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Proof step 484 from proof inv-rename-file-dentry (previous step)

(m6 = entries[str0] ⊃ mkfile(m, md3, # links(entries[str0], dirs0), content);mkfile(m8, md4, # links(m6, dirs0), content1)) = 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[datakey(m6, m7)] = mkpentry(false, content1[m7]), files[m6] = mkfile(m8, md4, # links(m6, dirs0), content1), 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, datakey(m6, m7) ∈ pcache, m7 ∈ content1, 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 ∧ content1[m7] = content0[m7]

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: m6 = entries[str0]

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws) Used formulas: m6 = entries[str0]