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Proof step 21 from proof crash-neutral-renam (previous step)

dirs[dirs[m4].entries[str]] = mkdir(m12, md3, m13, m14, entries), files[dirs[m4].entries[str]] = mkfile(m5, md1, m9, content), files[new_dent.ino] = mkfile(m10, md2, m11, content0), dirs[new_dent.ino] = mkdir(m15, md4, m16, m17, entries0), afs-cons(dirs, files), m4 ∈ dirs, str ∈ dirs[m4].entries, m ∈ dirs, m = m4 → md = md0, links(m4, dirs) ≠ ∅ ∨ m4 = ROOT_INO, dirs[m4].entries[str] ∈ dirs ∨ dirs[m4].entries[str] ∈ files, dirs[m4].entries[str] ∈ dirs ∧ m6 = m13 ∧ m8 = m12 ∧ m7 = m14 ∧ boolvar0 ∨ dirs[m4].entries[str] ∈ files ∧ m6 = m9 ∧ m7 = 0 ∧ ¬ boolvar0, (links(m, dirs) ≠ ∅ ∨ m = ROOT_INO) ∧ ¬ new_dent.name ∈ dirs[m].entries ∧ new_dent.negdentry? ∨ (links(m, dirs) ≠ ∅ ∨ m = ROOT_INO) ∧ (new_dent.ino ∈ dirs ∨ new_dent.ino ∈ files) ∧ new_dent.name ∈ dirs[m].entries ∧ new_dent.ino = dirs[m].entries[new_dent.name] ∧ new_dent.dentry? ∧ (new_dent.ino ∈ dirs ∧ m1 = m16 ∧ m3 = m15 ∧ m2 = m17 ∧ boolvar ∨ new_dent.ino ∈ files ∧ m1 = m11 ∧ m2 = 0 ∧ ¬ boolvar) ∧ m0 = new_dent.ino ∧ (new_dent.ino ∈ files ↔ dirs[m4].entries[str] ∈ files) ∧ (new_dent.ino ∈ dirs → new_dent.ino ≠ ROOT_INO ∧ entries0 = ∅) ⊦ ⟨fail#(; ; err); asynced := ?⟩ asynced

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 22:
dirs[new_dent.ino] = mkdir(m15, md4, m16, m17, entries0), files[new_dent.ino] = mkfile(m10, md2, m11, content0), files[dirs[m4].entries[str]] = mkfile(m5, md1, m9, content), dirs[dirs[m4].entries[str]] = mkdir(m12, md3, m13, m14, entries), dirs[m] = mkdir(m18, md5, m19, m20, entries1), afs-cons(dirs, files), m ∈ dirs, str ∈ dirs[m4].entries, m4 ∈ dirs, m = m4 → md = md0, (links(m, dirs) ≠ ∅ ∨ m = ROOT_INO) ∧ ¬ new_dent.name ∈ entries1 ∧ new_dent.negdentry? ∨ (links(m, dirs) ≠ ∅ ∨ m = ROOT_INO) ∧ (new_dent.ino ∈ dirs ∨ new_dent.ino ∈ files) ∧ new_dent.name ∈ entries1 ∧ new_dent.ino = entries1[new_dent.name] ∧ new_dent.dentry? ∧ (new_dent.ino ∈ dirs ∧ m1 = m16 ∧ m3 = m15 ∧ m2 = m17 ∧ boolvar ∨ new_dent.ino ∈ files ∧ m1 = m11 ∧ m2 = 0 ∧ ¬ boolvar) ∧ m0 = new_dent.ino ∧ (new_dent.ino ∈ files ↔ dirs[m4].entries[str] ∈ files) ∧ (new_dent.ino ∈ dirs → new_dent.ino ≠ ROOT_INO ∧ entries0 = ∅), dirs[m4].entries[str] ∈ dirs ∧ m6 = m13 ∧ m8 = m12 ∧ m7 = m14 ∧ boolvar0 ∨ dirs[m4].entries[str] ∈ files ∧ m6 = m9 ∧ m7 = 0 ∧ ¬ boolvar0, dirs[m4].entries[str] ∈ dirs ∨ dirs[m4].entries[str] ∈ files, links(m4, dirs) ≠ ∅ ∨ m4 = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ asynced

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] → [dirs[m], m18, md5, m19, m20, entries1]

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[m], m18, md5, m19, m20, entries1