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Proof step 134 from proof inv-evict (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 135:
files[m] = mkfile(m0, md, m1, content), err = ESUCCESS, m1 = 0, afs-cons(dirs, files), afs-cons(dirs, files -- m), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ files, asynced1 → synced(files, icache, pcache) ⊦ ⟪icache_delete#(m; err, icache); pcache_evict#(m; err, pcache)⟫ ( icache-cons(icache, dirs, files -- m) ∧ dcache-cons(dcache, dirs, files -- m) ∧ pcache-cons(pcache, dirs, files -- m) ∧ synced(dirs, icache, pcache) ∧ (asynced1 → synced(files -- m, icache, pcache))), m = ROOT_INO, m ∈ dirs

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files[m], m0, md, m1, content]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files[m], m0, md, m1, content