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Proof step 412 from proof refine-write_inode (previous step)

cache_icache[m].inode = mkinode(m0, md, false, m1, m3, m4), cache_files[m] = mkfile(m2, md0, # links(m, cache_dirs), content0), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_files, m ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ m1 = # links(m, cache_dirs)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 413:
cache_files[m] = mkfile(m2, md0, # links(m, cache_dirs), content0), cache_icache[m] = mkientry(boolvar, inode), inode = mkinode(m0, md, false, m1, m3, m4), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_icache, m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ m1 = # links(m, cache_dirs)

Rule argument

spec: icache-entry name: elim seq: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode) subst: [ie, boolvar, inode] → [cache_icache[m], boolvar, inode]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: cache_icache[m], boolvar, inode