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Proof step 838 from proof refine-truncate-buff-none-uncached (previous step)

m2 + n0 = m2 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, cache_icache[m1] = mkientry(boolvar, mkinode(m0, md, false, # links(m1, cache_dirs), m5, m6)), cache_files[m1] = mkfile(m3, md1, # links(m1, cache_dirs), content1), # (content1 ⊕ mkcontent(m1, cache_pcache0))[m2 / VFS_PAGE_SIZE] < VFS_PAGE_SIZE, afs-cons(cache_dirs, (cache_files ⊕ cache_pcache0) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache0), m1 ∈ cache_icache, m1 ∈ cache_files, m2 / VFS_PAGE_SIZE ∈ content1, m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data?, ∀ key. key ∈ cache_pcache0 → key.data? ∧ # cache_pcache0[key].page = VFS_PAGE_SIZE ∧ key.ino ∈ cache_files ∧ (¬ cache_pcache0[key].dirty → key.part ∈ cache_files[key.ino].content ∧ cache_pcache0[key].page = cache_files[key.ino].content[key.part]) ⊦ m2 = m2 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, datakey(m1, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0

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(m1, cache_pcache0), content1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache; (s)% ⊦ ¬ n ∈ content1 → (content0 ⊕ content1)[n] = content0[n]; (s)%⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s)% ⊦ ¬ n < n; (s) Used terms: m2 / VFS_PAGE_SIZE, mkcontent(m1, cache_pcache0), content1