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Proof step 6 from proof crash-neutral-lookup (previous step)

asynced ↔ true, afs-cons(dirs, files), p_ino ∈ dirs, links(p_ino, dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ⟨fail#(; ; err)⟩ true, ⟨if dent.name ∈ dirs[p_ino].entries then {dent := mkdentry(dent.name, dirs[p_ino].entries[dent.name]); err := ESUCCESS} else {dent := negdentry(dent.name); err := ENOENT}⟩ true

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
asynced ↔ true, dirs[p_ino] = mkdir(m, md, m0, m1, entries), afs-cons(dirs, files), p_ino ∈ dirs, links(p_ino, dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ⟨fail#(; ; err)⟩ true, ⟨if dent.name ∈ entries then {dent := mkdentry(dent.name, entries[dent.name]); err := ESUCCESS} else {dent := negdentry(dent.name); err := ENOENT}⟩ true

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, entries] → [dirs[p_ino], m, md, m0, 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: dirs[p_ino], m, md, m0, entries