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Proof step 200 from proof fsync-pages-overwrite (previous step)

pageno ∈ content0 ↔ pageno ∈ content, content0[pageno] = content[pageno], pcache[datakey(m, pageno)] = mkpentry(false, buf), files[m] = mkfile(m0, md0, # links(m, dirs), content0), files0[m] = mkfile(m0, md0, # links(m, dirs), content), pageno * 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, pageno) ∈ pcache, ∀ pageno0. (pageno0 < pageno ⊃ (pageno0 ∈ content0 ↔ pageno0 ∈ content ⊕ mkcontent(m, pcache1)) ∧ content0[pageno0] = (content ⊕ mkcontent(m, pcache1))[pageno0] ;(pageno0 ∈ content0 ↔ pageno0 ∈ content) ∧ content0[pageno0] = content[pageno0] ), ∀ key. (key ∈ pcache ↔ key ∈ pcache1) ∧ pcache[key].page = pcache1[key].page ∧ (pcache[key].dirty → pcache1[key].dirty) ⊦ datakey(m, pageno) ∈ pcache1, (pageno ∈ content → pageno ∈ content ⊕ mkcontent(m, pcache1)) ∧ content[pageno] = (content ⊕ mkcontent(m, pcache1))[pageno]

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 201:
pageno ∈ content0 ↔ pageno ∈ content, files0[m] = mkfile(m0, md0, # links(m, dirs), content), files[m] = mkfile(m0, md0, # links(m, dirs), content0), pcache[datakey(m, pageno)] = mkpentry(false, buf), content0[pageno] = content[pageno], pageno * VFS_PAGE_SIZE < m2, afs-cons(dirs, files0), afs-cons(dirs, files), pcache-cons(pcache1, dirs, files0), pcache-cons(pcache, dirs, files), datakey(m, pageno) ∈ pcache, m ∈ files0, m ∈ files, ∀ key. (key ∈ pcache ↔ key ∈ pcache1) ∧ pcache[key].page = pcache1[key].page ∧ (pcache[key].dirty → pcache1[key].dirty), ∀ pageno0. (pageno0 < pageno ⊃ (pageno0 ∈ content0 ↔ pageno0 ∈ content ⊕ mkcontent(m, pcache1)) ∧ content0[pageno0] = (content ⊕ mkcontent(m, pcache1))[pageno0] ;(pageno0 ∈ content0 ↔ pageno0 ∈ content) ∧ content0[pageno0] = content[pageno0] ) ⊦ content[pageno] = (content ⊕ mkcontent(m, pcache1))[pageno], datakey(m, pageno) ∈ pcache1, (pageno ∈ content → pageno ∈ content ⊕ mkcontent(m, pcache1)) ∧ content[pageno] = (content ⊕ mkcontent(m, pcache1))[pageno]

Rule argument

fma: content[pageno] = (content ⊕ mkcontent(m, pcache1))[pageno]

Additional information

Used simplifier rules: ⊦ ¬ n ∈ content → content[n] = (∅)[n]; (s)% ⊦ n ∈ content0 ⊕ content1 ↔ n ∈ content0 ∨ n ∈ content1; (ws) Used formulas: content[pageno] = (content ⊕ mkcontent(m, pcache1))[pageno]