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Proof step 818 from proof refine-truncate-buff-none-cached (previous step)

# buf0 = VFS_PAGE_SIZE, m2 + n0 = m2 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, cache_pcache0[datakey(m3, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), (∅)[m3] = mkientry(boolvar1, mkinode(m4, md, boolvar0, m5, m6, m7)), # (content1 ⊕ mkcontent(m3, cache_pcache0))[m2 / VFS_PAGE_SIZE] < VFS_PAGE_SIZE, afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache0) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache0, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache0), m3 ∈ cache_files, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ m2 = m2 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, m3 ∈ cache_icache

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: cache-base name: at-overwrite-content-new seq: ⊦ n ∈ content1 → (content0 ⊕ content1)[n] = content1[n] subst: [n, content1, content0] → [m2 / VFS_PAGE_SIZE, mkcontent(m3, cache_pcache0), content1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache; (s)% ⊦ mkcontent(ino, pcache)[n] = pcache[datakey(ino, n)].page; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ mkpentry(boolvar, buf).page = buf; (s)% ⊦ ¬ n < n; (s)% ⊦ ¬ n ∈ content1 → (content0 ⊕ content1)[n] = content0[n]; (s)% ⊦ ¬ key ∈ pcache → pcache[key] = (∅)[key]; (s) Used terms: m2 / VFS_PAGE_SIZE, mkcontent(m3, cache_pcache0), content1