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Proof step 263 from proof refine-write_inode (previous step)

cache_dirs[m] = mkdir(m7, md2, # links(m, cache_dirs), m9, entries), cache_files[m] = mkfile(m3, md0, m4, content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m5, md1, m6, 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), 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, ⌊err1⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ∃ err0. ⌊err0⌋ ∧ ⟨err := err0; asynced1 := ?⟩ ((asynced1 ↔ asynced0) ∧ err1 = err)

User applied rule exists right

And obtained the following new goals

Proof step 264:
((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m5, md1, m6, content0), cache_files[m] = mkfile(m3, md0, m4, content), cache_dirs[m] = mkdir(m7, md2, # links(m, cache_dirs), m9, entries), 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_dirs, ⌊err1⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⌊err1⌋ ∧ ⟨err := err1; asynced1 := ?⟩ ((asynced1 ↔ asynced0) ∧ err1 = err)

Rule argument

pos: right 1 terms: err1 abort: F discard: T computed: T

Additional information

Used terms: err1