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Proof step 239 from proof fsync-pages-overwrite (previous step)

files[m].nlink = # links(m, dirs), files0[m] = mkfile(files[m].size, files[m].meta, # links(m, dirs), content), afs-cons(dirs, files), afs-cons(dirs, files0), pcache-cons(pcache, dirs, files), pcache-cons(pcache1, dirs, files0), m ∈ files0, m ∈ files, m2 ≤ n * VFS_PAGE_SIZE, ∀ pageno. (pageno < n ⊃ (pageno ∈ files[m].content ↔ pageno ∈ content ⊕ mkcontent(m, pcache1)) ∧ files[m].content[pageno] = (content ⊕ mkcontent(m, pcache1))[pageno] ;(pageno ∈ files[m].content ↔ pageno ∈ content) ∧ files[m].content[pageno] = content[pageno] ), ∀ key. (key ∈ pcache ↔ key ∈ pcache1) ∧ pcache[key].page = pcache1[key].page ∧ (pcache[key].dirty → pcache1[key].dirty) ⊦ files[m].content:= (files[m].content upto m2) = mkfile(files[m].size, files[m].meta, # links(m, dirs), (content ⊕ mkcontent(m, pcache1)) upto m2)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 240:
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)

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files[m], m0, md, m1, content0]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files[m], m0, md, m1, content0