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Proof step 1004 from proof refine-truncate-buff-none-uncached (previous step)

((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content0), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), cache_icache[m3] = mkientry(boolvar0, mkinode(m, md, boolvar, m4, m5, m7)), # content0[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), pcache-cons(cache_pcache0, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache0), m2 / VFS_PAGE_SIZE ∈ content0, m3 ∈ cache_files, m2 ≤ m6, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, m2 / VFS_PAGE_SIZE ∈ content1, m3 ∈ cache_icache ∧ ¬ boolvar, m3 ∈ cache_icache ∧ boolvar

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: cache-base name: at-icache-overwrite-not-cached seq: ⊦ ¬ ino ∈ icache → (files ⊕ icache)[ino] = files[ino] subst: [ino, icache, files] → [m3, cache_icache, cache_files ⊕ cache_pcache0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)); (s)%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)% ⊦ ¬ ino ∈ icache → icache[ino] = (∅)[ino]; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkfile(m, md, m0, content).content = content; (s)% ⊦ n ∈ content0 ⊕ content1 ↔ n ∈ content0 ∨ n ∈ content1; (ws)% ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache; (s) Used terms: m3, cache_icache, cache_files ⊕ cache_pcache0