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Proof step 465 from proof fsync-pages-keep-abs (previous step)

# buf = VFS_PAGE_SIZE, files0[m] = mkfile(m0, md, m1, content), pcache[datakey(m, n)] = mkpentry(true, buf), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), datakey(m, n) ∈ pcache, m ∈ files0, ⌊err0⌋ , ∀ ino. (ino ∈ (files0 ⊕ pcache) ⊕ icache ↔ ino ∈ (files1 ⊕ pcache0) ⊕ icache) ∧ (ino ∈ (files0 ⊕ pcache) ⊕ icache → ((files0 ⊕ pcache) ⊕ icache)[ino] = ((files1 ⊕ pcache0) ⊕ icache)[ino]) ⊦ (ino ∈ files1 ↔ ino ∈ files0) ∧ (ino ∈ files1 → ((files1 ⊕ pcache0) ⊕ icache)[ino] = ((files0[m, mkfile(m0, md, m1, content[n, buf])] ⊕ pcache) ⊕ icache)[ino])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 466:
# buf = VFS_PAGE_SIZE, pcache[datakey(m, n)] = mkpentry(true, buf), files0[m] = mkfile(m0, md, m1, content), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), m ∈ files0, datakey(m, n) ∈ pcache, ⌊err0⌋ , ∀ ino0. (ino0 ∈ files0 ↔ ino0 ∈ files1) ∧ (ino0 ∈ files0 → ((files0 ⊕ pcache) ⊕ icache)[ino0] = ((files1 ⊕ pcache0) ⊕ icache)[ino0]) ⊦ (ino ∈ files1 ↔ ino ∈ files0) ∧ (ino ∈ files1 → ((files1 ⊕ pcache0) ⊕ icache)[ino] = ((files0[m, mkfile(m0, md, m1, content[n, buf])] ⊕ pcache) ⊕ icache)[ino])

Rule argument

Additional information

Used simplifier rules: ⊦ ino ∈ files ⊕ pcache ↔ ino ∈ files; (s)% ⊦ ino ∈ files ⊕ icache ↔ ino ∈ files; (s)