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Proof step 78 from proof refine-mkdir (previous step)

cache_dirs[m1] = mkdir(m0, md1, # links(m1, cache_dirs), m2, entries), (cache_dirs[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs), m2 + 1, entries[str, ino0])] ++ ino0)[m1] = mkdir(m, md0, m3, m4, entries0), 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), m2, m0), 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), m1 ∈ cache_dirs, ¬ ino0 ∈ cache_dirs, ¬ ino0 ∈ cache_files, ¬ str ∈ entries, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ⟨afs_mkdir#(md; p_inode0, p_inode1, dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( cache_dirs = (cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m1, (m1 = ino0 ∧ ino0 ∈ cache_dirs0[ino0, mkdir(m0 + 1, md1, # links(ino0, cache_dirs0), m2 + 1, entries[str, ino0])] ++ ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;(cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, ino0])] ++ ino0)[m1] ) .meta:= md2 ] ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, m3, m4, m))] [(ino0 ∈ cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, ino0])] ++ ino0 ⊃ mkinode (ino0, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md, 1, 0, ∅)).meta, true, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md, 1, 0, ∅)).nlink, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md, 1, 0, ∅)).nsubdirs, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md, 1, 0, ∅)).size) ;mkinode(ino0, cache_files[ino0].meta, false, cache_files[ino0].nlink, 0, cache_files[ino0].size) ) .ino, mkientry (false, (ino0 ∈ cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, ino0])] ++ ino0 ⊃ mkinode (ino0, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md, 1, 0, ∅)).meta, true, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md, 1, 0, ∅)).nlink, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md, 1, 0, ∅)).nsubdirs, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md, 1, 0, ∅)).size) ;mkinode(ino0, cache_files[ino0].meta, false, cache_files[ino0].nlink, 0, cache_files[ino0].size) )) ] ∧ (afs_asynced ↔ asynced0) ∧ (m1 ∈ cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, ino0])] ++ ino0 ⊃ mkinode (m1, md2, true, (m1 = ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;(cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, ino0])] ++ ino0)[m1] ) .nlink, (m1 = ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;(cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, ino0])] ++ ino0)[m1] ) .nsubdirs, (m1 = ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;(cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, ino0])] ++ ino0)[m1] ) .size) ;mkinode(m1, cache_files[m1].meta, false, cache_files[m1].nlink, 0, cache_files[m1].size) ) = p_inode0 ∧ (ino0 ∈ cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, ino0])] ++ ino0 ⊃ mkinode (ino0, (ino0 = m1 ⊃ mkdir(0, md2, 1, 0, ∅);mkdir(0, md, 1, 0, ∅)).meta, true, (ino0 = m1 ⊃ mkdir(0, md2, 1, 0, ∅);mkdir(0, md, 1, 0, ∅)).nlink, (ino0 = m1 ⊃ mkdir(0, md2, 1, 0, ∅);mkdir(0, md, 1, 0, ∅)).nsubdirs, (ino0 = m1 ⊃ mkdir(0, md2, 1, 0, ∅);mkdir(0, md, 1, 0, ∅)).size) ;mkinode(ino0, cache_files[ino0].meta, false, cache_files[ino0].nlink, 0, cache_files[ino0].size) ) = p_inode1 ∧ mkdentry(str, ino0) = dent0 ∧ ESUCCESS = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 79:
(ino0 ∈ cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, ino0])] ++ ino0 ⊃ mkinode (ino0, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md, 1, 0, ∅)).meta, true, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md, 1, 0, ∅)).nlink, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md, 1, 0, ∅)).nsubdirs, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md, 1, 0, ∅)).size) ;mkinode(ino0, cache_files[ino0].meta, false, cache_files[ino0].nlink, 0, cache_files[ino0].size) ) = mkinode(m5, md3, boolvar, m6, m7, m8), (cache_dirs[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs), m2 + 1, entries[str, ino0])] ++ ino0)[m1] = mkdir(m, md0, m3, m4, entries0), cache_dirs[m1] = mkdir(m0, md1, # links(m1, cache_dirs), m2, 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), m2, 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_mkdir#(md; p_inode0, p_inode1, dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( cache_dirs = (cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m1, (m1 = ino0 ∧ ino0 ∈ cache_dirs0[ino0, mkdir(m0 + 1, md1, # links(ino0, cache_dirs0), m2 + 1, entries[str, ino0])] ++ ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;(cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, ino0])] ++ ino0)[m1] ) .meta:= md2 ] ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, m3, m4, m))] [m5, mkientry (false, (ino0 ∈ cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, ino0])] ++ ino0 ⊃ mkinode (ino0, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md, 1, 0, ∅)).meta, true, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md, 1, 0, ∅)).nlink, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md, 1, 0, ∅)).nsubdirs, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md, 1, 0, ∅)).size) ;mkinode(ino0, cache_files[ino0].meta, false, cache_files[ino0].nlink, 0, cache_files[ino0].size) )) ] ∧ (afs_asynced ↔ asynced0) ∧ (m1 ∈ cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, ino0])] ++ ino0 ⊃ mkinode (m1, md2, true, (m1 = ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;(cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, ino0])] ++ ino0)[m1] ) .nlink, (m1 = ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;(cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, ino0])] ++ ino0)[m1] ) .nsubdirs, (m1 = ino0 ⊃ mkdir(0, md, 1, 0, ∅) ;(cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, ino0])] ++ ino0)[m1] ) .size) ;mkinode(m1, cache_files[m1].meta, false, cache_files[m1].nlink, 0, cache_files[m1].size) ) = p_inode0 ∧ (ino0 ∈ cache_dirs0[m1, mkdir(m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, ino0])] ++ ino0 ⊃ mkinode (ino0, (ino0 = m1 ⊃ mkdir(0, md2, 1, 0, ∅);mkdir(0, md, 1, 0, ∅)).meta, true, (ino0 = m1 ⊃ mkdir(0, md2, 1, 0, ∅);mkdir(0, md, 1, 0, ∅)).nlink, (ino0 = m1 ⊃ mkdir(0, md2, 1, 0, ∅);mkdir(0, md, 1, 0, ∅)).nsubdirs, (ino0 = m1 ⊃ mkdir(0, md2, 1, 0, ∅);mkdir(0, md, 1, 0, ∅)).size) ;mkinode(ino0, cache_files[ino0].meta, false, cache_files[ino0].nlink, 0, cache_files[ino0].size) ) = p_inode1 ∧ mkdentry(str, ino0) = dent0 ∧ ESUCCESS = err0), ino0 = 0, ino0 ∈ cache_dirs, ino0 ∈ cache_files, str ∈ entries

