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Proof step 91 from proof fsync-inode-inv (previous step)

icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino] = mkientry(boolvar1, inode0), pcache[datakey(ino, n)] = mkpentry(boolvar, buf), icache[m] = mkientry(true, mkinode(m1, md, false, # links(m1, dirs), 0, m4)), dirs[m1] = mkdir(m7, md2, m8, m9, entries), files[m1] = mkfile(m5, md1, # links(m1, dirs), content0), files[m] = mkfile(m0, md0, # links(m, dirs), content), icache[ino] = mkientry(boolvar0, inode), afs-cons(dirs, files[m1, mkfile(m4, md, # links(m1, dirs), content0)]), afs-cons(dirs, files), synced(dirs, icache, pcache), ino ∈ dirs, m ∈ files, m ∈ icache, m1 ∈ files, ino ∈ icache → ¬ boolvar0, datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty ⊦ (ino ∈ icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))] → ¬ boolvar1) ∧ (datakey(ino, n) ∈ pcache → ¬ boolvar)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 92:
icache[ino] = mkientry(false, inode), files[m] = mkfile(m0, md0, # links(m, dirs), content), files[m1] = mkfile(m5, md1, # links(m1, dirs), content0), dirs[m1] = mkdir(m7, md2, m8, m9, entries), icache[m] = mkientry(true, mkinode(m1, md, false, # links(m1, dirs), 0, m4)), pcache[datakey(ino, n)] = mkpentry(boolvar, buf), icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino] = mkientry(true, inode0), afs-cons(dirs, files), afs-cons(dirs, files[m1, mkfile(m4, md, # links(m1, dirs), content0)]), synced(dirs, icache, pcache), ino ∈ icache, ino ∈ icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))], m1 ∈ files, m ∈ icache, m ∈ files, ino ∈ dirs, datakey(ino, n) ∈ pcache → ¬ boolvar, ∀ 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)