Proof step 88 from proof refine-truncate-buff-some (previous step)

Heuristic conditional right split applied rule if right

And obtained the following new goals

• Proof step 89:

  # buf-opt0.buf = VFS_PAGE_SIZE, asynced ↔ cache_asynced, asynced0 ↔ asynced5, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, 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), afs_files = (cache_files ⊕ cache_pcache0) ⊕ cache_icache, buf = fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0), buf-opt = buf-opt0, buf-opt1 = some(fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)), buf-opt2 = buf-opt0, cache_dirs0 = cache_dirs, dirs = cache_dirs, err = err0, files = afs_files, inode = inode0, inode0 = mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2), n = m, pageno = m2 / VFS_PAGE_SIZE, 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), pre-truncate(inode, n, pageno, buf-opt, dirs, files), synced(cache_dirs, cache_icache, cache_pcache0), m3 ∈ cache_files, m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ⟨let old_ino = 0, size = 0 in afs_truncate_internal#(n, pageno; inode, buf-opt, old_ino, size, asynced0, err, dirs, files; asynced)⟩ ( dirs = cache_dirs0 ∧ files = ( cache_files [m3, mkfile(m, md, # links(m3, cache_dirs0), content1[m2 / VFS_PAGE_SIZE, fill(buf-opt2.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] ⊕ truncate(m3, m2, cache_pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, buf)]) ⊕ cache_icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, cache_dirs0), 0, m))] ∧ (asynced ↔ asynced1) ∧ buf-opt1 = buf-opt ∧ (m3 ∈ cache_dirs0 ⊃ mkinode(m3, cache_dirs0[m3].meta, true, cache_dirs0[m3].nlink, cache_dirs0[m3].nsubdirs, cache_dirs0[m3].size) ;mkinode(m3, md, false, # links(m3, cache_dirs0), 0, m) ) = inode ∧ asynced0 ∧ ESUCCESS = err), m2 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0

• Proof step 712:

  # buf-opt0.buf = VFS_PAGE_SIZE, asynced ↔ cache_asynced, asynced0 ↔ asynced5, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, 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), afs_files = (cache_files ⊕ cache_pcache0) ⊕ cache_icache, buf = fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0), buf-opt = buf-opt0, buf-opt1 = some(fill(buf-opt0.buf, zero, m2 % VFS_PAGE_SIZE, n0)), buf-opt2 = buf-opt0, cache_dirs0 = cache_dirs, dirs = cache_dirs, err = err0, files = afs_files, inode = inode0, inode0 = mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2), n = m, pageno = m2 / VFS_PAGE_SIZE, 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), m3 ∈ cache_files, m2 ≤ m, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ⟨abort⟩ ( dirs = cache_dirs0 ∧ files = ( cache_files [m3, mkfile(m, md, # links(m3, cache_dirs0), content1[m2 / VFS_PAGE_SIZE, fill(buf-opt2.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ] ⊕ truncate(m3, m2, cache_pcache0)[datakey(m3, m2 / VFS_PAGE_SIZE), mkpentry(false, buf)]) ⊕ cache_icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, cache_dirs0), 0, m))] ∧ (asynced ↔ asynced1) ∧ buf-opt1 = buf-opt ∧ (m3 ∈ cache_dirs0 ⊃ mkinode(m3, cache_dirs0[m3].meta, true, cache_dirs0[m3].nlink, cache_dirs0[m3].nsubdirs, cache_dirs0[m3].size) ;mkinode(m3, md, false, # links(m3, cache_dirs0), 0, m) ) = inode ∧ asynced0 ∧ ESUCCESS = err), m2 % VFS_PAGE_SIZE = 0, VFS_PAGE_SIZE = 0, pre-truncate(inode, n, pageno, buf-opt, dirs, files)

Rule argument

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