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Proof step 242 from proof inv-rename-file-negdentry (previous step)

#((links(entries5[str], dirs0) -- mklink(m, str)) ++ mklink(m, str0)) = # links(entries5[str], dirs0), dirs0[m] = mkdir(m1 + 1, md8, # links(m, dirs0), m20, entries5), files[entries5[str]] = mkfile(m3, md, # links(entries5[str], dirs0), content0), dcache0[dentrykey(m, str1)] = mkdentry(str1, entries5[str1]), afs-cons(dirs0[m, mkdir(m1 + 1, md0, # links(m, dirs0), m20, (entries5 -- str)[str0, entries5[str]])], files), afs-cons(dirs0, files), synced(dirs0, icache0, pcache), str ∈ entries5, entries5[str] ∈ files, m ∈ dirs0, dentrykey(m, str1) ∈ dcache0, str1 ∈ entries5, asynced2 → synced(files, icache0, pcache), ∀ key0. key0 ∈ dcache0 → key0.dentry? ∧ key0.name = dcache0[key0].name ∧ key0.ino ∈ dirs0 ∧ (links(key0.ino, dirs0) ≠ ∅ ∨ key0.ino = ROOT_INO) ∧ (dcache0[key0].ino ∈ dirs0 ∨ dcache0[key0].ino ∈ files) ∧ dcache0[key0].name ∈ dirs0[key0.ino].entries ∧ dcache0[key0].ino = dirs0[key0.ino].entries[dcache0[key0].name] ∧ dcache0[key0].dentry?, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, entries5[str1] ∈ dirs0 ∨ entries5[str1] ∈ files ⊦ entries5[str1] = (entries5 -- str)[str0, entries5[str]][str1], dentrykey(m, str1) = dentrykey(m, str0), dentrykey(m, str1) = dentrykey(m, str), str1 = str0, entries5[str] ∈ dirs0, str0 ∈ entries5

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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