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Proof step 240 from proof inv-rename-file-negdentry (previous step)

#((links(entries2[str], dirs0) -- mklink(m, str)) ++ mklink(m, str0)) = # links(entries2[str], dirs0), (m19 = m ⊃ mkdir(m1 + 1, md0, # links(m, dirs0), m9, (entries2 -- str)[str0, entries2[str]]) ;mkdir(m18, md8, # links(m19, dirs0), m20, entries5) ) = mkdir(m15, md7, m16, m17, entries4), files[entries2[str]] = mkfile(m3, md, # links(entries2[str], dirs0), content0), dirs0[m] = mkdir(m1 + 1, md4, # links(m, dirs0), m9, entries2), dirs0[m19] = mkdir(m18, md8, # links(m19, dirs0), m20, entries5), dcache0[dentrykey(m19, str1)] = mkdentry(str1, entries5[str1]), m19 = m, afs-cons(dirs0, files), afs-cons(dirs0[m, mkdir(m1 + 1, md0, # links(m, dirs0), m9, (entries2 -- str)[str0, entries2[str]])], files), synced(dirs0, icache0, pcache), str1 ∈ entries5, m19 ∈ dirs0, dentrykey(m19, str1) ∈ dcache0, m ∈ dirs0, entries2[str] ∈ files, str ∈ entries2, 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 ⊦ entries5[str1] = entries4[str1], dentrykey(m19, str1) = dentrykey(m, str), dentrykey(m19, str1) = dentrykey(m, str0), str0 ∈ entries2, entries2[str] ∈ dirs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 241:
#((links(entries5[str], dirs0) -- mklink(m, str)) ++ mklink(m, str0)) = # links(entries5[str], dirs0), dcache0[dentrykey(m, str1)] = mkdentry(str1, entries5[str1]), files[entries5[str]] = mkfile(m3, md, # links(entries5[str], dirs0), content0), dirs0[m] = mkdir(m1 + 1, md8, # links(m, dirs0), m20, entries5), afs-cons(dirs0, files), afs-cons(dirs0[m, mkdir(m1 + 1, md0, # links(m, dirs0), m20, (entries5 -- str)[str0, entries5[str]])], files), synced(dirs0, icache0, pcache), str1 ∈ entries5, dentrykey(m, str1) ∈ dcache0, m ∈ dirs0, entries5[str] ∈ files, str ∈ 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?, entries5[str1] ∈ dirs0 ∨ entries5[str1] ∈ files, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries5[str1] = (entries5 -- str)[str0, entries5[str]][str1], dentrykey(m, str1) = dentrykey(m, str), dentrykey(m, str1) = dentrykey(m, str0), str0 ∈ entries5, entries5[str] ∈ dirs0

Rule argument

Additional information

Used simplifier rules: ⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(m0, md0, n1, n2, entries) → links(ino0, dirs[ino, mkdir(m, md, n, n0, entries)]) = links(ino0, dirs); (s)%⊦ ino0 ∈ dirs → links(ino, dirs[ino0, mkdir(m, md, n0, n1, entries -- str)]) = (str ∈ entries ∧ entries[str] = ino ⊃ links(ino, dirs[ino0, mkdir(m, md, n0, n1, entries)]) -- mklink(ino0, str) ;links(ino, dirs[ino0, mkdir(m, md, n0, n1, entries)]) ); (s)%⊦ p_ino ∈ dirs → links (ino0, dirs[p_ino, mkdir(m0, md, n, n0, entries[str, ino])]) = (ino = ino0 ⊃ links(ino0, dirs[p_ino, mkdir(m0, md, n, n0, entries)]) ++ mklink(p_ino, str) ;(str ∈ entries ∧ entries[str] = ino0 ⊃ links(ino0, dirs[p_ino, mkdir(m0, md, n, n0, entries)]) -- mklink(p_ino, str) ;links(ino0, dirs[p_ino, mkdir(m0, md, n, n0, entries)]) ) ); (s)%afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)