Proof step 237 from proof inv-rename-file-negdentry (previous step)

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

• Proof step 238:

  # links(entries[str], dirs0[m8, mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]).meta:= md0][m, mkdir(m12, md5, m13, m14, entries3)]) = # links(entries[str], dirs0), (m19 = m ⊃ mkdir(m12, md5, m13, m14, entries3) ;(m19 = m8 ⊃ mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str);mkdir(m18, md8, # links(m19, dirs0), m20, entries5)) ) = mkdir(m15, md7, m16, m17, entries4), (m = m8 ⊃ mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str);mkdir(m7, md4, # links(m, dirs0), m9, entries2)) = mkdir(m1, md2, m4, m6, entries1), (m8 = m ⊃ mkdir(m1 + 1, md5, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str)) = mkdir(m0, md1, m10, m11, entries0), (m = m8 ⊃ mkdir(m1 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])) = mkdir(m12, md6, m13, m14, entries3), dirs0[m19] = mkdir(m18, md8, # links(m19, dirs0), m20, entries5), dirs0[m8] = mkdir(m2 + 1, md3, # links(m8, dirs0), m5, entries), files[entries[str]] = mkfile(m3, md, # links(entries[str], dirs0), content0), dirs0[m] = mkdir(m7, md4, # links(m, dirs0), m9, entries2), dcache0[dentrykey(m19, str1)] = mkdentry(str1, entries5[str1]), m8 = m, afs-cons(dirs0, files), afs-cons (dirs0[m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0] [m, mkdir(m12, md5, m13, m14, entries3) ], files), synced(dirs0, icache0, pcache), str ∈ entries, entries[str] ∈ files, m8 ∈ dirs0, m ∈ dirs0, dentrykey(m19, str1) ∈ dcache0, m19 ∈ dirs0, str1 ∈ entries5, asynced2 → synced(files, icache0, pcache), m = m8 → md5 = 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?, links(m8, dirs0) ≠ ∅ ∨ m8 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m19, dirs0) ≠ ∅ ∨ m19 = ROOT_INO, entries5[str1] ∈ dirs0 ∨ entries5[str1] ∈ files ⊦ entries5[str1] = entries4[str1], dentrykey(m19, str1) = dentrykey(m, str0), dentrykey(m19, str1) = dentrykey(m8, str), entries[str] ∈ dirs0, str0 ∈ entries2

• Proof step 245:

  # links(entries[str], dirs0[m8, mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str).meta:= md0][m, mkdir(m12, md5, m13, m14, entries3)]) = # links(entries[str], dirs0), (m19 = m ⊃ mkdir(m12, md5, m13, m14, entries3) ;(m19 = m8 ⊃ mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str);mkdir(m18, md8, # links(m19, dirs0), m20, entries5)) ) = mkdir(m15, md7, m16, m17, entries4), (m = m8 ⊃ mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str);mkdir(m7, md4, # links(m, dirs0), m9, entries2)) = mkdir(m1, md2, m4, m6, entries1), (m8 = m ⊃ mkdir(m1 + 1, md5, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str)) = mkdir(m0, md1, m10, m11, entries0), (m = m8 ⊃ mkdir(m1 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])) = mkdir(m12, md6, m13, m14, entries3), dirs0[m19] = mkdir(m18, md8, # links(m19, dirs0), m20, entries5), dirs0[m8] = mkdir(m2 + 1, md3, # links(m8, dirs0), m5, entries), files[entries[str]] = mkfile(m3, md, # links(entries[str], dirs0), content0), dirs0[m] = mkdir(m7, md4, # links(m, dirs0), m9, entries2), dcache0[dentrykey(m19, str1)] = mkdentry(str1, entries5[str1]), afs-cons(dirs0, files), afs-cons (dirs0[m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0] [m, mkdir(m12, md5, m13, m14, entries3) ], files), synced(dirs0, icache0, pcache), str ∈ entries, entries[str] ∈ files, m8 ∈ dirs0, m ∈ dirs0, dentrykey(m19, str1) ∈ dcache0, m19 ∈ dirs0, str1 ∈ entries5, asynced2 → synced(files, icache0, pcache), m = m8 → md5 = 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?, links(m8, dirs0) ≠ ∅ ∨ m8 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m19, dirs0) ≠ ∅ ∨ m19 = ROOT_INO, entries5[str1] ∈ dirs0 ∨ entries5[str1] ∈ files ⊦ entries5[str1] = entries4[str1], dentrykey(m19, str1) = dentrykey(m, str0), dentrykey(m19, str1) = dentrykey(m8, str), m8 = m, entries[str] ∈ dirs0, str0 ∈ entries2

Rule argument

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