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Proof step 92 from proof inv-link (previous step)

asynced ↔ false, 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), err = ESUCCESS, icache = icache0[m11, mkientry(false, mkinode(m11, md0, true, # links(m11, dirs0), m9, m1 + 1))], inode = getinode (mkdentry(str, entries0[str]).ino, dirs0[m11, mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)][entries1[str]].size:= m15 ] [entries1[str] ] .meta:= md ]), mkdentry(str, entries0[str]).dentry?, 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)]), dcache-cons(dcache, dirs0, files0), icache-cons(icache0, dirs0, files0), pcache-cons(pcache, dirs0, files0), 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, asynced1 → synced(files0, icache0, pcache), 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 ⊦ ⟪dcache_set#(m11, mkdentry(str0, mkdentry(str, entries0[str]).ino).name, mkdentry(str0, mkdentry(str, entries0[str]).ino); err, dcache)⟫ ( icache-cons (icache[inode.ino, mkientry(asynced, inode)], dirs0[m11, mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0) ]) ∧ dcache-cons (dcache, dirs0[m11, mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0) ]) ∧ pcache-cons (pcache, dirs0[m11, mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0) ]) ∧ synced (dirs0[m11, mkdir(m1 + 1, md0, # links(m11, dirs0), m9, entries3[str0, entries2[str]])], icache[inode.ino, mkientry(asynced, inode)], pcache) ∧ ( asynced1 → synced (files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], mkfile(m15, md, # links(entries2[str], dirs0) + 1, content0) ], icache[inode.ino, mkientry(asynced, inode)], pcache))), str0 ∈ entries3

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).meta:= md0 = mkfile(m, md0, m0, content); (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)%⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ mkfile(m, md, m0, content).size:= m1 = mkfile(m1, md, m0, content); (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ mkdentry(str, m).ino = m; (s)% ⊦ mkdentry(str, m).dentry?; (s)