| (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), dirs0[m20] = mkdir(m19, md8, # links(m20, dirs0), m21, entries6), dirs0[entries0[str]] = mkdir(m3, md2, # links(entries0[str], dirs0), m5, entries), dirs0[m] = mkdir(m4, md3, # links(m, dirs0), m7, entries2), dirs0[m9] = mkdir(m1 + 1, md, # links(m9, dirs0), m2 + 1, entries0), dcache0[dentrykey(m20, str1)] = mkdentry(str1, entries6[str1]), afs-cons (dirs0[m9, mkdir(m1, md0, # links(m9, dirs0), m2, entries0 -- str)] [m, mkdir(m4 + 1, md4, # links(m, dirs0), m7 + 1, entries2[str0, entries0[str]]) ], files), afs-cons(dirs0, files), synced(dirs0, icache0, pcache), entries0[str] ∈ dirs0, str ∈ entries0, m9 ∈ dirs0, m ∈ dirs0, dentrykey(m20, str1) ∈ dcache0, m20 ∈ dirs0, str1 ∈ entries6, 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(m9, dirs0) ≠ ∅ ∨ m9 = ROOT_INO, links(m20, dirs0) ≠ ∅ ∨ m20 = ROOT_INO, entries6[str1] ∈ dirs0 ∨ entries6[str1] ∈ files ⊦ entries6[str1] = entries5[str1], dentrykey(m20, str1) = dentrykey(m, str0), dentrykey(m20, str1) = dentrykey(m9, str), m = m9, m20 = m, str0 ∈ entries2 |
Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)%str ≠ str0 ⊦ (entries -- str0)[str] = entries[str]; (s) Used formulas: m20 = m9