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Proof step 347 from proof refine-truncate-buff-some (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, cache_icache[ino] = mkientry(boolvar1, mkinode(m0, md0, boolvar, 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, m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[ino] = ( ( 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))]) ⊕ cache_icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m))] )[ino ], ino = m3, ino ∈ cache_icache ∧ ¬ boolvar, ino ∈ cache_icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m))] ∧ cache_icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m))][ino].inode.directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 348:
# buf-opt0.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, cache_icache[ino] = mkientry(boolvar1, mkinode(m0, md0, boolvar, 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, m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[ino] = ( ( 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))]) ⊕ cache_icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m))] )[ino ], ino = m3, ino ∈ cache_icache ∧ ¬ boolvar, ino ∈ cache_icache ∧ boolvar

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkientry(boolvar, inode).inode = inode; (s)% ⊦ ino ≠ ino0 → icache[ino0, ie][ino] = icache[ino]; (s)% ⊦ ino ≠ ino0 → (ino ∈ icache[ino0, ie] ↔ ino ∈ icache); (s)