[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 62 from proof refine-truncate-buff-none-uncached (previous step)

VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, cache_files[m] = mkfile(m1, md2, # links(m, cache_dirs), content1), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, # links(m, cache_dirs), content0), dirs = cache_dirs, files0 = cache_files [m, mkfile(m1, md2, # links(m, cache_dirs), content1[m2 / VFS_PAGE_SIZE, fill(content1[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto m2) ], m2 % VFS_PAGE_SIZE ≠ 0, 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), m ∈ cache_files, m2 / VFS_PAGE_SIZE ∈ content1, m2 ≤ n, ¬ datakey(m, m2 / VFS_PAGE_SIZE) ∈ cache_pcache, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪afs_inode_sync#(mkinode(m, md, false, # links(m, cache_dirs), 0, n); dirs, files0); inode1 := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files0[m].meta, false, files0[m].nlink, 0, files0[m].size) ); err := ESUCCESS; asynced := ?; asynced1 := true; buf-opt := some(fill(cache_files[m].content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)); afs_files := (cache_files ⊕ cache_pcache) ⊕ cache_icache; if err = ESUCCESS then let asynced0 = false in {icache_set#(inode1, asynced0; err, cache_icache); pcache_truncate#(inode1.ino, m2, n; err, cache_pcache); if asynced1 then pcache_set#(inode1.ino, m2 / VFS_PAGE_SIZE, buf-opt.buf, asynced0; err, cache_pcache)}; if ¬ asynced1 ∨ err ≠ ESUCCESS then buf-opt := none⟫ ⟨buf-opt0 := none; inode0 := mkinode(m, md, false, # links(m, cache_dirs), 0, m2); afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt0, inode0, asynced5, err0, cache_dirs, afs_files, cache_asynced)⟩ ( cache_dirs = dirs ∧ afs_files = (files0 ⊕ cache_pcache) ⊕ cache_icache ∧ (cache_asynced ↔ asynced) ∧ buf-opt = buf-opt0 ∧ inode1 = inode0 ∧ (asynced1 ↔ asynced5) ∧ err = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 63:
VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, # links(m, cache_dirs), content0), cache_files[m] = mkfile(m1, md2, # links(m, cache_dirs), content1), cache_files[m] = mkfile(m3, md1, m4, content), dirs = cache_dirs, files0 = cache_files [m, mkfile(m1, md2, # links(m, cache_dirs), content1[m2 / VFS_PAGE_SIZE, fill(content1[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)] upto 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), m2 / VFS_PAGE_SIZE ∈ content1, m ∈ cache_files, m2 ≤ n, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪afs_inode_sync#(mkinode(m, md, false, # links(m, cache_dirs), 0, n); dirs, files0); inode1 := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files0[m].meta, false, files0[m].nlink, 0, files0[m].size) ); err := ESUCCESS; asynced := ?; asynced1 := true; buf-opt := some(fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n0)); afs_files := (cache_files ⊕ cache_pcache) ⊕ cache_icache; if err = ESUCCESS then let asynced0 = false in {icache_set#(inode1, asynced0; err, cache_icache); pcache_truncate#(inode1.ino, m2, n; err, cache_pcache); if asynced1 then pcache_set#(inode1.ino, m2 / VFS_PAGE_SIZE, buf-opt.buf, asynced0; err, cache_pcache)}; if ¬ asynced1 ∨ err ≠ ESUCCESS then buf-opt := none⟫ ⟨buf-opt0 := none; inode0 := mkinode(m, md, false, # links(m, cache_dirs), 0, m2); afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt0, inode0, asynced5, err0, cache_dirs, afs_files, cache_asynced)⟩ ( cache_dirs = dirs ∧ afs_files = (files0 ⊕ cache_pcache) ⊕ cache_icache ∧ (cache_asynced ↔ asynced) ∧ buf-opt = buf-opt0 ∧ inode1 = inode0 ∧ (asynced1 ↔ asynced5) ∧ err = err0), m2 % VFS_PAGE_SIZE = 0, datakey(m, m2 / VFS_PAGE_SIZE) ∈ cache_pcache

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [cache_files[m], m3, md1, m4, content]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: cache_files[m], m3, md1, m4, content