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Proof step 1031 from proof refine-truncate-buff-some (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, cache_icache[m3] = mkientry(boolvar, mkinode(m0, md0, false, # links(m3, cache_dirs), m11, m12)), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), cache_icache[ino] = mkientry(boolvar0, mkinode(m, md, true, m4, m5, m7)), cache_files[ino] = mkfile(m8, md3, # links(ino, cache_dirs), content), buf-opt0.some?, 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), pcache-cons(cache_pcache0, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache0), m3 ∈ cache_icache, ino ∈ cache_files, m3 ∈ cache_files, ino ∈ cache_icache, n ∈ content ⊕ mkcontent(ino, truncate(m3, min(m6, m2), cache_pcache0)), n ∈ content, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ content[n] = (content ⊕ mkcontent(ino, truncate(m3, min(m6, m2), cache_pcache0)))[n], ino = m3, datakey(ino, n) ∈ cache_pcache0, m2 ≤ m6 ∧ 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(ino, truncate(m3, min(m6, m2), cache_pcache0)), content] 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) Used terms: n, mkcontent(ino, truncate(m3, min(m6, m2), cache_pcache0)), content