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Proof step 296 from proof inv-truncate-buff-none-uncached (previous step)

files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), afs-cons(dirs, files0), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), synced(files0, icache, pcache0), m0 ∈ files0, ∀ key. key ∈ pcache0 → key.data? ⊦ datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, ∀ ino. (ino ∈ files0 → synced(ino, icache, pcache0)) → ino ∈ files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))] → synced(ino, icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))], truncate(m0, min(m5, m2), pcache0)), m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 297:
files0[m0] = mkfile(m1, md1, # links(m0, dirs), content0), afs-cons(dirs, files0[m0, mkfile(m5, md0, # links(m0, dirs), content0 upto min(m5, m2))]), afs-cons(dirs, files0), synced(files0, icache, pcache0), m0 ∈ files0, ino ∈ files0, ino ∈ icache → ¬ icache[ino].dirty, ∀ key. key ∈ pcache0 → key.data?, ∀ n. datakey(ino, n) ∈ pcache0 → ¬ pcache0[datakey(ino, n)].dirty ⊦ datakey(m0, m2 / VFS_PAGE_SIZE) ∈ pcache0, m2 ≤ m5 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ m2 / VFS_PAGE_SIZE ∈ content0, ( ino ∈ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))] → ¬ icache[m0, mkientry(false, mkinode(m0, md0, false, # links(m0, dirs), 0, m5))][ino].dirty) ∧ (datakey(ino, n) ∈ pcache0 ∧ (n * VFS_PAGE_SIZE < min(m5, m2) ∨ m0 ≠ ino) → ¬ truncate(m0, min(m5, m2), pcache0)[datakey(ino, n)].dirty)

Rule argument

Additional information

Used simplifier rules: ⊦ datakey(m, m0).ino = m; (s)% ⊦ datakey(m, m0).part = m0; (s)% ⊦ datakey(m, m0).data?; (s)%⊦ key ∈ truncate(ino, size, pcache) ↔ key.data? ∧ key ∈ pcache ∧ (key.part * VFS_PAGE_SIZE < size ∨ ino ≠ key.ino); (s)%⊦ synced(ino, icache, pcache) ↔ (ino ∈ icache → ¬ icache[ino].dirty) ∧ (∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty); (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)