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Proof step 146 from proof refine-truncate-buff-none-cached (previous step)

# buf0 = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, cache_pcache0[datakey(m3, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content0), ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m3] = mkfile(m4, md1, m5, content), afs_files0 = ((cache_files ⊕ cache_pcache0) ⊕ cache_icache )[m3, mkfile (m0, md0, # links(m3, cache_dirs), content0[m2 / VFS_PAGE_SIZE, fill(content0[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ], cache_dirs2 = cache_dirs, 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), m3 ∈ cache_files, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, m2 / VFS_PAGE_SIZE ∈ content0, m2 ≤ m, VFS_PAGE_SIZE ≤ # content0[m2 / VFS_PAGE_SIZE], cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ⟨afs_inode_sync#(mkinode(m3, md, false, # links(m3, cache_dirs), 0, m); cache_dirs, afs_files0); inode := (m3 ∈ cache_dirs ⊃ mkinode(m3, cache_dirs[m3].meta, true, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, cache_dirs[m3].size) ;mkinode(m3, afs_files0[m3].meta, false, afs_files0[m3].nlink, 0, afs_files0[m3].size) ); err := ESUCCESS; asynced := ?⟩ ( cache_dirs = cache_dirs2 ∧ afs_files0 = ( cache_files [m3, mkfile(m, md, # links(m3, cache_dirs2), content1[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ] ⊕ truncate(m3, m2, cache_pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n1))]) ⊕ cache_icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, cache_dirs2), 0, m))] ∧ ¬ asynced ∧ fill(buf0, zero, m2 % VFS_PAGE_SIZE, n1) = fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1) ∧ (m3 ∈ cache_dirs2 ⊃ mkinode(m3, cache_dirs2[m3].meta, true, cache_dirs2[m3].nlink, cache_dirs2[m3].nsubdirs, cache_dirs2[m3].size) ;mkinode(m3, md, false, # links(m3, cache_dirs2), 0, m) ) = inode ∧ ESUCCESS = err), m2 % VFS_PAGE_SIZE = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 147:
# buf0 = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m3] = mkfile(m4, md1, # links(m3, cache_dirs), content), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), cache_pcache0[datakey(m3, m2 / VFS_PAGE_SIZE)] = mkpentry(boolvar, buf0), afs_files0 = ((cache_files ⊕ cache_pcache0) ⊕ cache_icache )[m3, mkfile(m4, md1, # links(m3, cache_dirs), content[m2 / VFS_PAGE_SIZE, fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ], cache_dirs2 = cache_dirs, m2 % VFS_PAGE_SIZE ≠ 0, 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), m2 / VFS_PAGE_SIZE ∈ content, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, m3 ∈ cache_files, VFS_PAGE_SIZE ≤ # content[m2 / VFS_PAGE_SIZE], m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ⟨afs_inode_sync#(mkinode(m3, md, false, # links(m3, cache_dirs), 0, m); cache_dirs, afs_files0); inode := (m3 ∈ cache_dirs ⊃ mkinode(m3, cache_dirs[m3].meta, true, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, cache_dirs[m3].size) ;mkinode(m3, afs_files0[m3].meta, false, afs_files0[m3].nlink, 0, afs_files0[m3].size) ); err := ESUCCESS; asynced := ?⟩ ( cache_dirs = cache_dirs2 ∧ afs_files0 = ( cache_files [m3, mkfile(m, md, # links(m3, cache_dirs2), content1[m2 / VFS_PAGE_SIZE, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ] ⊕ truncate(m3, m2, cache_pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(buf0, zero, m2 % VFS_PAGE_SIZE, n1))]) ⊕ cache_icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, cache_dirs2), 0, m))] ∧ ¬ asynced ∧ fill(buf0, zero, m2 % VFS_PAGE_SIZE, n1) = fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1) ∧ (m3 ∈ cache_dirs2 ⊃ mkinode(m3, cache_dirs2[m3].meta, true, cache_dirs2[m3].nlink, cache_dirs2[m3].nsubdirs, cache_dirs2[m3].size) ;mkinode(m3, md, false, # links(m3, cache_dirs2), 0, m) ) = inode ∧ ESUCCESS = err)

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)