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Proof step 1077 from proof refine-truncate-buff-some (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, cache_files[m] = mkfile(m1, md2, # links(m, cache_dirs), content1), (∅)[m] = mkientry(boolvar1, mkinode(m10, md4, boolvar0, m11, m12, m13)), buf-opt0.some?, n * VFS_PAGE_SIZE < min(m8, m2), 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), n ∈ content1, m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ content1[n] = ((content1 upto min(m8, m2)) ⊕ mkcontent(m, truncate(m, min(m8, m2), cache_pcache0)))[n], datakey(m, n) ∈ cache_pcache0, m ∈ cache_icache, m2 ≤ m8 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Heuristic use patterns 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] → [n, mkcontent(m, truncate(m, min(m8, m2), cache_pcache0)), content1 upto min(m8, m2)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ mkcontent(ino, pcache)[n] = pcache[datakey(ino, n)].page; (s)% ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache; (s)%⊦ key ∈ truncate(ino, size, pcache) ↔ key.data? ∧ key ∈ pcache ∧ (key.part * VFS_PAGE_SIZE < size ∨ ino ≠ key.ino); (s)% ⊦ datakey(m, m0).data?; (s)% ⊦ ¬ n ∈ content1 → (content0 ⊕ content1)[n] = content0[n]; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%⊦ m * VFS_PAGE_SIZE < n ∧ m ∈ content → (content upto n)[m] = content[m]; (s) Used terms: n, mkcontent(m, truncate(m, min(m8, m2), cache_pcache0)), content1 upto min(m8, m2)