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Proof step 1376 from proof refine-truncate-buff-none-uncached (previous step)

cache_files[m] = mkfile(m1, md2, # links(m, cache_dirs), content1), cache_icache[m] = mkientry(boolvar0, mkinode(m0, md0, false, # links(m, cache_dirs), m11, m12)), cache_pcache0[datakey(m, n)] = mkpentry(boolvar, buf), 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 ⊕ mkcontent(m, cache_pcache0), m ∈ cache_files, m ∈ cache_icache, datakey(m, n) ∈ cache_pcache0, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ buf = ((content1 upto min(m8, m2)) ⊕ mkcontent(m, truncate(m, min(m8, m2), cache_pcache0)))[n], datakey(m, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, m2 ≤ m8 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content1, m2 ≤ m8 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content1 ⊕ mkcontent(m, cache_pcache0)

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1377:
⊦ n ∈ content1 → (content0 ⊕ content1)[n] = content1[n]
Proof step 1378:
cache_pcache0[datakey(m, n)] = mkpentry(boolvar, buf), cache_icache[m] = mkientry(boolvar0, mkinode(m0, md0, false, # links(m, cache_dirs), m11, m12)), cache_files[m] = mkfile(m1, md2, # links(m, cache_dirs), content1), n * VFS_PAGE_SIZE < min(m8, m2), 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), datakey(m, n) ∈ cache_pcache0, m ∈ cache_icache, m ∈ cache_files, n ∈ content1 ⊕ mkcontent(m, cache_pcache0), n ∈ mkcontent(m, truncate(m, min(m8, m2), cache_pcache0)), cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ buf = mkcontent(m, truncate(m, min(m8, m2), cache_pcache0))[n], datakey(m, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, m2 ≤ m8 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content1 ⊕ mkcontent(m, cache_pcache0), m2 ≤ m8 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content1

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: ⊦ ¬ n ∈ content1 → (content0 ⊕ content1)[n] = content0[n]; (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)% ⊦ datakey(m, m0).part = m0; (s) Used terms: n, mkcontent(m, truncate(m, min(m8, m2), cache_pcache0)), content1 upto min(m8, m2)