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Proof step 244 from proof fsync-pages-overwrite (previous step)

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] ) ⊦ content0 upto m2 = (content ⊕ mkcontent(m, pcache1)) upto m2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 245:
⊦ content = content0 ↔ (∀ n. (n ∈ content ↔ n ∈ content0) ∧ (n ∈ content → content[n] = content0[n]))
Proof step 246:
files[m] = mkfile(m0, md, # links(m, dirs), content0), files0[m] = mkfile(m0, md, # 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 ∈ 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. (n ∈ content0 upto m2 ↔ n ∈ (content ⊕ mkcontent(m, pcache1)) upto m2) ∧ (n ∈ content0 upto m2 → (content0 upto m2)[n] = ((content ⊕ mkcontent(m, pcache1)) upto m2)[n])

Rule argument

spec: store, inst: file-content name: k-Extension seq: ⊦ content = content0 ↔ (∀ n. (n ∈ content ↔ n ∈ content0) ∧ (n ∈ content → content[n] = content0[n])) subst: [content0, content] → [(content ⊕ mkcontent(m, pcache1)) upto m2, content0 upto m2] flags: <all paths>

Additional information

Used terms: (content ⊕ mkcontent(m, pcache1)) upto m2, content0 upto m2