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Proof step 392 from proof refine-truncate-buff-some (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, cache_icache[m3] = mkientry(boolvar0, mkinode(m4, md1, true, m5, m6, m7)), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), cache_icache[ino] = mkientry(boolvar1, mkinode(m0, md0, true, m8, m9, m10)), cache_files[ino] = mkfile(m11, md, # 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), ino ∈ cache_icache, m3 ∈ cache_icache, m3 ∈ cache_files, ino ∈ cache_files, m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, ino = m3, content ⊕ mkcontent(ino, cache_pcache0) = content ⊕ mkcontent (ino, truncate(m3, m2, cache_pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1))])

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 393:
⊦ content = content0 ↔ (∀ n. (n ∈ content ↔ n ∈ content0) ∧ (n ∈ content → content[n] = content0[n]))
Proof step 394:
# buf-opt0.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, cache_files[ino] = mkfile(m11, md, # links(ino, cache_dirs), content), cache_icache[ino] = mkientry(boolvar1, mkinode(m0, md0, true, m8, m9, m10)), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), cache_icache[m3] = mkientry(boolvar0, mkinode(m4, md1, true, m5, m6, m7)), buf-opt0.some?, 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), ino ∈ cache_files, m3 ∈ cache_files, m3 ∈ cache_icache, ino ∈ cache_icache, m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, ino = m3, ∀ n. ( n ∈ content ⊕ mkcontent(ino, cache_pcache0) ↔ n ∈ content ⊕ mkcontent (ino, truncate(m3, m2, cache_pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1))])) ∧ ( n ∈ content ⊕ mkcontent(ino, cache_pcache0) → (content ⊕ mkcontent(ino, cache_pcache0))[n] = ( content ⊕ mkcontent (ino, truncate(m3, m2, cache_pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1))]) )[n ])

Rule argument

spec: store, inst: file-content name: k-Extension seq: ⊦ content = content0 ↔ (∀ n. (n ∈ content ↔ n ∈ content0) ∧ (n ∈ content → content[n] = content0[n])) subst: [content, content0] → [content ⊕ mkcontent(ino, cache_pcache0), content ⊕ mkcontent (ino, truncate(m3, m2, cache_pcache0) [datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry (false, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)) ])] flags: <all paths>

Additional information

Used terms: content ⊕ mkcontent(ino, cache_pcache0), content ⊕ mkcontent (ino, truncate(m3, m2, cache_pcache0) [datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)) ])