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Proof step 43 from proof refine-iget (previous step)

cache_icache[m] = mkientry(false, mkinode(m, md, boolvar0, m0, m1, m2)), mkinode(m, md, boolvar0, m0, m1, m2) = (m ∈ cache_dirs ⊃ mkinode(m, cache_dirs[m].meta, true, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, cache_dirs[m].size) ;mkinode(m, cache_files[m].meta, false, cache_files[m].nlink, 0, cache_files[m].size) ), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), m ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ ino0. ino0 ∈ cache_icache → cache_icache[ino0].inode.ino = ino0 ∧ (cache_icache[ino0].dirty ⊃ cache_icache[ino0].inode.ino ∈ cache_files ∧ cache_icache[ino0].inode.nlink = cache_files[cache_icache[ino0].inode.ino].nlink ∧ cache_icache[ino0].inode.nsubdirs = 0 ∧ ¬ cache_icache[ino0].inode.directory ; (ino0 ∈ cache_dirs ∨ ino0 ∈ cache_files) ∧ cache_icache[ino0].inode = (cache_icache[ino0].inode.ino ∈ cache_dirs ⊃ mkinode (cache_icache[ino0].inode.ino, cache_dirs[cache_icache[ino0].inode.ino].meta, true, cache_dirs[cache_icache[ino0].inode.ino].nlink, cache_dirs[cache_icache[ino0].inode.ino].nsubdirs, cache_dirs[cache_icache[ino0].inode.ino].size) ;mkinode (cache_icache[ino0].inode.ino, cache_files[cache_icache[ino0].inode.ino].meta, false, cache_files[cache_icache[ino0].inode.ino].nlink, 0, cache_files[cache_icache[ino0].inode.ino].size) ) ), m ∈ cache_dirs ∨ m ∈ cache_files ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0⟩ (mkinode(m, md, boolvar0, m0, m1, m2) = inode ∧ ESUCCESS = err), mkinode(m, md, boolvar0, m0, m1, m2) = mkinode (m, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m].meta, false, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m].nlink, 0, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m].size), m ∈ cache_dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 44:
cache_icache[m] = mkientry(false, mkinode(m, cache_files[m].meta, false, cache_files[m].nlink, 0, cache_files[m].size)), mkinode(m, cache_files[m].meta, false, cache_files[m].nlink, 0, cache_files[m].size) ≠ mkinode (m, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m].meta, false, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m].nlink, 0, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m].size), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, 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, ¬ m ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), ∀ ino0. ino0 ∈ cache_icache → cache_icache[ino0].inode.ino = ino0 ∧ (cache_icache[ino0].dirty ⊃ cache_icache[ino0].inode.ino ∈ cache_files ∧ cache_icache[ino0].inode.nlink = cache_files[cache_icache[ino0].inode.ino].nlink ∧ cache_icache[ino0].inode.nsubdirs = 0 ∧ ¬ cache_icache[ino0].inode.directory ; (ino0 ∈ cache_dirs ∨ ino0 ∈ cache_files) ∧ cache_icache[ino0].inode = (cache_icache[ino0].inode.ino ∈ cache_dirs ⊃ mkinode (cache_icache[ino0].inode.ino, cache_dirs[cache_icache[ino0].inode.ino].meta, true, cache_dirs[cache_icache[ino0].inode.ino].nlink, cache_dirs[cache_icache[ino0].inode.ino].nsubdirs, cache_dirs[cache_icache[ino0].inode.ino].size) ;mkinode (cache_icache[ino0].inode.ino, cache_files[cache_icache[ino0].inode.ino].meta, false, cache_files[cache_icache[ino0].inode.ino].nlink, 0, cache_files[cache_icache[ino0].inode.ino].size) ) ) ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0⟩ (mkinode(m, cache_files[m].meta, false, cache_files[m].nlink, 0, cache_files[m].size) = inode ∧ ESUCCESS = err)

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2) = mkinode(m3, md0, boolvar0, m4, m5, m6) ↔ m = m3 ∧ md = md0 ∧ (boolvar ↔ boolvar0) ∧ m0 = m4 ∧ m1 = m5 ∧ m2 = m6; (ws)