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] → [( ino0 ∈ cache_dirs0 [m1, mkdir (m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, ino0]) ] ++ ino0 ⊃ mkinode (ino0, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0) ;mkdir(0, md, 1, 0, ∅) ) .meta, true, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0) ;mkdir(0, md, 1, 0, ∅) ) .nlink, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0) ;mkdir(0, md, 1, 0, ∅) ) .nsubdirs, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0) ;mkdir(0, md, 1, 0, ∅) ) .size) ;mkinode (ino0, cache_files[ino0].meta, false, cache_files[ino0].nlink, 0, cache_files[ino0].size) ), m5, md3, boolvar, m6, m7, m8]

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: ( ino0 ∈ cache_dirs0 [m1, mkdir (m0 + 1, md1, # links(m1, cache_dirs0), m2 + 1, entries[str, ino0]) ] ++ ino0 ⊃ mkinode (ino0, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md, 1, 0, ∅)) .meta, true, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md, 1, 0, ∅)) .nlink, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md, 1, 0, ∅)) .nsubdirs, (ino0 = m1 ⊃ mkdir(m, md2, m3, m4, entries0);mkdir(0, md, 1, 0, ∅)) .size) ;mkinode (ino0, cache_files[ino0].meta, false, cache_files[ino0].nlink, 0, cache_files[ino0].size) ), m5, md3, boolvar, m6, m7, m8