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Proof step 165 from proof inv-unlink (previous step)

# links(entries0[str], dirs0) = m2 + 1, 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), dcache-cons(dcache, dirs0, files0), synced(dirs0, icache0, pcache), m0 ∈ dirs0, entries0[str] ∈ files0, str ∈ entries0, key ∈ dcache, asynced1 → synced(files0, icache0, pcache), 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 ∈ (key.ino = m0 ⊃ mkdir(m8, md3, # links(key.ino, dirs0), m7, entries0 -- str);dirs0[key.ino]).entries ∧ dcache[key].ino = (key.ino = m0 ⊃ mkdir(m8, md3, # links(key.ino, dirs0), m7, entries0 -- str);dirs0[key.ino]).entries[dcache[key].name] ∧ dcache[key].dentry?

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 166:
# 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)]), dcache-cons(dcache, dirs0, files0), synced(dirs0, icache0, pcache), key ∈ dcache, str ∈ entries0, entries0[str] ∈ files0, m0 ∈ dirs0, asynced1 → synced(files0, icache0, pcache), 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

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [(key.ino = m0 ⊃ mkdir (m8, md3, # links(key.ino, dirs0), m7, entries0 -- str) ;dirs0[key.ino] ), m, md, m4, m5, entries]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: (key.ino = m0 ⊃ mkdir(m8, md3, # links(key.ino, dirs0), m7, entries0 -- str) ;dirs0[key.ino] ), m, md, m4, m5, entries