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Proof step 168 from proof inv-unlink (previous step)

# links(entries0[str], dirs0) = m2 + 1, (key.ino = m0 ⊃ mkdir(m8, md3, # links(key.ino, dirs0), m7, entries0 -- str);dirs0[key.ino]) = mkdir(m, md, m4, m5, entries), files0[entries0[str]] = mkfile(m1, md1, m2 + 1, content0), dirs0[m0] = mkdir(m8 + 1, md2, # links(m0, dirs0), m7, entries0), afs-cons(dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]), afs-cons(dirs0, files0), synced(dirs0, icache0, pcache), m0 ∈ dirs0, entries0[str] ∈ files0, str ∈ entries0, key ∈ dcache, asynced1 → synced(files0, icache0, pcache), ∀ key. key ∈ dcache → key.dentry? ∧ key.name = dcache[key].name ∧ valid-dentry(key.ino, dcache[key], dirs0, files0), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ key = dentrykey(m0, str), key.dentry? ∧ key.name = dcache[key].name ∧ key.ino ∈ dirs0 ∧ ((entries0[str] = key.ino ⊃ links(key.ino, dirs0) -- mklink(m0, str);links(key.ino, dirs0)) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ (dcache[key].ino ∈ dirs0 ∨ dcache[key].ino ∈ files0) ∧ dcache[key].name ∈ entries ∧ dcache[key].ino = entries[dcache[key].name] ∧ dcache[key].dentry?

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 169:
# links(entries0[str], dirs0) = m2 + 1, (key.ino = m0 ⊃ mkdir(m8, md3, # links(key.ino, dirs0), m7, entries0 -- str);dirs0[key.ino]) = mkdir(m, md, m4, m5, entries), dirs0[m0] = mkdir(m8 + 1, md2, # links(m0, dirs0), m7, entries0), files0[entries0[str]] = mkfile(m1, md1, m2 + 1, content0), afs-cons(dirs0, files0), afs-cons(dirs0[m0, mkdir(m8, md3, # links(m0, dirs0), m7, entries0 -- str)], files0[entries0[str], mkfile(m3, md0, m2, content0)]), synced(dirs0, icache0, pcache), key ∈ dcache, str ∈ entries0, entries0[str] ∈ files0, m0 ∈ dirs0, asynced1 → synced(files0, icache0, pcache), ∀ key0. key0 ∈ dcache → key0.dentry? ∧ key0.name = dcache[key0].name ∧ key0.ino ∈ dirs0 ∧ (links(key0.ino, dirs0) ≠ ∅ ∨ key0.ino = ROOT_INO) ∧ (dcache[key0].ino ∈ dirs0 ∨ dcache[key0].ino ∈ files0) ∧ dcache[key0].name ∈ dirs0[key0.ino].entries ∧ dcache[key0].ino = dirs0[key0.ino].entries[dcache[key0].name] ∧ dcache[key0].dentry?, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ key = dentrykey(m0, str), key.dentry? ∧ key.name = dcache[key].name ∧ key.ino ∈ dirs0 ∧ ((entries0[str] = key.ino ⊃ links(key.ino, dirs0) -- mklink(m0, str);links(key.ino, dirs0)) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ (dcache[key].ino ∈ dirs0 ∨ dcache[key].ino ∈ files0) ∧ dcache[key].name ∈ entries ∧ dcache[key].ino = entries[dcache[key].name] ∧ dcache[key].dentry?

Rule argument

Additional information

Used simplifier rules: ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)%⊦ valid-dentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ valid-ino(dent.ino, dirs, files) ∧ dent.name ∈ dirs[ino].entries ∧ dent.ino = dirs[ino].entries[dent.name] ∧ dent.dentry?; (s)