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Proof step 260 from proof refine-write_inode (previous step)

cache_dirs[m] = mkdir(m7, md2, m8, m9, entries), cache_files[m] = mkfile(m3, md0, m4, content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m5, md1, m6, content0), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, boolvar, cache_dirs0 = cache_dirs, 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), ⌊err0⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), cache_sync ∨ boolvar, m ∈ cache_dirs ∧ m0 = m8 ∧ m2 = m7 ∧ m1 = m9 ∧ boolvar ∨ m ∈ cache_files ∧ m0 = m4 ∧ m1 = 0 ∧ ¬ boolvar, m ∈ cache_dirs ∧ m0 = m8 ∧ m2 = m7 ∧ m1 = m9 ∧ boolvar ∨ m ∈ cache_files ∧ m0 = m6 ∧ m1 = 0 ∧ ¬ boolvar ⊦ ⟨fail#(; ; err); asynced1 := ?⟩ ((asynced1 ↔ asynced0) ∧ err0 = err), ∃ asynced. cache_dirs[m, cache_dirs[m].meta:= md] = cache_dirs0 ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (asynced ↔ asynced0) ∧ err0 = ESUCCESS

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 261:
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, ⌊err0⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟨fail#(; ; err); asynced1 := ?⟩ ((asynced1 ↔ asynced0) ∧ err0 = err)

Rule argument

Additional information

Used simplifier rules: afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base% ⊦ ⌊err⌋ → err ≠ ESUCCESS; (s)