino0 ] .inode, m0, md0, boolvar, m2, m3, m4