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Proof step 541 from proof refine-truncate-buff-some (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, cache_files[ino] = mkfile(m10, md3, # links(ino, cache_dirs), content), cache_icache[m3] = mkientry(boolvar, mkinode(m0, md0, false, # links(m3, cache_dirs), m5, m6)), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), (∅)[ino] = mkientry(boolvar1, mkinode(m4, md1, boolvar0, m7, m8, m9)), 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, m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, mkfile(m10, md3, # links(ino, cache_dirs), content ⊕ mkcontent(ino, cache_pcache0)) = ( cache_files [m3, mkfile(m, md, # links(m3, cache_dirs), content1[m2 / VFS_PAGE_SIZE, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ] ⊕ truncate(m3, m2, cache_pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n1))] )[ino ], ino ∈ cache_icache, ino ∈ cache_icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m))]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 542:
# buf-opt0.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, cache_files[ino] = mkfile(m10, md3, # links(ino, cache_dirs), content), cache_icache[m3] = mkientry(boolvar, mkinode(m0, md0, false, # links(m3, cache_dirs), m5, m6)), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), (∅)[ino] = mkientry(boolvar1, mkinode(m4, md1, boolvar0, m7, m8, m9)), 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, m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, mkfile(m10, md3, # links(ino, cache_dirs), content ⊕ mkcontent(ino, cache_pcache0)) = mkfile (m10, md3, # links(ino, cache_dirs), 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))])), ino ∈ cache_icache

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).content = content; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s)% ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ ino ∈ icache[ino0, ie] ↔ ino = ino0 ∨ ino ∈ icache; (ws)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)%⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)); (s)