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Proof step 37 from proof refine-write_inode (previous step)

cache_dirs[m] = mkdir(m0, md0, # links(m, cache_dirs), m3, entries), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = ESUCCESS, 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_icache, m ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪icache_set#(cache_icache[m].inode.meta:= md, false; err, cache_icache)⟫ ⟨cache_dirs0 := cache_dirs; afs_write_inode#(mkinode(m, md, true, # links(m, cache_dirs), m3, m0); err0, cache_dirs, afs_files; afs_asynced)⟩ ( cache_dirs = cache_dirs0[m, cache_dirs0[m].meta:= md] ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced0) ∧ err = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 38:
cache_dirs[m] = mkdir(m0, md0, # links(m, cache_dirs), m3, entries), cache_icache[m] = mkientry(boolvar, inode), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = ESUCCESS, 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_dirs, m ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪icache_set#(inode.meta:= md, false; err, cache_icache)⟫ ⟨cache_dirs0 := cache_dirs; afs_write_inode#(mkinode(m, md, true, # links(m, cache_dirs), m3, m0); err0, cache_dirs, afs_files; afs_asynced)⟩ ( cache_dirs = cache_dirs0[m, cache_dirs0[m].meta:= md] ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced0) ∧ err = err0)

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