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Proof step 36 from proof refine-rename-file-dentry (previous step)

cache_files[entries[str]] = mkfile(m4, md2, # links(entries[str], cache_dirs), content2), cache_dirs[m] = mkdir(m11, md5, # links(m, cache_dirs), m17, entries), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str0]] = mkfile(m8, md4, m15, content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m12, md3, m14, content), cache_dirs[m3] = mkdir(m0, md6, # links(m3, cache_dirs), m2, entries0), cache_files[entries0[str0]] = mkfile(m1, md1, # links(entries0[str0], cache_dirs), content1), 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), str ∈ entries, str0 ∈ entries0, m ∈ cache_dirs, m3 ∈ cache_dirs, entries[str] ∈ cache_files, entries0[str0] ∈ cache_files, m = m3 → md = md0, cache_sync → synced(cache_files, cache_icache, cache_pcache), entries0[str0] ∈ cache_icache → cache_icache[entries0[str0]].inode.ino = entries0[str0] ∧ (cache_icache[entries0[str0]].dirty ⊃ cache_icache[entries0[str0]].inode.ino ∈ cache_files ∧ cache_icache[entries0[str0]].inode.nlink = cache_files[cache_icache[entries0[str0]].inode.ino].nlink ∧ cache_icache[entries0[str0]].inode.nsubdirs = 0 ∧ ¬ cache_icache[entries0[str0]].inode.directory ; cache_icache[entries0[str0]].inode = (cache_icache[entries0[str0]].inode.ino ∈ cache_dirs ⊃ mkinode (cache_icache[entries0[str0]].inode.ino, cache_dirs[cache_icache[entries0[str0]].inode.ino].meta, true, cache_dirs[cache_icache[entries0[str0]].inode.ino].nlink, cache_dirs[cache_icache[entries0[str0]].inode.ino].nsubdirs, cache_dirs[cache_icache[entries0[str0]].inode.ino].size) ;mkinode (cache_icache[entries0[str0]].inode.ino, cache_files[cache_icache[entries0[str0]].inode.ino].meta, false, cache_files[cache_icache[entries0[str0]].inode.ino].nlink, 0, cache_files[cache_icache[entries0[str0]].inode.ino].size) ) ), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO ⊦ m15 = # links(entries0[str0], cache_dirs)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 37:
cache_icache[entries0[str0]].inode = mkinode(m5, md7, boolvar, m6, m7, m9), cache_files[entries0[str0]] = mkfile(m1, md1, # links(entries0[str0], cache_dirs), content1), cache_dirs[m3] = mkdir(m0, md6, # links(m3, cache_dirs), m2, entries0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m12, md3, m14, content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str0]] = mkfile(m8, md4, m15, content0), cache_dirs[m] = mkdir(m11, md5, # links(m, cache_dirs), m17, entries), cache_files[entries[str]] = mkfile(m4, md2, # links(entries[str], cache_dirs), content2), 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), entries0[str0] ∈ cache_files, entries[str] ∈ cache_files, m3 ∈ cache_dirs, m ∈ cache_dirs, str0 ∈ entries0, str ∈ entries, entries0[str0] ∈ cache_icache → m5 = entries0[str0] ∧ (cache_icache[entries0[str0]].dirty ⊃ m5 ∈ cache_files ∧ m6 = cache_files[m5].nlink ∧ m7 = 0 ∧ ¬ boolvar ; cache_icache[entries0[str0]].inode = (m5 ∈ cache_dirs ⊃ mkinode(m5, cache_dirs[m5].meta, true, cache_dirs[m5].nlink, cache_dirs[m5].nsubdirs, cache_dirs[m5].size) ;mkinode(m5, cache_files[m5].meta, false, cache_files[m5].nlink, 0, cache_files[m5].size) ) ), cache_sync → synced(cache_files, cache_icache, cache_pcache), m = m3 → md = md0, links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ m15 = # links(entries0[str0], 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[entries0[str0]].inode, m5, md1, boolvar, m6, m7, m9]

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[entries0[str0]].inode, m5, md1, boolvar, m6, m7, m9