| ⟨inode1 := mkinode(m, md, false, m1, 0, m2); afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt1, inode1, asynced0, err0, cache_dirs, afs_files, afs_asynced0)⟩ ( cache_dirs = cache_dirs0 ∧ afs_files = (cache_files0 ⊕ cache_pcache0) ⊕ cache_icache0 ∧ (afs_asynced0 ↔ cache_asynced0) ∧ buf-opt2 = buf-opt1 ∧ inode2 = inode1 ∧ (asynced1 ↔ asynced0) ∧ err1 = err0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, m1, content), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, buf-opt0 = none, buf-opt1 = none, inode0 = mkinode(m, md, false, m1, 0, m2), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), datakey(m, m2 / VFS_PAGE_SIZE) ∈ cache_pcache, m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟨afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt0, inode0, asynced0, err0, cache_dirs, afs_files, afs_asynced0)⟩ ( cache_dirs = cache_dirs0 ∧ afs_files = (cache_files0 ⊕ cache_pcache0) ⊕ cache_icache0 ∧ (afs_asynced0 ↔ cache_asynced0) ∧ buf-opt2 = buf-opt0 ∧ inode2 = inode0 ∧ (asynced1 ↔ asynced0) ∧ err1 = err0) |
⟨afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt1, inode1, asynced0, err0, cache_dirs, afs_files, afs_asynced0)⟩ ( cache_dirs = cache_dirs0 ∧ afs_files = (cache_files0 ⊕ cache_pcache0) ⊕ cache_icache0 ∧ (afs_asynced0 ↔ cache_asynced0) ∧ buf-opt2 = buf-opt1 ∧ inode2 = inode1 ∧ (asynced1 ↔ asynced0) ∧ err1 = err0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, m1, content), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, buf-opt0 = none, buf-opt1 = none, inode0 = mkinode(m, md, false, m1, 0, m2), inode1 = mkinode(m, md, false, m1, 0, m2), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ 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_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_files, datakey(m, m2 / VFS_PAGE_SIZE) ∈ cache_pcache, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟨afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt0, inode0, asynced0, err0, cache_dirs, afs_files, afs_asynced0)⟩ ( cache_dirs = cache_dirs0 ∧ afs_files = (cache_files0 ⊕ cache_pcache0) ⊕ cache_icache0 ∧ (afs_asynced0 ↔ cache_asynced0) ∧ buf-opt2 = buf-opt0 ∧ inode2 = inode0 ∧ (asynced1 ↔ asynced0) ∧ err1 = err0)