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Proof step 54 from proof refine-create (previous step)

cache_dirs[m] = mkdir(m0, md1, # links(m, cache_dirs), m2, entries), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = ESUCCESS, ino0 ≠ 0, 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, ¬ str ∈ entries, ¬ ino0 ∈ cache_files, ¬ ino0 ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪icache_set#(mkinode(m, md0, true, # links(m, cache_dirs), m2, m0 + 1), false; err, cache_icache); icache_set# (getinode (mkdentry(str, ino0).ino, cache_dirs[m, (m ∈ cache_dirs ⊃ mkdir(m0 + 1, md1, # links(m, cache_dirs), m2, entries[str, ino0]);cache_dirs[m]).meta:= md0], (cache_files ++ ino0)[ino0, mkfile(0, md, 1, ∅)]), false ; err, cache_icache); dcache_set# ((m ∈ cache_dirs ⊃ mkinode(m, md0, true, # links(m, cache_dirs), m2, m0 + 1) ;mkinode (m, (m = ino0 ∧ ino0 ∈ cache_files ++ ino0 ⊃ mkfile(0, md, 1, ∅);(cache_files ++ ino0)[m]).meta, false, (m = ino0 ∧ ino0 ∈ cache_files ++ ino0 ⊃ mkfile(0, md, 1, ∅);(cache_files ++ ino0)[m]).nlink, 0, (m = ino0 ∧ ino0 ∈ cache_files ++ ino0 ⊃ mkfile(0, md, 1, ∅);(cache_files ++ ino0)[m]).size) ) .ino, str, mkdentry(str, ino0) ; err, cache_dcache)⟫ ⟨dent0 := negdentry(str); p_inode0 := mkinode(m, md0, true, # links(m, cache_dirs), m2, m0); cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; cache_dirs2 := cache_dirs; cache_dirs3 := cache_dirs; afs_create#(md; p_inode0, p_inode1, dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( cache_dirs = cache_dirs2[m, (m ∈ cache_dirs2 ⊃ mkdir(m0 + 1, md1, # links(m, cache_dirs2), m2, entries[str, ino0]);cache_dirs2[m]).meta:= md0] ∧ afs_files = ((cache_files ++ ino0)[ino0, mkfile(0, md, 1, ∅)] ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced0) ∧ (m ∈ cache_dirs2 ⊃ mkinode(m, md0, true, # links(m, cache_dirs2), m2, m0 + 1) ;mkinode (m, (m = ino0 ⊃ mkfile(0, md, 1, ∅);(cache_files ++ ino0)[m]).meta, false, (m = ino0 ⊃ mkfile(0, md, 1, ∅);(cache_files ++ ino0)[m]).nlink, 0, (m = ino0 ⊃ mkfile(0, md, 1, ∅);(cache_files ++ ino0)[m]).size) ) = p_inode0 ∧ (ino0 ∈ cache_dirs3 ⊃ mkinode (ino0, (ino0 = m ⊃ mkdir(m0 + 1, md0, # links(m, cache_dirs3), m2, entries[str, m]);cache_dirs3[ino0]).meta, true, (ino0 = m ⊃ mkdir(m0 + 1, md0, # links(m, cache_dirs3), m2, entries[str, m]);cache_dirs3[ino0]).nlink, (ino0 = m ⊃ mkdir(m0 + 1, md0, # links(m, cache_dirs3), m2, entries[str, m]);cache_dirs3[ino0]).nsubdirs, (ino0 = m ⊃ mkdir(m0 + 1, md0, # links(m, cache_dirs3), m2, entries[str, m]);cache_dirs3[ino0]).size) ;mkinode(ino0, md, false, 1, 0, 0) ) = p_inode1 ∧ mkdentry(str, ino0) = dent0 ∧ err = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 55:
