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Proof step 45 from proof inv-create (previous step)

asynced ↔ false, dirs0[m] = mkdir(m0, md2, # links(m, dirs0), m2, entries1), dirs = dirs0[m, mkdir(m0 + 1, md2, # links(m, dirs0), m2, entries1[str, ino0])], err = ESUCCESS, files = (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)], ino = inode.ino, inode = mkinode(m, md0, true, # links(m, dirs0), m2, m0), mkdentry(str, ino0).dentry?, afs-cons(dirs[ino, dirs[ino].meta:= inode.meta], files), afs-cons(dirs0, files0), dcache-cons(dcache, dirs0, files0), icache-cons(icache, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache, pcache), ino ∈ dirs, m ∈ dirs0, asynced1 → synced(files0, 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, str ∈ entries1, ino0 ∈ files0, ino0 ∈ dirs0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 46:
dirs0[m] = mkdir(m0, md2, # links(m, dirs0), m2, entries1), err = ESUCCESS, ino0 ≠ 0, afs-cons(dirs0, files0), afs-cons(dirs0[m, mkdir(m0 + 1, md0, # links(m, dirs0), m2, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]), dcache-cons(dcache, dirs0, files0), icache-cons(icache, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache, pcache), m ∈ dirs0, ¬ ino0 ∈ dirs0, ¬ ino0 ∈ files0, ¬ str ∈ entries1, asynced1 → synced(files0, icache, pcache), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪icache_set#(mkinode(m, md0, true, # links(m, dirs0), m2, m0 + 1), false; err, icache); icache_set# (getinode (mkdentry(str, ino0).ino, dirs0[m, (m ∈ dirs0 ⊃ mkdir(m0 + 1, md2, # links(m, dirs0), m2, entries1[str, ino0]);dirs0[m]).meta:= md0], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]), false ; err, icache); dcache_set# ((m ∈ dirs0 ⊃ mkinode(m, md0, true, # links(m, dirs0), m2, m0 + 1) ;mkinode (m, (m = ino0 ∧ ino0 ∈ files0 ++ ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[m]).meta, false, (m = ino0 ∧ ino0 ∈ files0 ++ ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[m]).nlink, 0, (m = ino0 ∧ ino0 ∈ files0 ++ ino0 ⊃ mkfile(0, md, 1, ∅);(files0 ++ ino0)[m]).size) ) .ino, str, mkdentry(str, ino0) ; err, dcache)⟫ ( icache-cons(icache, dirs0[m, mkdir(m0 + 1, md0, # links(m, dirs0), m2, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]) ∧ dcache-cons(dcache, dirs0[m, mkdir(m0 + 1, md0, # links(m, dirs0), m2, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]) ∧ pcache-cons(pcache, dirs0[m, mkdir(m0 + 1, md0, # links(m, dirs0), m2, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]) ∧ synced(dirs0[m, mkdir(m0 + 1, md0, # links(m, dirs0), m2, entries1[str, ino0])], icache, pcache) ∧ (asynced1 → synced((files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)], icache, pcache)))

Rule argument

Additional information

Used simplifier rules: ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (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)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)%ino ≠ 0, ¬ ino ∈ files ⊦ ino0 ∈ files ++ ino ↔ ino0 = ino ∨ ino0 ∈ files; (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ dirs[ino, ad][ino, ad0] = dirs[ino, ad0]; (s)%⊦ mkdir(m, md, m0, m1, entries).meta:= md0 = mkdir(m, md0, m0, m1, entries); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)