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Proof step 44 from proof fsync-pages-inv (previous step)

files[m] = mkfile(m0, md1, # links(m, dirs), content0), files0[m] = mkfile(m1, md0, # links(m, dirs), content), pcache[datakey(m, n0)] = mkpentry(true, buf), err = ESUCCESS, n0 * VFS_PAGE_SIZE < m2, afs-cons(dirs, files0), afs-cons(dirs, files), dcache-cons(dcache, dirs, files0), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files0), icache-cons(icache, dirs, files), pcache-cons(pcache0, dirs, files0), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache0), synced(dirs, icache, pcache), m ∈ files0, m ∈ files, datakey(m, n0) ∈ pcache ⊦ ⟪afs_writepage#(mkinode(m, md, false, # links(m, dirs), 0, m2), n0, buf, dirs; err, files; asynced1); if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced1); n := n0; if err = ESUCCESS then {asynced := false; pcache_set_status#(m, n, asynced; err, pcache)}; n := n + 1⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ afs-cons(dirs, files) ∧ m ∈ files ∧ # links(m, dirs) = files[m].nlink ∧ (m2 + VFS_PAGE_SIZE - n * VFS_PAGE_SIZE) + n0 * VFS_PAGE_SIZE < m2 + VFS_PAGE_SIZE)

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: afs-asm name: inv-writepage seq: afs-cons(dirs, files), pre-writepage(inode, pageno, buf, dirs, files) ⊦ ⟪afs_writepage# (inode, pageno, buf, dirs; err, files; asynced)⟫ afs-cons(dirs, files) subst: [dirs, buf, pageno, inode, files, err, asynced] → [dirs, buf, n0, mkinode(m, md, false, # links(m, dirs), 0, m2), files, err, asynced1] flags: List([[1,0,0]])

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