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Proof step 79 from proof inv-writepage (previous step)

# buf = VFS_PAGE_SIZE, files[m] = mkfile(m0, md, # links(m, dirs), content), 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. key ∈ pcache[datakey(m, pageno), mkpentry(false, buf)] → key.data? ∧ # pcache[datakey(m, pageno), mkpentry(false, buf)][key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]) ∧ ( ¬ pcache[datakey(m, pageno), mkpentry(false, buf)][key].dirty → key.part ∈ files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])][key.ino].content ∧ pcache[datakey(m, pageno), mkpentry(false, buf)][key].page = files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])][key.ino].content[key.part])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 80:
# buf = VFS_PAGE_SIZE, 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? ∧ # pcache[datakey(m, pageno), mkpentry(false, buf)][key].page = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ ( ¬ pcache[datakey(m, pageno), mkpentry(false, buf)][key].dirty → key.part ∈ (key.ino = m ⊃ mkfile(m0, md, # links(key.ino, dirs), content[pageno, buf]);files[key.ino]).content ∧ pcache[datakey(m, pageno), mkpentry(false, buf)][key].page = (key.ino = m ⊃ mkfile(m0, md, # links(key.ino, dirs), content[pageno, buf]);files[key.ino]).content[key.part])

Rule argument

Additional information

Used simplifier rules: ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)