[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 186 from proof fsync-pages-keep-abs (previous step)

# buf = VFS_PAGE_SIZE, n0 ∈ content ↔ n0 ∈ content1, pcache[datakey(m, n)] = mkpentry(true, buf), (∅)[m] = mkientry(boolvar0, mkinode(m3, md0, boolvar, m4, m5, m6)), content[n0] = content1[n0], files1[m] = mkfile(m9, md2, m10, content1), files0[m] = mkfile(m9, md2, m10, content), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), n0 ∈ content1 ⊕ mkcontent(m, pcache0), m ∈ files0, m ∈ files1, datakey(m, n) ∈ pcache, ∀ ino0. (ino0 ∈ files0 ↔ ino0 ∈ files1) ∧ (ino0 ∈ files0 → ((files0 ⊕ pcache) ⊕ icache)[ino0] = ((files1 ⊕ pcache0) ⊕ icache)[ino0]) ⊦ (content1 ⊕ mkcontent(m, pcache0))[n0] = (content[n, buf] ⊕ mkcontent(m, pcache[datakey(m, n), mkpentry(false, buf)]))[n0], datakey(m, n0) = datakey(m, n), datakey(m, n0) ∈ pcache, datakey(m, n0) ∈ pcache0, m ∈ icache

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 187:
# buf = VFS_PAGE_SIZE, n0 ∈ content ↔ n0 ∈ content1, files0[m] = mkfile(m9, md2, m10, content), files1[m] = mkfile(m9, md2, m10, content1), content[n0] = content1[n0], (∅)[m] = mkientry(boolvar0, mkinode(m3, md0, boolvar, m4, m5, m6)), pcache[datakey(m, n)] = mkpentry(true, buf), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), datakey(m, n) ∈ pcache, m ∈ files1, m ∈ files0, n0 ∈ content1 ⊕ mkcontent(m, pcache0), n0 ∈ content, ∀ ino0. (ino0 ∈ files0 ↔ ino0 ∈ files1) ∧ (ino0 ∈ files0 → ((files0 ⊕ pcache) ⊕ icache)[ino0] = ((files1 ⊕ pcache0) ⊕ icache)[ino0]) ⊦ (content1 ⊕ mkcontent(m, pcache0))[n0] = (content[n, buf] ⊕ mkcontent(m, pcache[datakey(m, n), mkpentry(false, buf)]))[n0], datakey(m, n0) = datakey(m, n), m ∈ icache, datakey(m, n0) ∈ pcache0, datakey(m, n0) ∈ pcache

Rule argument

fma: n0 ∈ content

Additional information

Used simplifier rules: ⊦ ¬ n ∈ content → content[n] = (∅)[n]; (s)% ⊦ n ∈ content0 ⊕ content1 ↔ n ∈ content0 ∨ n ∈ content1; (ws)% ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache; (s) Used formulas: n0 ∈ content