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Proof step 240 from proof fsync-pages-overwrite (previous step)

files0[m] = mkfile(m0, md, # links(m, dirs), content), files[m] = mkfile(m0, md, m1, content0), m1 = # links(m, dirs), afs-cons(dirs, files0), afs-cons(dirs, files), pcache-cons(pcache1, dirs, files0), pcache-cons(pcache, dirs, files), m ∈ files, m ∈ files0, m2 ≤ n * VFS_PAGE_SIZE, ∀ 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] ) ⊦ files[m].content:= (content0 upto m2) = mkfile(m0, md, # links(m, dirs), (content ⊕ mkcontent(m, pcache1)) upto m2)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 241:
files0[m] = mkfile(m0, md, # links(m, dirs), content), files[m] = mkfile(m0, md, # links(m, dirs), content0), afs-cons(dirs, files0), afs-cons(dirs, files), pcache-cons(pcache1, dirs, files0), pcache-cons(pcache, dirs, files), m ∈ files, m ∈ files0, m2 ≤ n * VFS_PAGE_SIZE, ∀ 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] ) ⊦ mkfile(m0, md, # links(m, dirs), content0 upto m2) = mkfile(m0, md, # links(m, dirs), (content ⊕ mkcontent(m, pcache1)) upto m2)

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).content:= content0 = mkfile(m, md, m0, content0); (s)