Proof step 197 from proof inv-rmdir (previous step)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

• Proof step 198:

  icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m))][m5, mkientry(false, mkinode(m5, md5, true, m11, m12, m10))] [ino ] .inode = mkinode(m13, md6, boolvar, m14, m15, m16), (m5 = entries0[str] ⊃ mkdir(m3, md0, m7, m6, entries);mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str)) = mkdir(m10, md5, m11, m12, entries2), (entries0[str] = m5 ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)) = mkdir(m, md4, m8, m9, entries1), (entries0[str] = m5 ⊃ mkdir(m0 - 1, md1, # links(entries0[str], dirs0), m2 - 1, entries0 -- str) ;mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅) ) = mkdir(m3, md2, m7 + 1, m6, entries), dirs0[m5] = mkdir(m0, md1, # links(m5, dirs0), m2, entries0), dirs0[entries0[str]] = mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅), afs-cons (dirs0[m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], mkdir(m, md0, m8, m9, entries1) ], files), afs-cons(dirs0, files), icache-cons(icache0, dirs0, files), synced(dirs0, icache0, pcache), m5 ∈ dirs0, str ∈ entries0, entries0[str] ∈ dirs0, ino ∈ icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m))][m5, mkientry(false, mkinode(m5, md5, true, m11, m12, m10))], 1 ≤ m0, 1 ≤ m2, asynced1 → synced(files, icache0, pcache), links(m5, dirs0) ≠ ∅ ∨ m5 = ROOT_INO ⊦ entries0[str] = ROOT_INO, m0 = 0, m2 = 0, m13 = ino ∧ (icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m))][m5, mkientry(false, mkinode(m5, md5, true, m11, m12, m10))] [ino ] .dirty ⊃ m13 ∈ files ∧ m14 = files[m13].nlink ∧ m15 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino ∈ files) ∧ icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m))] [m5, mkientry(false, mkinode(m5, md5, true, m11, m12, m10)) ] [ino ] .inode = (m13 ∈ dirs0 ⊃ mkinode (m13, (m13 = entries0[str] ⊃ mkdir(m, md0, m8, m9, entries1) ;(m13 = m5 ⊃ mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str);dirs0[m13]) ) .meta, true, (m13 = entries0[str] ⊃ mkdir(m, md0, m8, m9, entries1) ;(m13 = m5 ⊃ mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str);dirs0[m13]) ) .nlink, (m13 = entries0[str] ⊃ mkdir(m, md0, m8, m9, entries1) ;(m13 = m5 ⊃ mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str);dirs0[m13]) ) .nsubdirs, (m13 = entries0[str] ⊃ mkdir(m, md0, m8, m9, entries1) ;(m13 = m5 ⊃ mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str);dirs0[m13]) ) .size) ;mkinode(m13, files[m13].meta, false, files[m13].nlink, 0, files[m13].size) ) )

Rule argument

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: icache0 [entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m)) ] [m5, mkientry(false, mkinode(m5, md5, true, m11, m12, m10)) ] [ino ] .inode, m13, md6, boolvar, m14, m15, m16