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Proof step 36 from proof recovery (previous step)

afs-cons(cache_dirs0, (cache_files0 ⊕ cache_pcache0) ⊕ cache_icache0), afs-cons(cache_dirs0, cache_files0), dcache-cons(cache_dcache0, cache_dirs0, cache_files0), icache-cons(cache_icache0, cache_dirs0, cache_files0), pcache-cons(cache_pcache0, cache_dirs0, cache_files0), synced(cache_dirs0, cache_icache0, cache_pcache0), ino ∈ cache_dirs0, cache_sync0 → synced(cache_files0, cache_icache0, cache_pcache0) ⊦ ¬ ino ∈ orphans(cache_dirs0, (cache_files0 ⊕ cache_pcache0) ⊕ cache_icache0) ↔ ¬ ino ∈ orphans(cache_dirs0, cache_files0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 37:
⊦ ino ∈ orphans(dirs, files) ↔ valid-ino(ino, dirs, files) ∧ links(ino, dirs) = ∅ ∧ ino ≠ ROOT_INO
Proof step 38:
afs-cons(cache_dirs0, cache_files0), afs-cons(cache_dirs0, (cache_files0 ⊕ cache_pcache0) ⊕ cache_icache0), dcache-cons(cache_dcache0, cache_dirs0, cache_files0), icache-cons(cache_icache0, cache_dirs0, cache_files0), pcache-cons(cache_pcache0, cache_dirs0, cache_files0), synced(cache_dirs0, cache_icache0, cache_pcache0), ino ∈ cache_dirs0, cache_sync0 → synced(cache_files0, cache_icache0, cache_pcache0) ⊦ ¬(valid-ino(ino, cache_dirs0, (cache_files0 ⊕ cache_pcache0) ⊕ cache_icache0) ∧ links(ino, cache_dirs0) = ∅ ∧ ino ≠ ROOT_INO) ↔ ¬ ino ∈ orphans(cache_dirs0, cache_files0)

Rule argument

spec: afs-base name: orphans seq: ⊦ ino ∈ orphans(dirs, files) ↔ valid-ino(ino, dirs, files) ∧ links(ino, dirs) = ∅ ∧ ino ≠ ROOT_INO subst: [files, dirs, ino] → [(cache_files0 ⊕ cache_pcache0) ⊕ cache_icache0, cache_dirs0, ino] flags: <all paths>

Additional information

Used terms: (cache_files0 ⊕ cache_pcache0) ⊕ cache_icache0, cache_dirs0, ino