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Proof step 89 from proof inv-writepage (previous step)

# files[key.ino].content[key.part] = VFS_PAGE_SIZE, # 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[key] = mkpentry(false, files[key.ino].content[key.part]), key.data?, afs-cons(dirs, files), afs-cons(dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]), synced(dirs, icache, pcache), synced(files, icache, pcache), key.part ∈ files[key.ino].content, m ∈ files, key ∈ pcache, key.ino ∈ files, ∀ key0. key0 ∈ pcache → key0.data? ∧ # pcache[key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ files ∧ (¬ pcache[key0].dirty → key0.part ∈ files[key0.ino].content ∧ pcache[key0].page = files[key0.ino].content[key0.part]) ⊦ key = datakey(m, pageno), key.part ∈ content0 ∧ files[key.ino].content[key.part] = content0[key.part]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 90:
# buf = VFS_PAGE_SIZE, # files[m3].content[m4] = VFS_PAGE_SIZE, (m3 = m ⊃ mkfile(m0, md, # links(m3, dirs), content[pageno, buf]);files[m3]) = mkfile(m1, md0, m2, content0), pcache[key] = mkpentry(false, files[m3].content[m4]), files[m] = mkfile(m0, md, # links(m, dirs), content), key = datakey(m3, m4), key.data?, afs-cons(dirs, files[m, mkfile(m0, md, # links(m, dirs), content[pageno, buf])]), afs-cons(dirs, files), synced(files, icache, pcache), synced(dirs, icache, pcache), m3 ∈ files, key ∈ pcache, m ∈ files, m4 ∈ files[m3].content, ∀ key0. key0 ∈ pcache → key0.data? ∧ # pcache[key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ files ∧ (¬ pcache[key0].dirty → key0.part ∈ files[key0.ino].content ∧ pcache[key0].page = files[key0.ino].content[key0.part]) ⊦ key = datakey(m, pageno), m4 ∈ content0 ∧ files[m3].content[m4] = content0[m4]

Rule argument

spec: key name: elim-02 seq: ⊦ key.data? → (m = key.ino ∧ m0 = key.part ↔ key = datakey(m, m0)) subst: [key, m, m0] → [key, m3, m4]

Additional information

Used simplifier rules: ⊦ key.data? → (m = key.ino ∧ m0 = key.part ↔ key = datakey(m, m0)); (elim) Used terms: key, m3, m4