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Proof step 7 from proof eq-io-lookup (previous step)

⟨afs_lookup#(pageno, dirs1, files1, asynced0; dent, err)⟩ (dent = old_dent ∧ err = err0), pageno ∈ dirs1, links(pageno, dirs1) ≠ ∅ ∨ pageno = ROOT_INO ⊦ ⟨fail#(; ; err)⟩ (dent = old_dent ∧ err = err0), ⟨if dent.name ∈ dirs1[pageno].entries then {dent := mkdentry(dent.name, dirs1[pageno].entries[dent.name]); err := ESUCCESS} else {dent := negdentry(dent.name); err := ENOENT}⟩ (dent = old_dent ∧ err = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
⟨afs_lookup#(pageno, dirs1, files1, asynced0; dent, err)⟩ (dent = old_dent ∧ err = err0), dirs1[pageno] = mkdir(m, md, m0, m1, entries), pageno ∈ dirs1, links(pageno, dirs1) ≠ ∅ ∨ pageno = ROOT_INO ⊦ ⟨fail#(; ; err)⟩ (dent = old_dent ∧ err = err0), ⟨if dent.name ∈ entries then {dent := mkdentry(dent.name, entries[dent.name]); err := ESUCCESS} else {dent := negdentry(dent.name); err := ENOENT}⟩ (dent = old_dent ∧ err = err0)

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] → [dirs1[pageno], m, md, m0, m1, 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: dirs1[pageno], m, md, m0, m1, entries