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Proof step 89 from proof fsync-inode-inv (previous step)

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, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty ⊦ ( ino ∈ icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))] → ¬ icache[m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4))][ino].dirty) ∧ (datakey(ino, n) ∈ pcache → ¬ boolvar)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 90:
icache[ino] = mkientry(boolvar0, 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(boolvar1, inode0), afs-cons(dirs, files), afs-cons(dirs, files[m1, mkfile(m4, md, # links(m1, dirs), content0)]), synced(dirs, icache, pcache), m1 ∈ files, m ∈ icache, m ∈ files, ino ∈ dirs, ino ∈ icache → ¬ boolvar0, ∀ 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)

Rule argument

spec: icache-entry name: elim seq: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode) subst: [ie, boolvar, inode] → [icache [m, mkientry (false, mkinode(m1, md, false, # links(m1, dirs), 0, m4)) ] [ino ], boolvar1, inode0]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: icache [m, mkientry(false, mkinode(m1, md, false, # links(m1, dirs), 0, m4)) ] [ino ], boolvar1, inode0