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Proof step 50 from proof inv-mkdir (previous step)

asynced ↔ false, dirs0[m] = mkdir(m3, md1, # links(m, dirs0), m5, entries0), dirs = (dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)], err = ESUCCESS, ino = inode.ino, inode = mkinode(m, md0, true, # links(m, dirs0), m5, m3), mkdentry(str, ino0).dentry?, afs-cons(dirs[ino, dirs[ino].meta:= inode.meta], files), afs-cons(dirs0, files), dcache-cons(dcache, dirs0, files), icache-cons(icache, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache, pcache), ino ∈ dirs, m ∈ dirs0, asynced1 → synced(files, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪icache_set# ((m ∈ dirs[ino, dirs[ino].meta:= inode.meta] ⊃ mkinode (m, dirs[ino, dirs[ino].meta:= inode.meta][m].meta, true, dirs[ino, dirs[ino].meta:= inode.meta][m].nlink, dirs[ino, dirs[ino].meta:= inode.meta][m].nsubdirs, dirs[ino, dirs[ino].meta:= inode.meta][m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ), asynced ; err, icache); icache_set#(getinode(mkdentry(str, ino0).ino, dirs[ino, dirs[ino].meta:= inode.meta], files), asynced; err, icache); dcache_set# ((m ∈ dirs[ino, dirs[ino].meta:= inode.meta] ⊃ mkinode (m, dirs[ino, dirs[ino].meta:= inode.meta][m].meta, true, dirs[ino, dirs[ino].meta:= inode.meta][m].nlink, dirs[ino, dirs[ino].meta:= inode.meta][m].nsubdirs, dirs[ino, dirs[ino].meta:= inode.meta][m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ) .ino, str, mkdentry(str, ino0) ; err, dcache)⟫ ( icache-cons(icache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ dcache-cons(dcache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ pcache-cons(pcache, dirs[ino, dirs[ino].meta:= inode.meta], files) ∧ synced(dirs[ino, dirs[ino].meta:= inode.meta], icache, pcache) ∧ (asynced1 → synced(files, icache, pcache))), ino0 = 0, ino ∈ files, ino0 ∈ dirs0, ino0 ∈ files, str ∈ entries0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
dirs0[m] = mkdir(m3, md1, # links(m, dirs0), m5, entries0), err = ESUCCESS, ino0 ≠ 0, afs-cons(dirs0, files), afs-cons ((dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m, (dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m].meta:= md0 ], files), dcache-cons(dcache, dirs0, files), icache-cons(icache, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache, pcache), m ∈ dirs0, ¬ str ∈ entries0, ¬ ino0 ∈ files, ¬ ino0 ∈ dirs0, asynced1 → synced(files, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪icache_set# (mkinode (m, md0, true, (dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m].nlink, (dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m].nsubdirs, (dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m].size), false ; err, icache); icache_set# (getinode (mkdentry(str, ino0).ino, (dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m, (m = ino0 ∧ ino0 ∈ dirs0[ino0, mkdir(m3 + 1, md1, # links(ino0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;(dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m] ) .meta:= md0 ], files), false ; err, icache); dcache_set# ((m ∈ dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0 ⊃ mkinode (m, md0, true, (m = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m]).nlink, (m = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m]).nsubdirs, (m = ino0 ⊃ mkdir(0, md, 1, 0, ∅);(dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m]).size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ) .ino, str, mkdentry(str, ino0) ; err, dcache)⟫ ( icache-cons (icache, (dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m, (dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m].meta:= md0 ], files) ∧ dcache-cons (dcache, (dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m, (dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m].meta:= md0 ], files) ∧ pcache-cons (pcache, (dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m, (dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m].meta:= md0 ], files) ∧ synced ((dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m, (dirs0[m, mkdir(m3 + 1, md1, # links(m, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[m].meta:= md0 ], icache, pcache) ∧ (asynced1 → synced(files, icache, pcache)))

Rule argument

Additional information

Used simplifier rules: ⊦ (ad.meta:= md).size = ad.size; (s)% ⊦ (ad.meta:= md).nsubdirs = ad.nsubdirs; (s)% ⊦ (ad.meta:= md).nlink = ad.nlink; (s)% ⊦ (ad.meta:= md).meta = md; (s)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).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)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)