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Proof step 22 from proof refine-write_inode (previous step)

¬ asynced2, err = ESUCCESS, inode = mkinode(m, md, true, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, cache_dirs[m].size), 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_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪icache_get#(m, cache_icache; asynced2, inode, err); afs_files := (cache_files ⊕ cache_pcache) ⊕ cache_icache; boolvar := true; m2 := cache_dirs[m].size; if err = ESUCCESS ∧ asynced2 then {inode.meta := md; if ¬ boolvar then inode.size := m2; icache_set#(inode, false; err, cache_icache)} else if false then err := EFAIL⟫ ⟨cache_dirs0 := cache_dirs; afs_write_inode#(mkinode(m, md, boolvar, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, m2); 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 ↔ asynced) ∧ err = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 23:
cache_dirs[m] = mkdir(m0, md0, m1, m3, entries), ¬ asynced2, err = ESUCCESS, inode = mkinode(m, md, true, m1, m3, m0), 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, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪icache_get#(m, cache_icache; asynced2, inode, err); afs_files := (cache_files ⊕ cache_pcache) ⊕ cache_icache; boolvar := true; m2 := m0; if err = ESUCCESS ∧ asynced2 then {inode.meta := md; if ¬ boolvar then inode.size := m2; icache_set#(inode, false; err, cache_icache)} else if false then err := EFAIL⟫ ⟨cache_dirs0 := cache_dirs; afs_write_inode#(mkinode(m, md, boolvar, m1, m3, m2); 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 ↔ asynced) ∧ err = err0)

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] → [cache_dirs[m], m0, md0, m1, m3, 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: cache_dirs[m], m0, md0, m1, m3, entries