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Proof step 143 from proof refine-mkdir (previous step)

cache_icache[ino] = mkientry(boolvar0, mkinode(m11, md5, false, m12, m13, m14)), cache_files[ino] = mkfile(m10, md4, # links(ino, cache_dirs), content), cache_icache[m1, mkientry(false, mkinode(m1, md2, true, m3, m4, m))][m5, mkientry(false, mkinode(m5, md3, true, 1, 0, 0))][ino] = mkientry(boolvar, mkinode(m0, md, true, m2, m7, m9)), cache_dirs[m1] = mkdir(m6, md1, # links(m1, cache_dirs), m8, entries1), (cache_dirs[m1, mkdir(m6 + 1, md1, # links(m1, cache_dirs), m8 + 1, entries1[str, m5])] ++ m5)[m1] = mkdir(m, md0, m3, m4, entries0), 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, m3, m4, m))][m5, mkientry(false, mkinode(m5, md3, true, 1, 0, 0))], ino ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ m5 = 0, str ∈ entries1, m5 ∈ cache_files, m5 ∈ cache_dirs, m14 = m10 ∧ md5 = md4 ∧ m12 = # links(ino, cache_dirs)

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 144:
⊦ ino ≠ ino0 → icache[ino0, ie][ino] = icache[ino]
Proof step 145:
(cache_dirs[m1, mkdir(m6 + 1, md1, # links(m1, cache_dirs), m8 + 1, entries1[str, m5])] ++ m5)[m1] = mkdir(m, md0, m3, m4, entries0), cache_dirs[m1] = mkdir(m6, md1, # links(m1, cache_dirs), m8, entries1), cache_icache[m1, mkientry(false, mkinode(m1, md2, true, m3, m4, m))][ino] = mkientry(boolvar, mkinode(m0, md, true, m2, m7, m9)), cache_files[ino] = mkfile(m10, md4, # links(ino, cache_dirs), content), cache_icache[ino] = mkientry(boolvar0, mkinode(m11, md5, false, m12, m13, m14)), 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), ino ∈ cache_icache, ino ∈ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, m3, m4, m))][m5, mkientry(false, mkinode(m5, md3, true, 1, 0, 0))], m1 ∈ cache_dirs, ino ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ino = m5, m5 = 0, m5 ∈ cache_dirs, m5 ∈ cache_files, str ∈ entries1, m14 = m10 ∧ md5 = md4 ∧ m12 = # links(ino, cache_dirs)

Rule argument

spec: store, inst: icache name: At-other seq: ⊦ ino ≠ ino0 → icache[ino0, ie][ino] = icache[ino] subst: [ino, ino0, icache, ie] → [ino, m5, cache_icache [m1, mkientry(false, mkinode(m1, md2, true, m3, m4, m)) ], mkientry(false, mkinode(m5, md3, true, 1, 0, 0))] flags: <all paths>

Additional information

Used terms: ino, m5, cache_icache[m1, mkientry(false, mkinode(m1, md2, true, m3, m4, m))], mkientry(false, mkinode(m5, md3, true, 1, 0, 0))