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Proof step 69 from proof fsync-pages-keep-abs (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 70:
⊦ files = files0 ↔ (∀ ino. (ino ∈ files ↔ ino ∈ files0) ∧ (ino ∈ files → files[ino] = files0[ino]))
Proof step 71:
# 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, ∀ 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[datakey(m, n), mkpentry(false, buf)]) ⊕ icache)[ino])

Rule argument

spec: heap, inst: file-heap name: ext seq: ⊦ files = files0 ↔ (∀ ino. (ino ∈ files ↔ ino ∈ files0) ∧ (ino ∈ files → files[ino] = files0[ino])) subst: [files0, files] → [(files1 ⊕ pcache0) ⊕ icache, (files0 ⊕ pcache) ⊕ icache] flags: <all paths>

Additional information

Used terms: (files1 ⊕ pcache0) ⊕ icache, (files0 ⊕ pcache) ⊕ icache