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Proof step 962 from proof refine-truncate-buff-none-uncached (previous step)

asynced0 ↔ asynced5, asynced ↔ cache_asynced, ((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content0), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), afs_files = (cache_files ⊕ cache_pcache0) ⊕ cache_icache, buf-opt = none, cache_dirs0 = cache_dirs, dirs = cache_dirs, err = err0, files = afs_files, inode = inode0, inode0 = mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m2), inode1 = mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m6), n = m6, old_ino = 0, pageno = m2 / VFS_PAGE_SIZE, 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), pre-truncate(inode, n, pageno, buf-opt, dirs, files), synced(cache_dirs, cache_icache, cache_pcache0), m3 ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ⟨afs_truncate_internal#(n, pageno; inode, buf-opt, old_ino, size, asynced0, err, dirs, files; asynced)⟩ ( dirs = cache_dirs0 ∧ files = (cache_files[m3, mkfile(m6, md1, # links(m3, cache_dirs0), content1 upto min(m6, m2))] ⊕ truncate(m3, min(m6, m2), cache_pcache0)) ⊕ cache_icache[m3, mkientry(false, mkinode(m3, md1, false, # links(m3, cache_dirs0), 0, m6))] ∧ ¬ asynced ∧ none = buf-opt ∧ inode1 = inode ∧ ¬ asynced0 ∧ ESUCCESS = err), VFS_PAGE_SIZE = 0, datakey(m3, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 963:
((cache_files ⊕ cache_pcache0) ⊕ cache_icache)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content0), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), afs_files = (cache_files ⊕ cache_pcache0) ⊕ cache_icache, buf-opt = none, dirs = cache_dirs, inode = mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m2), old_ino = 0, 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), m3 ∈ cache_files, ¬ datakey(m3, m2 / VFS_PAGE_SIZE) ∈ cache_pcache0, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ⟨afs_truncate_internal#(m6, m2 / VFS_PAGE_SIZE; inode, buf-opt, old_ino, size, asynced0, err, dirs, afs_files; asynced)⟩ ( dirs = cache_dirs ∧ afs_files = (cache_files[m3, mkfile(m6, md1, # links(m3, cache_dirs), content1 upto min(m6, m2))] ⊕ truncate(m3, min(m6, m2), cache_pcache0)) ⊕ cache_icache[m3, mkientry(false, mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m6))] ∧ ¬ asynced ∧ none = buf-opt ∧ mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m6) = inode ∧ ¬ asynced0 ∧ ESUCCESS = err), m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content1

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ ¬ none.some?; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ ino ∈ files ⊕ pcache ↔ ino ∈ files; (s)% ⊦ ino ∈ files ⊕ icache ↔ ino ∈ files; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)%⊦ pre-truncate(inode, n, pageno, buf-opt, dirs, files) ↔ valid-file-inode(inode, dirs, files) ∧ pageno = inode.size / VFS_PAGE_SIZE ∧ (buf-opt.some? → # buf-opt.buf = VFS_PAGE_SIZE); (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)