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Proof step 1251 from proof refine-truncate-buff-none-uncached (previous step)

(∅)[m] = mkientry(boolvar1, mkinode(m10, md4, boolvar0, m11, m12, m13)), 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), n ∈ content1 ⊕ mkcontent(m, cache_pcache0), m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ (content1 ⊕ mkcontent(m, cache_pcache0))[n] = ((content1 upto min(m8, m2)) ⊕ mkcontent(m, truncate(m, min(m8, m2), cache_pcache0)))[n], datakey(m, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, m ∈ cache_icache, 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 1252:
⊦ n ∈ content1 → (content0 ⊕ content1)[n] = content1[n]
Proof step 1253:
cache_files[m] = mkfile(m1, md2, # links(m, cache_dirs), content1), (∅)[m] = mkientry(boolvar1, mkinode(m10, md4, boolvar0, m11, m12, m13)), 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), m ∈ cache_files, n ∈ content1 ⊕ mkcontent(m, cache_pcache0), cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ (content1 ⊕ mkcontent(m, cache_pcache0))[n] = ((content1 upto min(m8, m2)) ⊕ mkcontent(m, truncate(m, min(m8, m2), cache_pcache0)))[n], m ∈ cache_icache, datakey(m, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, n ∈ mkcontent(m, 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
Proof step 1256:
cache_files[m] = mkfile(m1, md2, # links(m, cache_dirs), content1), (∅)[m] = mkientry(boolvar1, mkinode(m10, md4, boolvar0, m11, m12, m13)), 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), m ∈ cache_files, n ∈ content1 ⊕ mkcontent(m, cache_pcache0), n ∈ mkcontent(m, cache_pcache0), cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ mkcontent(m, cache_pcache0)[n] = ((content1 upto min(m8, m2)) ⊕ mkcontent(m, truncate(m, min(m8, m2), cache_pcache0)))[n], m ∈ cache_icache, 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, cache_pcache0), content1] flags: <all paths>

Additional information

Used terms: n, mkcontent(m, cache_pcache0), content1