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Proof step 58 from proof fsync-pages-overwrite (previous step)

# buf = VFS_PAGE_SIZE, files1[m] = mkfile(m1, md1, # links(m, dirs), content0), files0[m] = mkfile(m1, md1, # links(m, dirs), content1), pcache[datakey(m, n)] = mkpentry(true, buf), err = ESUCCESS, n * VFS_PAGE_SIZE < m2, afs-cons(dirs, files0), afs-cons(dirs, files1), afs-cons(dirs, files1[m, mkfile(m1, md1, # links(m, dirs), content0[n, buf])]), pcache-cons(pcache, dirs, files1), pcache-cons(pcache1, dirs, files0), datakey(m, n) ∈ pcache, m ∈ files1, m ∈ files0, ∀ pageno. (pageno < n ⊃ (pageno ∈ content0 ↔ pageno ∈ content1 ⊕ mkcontent(m, pcache1)) ∧ content0[pageno] = (content1 ⊕ mkcontent(m, pcache1))[pageno] ;(pageno ∈ content0 ↔ pageno ∈ content1) ∧ content0[pageno] = content1[pageno] ), ∀ key. (key ∈ pcache ↔ key ∈ pcache1) ∧ pcache[key].page = pcache1[key].page ∧ (pcache[key].dirty → pcache1[key].dirty) ⊦ [afs_check_commit#(dirs, files1[m, mkfile(m1, md1, # links(m, dirs), content0[n, buf])]; err; asynced1); ino := m; if err = ESUCCESS then {asynced := false; pcache_set_status#(ino, n, asynced; err, pcache)}; n0 := n + 1] ( pcache-cons(pcache, dirs, files1[m, files1[m].content:= files1[m].content[n, buf]]) ∧ mkinode(m, files1[m].meta, false, files1[m].nlink, 0, files1[m].size) = mkinode(m, md1, false, # links(m, dirs), 0, m1) ∧ ino = m ∧ (∀ key. (key ∈ pcache ↔ key ∈ pcache1) ∧ pcache[key].page = pcache1[key].page ∧ (pcache[key].dirty → pcache1[key].dirty)) ∧ ( err = ESUCCESS → (∀ pageno. (pageno < n0 ⊃ (pageno ∈ files1[m].content[n, buf] ↔ pageno ∈ content1 ⊕ mkcontent(m, pcache1)) ∧ files1[m].content[n, buf][pageno] = (content1 ⊕ mkcontent(m, pcache1))[pageno] ;(pageno ∈ files1[m].content[n, buf] ↔ pageno ∈ content1) ∧ files1[m].content[n, buf][pageno] = content1[pageno] ))))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 59:
# buf = VFS_PAGE_SIZE, pcache[datakey(m, n)] = mkpentry(true, buf), files0[m] = mkfile(m1, md1, # links(m, dirs), content1), files1[m] = mkfile(m1, md1, # links(m, dirs), content0), files1[m] = mkfile(m0, md, m3, content), err = ESUCCESS, n * VFS_PAGE_SIZE < m2, afs-cons(dirs, files1[m, mkfile(m1, md1, # links(m, dirs), content0[n, buf])]), afs-cons(dirs, files1), afs-cons(dirs, files0), pcache-cons(pcache1, dirs, files0), pcache-cons(pcache, dirs, files1), m ∈ files0, m ∈ files1, datakey(m, n) ∈ pcache, ∀ key. (key ∈ pcache ↔ key ∈ pcache1) ∧ pcache[key].page = pcache1[key].page ∧ (pcache[key].dirty → pcache1[key].dirty), ∀ pageno. (pageno < n ⊃ (pageno ∈ content0 ↔ pageno ∈ content1 ⊕ mkcontent(m, pcache1)) ∧ content0[pageno] = (content1 ⊕ mkcontent(m, pcache1))[pageno] ;(pageno ∈ content0 ↔ pageno ∈ content1) ∧ content0[pageno] = content1[pageno] ) ⊦ [afs_check_commit#(dirs, files1[m, mkfile(m1, md1, # links(m, dirs), content0[n, buf])]; err; asynced1); ino := m; if err = ESUCCESS then {asynced := false; pcache_set_status#(ino, n, asynced; err, pcache)}; n0 := n + 1] ( pcache-cons(pcache, dirs, files1[m, files1[m].content:= content[n, buf]]) ∧ mkinode(m, md, false, m3, 0, m0) = mkinode(m, md1, false, # links(m, dirs), 0, m1) ∧ ino = m ∧ (∀ key. (key ∈ pcache ↔ key ∈ pcache1) ∧ pcache[key].page = pcache1[key].page ∧ (pcache[key].dirty → pcache1[key].dirty)) ∧ ( err = ESUCCESS → (∀ pageno. (pageno < n0 ⊃ (pageno ∈ content[n, buf] ↔ pageno ∈ content1 ⊕ mkcontent(m, pcache1)) ∧ content[n, buf][pageno] = (content1 ⊕ mkcontent(m, pcache1))[pageno] ;(pageno ∈ content[n, buf] ↔ pageno ∈ content1) ∧ content[n, buf][pageno] = content1[pageno] ))))

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files1[m], m0, md, m3, content]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files1[m], m0, md, m3, content