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Proof step 110 from proof refine-iget (previous step)

mkinode(m, md, boolvar, m0, m1, m2) = 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), ino0 ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), ino ∈ cache_dirs ∨ ino ∈ cache_files ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino0] = ((cache_files ⊕ cache_pcache) ⊕ cache_icache[m, mkientry(false, mkinode(m, md, boolvar, m0, m1, m2))])[ino0], ino ∈ cache_icache, ino ∈ cache_dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 111:
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), ino ∈ cache_files, ino0 ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino0] = ( (cache_files ⊕ cache_pcache) ⊕ cache_icache[ino, mkientry(false, mkinode(ino, cache_files[ino].meta, false, cache_files[ino].nlink, 0, cache_files[ino].size))] )[ino0 ], ino ∈ cache_icache, ino ∈ cache_dirs

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)