Proof step 205 from proof inv-link (previous step)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

• Proof step 206:

  icache0[m11, mkientry(false, mkinode(m11, md0, true, # links(m11, dirs0), m9, m1 + 1))] [entries2[str], mkientry(false, mkinode(entries2[str], md, false, # links(entries2[str], dirs0) + 1, 0, m15)) ] [ino ] .inode = mkinode(m, md7, boolvar, m3, m13, m14), dirs0[ino3] = mkdir(m7, md4, # links(ino3, dirs0), m12, entries2), entries1[str] = entries2[str], dirs0[ino2] = mkdir(m4, md3, # links(ino2, dirs0), m6, entries0), dirs0[m11] = mkdir(m1, md5, # links(m11, dirs0), m9, entries3), files0[entries2[str]] = mkfile(m0, md6, # links(entries2[str], dirs0), content0), entries0[str] = entries2[str], dirs0[ino0] = mkdir(m2, md1, # links(ino0, dirs0), m8, entries), entries[str] = entries2[str], dirs0[ino1] = mkdir(m5, md2, # links(ino1, dirs0), m10, entries1), afs-cons (dirs0[m11, mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0)]), afs-cons(dirs0, files0), icache-cons(icache0, dirs0, files0), synced(dirs0, icache0, pcache), entries2[str] ∈ files0, m11 ∈ dirs0, str ∈ entries2, ino3 ∈ dirs0, str ∈ entries0, ino2 ∈ dirs0, ino0 ∈ dirs0, str ∈ entries, ino1 ∈ dirs0, str ∈ entries1, ino ∈ icache0[m11, mkientry(false, mkinode(m11, md0, true, # links(m11, dirs0), m9, m1 + 1))] [entries2[str], mkientry(false, mkinode(entries2[str], md, false, # links(entries2[str], dirs0) + 1, 0, m15)) ], asynced1 → synced(files0, icache0, pcache), links(ino3, dirs0) ≠ ∅ ∨ ino3 = ROOT_INO, links(m11, dirs0) ≠ ∅ ∨ m11 = ROOT_INO, links(ino2, dirs0) ≠ ∅ ∨ ino2 = ROOT_INO, links(ino0, dirs0) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ str0 ∈ entries3, m = ino ∧ (icache0[m11, mkientry(false, mkinode(m11, md0, true, # links(m11, dirs0), m9, m1 + 1))] [entries2[str], mkientry(false, mkinode(entries2[str], md, false, # links(entries2[str], dirs0) + 1, 0, m15)) ] [ino ] .dirty ⊃ m ∈ files0 ∧ m3 = (m = entries2[str] ⊃ mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0);files0[m]).nlink ∧ m13 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino ∈ files0) ∧ icache0[m11, mkientry(false, mkinode(m11, md0, true, # links(m11, dirs0), m9, m1 + 1))] [entries2[str], mkientry(false, mkinode(entries2[str], md, false, # links(entries2[str], dirs0) + 1, 0, m15)) ] [ino ] .inode = (m ∈ dirs0 ⊃ mkinode (m, (m = m11 ⊃ mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]]);dirs0[m]).meta, true, (m = m11 ⊃ mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]]);dirs0[m]).nlink, (m = m11 ⊃ mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]]);dirs0[m]).nsubdirs, (m = m11 ⊃ mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]]);dirs0[m]).size) ;mkinode (m, (m = entries2[str] ⊃ mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0);files0[m]).meta, false, (m = entries2[str] ⊃ mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0);files0[m]).nlink, 0, (m = entries2[str] ⊃ mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0);files0[m]).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 [m11, mkientry (false, mkinode(m11, md0, true, # links(m11, dirs0), m9, m1 + 1)) ] [entries2[str], mkientry (false, mkinode (entries2[str], md, false, # links(entries2[str], dirs0) + 1, 0, m15)) ] [ino ] .inode, m, md7, boolvar, m3, m13, m14