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Proof step 538 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), dirs0[m7] = mkdir(m1, md1, # links(m7, dirs0), m4, entries0), dirs0[entries0[str0]] = mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅), 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), dcache-cons(dcache0, dirs0, files), synced(dirs0, icache0, pcache), entries0[str0] ∈ dirs0, str0 ∈ entries0, m7 ∈ dirs0, asynced2 → synced(files, icache0, pcache), links(m7, dirs0) ≠ ∅ ∨ m7 = ROOT_INO ⊦ entries0[str0] = ROOT_INO, ∀ key. key ∈ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])] → key.dentry? ∧ key.name = dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].name ∧ valid-dentry (key.ino, dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key], dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)][entries0[str0], mkdir(m, md4, m8, m9, entries1)], files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 539:
(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), dirs0[entries0[str0]] = mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅), dirs0[m7] = mkdir(m1, md1, # links(m7, dirs0), m4, entries0), afs-cons(dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)][entries0[str0], mkdir(m, md4, m8, m9, entries1)], files), afs-cons(dirs0, files), dcache-cons(dcache0, dirs0, files), synced(dirs0, icache0, pcache), key ∈ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])], m7 ∈ dirs0, str0 ∈ entries0, entries0[str0] ∈ dirs0, asynced2 → synced(files, icache0, pcache), links(m7, dirs0) ≠ ∅ ∨ m7 = ROOT_INO ⊦ entries0[str0] = ROOT_INO, 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 ∈ (key.ino = entries0[str0] ⊃ mkdir(m, md4, m8, m9, entries1) ;(key.ino = m7 ⊃ mkdir(m1, md2, # links(key.ino, dirs0), m4, entries0);dirs0[key.ino]) ) .entries ∧ dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])][key].ino = (key.ino = entries0[str0] ⊃ mkdir(m, md4, m8, m9, entries1) ;(key.ino = m7 ⊃ mkdir(m1, md2, # links(key.ino, dirs0), m4, entries0);dirs0[key.ino]) ) .entries [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: ⊦ 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)