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Proof step 76 from proof refine-create (previous step)

(ino0 ∈ cache_dirs0 ⊃ mkinode (ino0, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).meta, true, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).nlink, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).nsubdirs, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).size) ;mkinode(ino0, md, false, 1, 0, 0) ) = mkinode(m, md0, boolvar, m2, m3, m5), cache_dirs[m1] = mkdir(m0, md1, # links(m1, cache_dirs), m4, entries), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_dirs0 = cache_dirs, dent0 = negdentry(str), p_inode0 = mkinode(m1, md2, true, # links(m1, cache_dirs), m4, m0), 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), m1 ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ⟨afs_create#(md; p_inode0, p_inode1, dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( cache_dirs = cache_dirs0[m1, (m1 ∈ cache_dirs0 ⊃ mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m4, entries[str, ino0]);cache_dirs0[m1]).meta:= md2] ∧ afs_files = ((cache_files ++ ino0)[ino0, mkfile(0, md, 1, ∅)] ⊕ cache_pcache) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, # links(m1, cache_dirs0), m4, m0 + 1))] [m, mkientry (false, (ino0 ∈ cache_dirs0 ⊃ mkinode (ino0, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).meta, true, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).nlink, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).nsubdirs, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).size) ;mkinode(ino0, md, false, 1, 0, 0) )) ] ∧ (afs_asynced ↔ asynced0) ∧ (m1 ∈ cache_dirs0 ⊃ mkinode(m1, md2, true, # links(m1, cache_dirs0), m4, m0 + 1) ;mkinode (m1, (m1 = ino0 ⊃ mkfile(0, md, 1, ∅);(cache_files ++ ino0)[m1]).meta, false, (m1 = ino0 ⊃ mkfile(0, md, 1, ∅);(cache_files ++ ino0)[m1]).nlink, 0, (m1 = ino0 ⊃ mkfile(0, md, 1, ∅);(cache_files ++ ino0)[m1]).size) ) = p_inode0 ∧ (ino0 ∈ cache_dirs0 ⊃ mkinode (ino0, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).meta, true, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).nlink, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).nsubdirs, (ino0 = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[ino0]).size) ;mkinode(ino0, md, false, 1, 0, 0) ) = p_inode1 ∧ mkdentry(str, ino0) = dent0 ∧ ESUCCESS = err0), ino0 = 0, str ∈ entries, ino0 ∈ cache_files, ino0 ∈ cache_dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 77:
cache_dirs[m1] = mkdir(m0, md1, # links(m1, cache_dirs), m4, entries), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_dirs0 = cache_dirs, dent0 = negdentry(str), p_inode0 = mkinode(m1, md2, true, # links(m1, cache_dirs), m4, m0), m ≠ 0, 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), m1 ∈ cache_dirs, ¬ str ∈ entries, ¬ m ∈ cache_files, ¬ m ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ⟨afs_create#(md0; p_inode0, p_inode1, dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( cache_dirs = cache_dirs0[m1, (m1 ∈ cache_dirs0 ⊃ mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m4, entries[str, m]);cache_dirs0[m1]).meta:= md2] ∧ afs_files = ((cache_files ++ m)[m, mkfile(0, md0, 1, ∅)] ⊕ cache_pcache) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, # links(m1, cache_dirs0), m4, m0 + 1))] [m, mkientry (false, (m ∈ cache_dirs0 ⊃ mkinode (m, (m = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[m]).meta, true, (m = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[m]).nlink, (m = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[m]).nsubdirs, (m = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[m]).size) ;mkinode(m, md0, false, 1, 0, 0) )) ] ∧ (afs_asynced ↔ asynced0) ∧ (m1 ∈ cache_dirs0 ⊃ mkinode(m1, md2, true, # links(m1, cache_dirs0), m4, m0 + 1) ;mkinode (m1, (m1 = m ⊃ mkfile(0, md0, 1, ∅);(cache_files ++ m)[m1]).meta, false, (m1 = m ⊃ mkfile(0, md0, 1, ∅);(cache_files ++ m)[m1]).nlink, 0, (m1 = m ⊃ mkfile(0, md0, 1, ∅);(cache_files ++ m)[m1]).size) ) = p_inode0 ∧ (m ∈ cache_dirs0 ⊃ mkinode (m, (m = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[m]).meta, true, (m = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[m]).nlink, (m = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[m]).nsubdirs, (m = m1 ⊃ mkdir(m0 + 1, md2, # links(m1, cache_dirs0), m4, entries[str, m1]);cache_dirs0[m]).size) ;mkinode(m, md0, false, 1, 0, 0) ) = p_inode1 ∧ mkdentry(str, m) = dent0 ∧ ESUCCESS = err0)

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)