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Proof step 82 from proof inv-rmdir (previous step)

(entries0[str] = m ⊃ mkdir(m3, md3, # links(entries0[str], dirs0), m0, entries0 -- str) ;mkdir(m1, md2, # links(entries0[str], dirs0), m4, ∅) ) = mkdir(m5, md1, m2 + 1, m7, entries), 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], mkdir(m5, md1, m2, m7, entries)], afs-cons(dirs0, files), afs-cons(dirs0[m, mkdir(m3, md3, # links(m, dirs0), m0, entries0 -- str)][entries0[str], mkdir(m5, md1, m2, m7, entries)], files), m ∈ dirs0, str ∈ entries0, entries0[str] ∈ dirs0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_inode_sync#(mkinode(m, md0, true, # links(m, dirs0), m0 + 1, m3 + 1); dirs, files)] ( afs-cons(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, entries0[str] = ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 83:
# links(entries0[str], dirs0) = m2 + 1, dirs0[m] = mkdir(m3 + 1, md3, # links(m, dirs0), m0 + 1, entries0), dirs0[entries0[str]] = mkdir(m5, md1, m2 + 1, m7, ∅), dirs = dirs0[m, mkdir(m3, md3, # links(m, dirs0), m0, entries0 -- str)][entries0[str], mkdir(m5, md1, m2, m7, ∅)], entries0[str] ≠ m, entries0[str] ≠ ROOT_INO, afs-cons(dirs0, files), afs-cons(dirs0[m, mkdir(m3, md3, # links(m, dirs0), m0, entries0 -- str)][entries0[str], mkdir(m5, md1, m2, m7, ∅)], files), m ∈ dirs0, str ∈ entries0, entries0[str] ∈ dirs0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_inode_sync#(mkinode(m, md0, true, # links(m, dirs0), m0 + 1, m3 + 1); dirs, files)] ( afs-cons(dirs, files) → ⟪afs_inode_sync#(mkinode(entries0[str], md, true, # links(entries0[str], dirs0), m7, 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 := getinode(entries0[str], dirs, files); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files))

Rule argument

Additional information

Used simplifier rules: afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)