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Proof step 51 from proof refine-write_inode (previous step)

# links(m, cache_dirs) = cache_dirs[m].nlink, cache_dirs[m] = mkdir(cache_dirs[m].size, md0, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, entries), cache_icache[m] = mkientry(boolvar, mkinode(m1, md1, boolvar0, m2, m4, m5)), 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), m ∈ cache_dirs, m ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟨fail#(; ; err); asynced1 := ?⟩ ( cache_dirs = cache_dirs[m, cache_dirs[m].meta:= md] ∧ (cache_files ⊕ cache_pcache) ⊕ cache_icache = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md, boolvar0, m2, m4, m5))] ∧ (asynced1 ↔ asynced0) ∧ ESUCCESS = err), ∃ asynced. cache_dirs[m, cache_dirs[m].meta:= md] = cache_dirs[m, cache_dirs[m].meta:= md] ∧ (cache_files ⊕ cache_pcache) ⊕ cache_icache = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md, boolvar0, m2, m4, m5))] ∧ (asynced ↔ asynced0) ∧ ESUCCESS = ESUCCESS

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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