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Proof step 180 from proof inv-rmdir (previous step)

(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), (entries0[str] = m5 ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)) = mkdir(m, md4, m8, m9, entries1), (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), (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), dcache[dentrykey(m16, str0)] = mkdentry(str0, entries4[str0]), dirs0[entries0[str]] = mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅), dirs0[m5] = mkdir(m0, md1, # links(m5, dirs0), m2, entries0), dirs0[m16] = mkdir(m17, md7, # links(m16, dirs0), m19, entries4), afs-cons(dirs0, files), 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), synced(dirs0, icache0, pcache), dentrykey(m16, str0) ∈ dcache, entries0[str] ∈ dirs0, str ∈ entries0, m5 ∈ dirs0, m16 ∈ dirs0, str0 ∈ entries4, 1 ≤ m2, 1 ≤ m0, 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?, links(m5, dirs0) ≠ ∅ ∨ m5 = ROOT_INO, links(m16, dirs0) ≠ ∅ ∨ m16 = ROOT_INO, entries4[str0] ∈ dirs0 ∨ entries4[str0] ∈ files ⊦ entries0[str] = ROOT_INO, 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 nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 181:
(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), str0 ∈ entries4, m16 ∈ dirs0, m5 ∈ dirs0, str ∈ entries0, entries0[str] ∈ dirs0, dentrykey(m16, str0) ∈ dcache, entries0[str] ∈ dirs0[m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md], 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, 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]

Rule argument

fma: entries0[str] ∈ dirs0 [m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries) ;mkdir (m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str) ) .meta:= md ]

Additional information

Used simplifier rules: ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s) Used formulas: entries0[str] ∈ dirs0 [m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries) ;mkdir (m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str) ) .meta:= md ]