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Proof step 189 from proof refine-create (previous step)

cache_icache[ino] = mkientry(boolvar0, mkinode(m8, md0, false, m9, m10, m11)), cache_dirs[m1] = mkdir(m2, md1, # links(m1, cache_dirs), m5, entries0), cache_icache[m1, mkientry(false, mkinode(m1, md2, true, # links(m1, cache_dirs), m5, m2 + 1))][ino] = mkientry(boolvar, mkinode(m0, md, false, m3, m4, m6)), cache_files[ino] = mkfile(m7, md3, # links(ino, cache_dirs), content), 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, m1 ∈ cache_dirs, ino ∈ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, # links(m1, cache_dirs), m5, m2 + 1))], ino ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ m = 0, m ∈ cache_files, m ∈ cache_dirs, str ∈ entries0, m11 = m6 ∧ md0 = md ∧ m9 = m3

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store, inst: icache name: At-other seq: ⊦ ino ≠ ino0 → icache[ino0, ie][ino] = icache[ino] subst: [ino, ino0, icache, ie] → [ino, m1, cache_icache, mkientry (false, mkinode (m1, md2, true, # links(m1, cache_dirs), m5, m2 + 1))] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ino ≠ ino0 → (ino ∈ icache[ino0, ie] ↔ ino ∈ icache); (s)%⊦ mkientry(boolvar, inode) = mkientry(boolvar0, inode0) ↔ (boolvar ↔ boolvar0) ∧ inode = inode0; (ws)%⊦ mkinode(m, md, boolvar, m0, m1, m2) = mkinode(m3, md0, boolvar0, m4, m5, m6) ↔ m = m3 ∧ md = md0 ∧ (boolvar ↔ boolvar0) ∧ m0 = m4 ∧ m1 = m5 ∧ m2 = m6; (ws)% ⊦ icache[ino, ie][ino] = ie; (s) Used terms: ino, m1, cache_icache, mkientry (false, mkinode(m1, md2, true, # links(m1, cache_dirs), m5, m2 + 1))