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Proof step 31 from proof refine-iget (previous step)

cache_icache[inode1.ino] = mkientry(boolvar, inode1), inode1 ≠ (inode1.ino ∈ cache_dirs ⊃ mkinode(inode1.ino, cache_dirs[inode1.ino].meta, true, cache_dirs[inode1.ino].nlink, cache_dirs[inode1.ino].nsubdirs, cache_dirs[inode1.ino].size) ;mkinode (inode1.ino, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[inode1.ino].meta, false, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[inode1.ino].nlink, 0, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[inode1.ino].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), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), inode1.ino ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache), (boolvar ⊃ inode1.ino ∈ cache_files ∧ inode1.nlink = cache_files[inode1.ino].nlink ∧ inode1.nsubdirs = 0 ∧ ¬ inode1.directory ; inode1 = (inode1.ino ∈ cache_dirs ⊃ mkinode (inode1.ino, cache_dirs[inode1.ino].meta, true, cache_dirs[inode1.ino].nlink, cache_dirs[inode1.ino].nsubdirs, cache_dirs[inode1.ino].size) ;mkinode(inode1.ino, cache_files[inode1.ino].meta, false, cache_files[inode1.ino].nlink, 0, cache_files[inode1.ino].size) ) ), ∀ 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) ) ), inode1.ino ∈ cache_dirs ∨ inode1.ino ∈ cache_files ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0⟩ (inode1 = inode ∧ ESUCCESS = err)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 32:
cache_icache[m] = mkientry(boolvar, inode1), inode1 = mkinode(m, md, boolvar0, m0, m1, m2), 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), (boolvar ⊃ m ∈ cache_files ∧ m0 = cache_files[m].nlink ∧ m1 = 0 ∧ ¬ boolvar0 ; inode1 = (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) ) ), ∀ 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⟩ (inode1 = inode ∧ ESUCCESS = err), inode1 = (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 ⊕ cache_pcache) ⊕ cache_icache)[m].meta, false, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m].nlink, 0, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m].size) )

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] → [inode1, m, md, boolvar0, m0, m1, m2]

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: inode1, m, md, boolvar0, m0, m1, m2