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Proof step 51 from proof inv-writepage (previous step)

# buf = VFS_PAGE_SIZE, pcache[datakey(m, pageno), mkpentry(false, buf)][datakey(ino, n)] = mkpentry(true, buf0), files[m] = mkfile(m0, md, # links(m, dirs), content), afs-cons(dirs, files), afs-cons(dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]), synced(files, icache, pcache), m ∈ files, ino ∈ files, datakey(ino, n) ∈ pcache[datakey(m, pageno), mkpentry(false, buf)], ino ∈ icache → ¬ icache[ino].dirty, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty ⊦

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 52:
# buf = VFS_PAGE_SIZE, files[m] = mkfile(m0, md, # links(m, dirs), content), pcache[datakey(m, pageno), mkpentry(false, buf)][datakey(ino, n)] = mkpentry(true, buf0), icache[ino] = mkientry(boolvar, inode), afs-cons(dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]), afs-cons(dirs, files), synced(files, icache, pcache), datakey(ino, n) ∈ pcache[datakey(m, pageno), mkpentry(false, buf)], ino ∈ files, m ∈ files, ino ∈ icache → ¬ boolvar, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty ⊦

Rule argument

spec: icache-entry name: elim seq: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode) subst: [ie, boolvar, inode] → [icache[ino], boolvar, inode]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: icache[ino], boolvar, inode