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Proof step 382 from proof refine-write_inode (previous step)

# links(m, cache_dirs) = cache_files[m].nlink, cache_files[m] = mkfile(m0, md0, cache_files[m].nlink, content), 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_files ⊦ ⟨fail#(; ; err); asynced0 := ?⟩ ((asynced0 ↔ asynced1) ∧ EFAIL = err), m ∈ cache_icache, ∃ asynced. ((cache_files ⊕ cache_pcache) ⊕ cache_icache )[m, mkfile(cache_files[m].size, md, cache_files[m].nlink, cache_files[m].content ⊕ mkcontent(m, cache_pcache)) ] [m, ((cache_files ⊕ cache_pcache) ⊕ cache_icache )[m, mkfile(cache_files[m].size, md, cache_files[m].nlink, cache_files[m].content ⊕ mkcontent(m, cache_pcache)) ] [m ] .size:= m2 ] = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (asynced ↔ asynced1) ∧ EFAIL = ESUCCESS

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 383:
# links(m, cache_dirs) = cache_files[m].nlink, cache_files[m] = mkfile(m0, md0, cache_files[m].nlink, content), 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), m ∈ cache_files, ¬ m ∈ cache_icache ⊦ ⟨fail#(; ; err); asynced0 := ?⟩ ((asynced0 ↔ asynced1) ∧ EFAIL = err)

Rule argument

Additional information

Used simplifier rules: ⊦ ESUCCESS ≠ EFAIL; (s)% ⊦ files[ino, af][ino, af0] = files[ino, af0]; (s)% ⊦ mkfile(m, md, m0, content).size:= m1 = mkfile(m1, md, m0, content); (s)% ⊦ ino ∈ files ⊕ pcache ↔ ino ∈ files; (s)% ⊦ ino ∈ files ⊕ icache ↔ ino ∈ files; (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)