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Proof step 11 from proof fsync-pages-keep-abs (previous step)

err = ESUCCESS, files0 = (files ⊕ pcache) ⊕ icache, inode = mkinode(m, md, boolvar, m0, m1, m2), n = 0, pcache-cons(pcache, dirs, files) ⊦ [while n * VFS_PAGE_SIZE < m2 ∧ err = ESUCCESS do {/* (fsync-pages-overwrite : invariant afs-cons(dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ getinode(m, dirs, files) = getinode(m, dirs, files`) ∧ m = inode.ino ∧ m ∈ 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[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] )))) */; pcache_check_page#(m, n, pcache; asynced0, asynced, err); 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}] (files0 = (files ⊕ pcache) ⊕ icache)

User applied rule invariant right

And obtained the following new goals

Proof step 12:
err = ESUCCESS, err0 = ESUCCESS, files0 = (files1 ⊕ pcache0) ⊕ icache, files0 = (files ⊕ pcache) ⊕ icache, inode = mkinode(m, md, boolvar, m0, m1, m2), n0 = 0, n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1) ⊦ [/* (fsync-pages-overwrite : invariant afs-cons(dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ getinode(m, dirs, files) = getinode(m, dirs, files`) ∧ m = inode.ino ∧ m ∈ 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[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] )))) */; pcache_check_page#(m, n, pcache; asynced0, asynced, err); 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] (files0 = (files ⊕ pcache) ⊕ icache)

Rule argument

fma: files0 = (files ⊕ pcache) ⊕ icache pos: right 1

Additional information

Used formulas: files0 = (files ⊕ pcache) ⊕ icache