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Proof step 76 from proof inv-readpage (previous step)

# buf0 = VFS_PAGE_SIZE, files[m] = mkfile(m0, md, # links(m, dirs), content), afs-cons(dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ files, pageno ∈ content, asynced2 → synced(files, icache, pcache) ⊦ content[pageno] = zeropage, pcache-cons(pcache[datakey(m, pageno), mkpentry(false, content[pageno])], dirs, files), datakey(m, pageno) ∈ pcache

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 77:
⊦ 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 78:
# buf0 = VFS_PAGE_SIZE, files[m] = mkfile(m0, md, # links(m, dirs), content), afs-cons(dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), pageno ∈ content, m ∈ files, asynced2 → synced(files, icache, pcache) ⊦ content[pageno] = zeropage, datakey(m, pageno) ∈ pcache, ∀ key. key ∈ pcache[datakey(m, pageno), mkpentry(false, content[pageno])] → key.data? ∧ # pcache[datakey(m, pageno), mkpentry(false, content[pageno])][key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs, files) ∧ ( ¬ pcache[datakey(m, pageno), mkpentry(false, content[pageno])][key].dirty → key.part ∈ files[key.ino].content ∧ pcache[datakey(m, pageno), mkpentry(false, content[pageno])][key].page = files[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, content[pageno])], dirs, files] flags: <all paths>

Additional information

Used terms: pcache[datakey(m, pageno), mkpentry(false, content[pageno])], dirs, files