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Proof step 11 from proof fsync-pages-overwrite (previous step)

asynced1 ↔ asynced2, files0[m] = mkfile(m0, md0, # links(m, dirs), content), err = ESUCCESS, files = files0, ino = inode.ino, inode = mkinode(m, md, false, # links(m, dirs), 0, m2), n = 0, pcache0 = pcache, afs-cons(dirs, files0), pcache-cons(pcache, dirs, files0), m ∈ files0 ⊦ [while n * VFS_PAGE_SIZE < inode.size ∧ err = ESUCCESS do {/* (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}] ( err = ESUCCESS → files[m].content:= (files[m].content upto m2) = mkfile(m0, md0, # links(m, dirs), (content ⊕ mkcontent(m, pcache0)) upto m2))

Heuristic annotation applied rule annotation right

And obtained the following new goals

Proof step 12:
asynced5 ↔ asynced2, files0[m] = mkfile(m0, md0, # links(m, dirs), content), err = ESUCCESS, err0 = ESUCCESS, files1 = files0, getinode(ino, dirs, files) = getinode(ino, dirs, files1), ino = inode.ino, inode = mkinode(m, md, false, # links(m, dirs), 0, m2), n0 = 0, pcache0 = pcache1, n * VFS_PAGE_SIZE < inode.size, afs-cons(dirs, files0), afs-cons(dirs, files), pcache-cons(pcache1, dirs, files0), pcache-cons(pcache, dirs, files), m ∈ files0, ino ∈ files, err = ESUCCESS → (∀ pageno. (pageno < n ⊃ (pageno ∈ files[ino].content ↔ pageno ∈ (files1 ⊕ pcache1)[ino].content) ∧ files[ino].content[pageno] = (files1 ⊕ pcache1)[ino].content[pageno] ;(pageno ∈ files[ino].content ↔ pageno ∈ files1[ino].content) ∧ files[ino].content[pageno] = files1[ino].content[pageno] )), ∀ key. (key ∈ pcache ↔ key ∈ pcache1) ∧ pcache[key].page = pcache1[key].page ∧ (pcache[key].dirty → pcache1[key].dirty) ⊦ [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] ( afs-cons(dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ getinode(ino, dirs, files) = getinode(ino, dirs, files1) ∧ ino = inode.ino ∧ ino ∈ files ∧ (∀ key. (key ∈ pcache ↔ key ∈ pcache1) ∧ pcache[key].page = pcache1[key].page ∧ (pcache[key].dirty → pcache1[key].dirty)) ∧ ( err = ESUCCESS → (∀ pageno. (pageno < n ⊃ (pageno ∈ files[ino].content ↔ pageno ∈ (files1 ⊕ pcache1)[ino].content) ∧ files[ino].content[pageno] = (files1 ⊕ pcache1)[ino].content[pageno] ;(pageno ∈ files[ino].content ↔ pageno ∈ files1[ino].content) ∧ files[ino].content[pageno] = files1[ino].content[pageno] ))))
Proof step 238:
asynced5 ↔ asynced2, files0[m] = mkfile(m0, md0, # links(m, dirs), content), err = ESUCCESS, err0 = ESUCCESS, files1 = files0, getinode(ino, dirs, files) = getinode(ino, dirs, files1), ino = inode.ino, inode = mkinode(m, md, false, # links(m, dirs), 0, m2), n0 = 0, pcache0 = pcache1, afs-cons(dirs, files0), afs-cons(dirs, files), pcache-cons(pcache1, dirs, files0), pcache-cons(pcache, dirs, files), m ∈ files0, ino ∈ files, err = ESUCCESS → (∀ pageno. (pageno < n ⊃ (pageno ∈ files[ino].content ↔ pageno ∈ (files1 ⊕ pcache1)[ino].content) ∧ files[ino].content[pageno] = (files1 ⊕ pcache1)[ino].content[pageno] ;(pageno ∈ files[ino].content ↔ pageno ∈ files1[ino].content) ∧ files[ino].content[pageno] = files1[ino].content[pageno] )), ∀ key. (key ∈ pcache ↔ key ∈ pcache1) ∧ pcache[key].page = pcache1[key].page ∧ (pcache[key].dirty → pcache1[key].dirty) ⊦ files[m].content:= (files[m].content upto m2) = mkfile(m0, md0, # links(m, dirs), (content ⊕ mkcontent(m, pcache0)) upto m2), n * VFS_PAGE_SIZE < inode.size ∧ err = ESUCCESS

Rule argument

rule: invariant right arg: fma: 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] ))) pos: right 1 pos: right 1

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)% ⊦ ¬ m < 0; (s) Used formulas: 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] )))