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Proof step 75 from proof refine-iget (previous step)

mkinode(m, md, boolvar, m0, m1, m2) = (ino ∈ cache_dirs ⊃ mkinode(ino, cache_dirs[ino].meta, true, cache_dirs[ino].nlink, cache_dirs[ino].nsubdirs, cache_dirs[ino].size) ;mkinode(ino, cache_files[ino].meta, false, cache_files[ino].nlink, 0, cache_files[ino].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), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), cache_sync → synced(cache_files, cache_icache, cache_pcache), ino ∈ cache_dirs ∨ ino ∈ cache_files ⊦ (cache_files ⊕ cache_pcache) ⊕ cache_icache = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))], ino ∈ cache_icache

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 76:
⊦ files = files0 ↔ (∀ ino. (ino ∈ files ↔ ino ∈ files0) ∧ (ino ∈ files → files[ino] = files0[ino]))
Proof step 77:
mkinode(m, md, boolvar, m0, m1, m2) = (ino ∈ cache_dirs ⊃ mkinode(ino, cache_dirs[ino].meta, true, cache_dirs[ino].nlink, cache_dirs[ino].nsubdirs, cache_dirs[ino].size) ;mkinode(ino, cache_files[ino].meta, false, cache_files[ino].nlink, 0, cache_files[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), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), cache_sync → synced(cache_files, cache_icache, cache_pcache), ino ∈ cache_dirs ∨ ino ∈ cache_files ⊦ ino ∈ cache_icache, ∀ ino. ( ino ∈ (cache_files ⊕ cache_pcache) ⊕ cache_icache ↔ ino ∈ (cache_files ⊕ cache_pcache) ⊕ cache_icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))]) ∧ ( ino ∈ (cache_files ⊕ cache_pcache) ⊕ cache_icache → ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino] = ((cache_files ⊕ cache_pcache) ⊕ cache_icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))])[ino])

Rule argument

spec: heap, inst: file-heap name: ext seq: ⊦ files = files0 ↔ (∀ ino. (ino ∈ files ↔ ino ∈ files0) ∧ (ino ∈ files → files[ino] = files0[ino])) subst: [files0, files] → [ (cache_files ⊕ cache_pcache) ⊕ cache_icache [m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2)) ], (cache_files ⊕ cache_pcache) ⊕ cache_icache] flags: <all paths>

Additional information

Used terms: (cache_files ⊕ cache_pcache) ⊕ cache_icache [m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2)) ], (cache_files ⊕ cache_pcache) ⊕ cache_icache