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Proof step 52 from proof inv-writepage (previous step)

# 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 ⊦

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 53:
# buf = VFS_PAGE_SIZE, icache[ino] = mkientry(boolvar, inode), 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 → ¬ boolvar, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty ⊦ datakey(ino, n) = datakey(m, pageno)

Rule argument

fma: datakey(ino, n) = datakey(m, pageno)

Additional information

Used simplifier rules: ⊦ datakey(m, m0) = datakey(m1, m2) ↔ m = m1 ∧ m0 = m2; (ws)% ⊦ pcache[key, pe][key] = pe; (s)%⊦ mkpentry(boolvar, buf) = mkpentry(boolvar0, buf0) ↔ (boolvar ↔ boolvar0) ∧ buf = buf0; (ws) Used formulas: datakey(ino, n) = datakey(m, pageno)