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Proof step 183 from proof inv-rmdir (previous step)

(m16 = entries0[str] ⊃ mkdir(m, md0, m8, m9, entries1) ;(m16 = m5 ⊃ mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str);mkdir(m17, md7, # links(m16, dirs0), m19, entries4)) ) = mkdir(m13, md6, m14, m15, entries3), (m5 = entries0[str] ⊃ mkdir(m3, md0, m7, m6, entries);mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str)) = mkdir(m10, md5, m11, m12, entries2), (entries0[str] = m5 ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)) = mkdir(m, md4, m8, m9, entries1), (entries0[str] = m5 ⊃ mkdir(m0 - 1, md1, # links(entries0[str], dirs0), m2 - 1, entries0 -- str) ;mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅) ) = mkdir(m3, md2, m7 + 1, m6, entries), dirs0[m16] = mkdir(m17, md7, # links(m16, dirs0), m19, entries4), dirs0[m5] = mkdir(m0, md1, # links(m5, dirs0), m2, entries0), dirs0[entries0[str]] = mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅), dcache[dentrykey(m16, str0)] = mkdentry(str0, entries4[str0]), afs-cons (dirs0[m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], mkdir(m, md0, m8, m9, entries1) ], files), afs-cons(dirs0, files), synced(dirs0, icache0, pcache), entries0[str] ∈ dirs0, str0 ∈ entries4, m16 ∈ dirs0, m5 ∈ dirs0, str ∈ entries0, dentrykey(m16, str0) ∈ dcache, 1 ≤ m0, 1 ≤ m2, asynced1 → synced(files, icache0, pcache), ∀ key0. key0 ∈ dcache → key0.dentry? ∧ key0.name = dcache[key0].name ∧ key0.ino ∈ dirs0 ∧ (links(key0.ino, dirs0) ≠ ∅ ∨ key0.ino = ROOT_INO) ∧ (dcache[key0].ino ∈ dirs0 ∨ dcache[key0].ino ∈ files) ∧ dcache[key0].name ∈ dirs0[key0.ino].entries ∧ dcache[key0].ino = dirs0[key0.ino].entries[dcache[key0].name] ∧ dcache[key0].dentry?, entries4[str0] ∈ dirs0 ∨ entries4[str0] ∈ files, links(m16, dirs0) ≠ ∅ ∨ m16 = ROOT_INO, links(m5, dirs0) ≠ ∅ ∨ m5 = ROOT_INO ⊦ entries0[str] = ROOT_INO, entries0[str] = m5, dentrykey(m16, str0) = dentrykey(m5, str), m0 = 0, m2 = 0, ( links (m16, dirs0 [m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str], mkdir(m, md0, m8, m9, entries1) ]) ≠ ∅ ∨ m16 = ROOT_INO) ∧ str0 ∈ entries3 ∧ entries4[str0] = entries3[str0]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 184:
# links(entries0[str], dirs0) = m8 + 1, (m16 = entries0[str] ⊃ mkdir(m, md0, m8, m9, ∅) ;(m16 = m5 ⊃ mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str);mkdir(m17, md7, # links(m16, dirs0), m19, entries4)) ) = mkdir(m13, md6, m14, m15, entries3), dirs0[m16] = mkdir(m17, md7, # links(m16, dirs0), m19, entries4), dirs0[m5] = mkdir(m0, md1, # links(m5, dirs0), m2, entries0), dirs0[entries0[str]] = mkdir(m, md3, m8 + 1, m9, ∅), dcache[dentrykey(m16, str0)] = mkdentry(str0, entries4[str0]), afs-cons(dirs0[m5, mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str)][entries0[str], mkdir(m, md0, m8, m9, ∅)], files), afs-cons(dirs0, files), synced(dirs0, icache0, pcache), entries0[str] ∈ dirs0, str0 ∈ entries4, m16 ∈ dirs0, m5 ∈ dirs0, str ∈ entries0, dentrykey(m16, str0) ∈ dcache, 1 ≤ m0, 1 ≤ m2, asynced1 → synced(files, icache0, pcache), ∀ key0. key0 ∈ dcache → key0.dentry? ∧ key0.name = dcache[key0].name ∧ key0.ino ∈ dirs0 ∧ (links(key0.ino, dirs0) ≠ ∅ ∨ key0.ino = ROOT_INO) ∧ (dcache[key0].ino ∈ dirs0 ∨ dcache[key0].ino ∈ files) ∧ dcache[key0].name ∈ dirs0[key0.ino].entries ∧ dcache[key0].ino = dirs0[key0.ino].entries[dcache[key0].name] ∧ dcache[key0].dentry?, entries4[str0] ∈ dirs0 ∨ entries4[str0] ∈ files, links(m16, dirs0) ≠ ∅ ∨ m16 = ROOT_INO, links(m5, dirs0) ≠ ∅ ∨ m5 = ROOT_INO ⊦ entries0[str] = ROOT_INO, entries0[str] = m5, dentrykey(m16, str0) = dentrykey(m5, str), m0 = 0, m2 = 0, ((entries0[str] = m16 ⊃ links(entries0[str], dirs0) -- mklink(m5, str);links(m16, dirs0)) ≠ ∅ ∨ m16 = ROOT_INO) ∧ str0 ∈ entries3 ∧ entries4[str0] = entries3[str0]

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(ino, dirs[p_ino, mkdir(m0, md, n0, n1 - 1, entries)]) = links(ino, dirs[p_ino, mkdir(m0, md, n0, n1, entries)]); (s)%⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(m0, md0, n1, n2, entries) ∧ ino ≠ ino1 → links(ino0, dirs[ino1, ad][ino, mkdir(m, md, n, n0, entries)]) = links(ino0, dirs[ino1, ad]); (s)%afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base%⊦ mkdir(m, md, m0, m1, entries).meta:= md0 = mkdir(m, md0, m0, m1, entries); (s)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)