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Proof step 22 from proof inv-evict (previous step)

dirs[m].nlink = 0, err = ESUCCESS, m ≠ ROOT_INO, afs-cons(dirs -- m, files), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ dirs, asynced1 → synced(files, icache, pcache) ⊦ ⟪icache_delete#(m; err, icache); skip⟫ ( icache-cons(icache, dirs -- m, files) ∧ dcache-cons(dcache, dirs -- m, files) ∧ pcache-cons(pcache, dirs -- m, files) ∧ synced(dirs -- m, icache, pcache) ∧ (asynced1 → synced(files, icache, pcache)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 23:
dirs[m] = mkdir(m0, md, m1, m2, entries), err = ESUCCESS, m1 = 0, afs-cons(dirs, files), afs-cons(dirs -- m, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ dirs, asynced1 → synced(files, icache, pcache) ⊦ ⟪icache_delete#(m; err, icache); skip⟫ ( icache-cons(icache, dirs -- m, files) ∧ dcache-cons(dcache, dirs -- m, files) ∧ pcache-cons(pcache, dirs -- m, files) ∧ synced(dirs -- m, icache, pcache) ∧ (asynced1 → synced(files, icache, pcache))), m = ROOT_INO

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [dirs[m], m0, md, m1, m2, entries]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: dirs[m], m0, md, m1, m2, entries