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Proof step 13 from proof fsync-pages-inv (previous step)

# links(m, dirs) = files[m].nlink, files0[m] = mkfile(m1, md0, # links(m, dirs), content), err = ESUCCESS, err0 = ESUCCESS, ino = m, inode = mkinode(m, md, false, # links(m, dirs), 0, m2), n = n0, n1 = 0, n * VFS_PAGE_SIZE < inode.size, 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 ⊦ ⟪/* (fsync-pages-overwrite : invariant afs-cons(dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ getinode(ino, dirs, files) = getinode(ino, dirs, files`) ∧ ino = inode.ino ∧ ino ∈ files ∧ (∀ key. (key ∈ pcache ↔ key ∈ pcache`) ∧ pcache[key].page = (pcache`)[key].page ∧ (pcache[key].dirty → (pcache`)[key].dirty)) ∧ ( err = ESUCCESS → (∀ pageno. (pageno < n ⊃ (pageno ∈ files[ino].content ↔ pageno ∈ (files` ⊕ pcache`)[ino].content) ∧ files[ino].content[pageno] = (files` ⊕ pcache`)[ino].content[pageno] ; (pageno ∈ files[ino].content ↔ pageno ∈ (files`)[ino].content) ∧ files[ino].content[pageno] = (files`)[ino].content[pageno] )))) */; pcache_check_page#(ino, n, pcache; asynced0, asynced, err); if asynced0 ∧ asynced then let buf = ? in {pcache_get#(ino, n, pcache; asynced0, buf, err); if err = ESUCCESS then afs_writepage#(inode, n, buf, dirs; err, files; asynced1); if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced1); if err = ESUCCESS then {asynced := false; pcache_set_status#(ino, 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) ∧ inode.size + VFS_PAGE_SIZE - n * VFS_PAGE_SIZE < inode.size + VFS_PAGE_SIZE - n0 * VFS_PAGE_SIZE)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
# links(m, dirs) = files[m].nlink, files0[m] = mkfile(m1, md0, files[m].nlink, content), 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 ⊦ ⟪/* (fsync-pages-overwrite : invariant afs-cons(dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ getinode(m, dirs, files) = getinode(m, dirs, files`) ∧ m = mkinode(m, md, false, # links(m, dirs), 0, m2).ino ∧ m ∈ files ∧ (∀ key. (key ∈ pcache ↔ key ∈ pcache`) ∧ pcache[key].page = (pcache`)[key].page ∧ (pcache[key].dirty → (pcache`)[key].dirty)) ∧ ( ESUCCESS = ESUCCESS → (∀ pageno. (pageno < n0 ⊃ (pageno ∈ files[m].content ↔ pageno ∈ (files` ⊕ pcache`)[m].content) ∧ files[m].content[pageno] = (files` ⊕ pcache`)[m].content[pageno] ;(pageno ∈ files[m].content ↔ pageno ∈ (files`)[m].content) ∧ files[m].content[pageno] = (files`)[m].content[pageno] )))) */; err := ESUCCESS; pcache_check_page#(m, n0, pcache; asynced0, asynced, err); n := n0; inode := mkinode(m, md, false, # links(m, dirs), 0, m2); if asynced0 ∧ asynced then let buf = ? in {pcache_get#(m, n, pcache; asynced0, buf, err); if err = ESUCCESS then afs_writepage#(inode, n, buf, dirs; err, files; asynced1); if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced1); 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 ∧ inode.size + VFS_PAGE_SIZE - n * VFS_PAGE_SIZE < inode.size + VFS_PAGE_SIZE - n0 * VFS_PAGE_SIZE)

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)