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Proof step 77 from proof inv-writepage (previous step)

# 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), m ∈ files ⊦ pcache-cons(pcache[datakey(m, pageno), mkpentry(false, buf)], dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])])

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 78:
⊦ pcache-cons(pcache, dirs, files) ↔ (∀ key. key ∈ pcache → key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs, files) ∧ (¬ pcache[key].dirty → key.part ∈ files[key.ino].content ∧ pcache[key].page = files[key.ino].content[key.part]))
Proof step 79:
# 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])

Rule argument

spec: cache-base name: pcache-cons seq: ⊦ pcache-cons(pcache, dirs, files) ↔ (∀ key. key ∈ pcache → key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs, files) ∧ ( ¬ pcache[key].dirty → key.part ∈ files[key.ino].content ∧ pcache[key].page = files[key.ino].content[key.part])) subst: [pcache, dirs, files] → [pcache[datakey(m, pageno), mkpentry(false, buf)], dirs, files [m, mkfile(m0, md, # links(m, dirs), content[pageno, buf]) ]] flags: <all paths>

Additional information

Used terms: pcache[datakey(m, pageno), mkpentry(false, buf)], dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]