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Proof step 72 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), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), m ∈ files0, datakey(m, n) ∈ pcache, ∀ 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[datakey(m, n), mkpentry(false, buf)]) ⊕ icache)[ino])

User applied rule all left

And obtained the following new goals

Proof step 73:
# buf = VFS_PAGE_SIZE, ino ∈ files0 ↔ ino ∈ files1, 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 ∈ files0 → ((files0 ⊕ pcache) ⊕ icache)[ino] = ((files1 ⊕ pcache0) ⊕ icache)[ino], ∀ 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[datakey(m, n), mkpentry(false, buf)]) ⊕ icache)[ino])

Rule argument

pos: left 8 terms: ino abort: F discard: F computed: T

Additional information

Used terms: ino