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Proof step 32 from proof crash-neutral-unlink (previous step)

c_inode.ino = entries0[str], c_inode.nlink = files1[entries0[str]].nlink, c_inode.nsubdirs = 0, dirs0[m] = mkdir(m1 + 1, md1, # links(m, dirs0), m2, entries0), dirs = dirs0[m, mkdir(m1, md1, # links(m, dirs0), m2, entries0 -- str)], files = files1[entries0[str], files1[entries0[str]].nlink:= (c_inode.nlink - 1)], c_inode.nlink ≠ 0, afs-cons(dirs0, files1), m ∈ dirs0, entries0[str] ∈ files1, str ∈ entries0, 1 ≤ c_inode.nlink, ¬ c_inode.directory, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_inode_sync#(mkinode(m, md, true, # links(m, dirs0), m2, m1 + 1); dirs, files); afs_inode_sync#(c_inode; 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 := (c_inode.ino ∈ dirs ⊃ mkinode(c_inode.ino, dirs[c_inode.ino].meta, true, dirs[c_inode.ino].nlink, dirs[c_inode.ino].nsubdirs, dirs[c_inode.ino].size) ;mkinode(c_inode.ino, files[c_inode.ino].meta, false, files[c_inode.ino].nlink, 0, files[c_inode.ino].size) ); err := ESUCCESS; asynced := ?⟩ (asynced ∧ dirs0 \ orphans(dirs0, files1) = dirs \ orphans(dirs, files) ∧ files1 \ orphans(dirs0, files1) = files \ orphans(dirs, files)), ⟨fail#(; ; err); asynced := ?⟩ asynced

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 33:
dirs0[m] = mkdir(m1 + 1, md1, # links(m, dirs0), m2, entries0), ¬ boolvar, c_inode = mkinode(m0, md0, boolvar, m3, m4, m5), dirs = dirs0[m, mkdir(m1, md1, # links(m, dirs0), m2, entries0 -- str)], files = files1[entries0[str], files1[entries0[str]].nlink:= (m3 - 1)], m0 = entries0[str], m3 = files1[entries0[str]].nlink, m4 = 0, afs-cons(dirs0, files1), str ∈ entries0, entries0[str] ∈ files1, m ∈ dirs0, 1 ≤ m3, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_inode_sync#(mkinode(m, md, true, # links(m, dirs0), m2, m1 + 1); dirs, files); afs_inode_sync#(c_inode; 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 := (c_inode.ino ∈ dirs ⊃ mkinode(c_inode.ino, dirs[c_inode.ino].meta, true, dirs[c_inode.ino].nlink, dirs[c_inode.ino].nsubdirs, dirs[c_inode.ino].size) ;mkinode(c_inode.ino, files[c_inode.ino].meta, false, files[c_inode.ino].nlink, 0, files[c_inode.ino].size) ); err := ESUCCESS; asynced := ?⟩ (asynced ∧ dirs0 \ orphans(dirs0, files1) = dirs \ orphans(dirs, files) ∧ files1 \ orphans(dirs0, files1) = files \ orphans(dirs, files)), ⟨fail#(; ; err); asynced := ?⟩ asynced, m3 = 0

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [c_inode, m0, md0, boolvar, m3, m4, m5]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: c_inode, m0, md0, boolvar, m3, m4, m5