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Proof step 332 from proof refine-write_inode (previous step)

cache_icache[m3] = mkientry(boolvar, mkinode(m3, md2, false, # links(m3, cache_dirs), 0, m6)), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content), cache_files[m3] = mkfile(m1, md1, # links(m3, cache_dirs), content0), 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), m3 ∈ cache_files, m3 ∈ cache_icache, ¬ boolvar → mkinode(m3, md2, false, # links(m3, cache_dirs), 0, m6) = mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m1) ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m3, mkfile(m2, md, # links(m3, cache_dirs), content)] = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m3, mkientry(true, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2))]

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 333:
⊦ files = files0 ↔ (∀ ino. (ino ∈ files ↔ ino ∈ files0) ∧ (ino ∈ files → files[ino] = files0[ino]))
Proof step 334:
cache_files[m3] = mkfile(m1, md1, # links(m3, cache_dirs), content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m3] = mkfile(m0, md0, # links(m3, cache_dirs), content), cache_icache[m3] = mkientry(boolvar, mkinode(m3, md2, false, # links(m3, cache_dirs), 0, m6)), 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), m3 ∈ cache_icache, m3 ∈ cache_files, ¬ boolvar → mkinode(m3, md2, false, # links(m3, cache_dirs), 0, m6) = mkinode(m3, md1, false, # links(m3, cache_dirs), 0, m1) ⊦ ∀ ino. ( ino ∈ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m3, mkfile(m2, md, # links(m3, cache_dirs), content)] ↔ ino ∈ (cache_files ⊕ cache_pcache) ⊕ cache_icache[m3, mkientry(true, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2))]) ∧ ( ino ∈ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m3, mkfile(m2, md, # links(m3, cache_dirs), content)] → ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m3, mkfile(m2, md, # links(m3, cache_dirs), content)][ino] = ((cache_files ⊕ cache_pcache) ⊕ cache_icache[m3, mkientry(true, mkinode(m3, md, false, # links(m3, cache_dirs), 0, 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: [files, files0] → [((cache_files ⊕ cache_pcache) ⊕ cache_icache )[m3, mkfile(m2, md, # links(m3, cache_dirs), content) ], (cache_files ⊕ cache_pcache) ⊕ cache_icache [m3, mkientry (true, mkinode (m3, md, false, # links(m3, cache_dirs), 0, m2)) ]] flags: <all paths>

Additional information

Used terms: ((cache_files ⊕ cache_pcache) ⊕ cache_icache )[m3, mkfile(m2, md, # links(m3, cache_dirs), content) ], (cache_files ⊕ cache_pcache) ⊕ cache_icache [m3, mkientry (true, mkinode(m3, md, false, # links(m3, cache_dirs), 0, m2)) ]