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Proof step 678 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(boolvar, mkinode(m0, md0, false, # links(m3, cache_dirs), m5, m6)), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), cache_icache[ino] = mkientry(boolvar0, mkinode(m4, md1, false, m7, m8, m9)), cache_files[ino] = mkfile(m10, md3, # links(ino, cache_dirs), content), 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 ∈ 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 ])

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 679:
# 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[ino] = mkientry(boolvar0, mkinode(m4, md1, false, m7, m8, m9)), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), cache_icache[m3] = mkientry(boolvar, mkinode(m0, md0, false, # links(m3, cache_dirs), m5, m6)), 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, 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))]), 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 ∈ 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

fma: 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)) ])

Additional information

Used simplifier rules: ⊦ n ∈ content0 ⊕ content1 ↔ n ∈ content0 ∨ n ∈ content1; (ws)% ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache; (s)% ⊦ key ∈ pcache[key0, pe] ↔ key = key0 ∨ key ∈ pcache; (ws)%⊦ 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)% ⊦ datakey(m, m0).ino = m; (s)% ⊦ key ≠ key0 → (key ∈ pcache[key0, pe] ↔ key ∈ pcache); (s) Used formulas: 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)) ])