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Proof step 477 from proof fsync-pages-keep-abs (previous step)

# buf = VFS_PAGE_SIZE, icache[ino] = mkientry(boolvar0, mkinode(m3, md0, boolvar, m4, m5, m6)), pcache[datakey(m, n)] = mkpentry(true, buf), files0[m] = mkfile(m0, md, m1, content), ((files0 ⊕ pcache) ⊕ icache)[ino] = ((files1 ⊕ pcache0) ⊕ icache)[ino], n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), m ∈ files0, datakey(m, n) ∈ pcache, ino ∈ files1, ino ∈ files0, ⌊err0⌋ ⊦ ((files1 ⊕ pcache0) ⊕ icache)[ino] = ((files0[m, mkfile(m0, md, m1, content[n, buf])] ⊕ pcache) ⊕ icache)[ino], ino ∈ icache, ino ∈ icache ∧ boolvar, ino ∈ icache ∧ ¬ boolvar

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 478:
# buf = VFS_PAGE_SIZE, files0[ino].meta = files1[ino].meta, files0[ino].nlink = files1[ino].nlink, files0[ino].size = files1[ino].size, files0[m] = mkfile(m0, md, m1, content), pcache[datakey(m, n)] = mkpentry(true, buf), (∅)[ino] = mkientry(boolvar0, mkinode(m3, md0, boolvar, m4, m5, m6)), files0[ino].content ⊕ mkcontent(ino, pcache) = files1[ino].content ⊕ mkcontent(ino, pcache0), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), ino ∈ files0, ino ∈ files1, datakey(m, n) ∈ pcache, m ∈ files0, ⌊err0⌋ ⊦ mkfile(files1[ino].size, files1[ino].meta, files1[ino].nlink, files1[ino].content ⊕ mkcontent(ino, pcache0)) = mkfile ((ino = m ⊃ mkfile(m0, md, m1, content[n, buf]);files0[ino]).size, (ino = m ⊃ mkfile(m0, md, m1, content[n, buf]);files0[ino]).meta, (ino = m ⊃ mkfile(m0, md, m1, content[n, buf]);files0[ino]).nlink, (ino = m ⊃ mkfile(m0, md, m1, content[n, buf]);files0[ino]).content ⊕ mkcontent(ino, pcache)), ino ∈ icache

Rule argument

Additional information

Used simplifier rules: ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ ¬ ino ∈ icache → icache[ino] = (∅)[ino]; (s)%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)%⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)); (s)% ⊦ ¬ ino ∈ icache → (files ⊕ icache)[ino] = files[ino]; (s)