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Proof step 58 from proof fsync-inode-inv (previous step)

files[m1] = mkfile(m5, md1, m6, content0), files[m] = mkfile(m0, md0, # links(m, dirs), content), icache[m] = mkientry(true, mkinode(m1, md, true, # links(m1, dirs), m9, m7)), dirs[m1] = mkdir(m7, md2, # links(m1, dirs), m9, entries), afs-cons(dirs, files), afs-cons(dirs[m1, mkdir(m7, md, # links(m1, dirs), m9, entries)], files), dcache-cons(dcache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m1 ∈ dirs, m ∈ files, m ∈ icache, ∀ ino. ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ valid-file-inode(icache[ino].inode, dirs, files);valid-ino(ino, dirs, files) ∧ valid-inode(icache[ino].inode, dirs, files)) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 59:
dirs[m1] = mkdir(m7, md2, # links(m1, dirs), m9, entries), icache[m] = mkientry(true, mkinode(m1, md, true, # links(m1, dirs), m9, m7)), files[m] = mkfile(m0, md0, # links(m, dirs), content), files[m1] = mkfile(m5, md1, m6, content0), afs-cons(dirs[m1, mkdir(m7, md, # links(m1, dirs), m9, entries)], files), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ icache, m ∈ files, m1 ∈ dirs, ∀ ino. ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ icache[ino].inode.ino ∈ files ∧ icache[ino].inode.nlink = files[icache[ino].inode.ino].nlink ∧ icache[ino].inode.nsubdirs = 0 ∧ ¬ icache[ino].inode.directory ; (ino ∈ dirs ∨ ino ∈ files) ∧ icache[ino].inode = (icache[ino].inode.ino ∈ dirs ⊃ mkinode (icache[ino].inode.ino, dirs[icache[ino].inode.ino].meta, true, dirs[icache[ino].inode.ino].nlink, dirs[icache[ino].inode.ino].nsubdirs, dirs[icache[ino].inode.ino].size) ;mkinode (icache[ino].inode.ino, files[icache[ino].inode.ino].meta, false, files[icache[ino].inode.ino].nlink, 0, files[icache[ino].inode.ino].size) ) ) ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ 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)