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Proof step 290 from proof afs-cons-rename-file-dentry (previous step)

# links(m0, dirs) = m4, # links(m, dirs) = dirs[m].nlink, dirs[m] = mkdir(dirs[m].size, md5, dirs[m].nlink, dirs[m].nsubdirs, entries), files[entries[str]] = mkfile(m3, md0, # links(entries[str], dirs), content0), files[entries0[str0]] = mkfile(m2, md, # links(entries0[str0], dirs), content1), dirs[m0] = mkdir(m1, md6, m4, m5, entries0), entries[str] = dirs[m].entries[str], entries0[str0] = entries1[str0], dirs[m0] = mkdir(m1, md3, m4, m5, entries1), afs-cons(dirs, files), str ∈ entries, str0 ∈ entries0, m ∈ dirs, m0 ∈ dirs, entries[str] ∈ files, entries0[str0] ∈ files, str ∈ dirs[m].entries, str0 ∈ entries1, m = m0 → md1 = md2, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪fail#(; ; err); asynced := ?⟫ true, entries[str] ∈ dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 291:
# links(m, dirs) = dirs[m].nlink, entries[str] = dirs[m].entries[str], dirs[m0] = mkdir(m1, md3, # links(m0, dirs), m5, entries1), files[entries1[str0]] = mkfile(m2, md, # links(entries1[str0], dirs), content1), files[entries[str]] = mkfile(m3, md0, # links(entries[str], dirs), content0), dirs[m] = mkdir(dirs[m].size, md5, dirs[m].nlink, dirs[m].nsubdirs, entries), afs-cons(dirs, files), str ∈ dirs[m].entries, entries1[str0] ∈ files, entries[str] ∈ files, m0 ∈ dirs, m ∈ dirs, str0 ∈ entries1, str ∈ entries, ¬ entries[str] ∈ dirs, m = m0 → md1 = md2, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪fail#(; ; err); asynced := ?⟫ true

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)