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Proof step 37 from proof inv-rmdir (previous step)

dirs0[entries0[str]] = mkdir(m1, md2, # links(entries0[str], dirs0), m4, ∅), dirs0[m] = mkdir(m3 + 1, md3, # links(m, dirs0), m0 + 1, entries0), dirs = dirs0[m, mkdir(m3, md3, # links(m, dirs0), m0, entries0 -- str)] [entries0[str], (entries0[str] = m ⊃ mkdir(m3, md3, # links(entries0[str], dirs0), m0, entries0 -- str) ;mkdir(m1, md2, # links(entries0[str], dirs0), m4, ∅) ) .nlink:= ( (entries0[str] = m ⊃ mkdir(m3, md3, # links(entries0[str], dirs0), m0, entries0 -- str) ;mkdir(m1, md2, # links(entries0[str], dirs0), m4, ∅) ) .nlink - 1) ], (entries0[str] = m ⊃ mkdir(m3, md3, # links(entries0[str], dirs0), m0, entries0 -- str) ;mkdir(m1, md2, # links(entries0[str], dirs0), m4, ∅) ) .nlink ≠ 0, entries0[str] ≠ ROOT_INO, afs-cons(dirs0, files), entries0[str] ∈ dirs0, str ∈ entries0, m ∈ dirs0, 1 ≤ (entries0[str] = m ⊃ mkdir(m3, md3, # links(entries0[str], dirs0), m0, entries0 -- str) ;mkdir(m1, md2, # links(entries0[str], dirs0), m4, ∅) ) .nlink, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪afs_inode_sync#(mkinode(m, md0, true, # links(m, dirs0), m0 + 1, m3 + 1); dirs, files); afs_inode_sync#(mkinode(entries0[str], md, true, # links(entries0[str], dirs0), m4, m1); 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)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 38:
(entries0[str] = m ⊃ mkdir(m3, md3, # links(entries0[str], dirs0), m0, entries0 -- str) ;mkdir(m1, md2, # links(entries0[str], dirs0), m4, ∅) ) .nlink = m2 + 1, dirs0[m] = mkdir(m3 + 1, md3, # links(m, dirs0), m0 + 1, entries0), dirs0[entries0[str]] = mkdir(m1, md2, # links(entries0[str], dirs0), m4, ∅), dirs = dirs0[m, mkdir(m3, md3, # links(m, dirs0), m0, entries0 -- str)] [entries0[str], (entries0[str] = m ⊃ mkdir(m3, md3, # links(entries0[str], dirs0), m0, entries0 -- str) ;mkdir(m1, md2, # links(entries0[str], dirs0), m4, ∅) ) .nlink:= m2 ], afs-cons(dirs0, files), m ∈ dirs0, str ∈ entries0, entries0[str] ∈ dirs0, 1 ≤ (entries0[str] = m ⊃ mkdir(m3, md3, # links(entries0[str], dirs0), m0, entries0 -- str) ;mkdir(m1, md2, # links(entries0[str], dirs0), m4, ∅) ) .nlink, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪afs_inode_sync#(mkinode(m, md0, true, # links(m, dirs0), m0 + 1, m3 + 1); dirs, files); afs_inode_sync#(mkinode(entries0[str], md, true, # links(entries0[str], dirs0), m4, m1); 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 ⊃ mkdir(m3, md3, # links(entries0[str], dirs0), m0, entries0 -- str) ;mkdir(m1, md2, # links(entries0[str], dirs0), m4, ∅) ) .nlink = 0, entries0[str] = ROOT_INO

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [(entries0[str] = m ⊃ mkdir (m3, md3, # links(entries0[str], dirs0), m0, entries0 -- str) ;mkdir(m1, md2, # links(entries0[str], dirs0), m4, ∅) ) .nlink, m2]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: (entries0[str] = m ⊃ mkdir(m3, md3, # links(entries0[str], dirs0), m0, entries0 -- str) ;mkdir(m1, md2, # links(entries0[str], dirs0), m4, ∅) ) .nlink, m2