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Proof step 31 from proof inv-recover (previous step)

afs-cons(dirs0, files1), dcache-cons(dcache1, dirs0, files1), synced(dirs0, icache1, pcache1), asynced4 → synced(files1, icache1, pcache1) ⊦ dcache-cons(∅, dirs0 \ orphans(dirs0, files1), files1 \ orphans(dirs0, files1))

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 32:
⊦ dcache-cons(dcache, dirs, files) ↔ (∀ key. key ∈ dcache → key.dentry? ∧ key.name = dcache[key].name ∧ valid-dentry(key.ino, dcache[key], dirs, files))

Rule argument

spec: cache-base name: dcache-cons seq: ⊦ dcache-cons(dcache, dirs, files) ↔ (∀ key. key ∈ dcache → key.dentry? ∧ key.name = dcache[key].name ∧ valid-dentry(key.ino, dcache[key], dirs, files)) subst: [dcache, dirs, files] → [∅, dirs0 \ orphans(dirs0, files1), files1 \ orphans(dirs0, files1)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ¬ key ∈ ∅; (s) Used terms: ∅, dirs0 \ orphans(dirs0, files1), files1 \ orphans(dirs0, files1)