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Proof step 480 from proof inv-rename-file-dentry (previous step)

# files[key.ino].content[key.part] = VFS_PAGE_SIZE, (key.ino = entries[str0] ⊃ mkfile(m, md3, # links(entries[str0], dirs0), content);files[key.ino]) = mkfile(m2, md, m5, content0), pcache[key] = mkpentry(false, files[key.ino].content[key.part]), dirs0[m3] = mkdir(m1, md1, # links(m3, dirs0), m4, entries), files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), key.data?, afs-cons(dirs0, files), afs-cons (dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)]), synced(dirs0, icache0, pcache), key.part ∈ files[key.ino].content, key ∈ pcache, m3 ∈ dirs0, str0 ∈ entries, entries[str0] ∈ files, key.ino ∈ files, asynced2 → synced(files, icache0, pcache), ∀ 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]), links(m3, dirs0) ≠ ∅ ∨ m3 = ROOT_INO ⊦ entries[str0] ∈ dirs0, 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 481:
# files[m6].content[m7] = VFS_PAGE_SIZE, (m6 = entries[str0] ⊃ mkfile(m, md3, # links(entries[str0], dirs0), content);files[m6]) = mkfile(m2, md, m5, content0), files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), dirs0[m3] = mkdir(m1, md1, # links(m3, dirs0), m4, entries), pcache[key] = mkpentry(false, files[m6].content[m7]), key = datakey(m6, m7), key.data?, afs-cons (dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)]), afs-cons(dirs0, files), synced(dirs0, icache0, pcache), m6 ∈ files, entries[str0] ∈ files, str0 ∈ entries, m3 ∈ dirs0, key ∈ pcache, m7 ∈ files[m6].content, asynced2 → synced(files, icache0, pcache), ∀ 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]), links(m3, dirs0) ≠ ∅ ∨ m3 = ROOT_INO ⊦ entries[str0] ∈ dirs0, m7 ∈ content0 ∧ files[m6].content[m7] = content0[m7]

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, m6, m7]

Additional information

Used simplifier rules: ⊦ key.data? → (m = key.ino ∧ m0 = key.part ↔ key = datakey(m, m0)); (elim) Used terms: key, m6, m7