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Proof step 359 from proof inv-write_inode (previous step)

afs-cons(dirs, files), afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), synced(files, icache, pcache), m ∈ files ⊦ m ∈ icache, ∀ ino. (ino ∈ files → synced(ino, icache, pcache)) → ino ∈ files[m, (files[m].meta:= md).size:= m2] → synced(ino, icache, pcache)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 360:
pcache[datakey(ino, n)].dirty, afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), afs-cons(dirs, files), synced(files, icache, pcache), m ∈ files, ino ∈ files, datakey(ino, n) ∈ pcache, ino ∈ icache → ¬ icache[ino].dirty, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty ⊦ m ∈ icache

Rule argument

Additional information

Used simplifier rules: ⊦ 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)