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Proof step 34 from proof crash-neutral-unlink (previous step)

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:= (files1[entries0[str]].nlink - 1)], files1[entries0[str]].nlink ≠ 0, afs-cons(dirs0, files1), m ∈ dirs0, entries0[str] ∈ files1, str ∈ entries0, 1 ≤ files1[entries0[str]].nlink, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ asynced, ⟨afs_inode_sync#(mkinode(m, md, true, # links(m, dirs0), m2, m1 + 1); dirs, files); afs_inode_sync#(mkinode(entries0[str], md0, false, files1[entries0[str]].nlink, 0, 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 := (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, files1) = dirs \ orphans(dirs, files) ∧ files1 \ orphans(dirs0, files1) = files \ orphans(dirs, files))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 35:
files1[entries0[str]].nlink = m0 + 1, 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:= m0], afs-cons(dirs0, files1), str ∈ entries0, entries0[str] ∈ files1, m ∈ dirs0, 1 ≤ files1[entries0[str]].nlink, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ asynced, ⟨afs_inode_sync#(mkinode(m, md, true, # links(m, dirs0), m2, m1 + 1); dirs, files); afs_inode_sync#(mkinode(entries0[str], md0, false, files1[entries0[str]].nlink, 0, 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 := (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, files1) = dirs \ orphans(dirs, files) ∧ files1 \ orphans(dirs0, files1) = files \ orphans(dirs, files)), files1[entries0[str]].nlink = 0

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [files1[entries0[str]].nlink, m0]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: files1[entries0[str]].nlink, m0