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Proof step 203 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), 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), 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), dcache-cons(dcache0, dirs0, files), synced(dirs0, icache0, pcache), m8 ∈ dirs0, m ∈ dirs0, entries[str] ∈ files, str ∈ entries, m = m8 → md5 = md0, asynced2 → synced(files, icache0, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m8, dirs0) ≠ ∅ ∨ m8 = ROOT_INO ⊦ str0 ∈ entries2, entries[str] ∈ dirs0, ∀ key. key ∈ (dcache0 -- dentrykey(m8, str))[dentrykey(m, str0), mkdentry(str0, entries[str])] → key.dentry? ∧ key.name = (dcache0 -- dentrykey(m8, str))[dentrykey(m, str0), mkdentry(str0, entries[str])][key].name ∧ valid-dentry (key.ino, (dcache0 -- dentrykey(m8, str))[dentrykey(m, str0), mkdentry(str0, entries[str])][key], 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 204:
# 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(m2, md3, # links(m8, dirs0), m5, entries -- str);mkdir(m7, md4, # links(m, dirs0), m9, entries2)) = mkdir(m1, md2, m4, m6, entries1), (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(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), dirs0[m8] = mkdir(m2 + 1, md3, # links(m8, dirs0), m5, entries), files[entries[str]] = mkfile(m3, md, # links(entries[str], dirs0), content0), dirs0[m] = mkdir(m7, md4, # links(m, dirs0), m9, entries2), afs-cons(dirs0, files), 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), dcache-cons(dcache0, dirs0, files), synced(dirs0, icache0, pcache), key ∈ (dcache0 -- dentrykey(m8, str))[dentrykey(m, str0), mkdentry(str0, entries[str])], str ∈ entries, entries[str] ∈ files, m ∈ dirs0, m8 ∈ dirs0, asynced2 → synced(files, icache0, pcache), m = m8 → md5 = md0, links(m8, dirs0) ≠ ∅ ∨ m8 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries[str] ∈ dirs0, str0 ∈ entries2, key.dentry? ∧ key.name = (dcache0 -- dentrykey(m8, str))[dentrykey(m, str0), mkdentry(str0, entries[str])][key].name ∧ key.ino ∈ dirs0 ∧ ( links (key.ino, 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) ]) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ ( (dcache0 -- dentrykey(m8, str))[dentrykey(m, str0), mkdentry(str0, entries[str])][key].ino ∈ dirs0 ∨ (dcache0 -- dentrykey(m8, str))[dentrykey(m, str0), mkdentry(str0, entries[str])][key].ino ∈ files) ∧ (dcache0 -- dentrykey(m8, str))[dentrykey(m, str0), mkdentry(str0, entries[str])][key].name ∈ (key.ino = m ⊃ mkdir(m12, md5, m13, m14, entries3) ;(key.ino = m8 ⊃ mkdir(m2, md0, # links(key.ino, dirs0), m5, entries -- str);dirs0[key.ino]) ) .entries ∧ (dcache0 -- dentrykey(m8, str))[dentrykey(m, str0), mkdentry(str0, entries[str])][key].ino = (key.ino = m ⊃ mkdir(m12, md5, m13, m14, entries3) ;(key.ino = m8 ⊃ mkdir(m2, md0, # links(key.ino, dirs0), m5, entries -- str);dirs0[key.ino]) ) .entries [(dcache0 -- dentrykey(m8, str))[dentrykey(m, str0), mkdentry(str0, entries[str])][key].name ] ∧ (dcache0 -- dentrykey(m8, str))[dentrykey(m, str0), mkdentry(str0, entries[str])][key].dentry?

Rule argument

Additional information

Used simplifier rules: ⊦ 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)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)%⊦ valid-dentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ valid-ino(dent.ino, dirs, files) ∧ dent.name ∈ dirs[ino].entries ∧ dent.ino = dirs[ino].entries[dent.name] ∧ dent.dentry?; (s)