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Proof step 222 from proof inv-rename-file-negdentry (previous step)

# links (entries[str], 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) ]) = # links(entries[str], dirs0), (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), (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(m2, md3, # links(m8, dirs0), m5, entries -- str);mkdir(m7, md4, # links(m, dirs0), m9, entries2)) = mkdir(m1, md2, m4, m6, entries1), (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), dcache0[dentrykey(m19, str1)] = mkdentry(str1, entries5[str1]), dirs0[m] = mkdir(m7, md4, # links(m, dirs0), m9, entries2), files[entries[str]] = mkfile(m3, md, # links(entries[str], dirs0), content0), dirs0[m8] = mkdir(m2 + 1, md3, # links(m8, dirs0), m5, entries), dirs0[m19] = mkdir(m18, md8, # links(m19, dirs0), m20, entries5), links (m19, 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) ]) = ∅, 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), afs-cons(dirs0, files), synced(dirs0, icache0, pcache), str1 ∈ entries5, m19 ∈ dirs0, dentrykey(m19, str1) ∈ dcache0, m ∈ dirs0, m8 ∈ dirs0, entries[str] ∈ files, str ∈ entries, m = m8 → md5 = md0, 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?, entries5[str1] ∈ dirs0 ∨ entries5[str1] ∈ files, links(m19, dirs0) ≠ ∅ ∨ m19 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m8, dirs0) ≠ ∅ ∨ m8 = ROOT_INO ⊦ dentrykey(m19, str1) = dentrykey(m8, str), dentrykey(m19, str1) = dentrykey(m, str0), m19 = ROOT_INO, str0 ∈ entries2, entries[str] ∈ dirs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 223:
# links (entries[str], 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) ]) = # links(entries[str], dirs0), (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), (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(m2, md3, # links(m8, dirs0), m5, entries -- str);mkdir(m7, md4, # links(m, dirs0), m9, entries2)) = mkdir(m1, md2, m4, m6, entries1), (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, 0, m17, entries4), dcache0[dentrykey(m19, str1)] = mkdentry(str1, entries5[str1]), dirs0[m] = mkdir(m7, md4, # links(m, dirs0), m9, entries2), files[entries[str]] = mkfile(m3, md, # links(entries[str], dirs0), content0), dirs0[m8] = mkdir(m2 + 1, md3, # links(m8, dirs0), m5, entries), dirs0[m19] = mkdir(m18, md8, # links(m19, dirs0), m20, entries5), 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), afs-cons(dirs0, files), synced(dirs0, icache0, pcache), str1 ∈ entries5, m19 ∈ dirs0, dentrykey(m19, str1) ∈ dcache0, m ∈ dirs0, m8 ∈ dirs0, entries[str] ∈ files, str ∈ entries, m = m8 → md5 = md0, 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, links(m8, dirs0) ≠ ∅ ∨ m8 = ROOT_INO, entries5[str1] ∈ dirs0 ∨ entries5[str1] ∈ files ⊦ # links(m19, dirs0) = 0, dentrykey(m19, str1) = dentrykey(m8, str), dentrykey(m19, str1) = dentrykey(m, str0), links(m19, dirs0) = ∅, m19 = ROOT_INO, str0 ∈ entries2, entries[str] ∈ dirs0

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)%size-zero: ⊦ # ls ≠ 0 → ls ≠ ∅; (forward) from specification set-basic[alink-set]%size-zero-01: ⊦ ls ≠ ∅ → # ls ≠ 0; (forward) from specification set-basic[alink-set]% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)%⊦ mkdir(m, md, m0, m1, entries).meta:= md0 = mkdir(m, md0, m0, m1, entries); (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)%⊦ afs-cons(dirs, files) → ( links(ino, dirs) = ∅ ↔ (ino ∈ dirs → dirs[ino].nlink = 0) ∧ (ino ∈ files → files[ino].nlink = 0)); (ws)