(m ∈ cache_dirs ⊃ mkinode(m, md0, true, # links(m, cache_dirs), m2, m0 + 1) ;mkinode (m, (m = ino0 ∧ ino0 ∈ cache_files ++ ino0 ⊃ mkfile(0, md, 1, ∅);(cache_files ++ ino0)[m]).meta, false, (m = ino0 ∧ ino0 ∈ cache_files ++ ino0 ⊃ mkfile(0, md, 1, ∅);(cache_files ++ ino0)[m]).nlink, 0, (m = ino0 ∧ ino0 ∈ cache_files ++ ino0 ⊃ mkfile(0, md, 1, ∅);(cache_files ++ ino0)[m]).size) ) = mkinode(m1, md2, boolvar, m3, m4, m5), cache_dirs[m] = mkdir(m0, md1, # links(m, cache_dirs), m2, entries), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = ESUCCESS, 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, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪icache_set#(mkinode(m, md0, true, # links(m, cache_dirs), m2, m0 + 1), false; err, cache_icache); icache_set# (getinode (mkdentry(str, ino0).ino, cache_dirs[m, (m ∈ cache_dirs ⊃ mkdir(m0 + 1, md1, # links(m, cache_dirs), m2, entries[str, ino0]);cache_dirs[m]).meta:= md0], (cache_files ++ ino0)[ino0, mkfile(0, md, 1, ∅)]), false ; err, cache_icache); dcache_set#(m1, str, mkdentry(str, ino0); err, cache_dcache)⟫ ⟨dent0 := negdentry(str); p_inode0 := mkinode(m, md0, true, # links(m, cache_dirs), m2, m0); cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; cache_dirs2 := cache_dirs; cache_dirs3 := cache_dirs; afs_create#(md; p_inode0, p_inode1, dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( cache_dirs = cache_dirs2[m, (m ∈ cache_dirs2 ⊃ mkdir(m0 + 1, md1, # links(m, cache_dirs2), m2, entries[str, ino0]);cache_dirs2[m]).meta:= md0] ∧ afs_files = ((cache_files ++ ino0)[ino0, mkfile(0, md, 1, ∅)] ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced0) ∧ (m ∈ cache_dirs2 ⊃ mkinode(m, md0, true, # links(m, cache_dirs2), m2, m0 + 1) ;mkinode (m, (m = ino0 ⊃ mkfile(0, md, 1, ∅);(cache_files ++ ino0)[m]).meta, false, (m = ino0 ⊃ mkfile(0, md, 1, ∅);(cache_files ++ ino0)[m]).nlink, 0, (m = ino0 ⊃ mkfile(0, md, 1, ∅);(cache_files ++ ino0)[m]).size) ) = p_inode0 ∧ (ino0 ∈ cache_dirs3 ⊃ mkinode (ino0, (ino0 = m ⊃ mkdir(m0 + 1, md0, # links(m, cache_dirs3), m2, entries[str, m]);cache_dirs3[ino0]).meta, true, (ino0 = m ⊃ mkdir(m0 + 1, md0, # links(m, cache_dirs3), m2, entries[str, m]);cache_dirs3[ino0]).nlink, (ino0 = m ⊃ mkdir(m0 + 1, md0, # links(m, cache_dirs3), m2, entries[str, m]);cache_dirs3[ino0]).nsubdirs, (ino0 = m ⊃ mkdir(m0 + 1, md0, # links(m, cache_dirs3), m2, entries[str, m]);cache_dirs3[ino0]).size) ;mkinode(ino0, md, false, 1, 0, 0) ) = p_inode1 ∧ mkdentry(str, ino0) = dent0 ∧ err = err0), ino0 = 0, str ∈ entries, ino0 ∈ cache_files, ino0 ∈ cache_dirs

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [(m ∈ cache_dirs ⊃ mkinode (m, md0, true, # links(m, cache_dirs), m2, m0 + 1) ;mkinode (m, (m = ino0 ∧ ino0 ∈ cache_files ++ ino0 ⊃ mkfile(0, md, 1, ∅) ;(cache_files ++ ino0)[m] ) .meta, false, (m = ino0 ∧ ino0 ∈ cache_files ++ ino0 ⊃ mkfile(0, md, 1, ∅) ;(cache_files ++ ino0)[m] ) .nlink, 0, (m = ino0 ∧ ino0 ∈ cache_files ++ ino0 ⊃ mkfile(0, md, 1, ∅) ;(cache_files ++ ino0)[m] ) .size) ), m1, md2, boolvar, m3, m4, m5]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: (m ∈ cache_dirs ⊃ mkinode(m, md0, true, # links(m, cache_dirs), m2, m0 + 1) ;mkinode (m, (m = ino0 ∧ ino0 ∈ cache_files ++ ino0 ⊃ mkfile(0, md, 1, ∅) ;(cache_files ++ ino0)[m] ) .meta, false, (m = ino0 ∧ ino0 ∈ cache_files ++ ino0 ⊃ mkfile(0, md, 1, ∅) ;(cache_files ++ ino0)[m] ) .nlink, 0, (m = ino0 ∧ ino0 ∈ cache_files ++ ino0 ⊃ mkfile(0, md, 1, ∅) ;(cache_files ++ ino0)[m] ) .size) ), m1, md2, boolvar, m3, m4, m5