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Proof step 16 from proof inv-truncate (previous step)

files[m] = mkfile(m0, md0, # links(m, dirs), content), buf-opt = none, 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), datakey(m, m2 / VFS_PAGE_SIZE) ∈ pcache, m ∈ files, asynced → synced(files, icache, pcache) ⊦ ⟪cache_truncate#(n, m2 / VFS_PAGE_SIZE; buf-opt, inode, asynced0, err, dirs, files, asynced1, icache, pcache)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)) ∧ afs-cons(dirs, files))

User applied rule insert program lemma

And obtained the following new goals

Proof step 17:
valid-file-inode(inode, dirs, files), pageno = inode.size / VFS_PAGE_SIZE, buf-opt.none?, datakey(inode.ino, pageno) ∈ pcache, icache-cons(icache, dirs, files), dcache-cons(dcache, dirs, files), pcache-cons(pcache, dirs, files), afs-cons(dirs, files), synced(dirs, icache, pcache), asynced → synced(files, icache, pcache) ⊦ ⟪cache_truncate#(n, pageno; buf-opt, inode, asynced0, err, dirs, files, asynced1, icache, pcache)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)))

Rule argument

spec: <toplevel> name: inv-truncate-buff-none-cached seq: valid-file-inode(inode, dirs, files), pageno = inode.size / VFS_PAGE_SIZE, buf-opt.none?, datakey(inode.ino, pageno) ∈ pcache, icache-cons(icache, dirs, files), dcache-cons(dcache, dirs, files), pcache-cons(pcache, dirs, files), afs-cons(dirs, files), synced(dirs, icache, pcache), asynced → synced(files, icache, pcache) ⊦ ⟪cache_truncate# (n, pageno ; buf-opt, inode, asynced0, err, dirs, files, asynced1, icache, pcache)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ afs-cons(dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache))) subst: [dcache, asynced, pageno, n, pcache, icache, asynced1, files, dirs, err, asynced0, inode, buf-opt] → [dcache, asynced, m2 / VFS_PAGE_SIZE, n, pcache, icache, asynced1, files, dirs, err, asynced0, inode, buf-opt] flags: List([[1,0,0]])

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (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)% ⊦ 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)% ⊦ none.none?; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)