[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 241 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] ) ⊦ mkfile(m0, md, # links(m, dirs), content0 upto m2) = mkfile(m0, md, # links(m, dirs), (content ⊕ mkcontent(m, pcache1)) upto m2)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 242:
⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0
Proof step 243:
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) ⊦ m0 = m0 ∧ md = md ∧ # links(m, dirs) = # links(m, dirs) ∧ content0 upto m2 = (content ⊕ mkcontent(m, pcache1)) upto m2

Rule argument

spec: abstract-file name: inj seq: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0 subst: [content0, m2, md0, m1, content, m0, md, m] → [(content ⊕ mkcontent(m, pcache1)) upto m2, # links(m, dirs), md, m0, content0 upto m2, # links(m, dirs), md, m0] flags: <all paths>

Additional information

Used terms: (content ⊕ mkcontent(m, pcache1)) upto m2, # links(m, dirs), md, m0, content0 upto m2, # links(m, dirs), md, m0