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Proof step 42 from proof refine-write_inode (previous step)

cache_dirs[m] = mkdir(m0, md0, # links(m, cache_dirs), m3, entries), cache_icache[m] = mkientry(boolvar, inode0), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_dirs0 = cache_dirs, 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) ⊦ ⟨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[inode0.ino, mkientry(false, inode0.meta:= md)] ∧ (afs_asynced ↔ asynced0) ∧ ESUCCESS = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 43:
cache_icache[m] = mkientry(boolvar, inode0), cache_dirs[m] = mkdir(m0, md0, # links(m, cache_dirs), m3, entries), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_dirs0 = cache_dirs, inode0 = mkinode(m1, md1, boolvar0, m2, m4, m5), 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) ⊦ ⟨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[m1, mkientry(false, inode0.meta:= md)] ∧ (afs_asynced ↔ asynced0) ∧ ESUCCESS = err0)

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [inode0, m1, md1, boolvar0, m2, m4, m5]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: inode0, m1, md1, boolvar0, m2, m4, m5