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Proof step 371 from proof inv-write_inode (previous step)

afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), afs-cons(dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), synced(files, icache, pcache), m ∈ files ⊦ m ∈ icache, ∀ key. key ∈ pcache → key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ valid-file-ino(key.ino, dirs, files[m, (files[m].meta:= md).size:= m2]) ∧ ( ¬ pcache[key].dirty → key.part ∈ files[m, (files[m].meta:= md).size:= m2][key.ino].content ∧ pcache[key].page = files[m, (files[m].meta:= md).size:= m2][key.ino].content[key.part])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 372:
afs-cons(dirs, files), afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), pcache-cons(pcache, dirs, files), synced(files, icache, pcache), synced(dirs, icache, pcache), key ∈ pcache, m ∈ files ⊦ m ∈ icache, key.data? ∧ # pcache[key].page = VFS_PAGE_SIZE ∧ key.ino ∈ files ∧ ( ¬ pcache[key].dirty → key.part ∈ (key.ino = m ⊃ (files[key.ino].meta:= md).size:= m2;files[key.ino]).content ∧ pcache[key].page = (key.ino = m ⊃ (files[key.ino].meta:= md).size:= m2;files[key.ino]).content[key.part])

Rule argument

Additional information

Used simplifier rules: ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)