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Proof step 23 from proof refine-write_inode (previous step)

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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
cache_dirs[m] = mkdir(m0, md0, # links(m, cache_dirs), m3, entries), ¬ asynced2, err = ESUCCESS, inode = mkinode(m, md, true, # links(m, cache_dirs), 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, # links(m, cache_dirs), 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

Additional information

Used simplifier rules: afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base