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Proof step 33 from proof inv-truncate-buff-none-uncached (previous step)

files[m] = mkfile(m1, md1, # links(m, dirs), content0), buf-opt = none, err = ESUCCESS, inode = mkinode(m, md, false, # links(m, dirs), 0, m2), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ files, ¬ datakey(m, m2 / VFS_PAGE_SIZE) ∈ pcache, asynced2 → synced(files, icache, pcache) ⊦ ⟪afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt, inode, asynced4, err, dirs, files, asynced3); if err = ESUCCESS then let asynced = false in {icache_set#(inode, asynced; err, icache); pcache_truncate#(inode.ino, m2, n; err, pcache); if asynced4 then pcache_set#(inode.ino, m2 / VFS_PAGE_SIZE, buf-opt.buf, asynced; err, pcache)}; if ¬ asynced4 ∨ err ≠ ESUCCESS then buf-opt := none⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced2 → synced(files, icache, pcache)))

User applied rule insert program lemma

And obtained the following new goals

Proof step 34:
afs-cons(dirs, files), pre-truncate(inode, n, pageno, buf-opt, dirs, files) ⊦ ⟪afs_truncate#(n, pageno; buf-opt, inode, asynced, err, dirs, files, asynced0)⟫ afs-cons(dirs, files)
Proof step 35:
files[m] = mkfile(m1, md1, # links(m, dirs), content0), buf-opt = none, err = ESUCCESS, inode = mkinode(m, md, false, # links(m, dirs), 0, m2), n0 = n, pageno0 = m2 / VFS_PAGE_SIZE, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), pre-truncate(inode, n, m2 / VFS_PAGE_SIZE, buf-opt, dirs, files), synced(dirs, icache, pcache), m ∈ files, asynced2 → synced(files, icache, pcache) ⊦ [afs_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt, inode, asynced4, err, dirs, files, asynced3)] ( afs-cons(dirs, files) → ⟪if err = ESUCCESS then let asynced = false in {icache_set#(inode, asynced; err, icache); pcache_truncate#(inode.ino, m2, n; err, pcache); if asynced4 then pcache_set#(inode.ino, m2 / VFS_PAGE_SIZE, buf-opt.buf, asynced; err, pcache)}; if ¬ asynced4 ∨ err ≠ ESUCCESS then buf-opt := none⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced2 → synced(files, icache, pcache)))), datakey(m, m2 / VFS_PAGE_SIZE) ∈ pcache

Rule argument

spec: afs-asm name: inv-truncate seq: afs-cons(dirs, files), pre-truncate(inode, n, pageno, buf-opt, dirs, files) ⊦ ⟪afs_truncate# (n, pageno ; buf-opt, inode, asynced, err, dirs, files, asynced0)⟫ afs-cons(dirs, files) subst: [pageno, n, asynced0, files, dirs, err, asynced, inode, buf-opt] → [m2 / VFS_PAGE_SIZE, n, asynced3, files, dirs, err, asynced4, inode, buf-opt] flags: List([[1,0,0]])

Additional information

Used simplifier rules: ⊦ 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)%⊦ 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)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ ¬ none.some?; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)