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Proof step 489 from proof inv-rename-file-dentry (previous step)

files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), dirs0[m3] = mkdir(m1, md1, # links(m3, dirs0), m4, entries), 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), dcache-cons(dcache0, dirs0, files), synced(dirs0, icache0, pcache), entries[str0] ∈ files, str0 ∈ entries, m3 ∈ dirs0, asynced2 → synced(files, icache0, pcache), links(m3, dirs0) ≠ ∅ ∨ m3 = ROOT_INO ⊦ dcache-cons (dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])], dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)]), entries[str0] ∈ dirs0

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 490:
⊦ dcache-cons(dcache, dirs, files) ↔ (∀ key. key ∈ dcache → key.dentry? ∧ key.name = dcache[key].name ∧ valid-dentry(key.ino, dcache[key], dirs, files))
Proof step 491:
dirs0[m3] = mkdir(m1, md1, # links(m3, dirs0), m4, entries), files[entries[str0]] = mkfile(m0, md0, # links(entries[str0], dirs0), content), 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)]), dcache-cons(dcache0, dirs0, files), synced(dirs0, icache0, pcache), m3 ∈ dirs0, str0 ∈ entries, entries[str0] ∈ files, asynced2 → synced(files, icache0, pcache), links(m3, dirs0) ≠ ∅ ∨ m3 = ROOT_INO ⊦ entries[str0] ∈ dirs0, ∀ key. key ∈ dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])] → key.dentry? ∧ key.name = dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])][key].name ∧ valid-dentry (key.ino, dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])][key], dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files[entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content)])

Rule argument

spec: cache-base name: dcache-cons seq: ⊦ dcache-cons(dcache, dirs, files) ↔ (∀ key. key ∈ dcache → key.dentry? ∧ key.name = dcache[key].name ∧ valid-dentry(key.ino, dcache[key], dirs, files)) subst: [dcache, dirs, files] → [dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])], dirs0 [m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries) ], files [entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content) ]] flags: <all paths>

Additional information

Used terms: dcache0[dentrykey(m3, str0), mkdentry(str0, entries[str0])], dirs0[m3, mkdir(m1, md2, # links(m3, dirs0), m4, entries)], files [entries[str0], mkfile(m, md3, # links(entries[str0], dirs0), content) ]