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Proof step 84 from proof inv-write_inode (previous step)

icache[m1, mkientry(false, mkinode(m1, md, boolvar0, m3, m4, m5))][ino] = mkientry(boolvar3, inode0), pcache[datakey(ino, n)] = mkpentry(boolvar1, buf), icache[m] = mkientry(boolvar, mkinode(m1, md1, boolvar0, m3, m4, m5)), dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), icache[ino] = mkientry(boolvar2, inode), afs-cons(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files), afs-cons(dirs, files), synced(dirs, icache, pcache), m ∈ icache, m ∈ dirs, ino ∈ dirs, asynced2 → synced(files, icache, pcache), ino ∈ icache → ¬ boolvar2, datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty ⊦ (ino ∈ icache[m1, mkientry(false, mkinode(m1, md, boolvar0, m3, m4, m5))] → ¬ boolvar3) ∧ (datakey(ino, n) ∈ pcache → ¬ boolvar1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 85:
icache[ino] = mkientry(false, inode), dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), icache[m] = mkientry(boolvar, mkinode(m1, md1, boolvar0, m3, m4, m5)), pcache[datakey(ino, n)] = mkpentry(boolvar1, buf), icache[m1, mkientry(false, mkinode(m1, md, boolvar0, m3, m4, m5))][ino] = mkientry(true, inode0), afs-cons(dirs, files), afs-cons(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files), synced(dirs, icache, pcache), ino ∈ icache, ino ∈ icache[m1, mkientry(false, mkinode(m1, md, boolvar0, m3, m4, m5))], ino ∈ dirs, m ∈ dirs, m ∈ icache, asynced2 → synced(files, icache, pcache), datakey(ino, n) ∈ pcache → ¬ boolvar1, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ mkientry(boolvar, inode) = mkientry(boolvar0, inode0) ↔ (boolvar ↔ boolvar0) ∧ inode = inode0; (ws)% ⊦ ino = ino0 → icache[ino0, ie][ino] = ie; (s)% ⊦ ino ∈ icache[ino0, ie] ↔ ino = ino0 ∨ ino ∈ icache; (ws)% ⊦ ¬ ino ∈ icache → icache[ino] = (∅)[ino]; (s)% ⊦ mkpentry(boolvar, buf).dirty ↔ boolvar; (s)