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Proof step 157 from proof refine-write_inode (previous step)

cache_files[m] = mkfile(m1, md1, # links(m, cache_dirs), content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, # links(m, cache_dirs), content), cache_icache[m] = mkientry(boolvar, mkinode(m3, md2, boolvar0, m4, m5, m6)), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_files, cache_icache, cache_pcache), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_files, m ∈ cache_icache, ino ∈ cache_files, m ∈ cache_icache → cache_icache[m].inode.ino = m ∧ (cache_icache[m].dirty ⊃ valid-file-inode(cache_icache[m].inode, cache_dirs, cache_files) ;valid-ino(m, cache_dirs, cache_files) ∧ valid-inode(cache_icache[m].inode, cache_dirs, cache_files) ), ∀ ino. ino ∈ cache_icache → cache_icache[ino].inode.ino = ino ∧ (cache_icache[ino].dirty ⊃ valid-file-inode(cache_icache[ino].inode, cache_dirs, cache_files) ;valid-ino(ino, cache_dirs, cache_files) ∧ valid-inode(cache_icache[ino].inode, cache_dirs, cache_files) ) ⊦ (ino = m ⊃ mkfile(m2, md, # links(m, cache_dirs), content);((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino]) = ( (cache_files[m, mkfile(m2, md, # links(m, cache_dirs), content0)] ⊕ cache_pcache) ⊕ cache_icache[m3, mkientry(false, mkinode(m3, md, boolvar0, m4, m5, m2))] )[ino ]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 158:
cache_files[m3] = mkfile(m1, md1, # links(m3, cache_dirs), content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content), cache_icache[m3] = mkientry(boolvar, mkinode(m3, md2, boolvar0, m4, m5, m6)), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_files, cache_icache, cache_pcache), synced(cache_dirs, cache_icache, cache_pcache), ino ∈ cache_files, m3 ∈ cache_files, m3 ∈ cache_icache, (boolvar ⊃ m4 = # links(m3, cache_dirs) ∧ m5 = 0 ∧ ¬ boolvar0 ;mkinode(m3, md2, boolvar0, m4, m5, m6) = mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m1) ), ∀ ino0. ino0 ∈ cache_icache → cache_icache[ino0].inode.ino = ino0 ∧ (cache_icache[ino0].dirty ⊃ cache_icache[ino0].inode.ino ∈ cache_files ∧ cache_icache[ino0].inode.nlink = cache_files[cache_icache[ino0].inode.ino].nlink ∧ cache_icache[ino0].inode.nsubdirs = 0 ∧ ¬ cache_icache[ino0].inode.directory ; (ino0 ∈ cache_dirs ∨ ino0 ∈ cache_files) ∧ cache_icache[ino0].inode = (cache_icache[ino0].inode.ino ∈ cache_dirs ⊃ mkinode (cache_icache[ino0].inode.ino, cache_dirs[cache_icache[ino0].inode.ino].meta, true, cache_dirs[cache_icache[ino0].inode.ino].nlink, cache_dirs[cache_icache[ino0].inode.ino].nsubdirs, cache_dirs[cache_icache[ino0].inode.ino].size) ;mkinode (cache_icache[ino0].inode.ino, cache_files[cache_icache[ino0].inode.ino].meta, false, cache_files[cache_icache[ino0].inode.ino].nlink, 0, cache_files[cache_icache[ino0].inode.ino].size) ) ) ⊦ (ino = m3 ⊃ mkfile(m2, md, # links(m3, cache_dirs), content);((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino]) = ( (cache_files[m3, mkfile(m2, md, # links(m3, cache_dirs), content0)] ⊕ cache_pcache) ⊕ cache_icache[m3, mkientry(false, mkinode(m3, md, boolvar0, m4, m5, m2))] )[ino ]

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ mkientry(boolvar, inode).dirty ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ mkientry(boolvar, inode).inode = inode; (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)%⊦ valid-inode(inode, dirs, files) ↔ inode = getinode(inode.ino, dirs, files); (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)