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Proof step 133 from proof refine-iget (previous step)

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)), 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 ∧ ¬ cache_icache[ino0].inode.directory

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 134:
cache_icache[ino0].inode = 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

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[ino0].inode, m5, md2, boolvar0, m6, m7, m8]

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[ino0].inode, m5, md2, boolvar0, m6, m7, m8