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Proof step 212 from proof fsync-pages-overwrite (previous step)

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, buf0), content0[pageno] = content[pageno], pcache1[datakey(m, pageno)] = mkpentry(boolvar, buf0), 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) ∈ pcache1, 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] ) ⊦ pageno ∈ content ∧ content[pageno] = buf0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 213:
⊦ pcache-cons(pcache, dirs, files) ↔ (∀ key. key ∈ pcache → key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs, files) ∧ (¬ pcache[key].dirty → key.part ∈ files[key.ino].content ∧ pcache[key].page = files[key.ino].content[key.part]))
Proof step 214:
pageno ∈ content0 ↔ pageno ∈ content, pcache1[datakey(m, pageno)] = mkpentry(boolvar, buf0), content0[pageno] = content[pageno], pcache[datakey(m, pageno)] = mkpentry(false, buf0), 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(pcache1, dirs, files0), m ∈ files, m ∈ files0, datakey(m, pageno) ∈ pcache, datakey(m, pageno) ∈ pcache1, ∀ 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), ∀ key. key ∈ pcache → key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs, files) ∧ (¬ pcache[key].dirty → key.part ∈ files[key.ino].content ∧ pcache[key].page = files[key.ino].content[key.part]) ⊦ pageno ∈ content ∧ content[pageno] = buf0

Rule argument

spec: cache-base name: pcache-cons seq: ⊦ pcache-cons(pcache, dirs, files) ↔ (∀ key. key ∈ pcache → key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs, files) ∧ ( ¬ pcache[key].dirty → key.part ∈ files[key.ino].content ∧ pcache[key].page = files[key.ino].content[key.part])) subst: [files, dirs, pcache] → [files, dirs, pcache] flags: <all paths>

Additional information

Used terms: files, dirs, pcache