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Proof step 107 from proof inv-truncate-buff-some (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, truncate(m3, m2, pcache0)[datakey(ino, n)] = mkpentry(boolvar, buf), files0[m3] = mkfile(m1, md1, # links(m3, dirs), content0), icache[ino] = mkientry(boolvar0, inode), icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino] = mkientry(boolvar1, inode0), buf-opt.some?, afs-cons (dirs, files0[m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]), afs-cons(dirs, files0), synced(files0, icache, pcache0), m3 ∈ files0, ino ∈ files0, m2 ≤ m, ino ∈ icache → ¬ boolvar0, ∀ key. key ∈ pcache0 → key.data?, ∀ n. datakey(ino, n) ∈ pcache0 → ¬ pcache0[datakey(ino, n)].dirty ⊦ m2 % VFS_PAGE_SIZE = 0, datakey(ino, n) = datakey(m3, m2 / VFS_PAGE_SIZE), (ino ∈ icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))] → ¬ boolvar1) ∧ (datakey(ino, n) ∈ pcache0 ∧ (n * VFS_PAGE_SIZE < m2 ∨ m3 ≠ ino) → ¬ boolvar), datakey(ino, n).data? ∧ datakey(ino, n) ∈ pcache0 ∧ (datakey(ino, n).part * VFS_PAGE_SIZE < m2 ∨ m3 ≠ datakey(ino, n).ino)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 108:
# buf-opt.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n0 + m2 % VFS_PAGE_SIZE, icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))][ino] = mkientry(true, inode0), icache[ino] = mkientry(false, inode), files0[m3] = mkfile(m1, md1, # links(m3, dirs), content0), truncate(m3, m2, pcache0)[datakey(ino, n)] = mkpentry(boolvar, buf), buf-opt.some?, afs-cons(dirs, files0), afs-cons (dirs, files0[m3, mkfile(m, md, # links(m3, dirs), content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n0)] upto m2)]), synced(files0, icache, pcache0), ino ∈ icache, ino ∈ files0, m3 ∈ files0, ino ∈ icache[m3, mkientry(false, mkinode(m3, md, false, # links(m3, dirs), 0, m))], m2 ≤ m, ∀ n. datakey(ino, n) ∈ pcache0 → ¬ pcache0[datakey(ino, n)].dirty, ∀ key. key ∈ pcache0 → key.data? ⊦ m2 % VFS_PAGE_SIZE = 0, datakey(ino, n) = datakey(m3, m2 / VFS_PAGE_SIZE), datakey(ino, n) ∈ pcache0 ∧ (n * VFS_PAGE_SIZE < m2 ∨ m3 ≠ ino)

Rule argument

Additional information

Used simplifier rules: ⊦ mkientry(boolvar, inode) = mkientry(boolvar0, inode0) ↔ (boolvar ↔ boolvar0) ∧ inode = inode0; (ws)% ⊦ ino = ino0 → icache[ino0, ie][ino] = ie; (s)% ⊦ ino ∈ icache[ino0, ie] ↔ ino = ino0 ∨ ino ∈ icache; (ws)% ⊦ ¬ ino ∈ icache → icache[ino] = (∅)[ino]; (s)% ⊦ datakey(m, m0).ino = m; (s)% ⊦ datakey(m, m0).part = m0; (s)% ⊦ datakey(m, m0).data?; (s)