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Proof step 141 from proof refine-truncate-buff-none-uncached (previous step)

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

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 142:
VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, cache_files[m1] = mkfile(m3, md1, # links(m1, cache_dirs), content1), ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m1] = mkfile(m4, md2, # links(m1, cache_dirs), content), afs_files0 = ((cache_files ⊕ cache_pcache0) ⊕ cache_icache )[m1, mkfile(m4, md2, # links(m1, 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, dirs = cache_dirs, files = afs_files0, inode = mkinode(m1, md, false, # links(m1, cache_dirs), 0, m), 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), m2 / VFS_PAGE_SIZE ∈ content1, m1 ∈ cache_files, m2 / VFS_PAGE_SIZE ∈ content, m2 ≤ m, VFS_PAGE_SIZE ≤ # content[m2 / VFS_PAGE_SIZE], cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ⟨let ino = inode.ino in if ino ∈ files then {files[ino].size := inode.size; files[ino].meta := inode.meta} else if ino ∈ dirs then dirs[ino].meta := inode.meta; inode := (m1 ∈ dirs ⊃ mkinode(m1, dirs[m1].meta, true, dirs[m1].nlink, dirs[m1].nsubdirs, dirs[m1].size) ;mkinode(m1, files[m1].meta, false, files[m1].nlink, 0, files[m1].size) ); err := ESUCCESS; asynced := ?⟩ ( dirs = cache_dirs2 ∧ files = ( cache_files [m1, mkfile (m, md, # links(m1, cache_dirs2), content1[m2 / VFS_PAGE_SIZE, fill(content1[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)] upto m2) ] ⊕ truncate(m1, m2, cache_pcache0) [datakey(m1, m2 / VFS_PAGE_SIZE), mkpentry(false, fill(content1[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)) ]) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md, false, # links(m1, cache_dirs2), 0, m))] ∧ ¬ asynced ∧ fill(content1[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1) = fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1) ∧ (m1 ∈ cache_dirs2 ⊃ mkinode(m1, cache_dirs2[m1].meta, true, cache_dirs2[m1].nlink, cache_dirs2[m1].nsubdirs, cache_dirs2[m1].size) ;mkinode(m1, md, false, # links(m1, cache_dirs2), 0, m) ) = inode ∧ ESUCCESS = err), m2 % VFS_PAGE_SIZE = 0, datakey(m1, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_inode_sync#(INODE; DIRS, FILES) {let INO = INODE.ino in if INO ∈ FILES then {FILES[INO].size := INODE.size; FILES[INO].meta := INODE.meta} else if INO ∈ DIRS then DIRS[INO].meta := INODE.meta };