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Proof step 435 from proof fsync-pages-keep-abs (previous step)

# buf = VFS_PAGE_SIZE, files1[m] = mkfile(m9, md2, m10, content1), content0[n0] = content1[n0], files0[m] = mkfile(m7, md1, m8, content0), pcache[datakey(m, n)] = mkpentry(true, buf), icache[m] = mkientry(boolvar, mkinode(m3, md0, false, m4, m5, m6)), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), n0 ∈ content0, n0 ∈ content1 ⊕ mkcontent(m, pcache0), m ∈ files0, m ∈ files1, datakey(m, n) ∈ pcache, m ∈ icache, n0 ∈ content1, ∀ ino0. (ino0 ∈ files0 ↔ ino0 ∈ files1) ∧ (ino0 ∈ files0 → ((files0 ⊕ pcache) ⊕ icache)[ino0] = ((files1 ⊕ pcache0) ⊕ icache)[ino0]) ⊦ (content1 ⊕ mkcontent(m, pcache0))[n0] = (content0[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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 436:
⊦ n ∈ content1 → (content0 ⊕ content1)[n] = content1[n]
Proof step 437:
# buf = VFS_PAGE_SIZE, icache[m] = mkientry(boolvar, mkinode(m3, md0, false, m4, m5, m6)), pcache[datakey(m, n)] = mkpentry(true, buf), files0[m] = mkfile(m7, md1, m8, content0), content0[n0] = content1[n0], files1[m] = mkfile(m9, md2, m10, content1), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), n0 ∈ content1, m ∈ icache, datakey(m, n) ∈ pcache, m ∈ files1, m ∈ files0, n0 ∈ content1 ⊕ mkcontent(m, pcache0), n0 ∈ content0, ∀ ino0. (ino0 ∈ files0 ↔ ino0 ∈ files1) ∧ (ino0 ∈ files0 → ((files0 ⊕ pcache) ⊕ icache)[ino0] = ((files1 ⊕ pcache0) ⊕ icache)[ino0]) ⊦ (content1 ⊕ mkcontent(m, pcache0))[n0] = (content0[n, buf] ⊕ mkcontent(m, pcache[datakey(m, n), mkpentry(false, buf)]))[n0], datakey(m, n0) = datakey(m, n), datakey(m, n0) ∈ pcache0, datakey(m, n0) ∈ pcache, n0 ∈ mkcontent(m, pcache[datakey(m, n), mkpentry(false, buf)])

Rule argument

spec: cache-base name: at-overwrite-content-new seq: ⊦ n ∈ content1 → (content0 ⊕ content1)[n] = content1[n] subst: [n, content1, content0] → [n0, mkcontent(m, pcache[datakey(m, n), mkpentry(false, buf)]), content0[n, buf]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ mkcontent(ino, pcache)[n] = pcache[datakey(ino, n)].page; (s)% ⊦ key ≠ key0 → pcache[key0, pe][key] = pcache[key]; (s)% ⊦ ¬ key ∈ pcache → pcache[key] = (∅)[key]; (s)% ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache; (s)% ⊦ key ≠ key0 → (key ∈ pcache[key0, pe] ↔ key ∈ pcache); (s) Used terms: n0, mkcontent(m, pcache[datakey(m, n), mkpentry(false, buf)]), content0[n, buf]