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Proof step 81 from proof fsync-pages-keep-abs (previous step)

# buf = VFS_PAGE_SIZE, ((files0 ⊕ pcache) ⊕ icache)[ino] = ((files1 ⊕ pcache0) ⊕ icache)[ino], files0[m] = mkfile(m0, md, m1, content), pcache[datakey(m, n)] = mkpentry(true, buf), icache[ino] = mkientry(boolvar0, mkinode(m3, md0, boolvar, m4, m5, m6)), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), ino ∈ files0, ino ∈ files1, datakey(m, n) ∈ pcache, m ∈ files0, ∀ ino0. (ino0 ∈ files0 ↔ ino0 ∈ files1) ∧ (ino0 ∈ files0 → ((files0 ⊕ pcache) ⊕ icache)[ino0] = ((files1 ⊕ pcache0) ⊕ icache)[ino0]) ⊦ ((files1 ⊕ pcache0) ⊕ icache)[ino] = ((files0[m, mkfile(m0, md, m1, content[n, buf])] ⊕ pcache[datakey(m, n), mkpentry(false, buf)]) ⊕ icache)[ino], ino ∈ icache ∧ ¬ boolvar, ino ∈ icache ∧ icache[ino].inode.directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 82:
# buf = VFS_PAGE_SIZE, ((files0 ⊕ pcache) ⊕ icache)[ino] = ((files1 ⊕ pcache0) ⊕ icache)[ino], files0[m] = mkfile(m0, md, m1, content), pcache[datakey(m, n)] = mkpentry(true, buf), icache[ino] = mkientry(boolvar0, mkinode(m3, md0, boolvar, m4, m5, m6)), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), ino ∈ files0, ino ∈ files1, datakey(m, n) ∈ pcache, m ∈ files0, ∀ ino0. (ino0 ∈ files0 ↔ ino0 ∈ files1) ∧ (ino0 ∈ files0 → ((files0 ⊕ pcache) ⊕ icache)[ino0] = ((files1 ⊕ pcache0) ⊕ icache)[ino0]) ⊦ ((files1 ⊕ pcache0) ⊕ icache)[ino] = ((files0[m, mkfile(m0, md, m1, content[n, buf])] ⊕ pcache[datakey(m, n), mkpentry(false, buf)]) ⊕ icache)[ino], ino ∈ icache ∧ ¬ boolvar, ino ∈ icache ∧ boolvar

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkientry(boolvar, inode).inode = inode; (s)