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Proof step 90 from proof inv-rmdir (previous step)

# links(entries0[str], dirs0) = m2 + 1, dirs0[entries0[str]] = mkdir(m5, md1, m2 + 1, m7, ∅), dirs0[m] = mkdir(m3 + 1, md3, # links(m, dirs0), m0 + 1, entries0), dirs = dirs1[ino, dirs1[ino].meta:= inode.meta], dirs1 = dirs0[m, mkdir(m3, md3, # links(m, dirs0), m0, entries0 -- str)][entries0[str], mkdir(m5, md1, m2, m7, ∅)], ino = inode.ino, inode = mkinode(m, md0, true, # links(m, dirs0), m0 + 1, m3 + 1), afs-cons(dirs, files), afs-cons(dirs0[m, mkdir(m3, md3, # links(m, dirs0), m0, entries0 -- str)][entries0[str], mkdir(m5, md1, m2, m7, ∅)], files), afs-cons(dirs0, files), entries0[str] ∈ dirs0, str ∈ entries0, m ∈ dirs0, ino ∈ dirs1, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪afs_inode_sync#(mkinode(entries0[str], md, true, # links(entries0[str], dirs0), m7, m5); dirs, files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := getinode(entries0[str], dirs, files); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files), entries0[str] = m, entries0[str] = ROOT_INO, ino ∈ files

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 91:
# links(entries0[str], dirs0) = m2 + 1, dirs0[m] = mkdir(m3 + 1, md3, # links(m, dirs0), m0 + 1, entries0), dirs0[entries0[str]] = mkdir(m5, md1, m2 + 1, m7, ∅), dirs = dirs0[entries0[str], mkdir(m5, md1, m2, m7, ∅)][m, mkdir(m3, md0, # links(m, dirs0), m0, entries0 -- str)], entries0[str] ≠ ROOT_INO, entries0[str] ≠ m, afs-cons(dirs0, files), afs-cons(dirs0[m, mkdir(m3, md3, # links(m, dirs0), m0, entries0 -- str)][entries0[str], mkdir(m5, md1, m2, m7, ∅)], files), afs-cons(dirs0[entries0[str], mkdir(m5, md1, m2, m7, ∅)][m, mkdir(m3, md0, # links(m, dirs0), m0, entries0 -- str)], files), m ∈ dirs0, str ∈ entries0, entries0[str] ∈ dirs0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪afs_inode_sync#(mkinode(entries0[str], md, true, # links(entries0[str], dirs0), m7, m5); dirs, files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := getinode(entries0[str], dirs, files); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files)

Rule argument

Additional information

Used simplifier rules: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ dirs[ino, ad][ino0, ad0][ino, ad1] = dirs[ino0, ad0][ino, ad1]; (s)%⊦ mkdir(m, md, m0, m1, entries).meta:= md0 = mkdir(m, md0, m0, m1, entries); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)