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Proof step 142 from proof inv-create (previous step)

(key.ino = m1 ⊃ mkdir(m0 + 1, md1, # links(key.ino, dirs0), m4, entries1[str, ino0]);dirs0[key.ino]) = mkdir(m, md0, m2, m3, entries), 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, key ∈ dcache[dentrykey(m1, str), mkdentry(str, ino0)], asynced1 → synced(files0, icache0, pcache), links(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ino0 = 0, str ∈ entries1, ino0 ∈ files0, ino0 ∈ dirs0, key.dentry? ∧ key.name = dcache[dentrykey(m1, str), mkdentry(str, ino0)][key].name ∧ key.ino ∈ dirs0 ∧ (links(key.ino, dirs0) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ ( dcache[dentrykey(m1, str), mkdentry(str, ino0)][key].ino ∈ dirs0 ∨ dcache[dentrykey(m1, str), mkdentry(str, ino0)][key].ino = ino0 ∨ dcache[dentrykey(m1, str), mkdentry(str, ino0)][key].ino ∈ files0) ∧ dcache[dentrykey(m1, str), mkdentry(str, ino0)][key].name ∈ entries ∧ dcache[dentrykey(m1, str), mkdentry(str, ino0)][key].ino = entries[dcache[dentrykey(m1, str), mkdentry(str, ino0)][key].name] ∧ dcache[dentrykey(m1, str), mkdentry(str, ino0)][key].dentry?

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 143:
⊦ 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 144:
(key.ino = m1 ⊃ mkdir(m0 + 1, md1, # links(key.ino, dirs0), m4, entries1[str, ino0]);dirs0[key.ino]) = mkdir(m, md0, m2, m3, entries), 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, ∅)]), synced(dirs0, icache0, pcache), key ∈ dcache[dentrykey(m1, str), mkdentry(str, ino0)], m1 ∈ dirs0, asynced1 → synced(files0, icache0, pcache), ∀ key. key ∈ dcache → key.dentry? ∧ key.name = dcache[key].name ∧ valid-dentry(key.ino, dcache[key], dirs0, files0), links(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ino0 = 0, ino0 ∈ dirs0, ino0 ∈ files0, str ∈ entries1, key.dentry? ∧ key.name = dcache[dentrykey(m1, str), mkdentry(str, ino0)][key].name ∧ key.ino ∈ dirs0 ∧ (links(key.ino, dirs0) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ ( dcache[dentrykey(m1, str), mkdentry(str, ino0)][key].ino ∈ dirs0 ∨ dcache[dentrykey(m1, str), mkdentry(str, ino0)][key].ino = ino0 ∨ dcache[dentrykey(m1, str), mkdentry(str, ino0)][key].ino ∈ files0) ∧ dcache[dentrykey(m1, str), mkdentry(str, ino0)][key].name ∈ entries ∧ dcache[dentrykey(m1, str), mkdentry(str, ino0)][key].ino = entries[dcache[dentrykey(m1, str), mkdentry(str, ino0)][key].name] ∧ dcache[dentrykey(m1, str), mkdentry(str, ino0)][key].dentry?

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, dirs0, files0] flags: <all paths>

Additional information

Used terms: dcache, dirs0, files0