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Proof step 189 from proof inv-rmdir (previous step)

# links(entries0[str], dirs0) = m8 + 1, (m16 = entries0[str] ⊃ mkdir(m, md0, m8, m9, ∅) ;(m16 = m5 ⊃ mkdir(m1, md, # links(m5, dirs0), m0, entries0 -- str);mkdir(m17, md7, # links(m16, dirs0), m19, entries4)) ) = mkdir(m13, md6, m14, m15, entries3), dcache[dentrykey(m16, str0)] = mkdentry(str0, entries4[str0]), dirs0[entries0[str]] = mkdir(m, md3, m8 + 1, m9, ∅), dirs0[m5] = mkdir(m1 + 1, md1, # links(m5, dirs0), m0 + 1, entries0), dirs0[m16] = mkdir(m17, md7, # links(m16, dirs0), m19, entries4), afs-cons(dirs0, files), afs-cons(dirs0[m5, mkdir(m1, md, # links(m5, dirs0), m0, entries0 -- str)][entries0[str], mkdir(m, md0, m8, m9, ∅)], files), synced(dirs0, icache0, pcache), dentrykey(m16, str0) ∈ dcache, str ∈ entries0, m5 ∈ dirs0, m16 ∈ dirs0, str0 ∈ entries4, entries0[str] ∈ dirs0, asynced1 → synced(files, icache0, pcache), ∀ key0. key0 ∈ dcache → key0.dentry? ∧ key0.name = dcache[key0].name ∧ key0.ino ∈ dirs0 ∧ (links(key0.ino, dirs0) ≠ ∅ ∨ key0.ino = ROOT_INO) ∧ (dcache[key0].ino ∈ dirs0 ∨ dcache[key0].ino ∈ files) ∧ dcache[key0].name ∈ dirs0[key0.ino].entries ∧ dcache[key0].ino = dirs0[key0.ino].entries[dcache[key0].name] ∧ dcache[key0].dentry?, links(m5, dirs0) ≠ ∅ ∨ m5 = ROOT_INO, links(m16, dirs0) ≠ ∅ ∨ m16 = ROOT_INO, entries4[str0] ∈ dirs0 ∨ entries4[str0] ∈ files ⊦ entries0[str] = m5, entries0[str] = ROOT_INO, dentrykey(m16, str0) = dentrykey(m5, str), m16 = entries0[str], ((entries0[str] = m16 ⊃ links(entries0[str], dirs0) -- mklink(m5, str);links(m16, dirs0)) ≠ ∅ ∨ m16 = ROOT_INO) ∧ str0 ∈ entries3 ∧ entries4[str0] = entries3[str0]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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