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Proof step 60 from proof inv-mkdir (previous step)

asynced ↔ false, dirs0[m0] = mkdir(m3, md1, # links(m0, dirs0), m5, entries0), (dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m0] = mkdir(m, md0, m1, m2, entries), err = ESUCCESS, icache = icache0[m0, mkientry(false, mkinode(m0, md2, true, m1, m2, m))], inode = getinode (mkdentry(str, ino0).ino, (dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m, md2, m1, m2, entries) ], files), mkdentry(str, ino0).dentry?, afs-cons(dirs0, files), afs-cons ((dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m, md2, m1, m2, entries) ], files), dcache-cons(dcache, dirs0, files), icache-cons(icache0, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), m0 ∈ dirs0, asynced1 → synced(files, icache0, pcache), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪dcache_set#(m0, str, mkdentry(str, ino0); err, dcache)⟫ ( icache-cons (icache[inode.ino, mkientry(asynced, inode)], (dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m, md2, m1, m2, entries) ], files) ∧ dcache-cons (dcache, (dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m, md2, m1, m2, entries) ], files) ∧ pcache-cons (pcache, (dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m, md2, m1, m2, entries) ], files) ∧ synced ((dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m, md2, m1, m2, entries) ], icache[inode.ino, mkientry(asynced, inode)], pcache) ∧ (asynced1 → synced(files, icache[inode.ino, mkientry(asynced, inode)], pcache))), ino0 = 0, str ∈ entries0, ino0 ∈ files, ino0 ∈ dirs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 61:
(dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m0] = mkdir(m, md0, m1, m2, entries), dirs0[m0] = mkdir(m3, md1, # links(m0, dirs0), m5, entries0), err = ESUCCESS, ino0 ≠ 0, afs-cons ((dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m, md2, m1, m2, entries) ], files), afs-cons(dirs0, files), dcache-cons(dcache, dirs0, files), icache-cons(icache0, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), m0 ∈ dirs0, ¬ ino0 ∈ dirs0, ¬ ino0 ∈ files, ¬ str ∈ entries0, asynced1 → synced(files, icache0, pcache), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪dcache_set#(m0, str, mkdentry(str, ino0); err, dcache)⟫ ( icache-cons (icache0[m0, mkientry(false, mkinode(m0, md2, true, m1, m2, m))][ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0))], (dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m, md2, m1, m2, entries) ], files) ∧ dcache-cons (dcache, (dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m, md2, m1, m2, entries) ], files) ∧ pcache-cons (pcache, (dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m, md2, m1, m2, entries) ], files) ∧ synced ((dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m, md2, m1, m2, entries) ], icache0[m0, mkientry(false, mkinode(m0, md2, true, m1, m2, m))][ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0))], pcache) ∧ ( asynced1 → synced (files, icache0[m0, mkientry(false, mkinode(m0, md2, true, m1, m2, m))][ino0, mkientry(false, mkinode(ino0, md, true, 1, 0, 0))], pcache)))

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)% ⊦ mkdir(m, md, m0, m1, entries).nsubdirs = m1; (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)% ⊦ mkdir(m, md, m0, m1, entries).meta = md; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)%ino ≠ 0, ¬ ino ∈ dirs ⊦ ino0 ∈ dirs ++ ino ↔ ino0 = ino ∨ ino0 ∈ dirs; (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)% ⊦ mkdentry(str, m).ino = m; (s)% ⊦ mkdentry(str, m).dentry?; (s)