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Proof step 112 from proof refine-mkdir (previous step)

(cache_dirs[m1, mkdir(m6 + 1, md1, # links(m1, cache_dirs), m8 + 1, entries1[str, m5])] ++ m5)[m1] = mkdir(m, md0, m3, m4, entries0), cache_dirs[m1] = mkdir(m6, md1, # links(m1, cache_dirs), m8, entries1), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dirs = (cache_dirs[m1, mkdir(m6 + 1, md1, # links(m1, cache_dirs), m8 + 1, entries1[str, m5])] ++ m5)[m5, mkdir(0, md3, 1, 0, ∅)], files = afs_files, ino = inode.ino, inode = mkinode(m1, md2, true, # links(m1, cache_dirs), m8, m6), mkdentry(str, m5).dentry?, afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), ino ∈ dirs, m1 ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ m5 = 0, ino ∈ files, m5 ∈ cache_dirs, m5 ∈ cache_files, str ∈ entries1, ∃ asynced. dirs[ino, dirs[ino].meta:= inode.meta] = (cache_dirs[m1, mkdir(m6 + 1, md1, # links(m1, cache_dirs), m8 + 1, entries1[str, m5])] ++ m5)[m5, mkdir(0, md3, 1, 0, ∅)] [m1, mkdir(m, md2, m3, m4, entries0) ] ∧ files = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, m3, m4, m))][m5, mkientry(false, mkinode(m5, md3, true, 1, 0, 0))] ∧ (asynced ↔ asynced0) ∧ mkinode(m1, md2, true, m3, m4, m) = (m1 ∈ dirs[ino, dirs[ino].meta:= inode.meta] ⊃ mkinode (m1, dirs[ino, dirs[ino].meta:= inode.meta][m1].meta, true, dirs[ino, dirs[ino].meta:= inode.meta][m1].nlink, dirs[ino, dirs[ino].meta:= inode.meta][m1].nsubdirs, dirs[ino, dirs[ino].meta:= inode.meta][m1].size) ;mkinode(m1, files[m1].meta, false, files[m1].nlink, 0, files[m1].size) ) ∧ mkinode(m5, md3, true, 1, 0, 0) = getinode(mkdentry(str, m5).ino, dirs[ino, dirs[ino].meta:= inode.meta], files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

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