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Proof step 381 from proof inv-write_inode (previous step)

# files[m3].content[m4] = VFS_PAGE_SIZE, (m3 = m ⊃ (files[m].meta:= md).size:= m2;files[m3]) = mkfile(m0, md0, m1, content), pcache[datakey(m3, m4)] = mkpentry(false, files[m3].content[m4]), afs-cons(dirs, files), afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), synced(files, icache, pcache), synced(dirs, icache, pcache), m4 ∈ files[m3].content, datakey(m3, m4) ∈ pcache, m ∈ files, 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]) ⊦ m ∈ icache, m4 ∈ content ∧ files[m3].content[m4] = content[m4]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 382:
# content0[m4] = VFS_PAGE_SIZE, (m3 = m ⊃ (files[m].meta:= md).size:= m2;files[m3]) = mkfile(m0, md0, m1, content), pcache[datakey(m3, m4)] = mkpentry(false, content0[m4]), files[m3] = mkfile(m5, md1, m6, content0), afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), afs-cons(dirs, files), synced(dirs, icache, pcache), synced(files, icache, pcache), m3 ∈ files, m ∈ files, datakey(m3, m4) ∈ pcache, m4 ∈ content0, ∀ 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]) ⊦ m ∈ icache, m4 ∈ content ∧ content0[m4] = content[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, content0]

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, content0