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Proof step 557 from proof inv-rename-file-dentry (previous step)

dirs[m0] = mkdir(m6, md6, # links(m0, dirs), m9, entries0), files[entries0[str0]] = mkfile(m4, md4, # links(entries0[str0], dirs), content0), files[entries[str]] = mkfile(m1, md3, # links(entries[str], dirs), content), dirs[m] = mkdir(m5, md5, # links(m, dirs), m7, entries), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), entries0[str0] ∈ files, entries[str] ∈ files, m0 ∈ dirs, m ∈ dirs, str0 ∈ entries0, str ∈ entries, asynced → synced(files, icache, pcache), m = m0 → md1 = md2, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ str0 ∈ entries0 ∧ (str0 ∈ entries0 ∧ str0 ∈ entries0) ∧ str ∈ entries ∧ str ∈ entries ∧ str ∈ entries

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: cache-base name: icache-cons seq: ⊦ icache-cons(icache, dirs, files) ↔ (∀ 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) )) subst: [icache, dirs, files] → [icache, dirs, files] flags: <all paths>

Additional information

Used simplifier rules: ⊦ 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)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)%⊦ valid-inode(inode, dirs, files) ↔ inode = getinode(inode.ino, dirs, files); (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) Used terms: icache, dirs, files