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Proof step 190 from proof refine-link (previous step)

cache_icache[entries2[str]].inode = mkinode(m8, md, boolvar, m13, m14, m15), cache_dirs[ino3] = mkdir(m1, md4, # links(ino3, cache_dirs), m12, entries2), cache_dirs[ino0] = mkdir(m4, md2, # links(ino0, cache_dirs), m10, entries), cache_dirs[ino1] = mkdir(m0, md3, # links(ino1, cache_dirs), m2, entries0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries2[str]] = mkfile(m5, md1, # links(entries2[str], cache_dirs), content), cache_dirs[m9] = mkdir(m, md7, # links(m9, cache_dirs), m6, entries3), entries0[str] = entries2[str], cache_files[entries2[str]] = mkfile(m3, md6, # links(entries2[str], cache_dirs), content0), entries[str] = entries2[str], cache_dirs[ino2] = mkdir(m7, md5, # links(ino2, cache_dirs), m11, entries1), entries1[str] = entries2[str], 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), m9 ∈ cache_dirs, str ∈ entries0, str ∈ entries, ino1 ∈ cache_dirs, ino0 ∈ cache_dirs, ino2 ∈ cache_dirs, str ∈ entries1, ino3 ∈ cache_dirs, str ∈ entries2, entries2[str] ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m9, cache_dirs) ≠ ∅ ∨ m9 = ROOT_INO, links(ino1, cache_dirs) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino0, cache_dirs) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino2, cache_dirs) ≠ ∅ ∨ ino2 = ROOT_INO, links(ino3, cache_dirs) ≠ ∅ ∨ ino3 = ROOT_INO ⊦ str0 ∈ entries3, entries2[str] ∈ cache_icache ∧ ¬ boolvar, (n ∈ content ↔ n ∈ content0 ⊕ mkcontent(entries2[str], cache_pcache)) ∧ (n ∈ content → content[n] = (content0 ⊕ mkcontent(entries2[str], cache_pcache))[n])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 191:
entries1[str] = entries2[str], cache_dirs[ino2] = mkdir(m7, md5, # links(ino2, cache_dirs), m11, entries1), entries[str] = entries2[str], cache_files[entries2[str]] = mkfile(m3, md6, # links(entries2[str], cache_dirs), content0), entries0[str] = entries2[str], cache_dirs[m9] = mkdir(m, md7, # links(m9, cache_dirs), m6, entries3), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries2[str]] = mkfile(m5, md1, # links(entries2[str], cache_dirs), content), cache_dirs[ino1] = mkdir(m0, md3, # links(ino1, cache_dirs), m2, entries0), cache_dirs[ino0] = mkdir(m4, md2, # links(ino0, cache_dirs), m10, entries), cache_dirs[ino3] = mkdir(m1, md4, # links(ino3, cache_dirs), m12, entries2), cache_icache[entries2[str]] = mkientry(boolvar0, inode), inode = mkinode(m8, md, boolvar, m13, m14, m15), 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), entries2[str] ∈ cache_files, str ∈ entries2, ino3 ∈ cache_dirs, str ∈ entries1, ino2 ∈ cache_dirs, ino0 ∈ cache_dirs, ino1 ∈ cache_dirs, str ∈ entries, str ∈ entries0, m9 ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(ino3, cache_dirs) ≠ ∅ ∨ ino3 = ROOT_INO, links(ino2, cache_dirs) ≠ ∅ ∨ ino2 = ROOT_INO, links(ino0, cache_dirs) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino1, cache_dirs) ≠ ∅ ∨ ino1 = ROOT_INO, links(m9, cache_dirs) ≠ ∅ ∨ m9 = ROOT_INO ⊦ str0 ∈ entries3, (n ∈ content ↔ n ∈ content0 ⊕ mkcontent(entries2[str], cache_pcache)) ∧ (n ∈ content → content[n] = (content0 ⊕ mkcontent(entries2[str], cache_pcache))[n]), entries2[str] ∈ cache_icache ∧ ¬ boolvar

Rule argument

spec: icache-entry name: elim seq: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode) subst: [ie, boolvar, inode] → [cache_icache[entries2[str]], boolvar0, inode]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: cache_icache[entries2[str]], boolvar0, inode