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Proof step 194 from proof fsync-pages-overwrite (previous step)

pcache[datakey(m, n)] = mkpentry(false, buf), files[m] = mkfile(m0, md0, # links(m, dirs), content0), files0[m] = mkfile(m0, md0, # links(m, dirs), content), n * VFS_PAGE_SIZE < m2, afs-cons(dirs, files), afs-cons(dirs, files0), pcache-cons(pcache, dirs, files), pcache-cons(pcache1, dirs, files0), m ∈ files, m ∈ files0, datakey(m, n) ∈ pcache, ∀ 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) ⊦ (¬ n < pageno ⊃ (pageno ∈ content0 ↔ pageno ∈ content ⊕ mkcontent(m, pcache1)) ∧ content0[pageno] = (content ⊕ mkcontent(m, pcache1))[pageno] ;(pageno ∈ content0 ↔ pageno ∈ content) ∧ content0[pageno] = content[pageno] )

User applied rule all left

And obtained the following new goals

Proof step 195:
files0[m] = mkfile(m0, md0, # links(m, dirs), content), files[m] = mkfile(m0, md0, # links(m, dirs), content0), pcache[datakey(m, n)] = mkpentry(false, buf), n * VFS_PAGE_SIZE < m2, afs-cons(dirs, files0), afs-cons(dirs, files), pcache-cons(pcache1, dirs, files0), pcache-cons(pcache, dirs, files), datakey(m, n) ∈ pcache, m ∈ files0, m ∈ files, (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), ∀ 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] ) ⊦ (¬ n < pageno ⊃ (pageno ∈ content0 ↔ pageno ∈ content ⊕ mkcontent(m, pcache1)) ∧ content0[pageno] = (content ⊕ mkcontent(m, pcache1))[pageno] ;(pageno ∈ content0 ↔ pageno ∈ content) ∧ content0[pageno] = content[pageno] )

Rule argument

pos: left 12 terms: pageno abort: F discard: F computed: T

Additional information

Used terms: pageno