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Proof step 82 from proof inv-writepage (previous step)

# buf = VFS_PAGE_SIZE, (key.ino = m ⊃ mkfile(m0, md, # links(key.ino, dirs), content[pageno, buf]);files[key.ino]) = mkfile(m1, md0, m2, content0), pcache[datakey(m, pageno), mkpentry(false, buf)][key] = mkpentry(boolvar, 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])]), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), synced(files, icache, pcache), key ∈ pcache[datakey(m, pageno), mkpentry(false, buf)], m ∈ files ⊦ key.data? ∧ # buf0 = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ (¬ boolvar → key.part ∈ content0 ∧ buf0 = content0[key.part])

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 83:
# buf = VFS_PAGE_SIZE, (key.ino = m ⊃ mkfile(m0, md, # links(key.ino, dirs), content[pageno, buf]);files[key.ino]) = mkfile(m1, md0, m2, content0), files[m] = mkfile(m0, md, # links(m, dirs), content), pcache[datakey(m, pageno), mkpentry(false, buf)][key] = mkpentry(boolvar, buf0), afs-cons(dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]), afs-cons(dirs, files), pcache-cons(pcache, dirs, files), synced(files, icache, pcache), synced(dirs, icache, pcache), m ∈ files, key ∈ pcache[datakey(m, pageno), mkpentry(false, buf)] ⊦ key = datakey(m, pageno), key.data? ∧ # buf0 = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ (¬ boolvar → key.part ∈ content0 ∧ buf0 = content0[key.part])

Rule argument

fma: key = datakey(m, pageno)

Additional information

Used simplifier rules: ⊦ pcache[key, pe][key] = pe; (s)%⊦ mkpentry(boolvar, buf) = mkpentry(boolvar0, buf0) ↔ (boolvar ↔ boolvar0) ∧ buf = buf0; (ws)% ⊦ datakey(m, m0).ino = m; (s)%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)% ⊦ key ∈ pcache[key, pe]; (s)% ⊦ datakey(m, m0).data?; (s)% ⊦ datakey(m, m0).part = m0; (s)% ⊦ content[n, buf][n] = buf; (s)% ⊦ n ∈ content[n, buf]; (s) Used formulas: key = datakey(m, pageno)