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Proof step 75 from proof crash-neutral-rmdir (previous step)

(entries0[str] = m ⊃ mkdir(m1, md3, # links(entries0[str], dirs0), m0, entries0 -- str) ;mkdir(m3, md1, # links(entries0[str], dirs0), m2, ∅) ) = mkdir(m5, md0, m4 + 1, m7, entries), dirs0[entries0[str]] = mkdir(m3, md1, # links(entries0[str], dirs0), m2, ∅), dirs0[m] = mkdir(m1 + 1, md3, # links(m, dirs0), m0 + 1, entries0), dirs = dirs0[m, mkdir(m1, md3, # links(m, dirs0), m0, entries0 -- str)][entries0[str], mkdir(m5, md0, m4, m7, entries)], files0 = files, ino = inode.ino, inode = mkinode(m, md, true, # links(m, dirs0), m0 + 1, m1 + 1), afs-cons(dirs0, files), m ∈ dirs0, entries0[str] ∈ dirs0, str ∈ entries0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_inode_sync#(mkinode(entries0[str], md2, true, # links(entries0[str], dirs0), m2, m3); 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 := (entries0[str] ∈ dirs ⊃ mkinode(entries0[str], dirs[entries0[str]].meta, true, dirs[entries0[str]].nlink, dirs[entries0[str]].nsubdirs, dirs[entries0[str]].size) ;mkinode(entries0[str], files[entries0[str]].meta, false, files[entries0[str]].nlink, 0, files[entries0[str]].size) ); err := ESUCCESS; asynced := ?⟩ (asynced ∧ dirs0 \ orphans(dirs0, files0) = dirs \ orphans(dirs, files) ∧ files0 \ orphans(dirs0, files0) = files \ orphans(dirs, files)), ⟨fail#(; ; err); asynced := ?⟩ asynced, entries0[str] = ROOT_INO, ino ∈ dirs, ino ∈ files

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

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