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Proof step 80 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), 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])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 81:
# buf = VFS_PAGE_SIZE, 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.data? ∧ # buf0 = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ ( ¬ boolvar → key.part ∈ (key.ino = m ⊃ mkfile(m0, md, # links(key.ino, dirs), content[pageno, buf]);files[key.ino]).content ∧ buf0 = (key.ino = m ⊃ mkfile(m0, md, # links(key.ino, dirs), content[pageno, buf]);files[key.ino]).content[key.part])

Rule argument

spec: pcache-entry name: elim seq: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf) subst: [pe, boolvar, buf] → [pcache[datakey(m, pageno), mkpentry(false, buf)][key], boolvar, buf0]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf); (elim) Used terms: pcache[datakey(m, pageno), mkpentry(false, buf)][key], boolvar, buf0