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Proof step 223 from proof inv-rename-dir-negdentry (previous step)

(m = m9 ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]])) = mkdir(m13, md6, m14, m15, entries4), (m9 = m ⊃ mkdir(m4 + 1, md4, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md0, # links(m9, dirs0), m2, entries0 -- str)) = mkdir(m0, md1, m11, m12, entries1), (m = m9 ⊃ mkdir(m1, md, # links(m9, dirs0), m2, entries0 -- str);mkdir(m8, md5, # links(m, dirs0), m10, entries3)) = mkdir(m4, md3, m6, m7, entries2), (m20 = m ⊃ mkdir(m13, md4, m14, m15, entries4) ;(m20 = m9 ⊃ mkdir(m1, md0, # links(m9, dirs0), m2, entries0 -- str);mkdir(m19, md8, # links(m20, dirs0), m21, entries6)) ) = mkdir(m16, md7, m17, m18, entries5), dcache0[dentrykey(m20, str1)] = mkdentry(str1, entries6[str1]), dirs0[m9] = mkdir(m1 + 1, md, # links(m9, dirs0), m2 + 1, entries0), dirs0[m] = mkdir(m8, md5, # links(m, dirs0), m10, entries3), dirs0[entries0[str]] = mkdir(m3, md2, # links(entries0[str], dirs0), m5, entries), dirs0[m20] = mkdir(m19, md8, # links(m20, dirs0), m21, entries6), afs-cons (dirs0 [m9, (m9 = m ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries2[str0, entries0[str]]);mkdir(m1, md, # links(m9, dirs0), m2, entries0 -- str)).meta:= md0 ] [m, mkdir(m13, md4, m14, m15, entries4) ], files), afs-cons(dirs0, files), synced(dirs0, icache0, pcache), str1 ∈ entries6, m20 ∈ dirs0, dentrykey(m20, str1) ∈ dcache0, m ∈ dirs0, m9 ∈ dirs0, str ∈ entries0, entries0[str] ∈ dirs0, asynced2 → synced(files, icache0, pcache), m = m9 → md4 = md0, ∀ 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?, entries6[str1] ∈ dirs0 ∨ entries6[str1] ∈ files, links(m20, dirs0) ≠ ∅ ∨ m20 = ROOT_INO, links(m9, dirs0) ≠ ∅ ∨ m9 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ dentrykey(m20, str1) = dentrykey(m9, str), dentrykey(m20, str1) = dentrykey(m, str0), str0 ∈ entries3, str1 ∈ entries5

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Rule argument

pos: left 1

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