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Proof step 32 from proof inv-unlink (previous step)

dirs0[m] = mkdir(m2 + 1, md2, # links(m, dirs0), m3, entries0), files0[entries0[str]] = mkfile(m0, md1, # links(entries0[str], dirs0), content), dirs = dirs0[m, mkdir(m2, md2, # links(m, dirs0), m3, entries0 -- str)], files = files0[entries0[str], mkfile(m0, md1, # links(entries0[str], dirs0) - 1, content)], # links(entries0[str], dirs0) ≠ 0, afs-cons(dirs0, files0), entries0[str] ∈ files0, str ∈ entries0, m ∈ dirs0, 1 ≤ # links(entries0[str], dirs0), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪afs_inode_sync#(mkinode(m, md, true, # links(m, dirs0), m3, m2 + 1); dirs, files); afs_inode_sync#(mkinode(entries0[str], md0, false, # links(entries0[str], dirs0), 0, m6); 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 := ?⟫ afs-cons(dirs, files)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 33:
# links(entries0[str], dirs0) = m1 + 1, files0[entries0[str]] = mkfile(m0, md1, # links(entries0[str], dirs0), content), dirs0[m] = mkdir(m2 + 1, md2, # links(m, dirs0), m3, entries0), dirs = dirs0[m, mkdir(m2, md2, # links(m, dirs0), m3, entries0 -- str)], files = files0[entries0[str], mkfile(m0, md1, m1, content)], afs-cons(dirs0, files0), m ∈ dirs0, str ∈ entries0, entries0[str] ∈ files0, 1 ≤ # links(entries0[str], dirs0), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪afs_inode_sync#(mkinode(m, md, true, # links(m, dirs0), m3, m2 + 1); dirs, files); afs_inode_sync#(mkinode(entries0[str], md0, false, # links(entries0[str], dirs0), 0, m6); 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 := ?⟫ afs-cons(dirs, files), # links(entries0[str], dirs0) = 0

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [# links(entries0[str], dirs0), m1]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: # links(entries0[str], dirs0), m1