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Proof step 40 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, ∅) ) .nlink = m4 + 1, 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], (entries0[str] = m ⊃ mkdir(m1, md3, # links(entries0[str], dirs0), m0, entries0 -- str) ;mkdir(m3, md1, # links(entries0[str], dirs0), m2, ∅) ) .nlink:= m4 ], files0 = files, afs-cons(dirs0, files), m ∈ dirs0, entries0[str] ∈ dirs0, str ∈ entries0, 1 ≤ (entries0[str] = m ⊃ mkdir(m1, md3, # links(entries0[str], dirs0), m0, entries0 -- str) ;mkdir(m3, md1, # links(entries0[str], dirs0), m2, ∅) ) .nlink, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_inode_sync#(mkinode(m, md, true, # links(m, dirs0), m0 + 1, m1 + 1); dirs, files); 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] = m ⊃ mkdir(m1, md3, # links(entries0[str], dirs0), m0, entries0 -- str) ;mkdir(m3, md1, # links(entries0[str], dirs0), m2, ∅) ) .nlink = 0, entries0[str] = ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 41:
(entries0[str] = m ⊃ mkdir(m1, md3, # links(entries0[str], dirs0), m0, entries0 -- str) ;mkdir(m3, md1, # links(entries0[str], dirs0), m2, ∅) ) .nlink = m4 + 1, 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], (entries0[str] = m ⊃ mkdir(m1, md3, # links(entries0[str], dirs0), m0, entries0 -- str) ;mkdir(m3, md1, # links(entries0[str], dirs0), m2, ∅) ) .nlink:= m4 ], files0 = files, entries0[str] ≠ ROOT_INO, afs-cons(dirs0, files), m ∈ dirs0, entries0[str] ∈ dirs0, str ∈ entries0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ asynced, ⟨afs_inode_sync#(mkinode(m, md, true, # links(m, dirs0), m0 + 1, m1 + 1); dirs, files); 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))

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m + n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)%not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat