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Proof step 138 from proof inv-create (previous step)

dirs0[m1] = mkdir(m0, md2, # links(m1, dirs0), m4, entries1), afs-cons(dirs0, files0), afs-cons(dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]), dcache-cons(dcache, dirs0, files0), synced(dirs0, icache0, pcache), m1 ∈ dirs0, asynced1 → synced(files0, icache0, pcache), links(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ino0 = 0, dcache-cons (dcache[dentrykey(m1, str), mkdentry(str, ino0)], dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]), ino0 ∈ dirs0, ino0 ∈ files0, str ∈ entries1

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 139:
⊦ 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 140:
dirs0[m1] = mkdir(m0, md2, # links(m1, dirs0), m4, entries1), afs-cons(dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]), afs-cons(dirs0, files0), dcache-cons(dcache, dirs0, files0), synced(dirs0, icache0, pcache), m1 ∈ dirs0, asynced1 → synced(files0, icache0, pcache), links(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ino0 = 0, str ∈ entries1, ino0 ∈ files0, ino0 ∈ dirs0, ∀ key. key ∈ dcache[dentrykey(m1, str), mkdentry(str, ino0)] → key.dentry? ∧ key.name = dcache[dentrykey(m1, str), mkdentry(str, ino0)][key].name ∧ valid-dentry (key.ino, dcache[dentrykey(m1, str), mkdentry(str, ino0)][key], dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)])

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] → [dcache[dentrykey(m1, str), mkdentry(str, ino0)], dirs0 [m1, mkdir (m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0]) ], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]] flags: <all paths>

Additional information

Used terms: dcache[dentrykey(m1, str), mkdentry(str, ino0)], dirs0 [m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0]) ], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]