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Proof step 41 from proof fsync-pages-overwrite (previous step)

files[m] = mkfile(m0, md0, # links(m, dirs), content0), files0[m] = mkfile(m0, md0, # links(m, dirs), content), pcache[datakey(m, n)] = mkpentry(true, buf), files0[m] = mkfile(m1, md1, m3, content1), err = ESUCCESS, n * VFS_PAGE_SIZE < m2, afs-cons(dirs, files), afs-cons(dirs, files0), pcache-cons(pcache, dirs, files), pcache-cons(pcache1, dirs, files0), datakey(m, n) ∈ pcache, m ∈ files, m ∈ files0, ∀ pageno. (pageno < n ⊃ (pageno ∈ content0 ↔ pageno ∈ content ⊕ mkcontent(m, pcache1)) ∧ content0[pageno] = (content ⊕ mkcontent(m, pcache1))[pageno] ;(pageno ∈ content0 ↔ pageno ∈ content) ∧ content0[pageno] = content[pageno] ), ∀ key. (key ∈ pcache ↔ key ∈ pcache1) ∧ pcache[key].page = pcache1[key].page ∧ (pcache[key].dirty → pcache1[key].dirty) ⊦ [afs_writepage#(mkinode(m, md, false, # links(m, dirs), 0, m2), n, buf, dirs; err, files; asynced1); if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced1); ino := m; 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) ∧ mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) = mkinode(m, md1, false, m3, 0, m1) ∧ ino = m ∧ m ∈ 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[m].content ↔ pageno ∈ content1 ⊕ mkcontent(m, pcache1)) ∧ files[m].content[pageno] = (content1 ⊕ mkcontent(m, pcache1))[pageno] ;(pageno ∈ files[m].content ↔ pageno ∈ content1) ∧ files[m].content[pageno] = content1[pageno] ))))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
pcache[datakey(m, n)] = mkpentry(true, buf), files0[m] = mkfile(m1, md1, # links(m, dirs), content1), files[m] = mkfile(m1, md1, # links(m, dirs), content0), err = ESUCCESS, n * VFS_PAGE_SIZE < m2, afs-cons(dirs, files0), afs-cons(dirs, files), pcache-cons(pcache1, dirs, files0), pcache-cons(pcache, dirs, files), m ∈ files0, m ∈ files, 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_writepage#(mkinode(m, md, false, # links(m, dirs), 0, m2), n, buf, dirs; err, files; asynced1); if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced1); ino := m; 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) ∧ mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) = mkinode(m, md1, false, # links(m, dirs), 0, m1) ∧ ino = m ∧ m ∈ 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[m].content ↔ pageno ∈ content1 ⊕ mkcontent(m, pcache1)) ∧ files[m].content[pageno] = (content1 ⊕ mkcontent(m, pcache1))[pageno] ;(pageno ∈ files[m].content ↔ pageno ∈ content1) ∧ files[m].content[pageno] = content1[pageno] ))))

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)%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