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Proof step 94 from proof inv-create (previous step)

# links(ino0, dirs0) = m0, dirs0[ino0] = mkdir(m, md0, # links(ino0, dirs0), m1, entries), dent = negdentry(str), dirs = dirs0[p_ino, dirs0[p_ino].entries:= dirs0[p_ino].entries[dent.name, ino]] [p_ino, dirs0[p_ino, dirs0[p_ino].entries:= dirs0[p_ino].entries[dent.name, ino]][p_ino] .size:= (dirs0[p_ino, dirs0[p_ino].entries:= dirs0[p_ino].entries[dent.name, ino]][p_ino].size + 1) ], err = ESUCCESS, files = (files0 ++ ino)[ino, mkfile(0, md, 1, ∅)], p_ino = ino0, afs-cons(dirs0, files0), ispath(q, ROOT_INO, ino0, dirs0, files0), of-cons(of, dirs0, files0), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs0, files0), ino0 ∈ dirs0, links(ino0, dirs0) ≠ ∅ ∨ ino0 = ROOT_INO ⊦ [afs_inode_sync#(mkinode(ino0, md0, true, m0, m1, m); dirs, files); inode := (ino0 ∈ dirs ⊃ mkinode(ino0, dirs[ino0].meta, true, dirs[ino0].nlink, dirs[ino0].nsubdirs, dirs[ino0].size) ;mkinode(ino0, files[ino0].meta, false, files[ino0].nlink, 0, files[ino0].size) ); c_inode := getinode(mkdentry(dent.name, ino).ino, dirs, files); asynced := ?] (afs-cons(dirs, files) → of-cons(of, dirs, files)), ino = 0, ino ∈ dirs0, ino ∈ files0, str ∈ entries

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 95:
# links(ino0, dirs0) = m0, dirs0[ino0] = mkdir(m, md0, # links(ino0, dirs0), m1, entries), dirs0[p_ino, dirs0[p_ino].entries:= dirs0[p_ino].entries[dent.name, ino]][p_ino] = mkdir(m2, md1, m3, m4, entries0), dent = negdentry(str), dirs = dirs0[p_ino, dirs0[p_ino].entries:= dirs0[p_ino].entries[dent.name, ino]] [p_ino, dirs0[p_ino, dirs0[p_ino].entries:= dirs0[p_ino].entries[dent.name, ino]][p_ino].size:= (m2 + 1) ], err = ESUCCESS, files = (files0 ++ ino)[ino, mkfile(0, md, 1, ∅)], p_ino = ino0, afs-cons(dirs0, files0), ispath(q, ROOT_INO, ino0, dirs0, files0), of-cons(of, dirs0, files0), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs0, files0), ino0 ∈ dirs0, links(ino0, dirs0) ≠ ∅ ∨ ino0 = ROOT_INO ⊦ [afs_inode_sync#(mkinode(ino0, md0, true, m0, m1, m); dirs, files); inode := (ino0 ∈ dirs ⊃ mkinode(ino0, dirs[ino0].meta, true, dirs[ino0].nlink, dirs[ino0].nsubdirs, dirs[ino0].size) ;mkinode(ino0, files[ino0].meta, false, files[ino0].nlink, 0, files[ino0].size) ); c_inode := getinode(mkdentry(dent.name, ino).ino, dirs, files); asynced := ?] (afs-cons(dirs, files) → of-cons(of, dirs, files)), ino = 0, str ∈ entries, ino ∈ files0, ino ∈ dirs0

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [dirs0 [p_ino, dirs0[p_ino].entries:= dirs0[p_ino].entries[dent.name, ino] ] [p_ino ], m2, md1, m3, m4, entries0]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: dirs0 [p_ino, dirs0[p_ino].entries:= dirs0[p_ino].entries[dent.name, ino] ] [p_ino ], m2, md1, m3, m4, entries0