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Proof step 91 from proof inv-writepage (previous step)

# files[m3].content[m4] = VFS_PAGE_SIZE, # buf = VFS_PAGE_SIZE, (m3 = m ⊃ mkfile(m0, md, # links(m, dirs), content[pageno, buf]);files[m3]) = mkfile(m1, md0, m2, content0), files[m] = mkfile(m0, md, # links(m, dirs), content), pcache[datakey(m3, m4)] = mkpentry(false, files[m3].content[m4]), 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), m4 ∈ files[m3].content, m ∈ files, datakey(m3, m4) ∈ pcache, m3 ∈ 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]) ⊦ datakey(m3, m4) = datakey(m, pageno), m4 ∈ content0 ∧ files[m3].content[m4] = content0[m4]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 92:
# buf = VFS_PAGE_SIZE, # content1[m4] = VFS_PAGE_SIZE, (m3 = m ⊃ mkfile(m0, md, # links(m, dirs), content[pageno, buf]);files[m3]) = mkfile(m1, md0, m2, content0), pcache[datakey(m3, m4)] = mkpentry(false, content1[m4]), files[m] = mkfile(m0, md, # links(m, dirs), content), files[m3] = mkfile(m5, md1, m6, content1), 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, datakey(m3, m4) ∈ pcache, m ∈ files, m4 ∈ content1, ∀ 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]) ⊦ datakey(m3, m4) = datakey(m, pageno), m4 ∈ content0 ∧ content1[m4] = content0[m4]

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files[m3], m5, md1, m6, content1]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files[m3], m5, md1, m6, content1