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Proof step 549 from proof inv-rename-dir-dentry (previous step)

(entries0[str0] = m7 ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0) ;mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅) ) .meta:= md0 = mkdir(m, md4, m8, m9, entries1), (m7 = entries0[str0] ⊃ mkdir(m1, md0, # links(entries0[str0], dirs0), m4, entries0);mkdir(m1, md2, # links(m7, dirs0), m4, entries0)) = mkdir(m0, md, m2, m5, entries), (key.ino = entries0[str0] ⊃ mkdir(m, md4, m8, m9, entries1) ;(key.ino = m7 ⊃ mkdir(m1, md2, # links(key.ino, dirs0), m4, entries0);mkdir(m13, md6, m14, m15, entries3)) ) = mkdir(m10, md5, m11, m12, entries2), dirs0[m7] = mkdir(m1, md1, # links(m7, dirs0), m4, entries0), dirs0[entries0[str0]] = mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅), dirs0[key.ino] = mkdir(m13, md6, m14, m15, entries3), afs-cons(dirs0, files), afs-cons(dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)][entries0[str0], mkdir(m, md4, m8, m9, entries1)], files), synced(dirs0, icache0, pcache), entries0[str0] ∈ dirs0, str0 ∈ entries0, m7 ∈ dirs0, key ∈ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])], key ∈ dcache0 → key.dentry? ∧ key.name = dcache0[key].name ∧ key.ino ∈ dirs0 ∧ (links(key.ino, dirs0) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ (dcache0[key].ino ∈ dirs0 ∨ dcache0[key].ino ∈ files) ∧ dcache0[key].name ∈ entries3 ∧ dcache0[key].ino = entries3[dcache0[key].name] ∧ dcache0[key].dentry?, 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(m7, dirs0) ≠ ∅ ∨ m7 = ROOT_INO ⊦ entries0[str0] = ROOT_INO, entries0[str0] = m7, key.dentry? ∧ key.name = dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].name ∧ key.ino ∈ dirs0 ∧ ( links(key.ino, dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)][entries0[str0], mkdir(m, md4, m8, m9, entries1)]) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ ( dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].ino ∈ dirs0 ∨ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].ino ∈ files) ∧ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].name ∈ entries2 ∧ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].ino = entries2[dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].name] ∧ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].dentry?

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 550:
(key.ino = entries0[str0] ⊃ mkdir(m, md4, # links(entries0[str0], dirs0), m9, ∅) ;(key.ino = m7 ⊃ mkdir(m1, md2, # links(key.ino, dirs0), m4, entries0);mkdir(m13, md6, m14, m15, entries3)) ) = mkdir(m10, md5, m11, m12, entries2), dirs0[m7] = mkdir(m1, md1, # links(m7, dirs0), m4, entries0), dirs0[entries0[str0]] = mkdir(m, md3, # links(entries0[str0], dirs0), m9, ∅), dirs0[key.ino] = mkdir(m13, md6, m14, m15, entries3), afs-cons(dirs0, files), afs-cons (dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)][entries0[str0], mkdir(m, md4, # links(entries0[str0], dirs0), m9, ∅)], files), synced(dirs0, icache0, pcache), entries0[str0] ∈ dirs0, str0 ∈ entries0, m7 ∈ dirs0, key ∈ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])], key ∈ dcache0 → key.dentry? ∧ key.name = dcache0[key].name ∧ key.ino ∈ dirs0 ∧ (links(key.ino, dirs0) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ (dcache0[key].ino ∈ dirs0 ∨ dcache0[key].ino ∈ files) ∧ dcache0[key].name ∈ entries3 ∧ dcache0[key].ino = entries3[dcache0[key].name] ∧ dcache0[key].dentry?, 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(m7, dirs0) ≠ ∅ ∨ m7 = ROOT_INO ⊦ entries0[str0] = ROOT_INO, entries0[str0] = m7, key.dentry? ∧ key.name = dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].name ∧ key.ino ∈ dirs0 ∧ (links(key.ino, dirs0) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ ( dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].ino ∈ dirs0 ∨ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].ino ∈ files) ∧ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].name ∈ entries2 ∧ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].ino = entries2[dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].name] ∧ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].dentry?

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)%⊦ 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)%⊦ 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)