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Proof step 21 from proof refine-unlink (previous step)

cache_files[entries[str]] = mkfile(m2, md0, # links(entries[str], cache_dirs), content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m0, md, m1, content), cache_dirs[m] = mkdir(m3, md1, # links(m, cache_dirs), m5, 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), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_dirs, str ∈ entries, entries[str] ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), entries[str] ∈ cache_icache → cache_icache[entries[str]].inode.ino = entries[str] ∧ (cache_icache[entries[str]].dirty ⊃ cache_icache[entries[str]].inode.ino ∈ cache_files ∧ cache_icache[entries[str]].inode.nlink = cache_files[cache_icache[entries[str]].inode.ino].nlink ∧ cache_icache[entries[str]].inode.nsubdirs = 0 ∧ ¬ cache_icache[entries[str]].inode.directory ; cache_icache[entries[str]].inode = (cache_icache[entries[str]].inode.ino ∈ cache_dirs ⊃ mkinode (cache_icache[entries[str]].inode.ino, cache_dirs[cache_icache[entries[str]].inode.ino].meta, true, cache_dirs[cache_icache[entries[str]].inode.ino].nlink, cache_dirs[cache_icache[entries[str]].inode.ino].nsubdirs, cache_dirs[cache_icache[entries[str]].inode.ino].size) ;mkinode (cache_icache[entries[str]].inode.ino, cache_files[cache_icache[entries[str]].inode.ino].meta, false, cache_files[cache_icache[entries[str]].inode.ino].nlink, 0, cache_files[cache_icache[entries[str]].inode.ino].size) ) ), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ m1 = # links(entries[str], cache_dirs)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 22:
cache_icache[entries[str]].inode = mkinode(m4, md2, boolvar, m6, m7, m8), cache_dirs[m] = mkdir(m3, md1, # links(m, cache_dirs), m5, entries), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m0, md, m1, content), cache_files[entries[str]] = mkfile(m2, md0, # links(entries[str], 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), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), entries[str] ∈ cache_files, str ∈ entries, m ∈ cache_dirs, entries[str] ∈ cache_icache → m4 = entries[str] ∧ (cache_icache[entries[str]].dirty ⊃ m4 ∈ cache_files ∧ m6 = cache_files[m4].nlink ∧ m7 = 0 ∧ ¬ boolvar ; cache_icache[entries[str]].inode = (m4 ∈ cache_dirs ⊃ mkinode(m4, cache_dirs[m4].meta, true, cache_dirs[m4].nlink, cache_dirs[m4].nsubdirs, cache_dirs[m4].size) ;mkinode(m4, cache_files[m4].meta, false, cache_files[m4].nlink, 0, cache_files[m4].size) ) ), cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ m1 = # links(entries[str], cache_dirs)

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[entries[str]].inode, m4, md2, boolvar, 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[entries[str]].inode, m4, md2, boolvar, m6, m7, m8