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Proof step 220 from proof inv-link (previous step)

icache0[ino] = mkientry(boolvar2, mkinode(m16, md8, boolvar1, m17, m18, m19)), 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 ] = mkientry(boolvar0, 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), 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, asynced1 → synced(files0, icache0, pcache), ino ∈ icache0 → m16 = ino ∧ (boolvar2 ⊃ ino ∈ files0 ∧ m17 = files0[ino].nlink ∧ m18 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs0 ∨ ino ∈ files0) ∧ mkinode(ino, md8, boolvar1, m17, m18, m19) = (ino ∈ dirs0 ⊃ mkinode(ino, dirs0[ino].meta, true, dirs0[ino].nlink, dirs0[ino].nsubdirs, dirs0[ino].size) ;mkinode(ino, files0[ino].meta, false, files0[ino].nlink, 0, files0[ino].size) ) ), ∀ ino4. ino4 ∈ icache0 → icache0[ino4].inode.ino = ino4 ∧ (icache0[ino4].dirty ⊃ icache0[ino4].inode.ino ∈ files0 ∧ icache0[ino4].inode.nlink = files0[icache0[ino4].inode.ino].nlink ∧ icache0[ino4].inode.nsubdirs = 0 ∧ ¬ icache0[ino4].inode.directory ; (ino4 ∈ dirs0 ∨ ino4 ∈ files0) ∧ icache0[ino4].inode = (icache0[ino4].inode.ino ∈ dirs0 ⊃ mkinode (icache0[ino4].inode.ino, dirs0[icache0[ino4].inode.ino].meta, true, dirs0[icache0[ino4].inode.ino].nlink, dirs0[icache0[ino4].inode.ino].nsubdirs, dirs0[icache0[ino4].inode.ino].size) ;mkinode (icache0[ino4].inode.ino, files0[icache0[ino4].inode.ino].meta, false, files0[icache0[ino4].inode.ino].nlink, 0, files0[icache0[ino4].inode.ino].size) ) ), ino = entries2[str] ∨ ino ∈ icache0[m11, mkientry(false, mkinode(m11, md0, true, # links(m11, dirs0), m9, m1 + 1))], 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 ⊦ ino = entries2[str], str0 ∈ entries3, m = ino ∧ (boolvar0 ⊃ ino ∈ files0 ∧ m3 = (ino = entries2[str] ⊃ mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0);files0[ino]).nlink ∧ m13 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino ∈ files0) ∧ mkinode(ino, md7, boolvar, m3, m13, m14) = (ino ∈ dirs0 ⊃ mkinode (ino, (ino = m11 ⊃ mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]]);dirs0[ino]).meta, true, (ino = m11 ⊃ mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]]);dirs0[ino]).nlink, (ino = m11 ⊃ mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]]);dirs0[ino]).nsubdirs, (ino = m11 ⊃ mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]]);dirs0[ino]).size) ;mkinode (ino, (ino = entries2[str] ⊃ mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0);files0[ino]).meta, false, (ino = entries2[str] ⊃ mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0);files0[ino]).nlink, 0, (ino = entries2[str] ⊃ mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0);files0[ino]).size) ) )

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 221:
icache0[ino] = mkientry(boolvar2, mkinode(m16, md8, boolvar1, m17, m18, m19)), dirs0[ino1] = mkdir(m5, md2, # links(ino1, dirs0), m10, entries1), entries[str] = entries2[str], dirs0[ino0] = mkdir(m2, md1, # links(ino0, dirs0), m8, entries), entries0[str] = entries2[str], files0[entries2[str]] = mkfile(m0, md6, # links(entries2[str], dirs0), content0), dirs0[m11] = mkdir(m1, md5, # links(m11, dirs0), m9, entries3), dirs0[ino2] = mkdir(m4, md3, # links(ino2, dirs0), m6, entries0), entries1[str] = entries2[str], dirs0[ino3] = mkdir(m7, md4, # links(ino3, dirs0), m12, entries2), icache0[m11, mkientry(false, mkinode(m11, md0, true, # links(m11, dirs0), m9, m1 + 1))][ino] = mkientry(boolvar0, mkinode(m, md7, boolvar, m3, m13, m14)), afs-cons(dirs0, files0), 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)]), synced(dirs0, icache0, pcache), str ∈ entries1, ino1 ∈ dirs0, str ∈ entries, ino0 ∈ dirs0, ino2 ∈ dirs0, str ∈ entries0, ino3 ∈ dirs0, str ∈ entries2, m11 ∈ dirs0, entries2[str] ∈ files0, ino ∈ icache0[m11, mkientry(false, mkinode(m11, md0, true, # links(m11, dirs0), m9, m1 + 1))], ino ∈ icache0 → m16 = ino ∧ (boolvar2 ⊃ ino ∈ files0 ∧ m17 = files0[ino].nlink ∧ m18 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs0 ∨ ino ∈ files0) ∧ mkinode(ino, md8, boolvar1, m17, m18, m19) = (ino ∈ dirs0 ⊃ mkinode(ino, dirs0[ino].meta, true, dirs0[ino].nlink, dirs0[ino].nsubdirs, dirs0[ino].size) ;mkinode(ino, files0[ino].meta, false, files0[ino].nlink, 0, files0[ino].size) ) ), asynced1 → synced(files0, icache0, pcache), ∀ ino4. ino4 ∈ icache0 → icache0[ino4].inode.ino = ino4 ∧ (icache0[ino4].dirty ⊃ icache0[ino4].inode.ino ∈ files0 ∧ icache0[ino4].inode.nlink = files0[icache0[ino4].inode.ino].nlink ∧ icache0[ino4].inode.nsubdirs = 0 ∧ ¬ icache0[ino4].inode.directory ; (ino4 ∈ dirs0 ∨ ino4 ∈ files0) ∧ icache0[ino4].inode = (icache0[ino4].inode.ino ∈ dirs0 ⊃ mkinode (icache0[ino4].inode.ino, dirs0[icache0[ino4].inode.ino].meta, true, dirs0[icache0[ino4].inode.ino].nlink, dirs0[icache0[ino4].inode.ino].nsubdirs, dirs0[icache0[ino4].inode.ino].size) ;mkinode (icache0[ino4].inode.ino, files0[icache0[ino4].inode.ino].meta, false, files0[icache0[ino4].inode.ino].nlink, 0, files0[icache0[ino4].inode.ino].size) ) ), links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino0, dirs0) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino2, dirs0) ≠ ∅ ∨ ino2 = ROOT_INO, links(m11, dirs0) ≠ ∅ ∨ m11 = ROOT_INO, links(ino3, dirs0) ≠ ∅ ∨ ino3 = ROOT_INO ⊦ ino = entries2[str], str0 ∈ entries3, m = ino ∧ (boolvar0 ⊃ ino ∈ files0 ∧ m3 = files0[ino].nlink ∧ m13 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino ∈ files0) ∧ mkinode(ino, md7, boolvar, m3, m13, m14) = (ino ∈ dirs0 ⊃ mkinode (ino, (ino = m11 ⊃ mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]]);dirs0[ino]).meta, true, (ino = m11 ⊃ mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]]);dirs0[ino]).nlink, (ino = m11 ⊃ mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]]);dirs0[ino]).nsubdirs, (ino = m11 ⊃ mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]]);dirs0[ino]).size) ;mkinode(ino, files0[ino].meta, false, files0[ino].nlink, 0, files0[ino].size) ) )

Rule argument

Additional information

Used simplifier rules: ⊦ ino ≠ ino0 → icache[ino0, ie][ino] = icache[ino]; (s)