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Proof step 259 from proof inv-write_inode (previous step)

pcache[datakey(ino, n)] = mkpentry(boolvar1, buf), icache[m] = mkientry(boolvar, mkinode(m0, md0, boolvar0, m1, m3, m4)), icache[ino] = mkientry(boolvar2, inode), afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), afs-cons(dirs, files), synced(files, icache, pcache), m ∈ files, m ∈ icache, ino ∈ files, ino ∈ icache → ¬ boolvar2, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty ⊦ ( ino ∈ icache[m0, mkientry(false, mkinode(m0, md, boolvar0, m1, m3, m2))] → ¬ icache[m0, mkientry(false, mkinode(m0, md, boolvar0, m1, m3, m2))][ino].dirty) ∧ (datakey(ino, n) ∈ pcache → ¬ boolvar1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 260:
icache[ino] = mkientry(boolvar2, inode), icache[m] = mkientry(boolvar, mkinode(m0, md0, boolvar0, m1, m3, m4)), pcache[datakey(ino, n)] = mkpentry(boolvar1, buf), icache[m0, mkientry(false, mkinode(m0, md, boolvar0, m1, m3, m2))][ino] = mkientry(boolvar3, inode0), afs-cons(dirs, files), afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), synced(files, icache, pcache), ino ∈ files, m ∈ icache, m ∈ files, ino ∈ icache → ¬ boolvar2, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty ⊦ (ino ∈ icache[m0, mkientry(false, mkinode(m0, md, boolvar0, m1, m3, m2))] → ¬ boolvar3) ∧ (datakey(ino, n) ∈ pcache → ¬ boolvar1)

Rule argument

spec: icache-entry name: elim seq: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode) subst: [ie, boolvar, inode] → [icache [m0, mkientry(false, mkinode(m0, md, boolvar0, m1, m3, m2)) ] [ino ], boolvar3, inode0]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: icache[m0, mkientry(false, mkinode(m0, md, boolvar0, m1, m3, m2))] [ino ], boolvar3, inode0