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Proof step 166 from proof refine-rmdir (previous step)

(m6 = entries3[str] ⊃ mkdir(m5, md0, m3, m7, entries);mkdir(m0, md, # links(m6, cache_dirs), m1, entries3 -- str)) = mkdir(m4, md3, m14, m15, entries0), (entries3[str] = m6 ⊃ mkdir(m0, md6, # links(entries3[str], cache_dirs), m1, entries3 -- str) ;mkdir(m2, md1, # links(entries3[str], cache_dirs), m13, ∅) ) = mkdir(m5, md2, m3 + 1, m7, entries), (entries3[str] = m6 ⊃ mkdir(m5, md, m3, m7, entries);mkdir(m5, md2, m3, m7, entries)) = mkdir(m, md4, m8, m9, entries1), cache_dirs[m6] = mkdir(m0 + 1, md6, # links(m6, cache_dirs), m1 + 1, entries3), cache_dirs[entries3[str]] = mkdir(m2, md1, # links(entries3[str], cache_dirs), m13, ∅), cache_icache[entries3[str], mkientry(false, mkinode(entries3[str], md0, true, m8, m9, m))][m6, mkientry(false, mkinode(m6, md3, true, m14, m15, m4))] [ino ] .inode .directory, afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), afs-cons (cache_dirs[m6, (m6 = entries3[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md6, # links(m6, cache_dirs), m1, entries3 -- str)).meta:= md] [entries3[str], mkdir(m, md0, m8, m9, entries1) ], cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), dcache-cons (cache_dcache -- dentrykey(m6, str), cache_dirs[m6, (m6 = entries3[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md6, # links(m6, cache_dirs), m1, entries3 -- str)).meta:= md] [entries3[str], mkdir(m, md0, m8, m9, entries1) ], cache_files), icache-cons(cache_icache, cache_dirs, cache_files), icache-cons (cache_icache[entries3[str], mkientry(false, mkinode(entries3[str], md0, true, m8, m9, m))][m6, mkientry(false, mkinode(m6, md3, true, m14, m15, m4))], cache_dirs[m6, (m6 = entries3[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md6, # links(m6, cache_dirs), m1, entries3 -- str)).meta:= md] [entries3[str], mkdir(m, md0, m8, m9, entries1) ], cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), pcache-cons (cache_pcache, cache_dirs[m6, (m6 = entries3[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md6, # links(m6, cache_dirs), m1, entries3 -- str)).meta:= md] [entries3[str], mkdir(m, md0, m8, m9, entries1) ], cache_files), synced (cache_dirs[m6, (m6 = entries3[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md6, # links(m6, cache_dirs), m1, entries3 -- str)).meta:= md] [entries3[str], mkdir(m, md0, m8, m9, entries1) ], cache_icache[entries3[str], mkientry(false, mkinode(entries3[str], md0, true, m8, m9, m))][m6, mkientry(false, mkinode(m6, md3, true, m14, m15, m4))], cache_pcache), synced(cache_dirs, cache_icache, cache_pcache), ino ∈ cache_files, str ∈ entries3, entries3[str] ∈ cache_dirs, m6 ∈ cache_dirs, ino ∈ cache_icache[entries3[str], mkientry(false, mkinode(entries3[str], md0, true, m8, m9, m))] [m6, mkientry(false, mkinode(m6, md3, true, m14, m15, m4)) ], cache_sync → synced(cache_files, cache_icache, cache_pcache), cache_sync → synced (cache_files, cache_icache[entries3[str], mkientry(false, mkinode(entries3[str], md0, true, m8, m9, m))] [m6, mkientry(false, mkinode(m6, md3, true, m14, m15, m4)) ], cache_pcache), links(m6, cache_dirs) ≠ ∅ ∨ m6 = ROOT_INO ⊦ entries3[str] = ROOT_INO, ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino] = mkfile(cache_files[ino].size, cache_files[ino].meta, cache_files[ino].nlink, cache_files[ino].content ⊕ mkcontent(ino, cache_pcache))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 167:
cache_icache[entries3[str], mkientry(false, mkinode(entries3[str], md0, true, m8, m9, m))] [m6, mkientry(false, mkinode(m6, md3, true, m14, m15, m4)) ] [ino ] .inode = mkinode(m10, md5, boolvar, m11, m12, m16), (entries3[str] = m6 ⊃ mkdir(m5, md, m3, m7, entries);mkdir(m5, md2, m3, m7, entries)) = mkdir(m, md4, m8, m9, entries1), (entries3[str] = m6 ⊃ mkdir(m0, md6, # links(entries3[str], cache_dirs), m1, entries3 -- str) ;mkdir(m2, md1, # links(entries3[str], cache_dirs), m13, ∅) ) = mkdir(m5, md2, m3 + 1, m7, entries), (m6 = entries3[str] ⊃ mkdir(m5, md0, m3, m7, entries);mkdir(m0, md, # links(m6, cache_dirs), m1, entries3 -- str)) = mkdir(m4, md3, m14, m15, entries0), cache_dirs[entries3[str]] = mkdir(m2, md1, # links(entries3[str], cache_dirs), m13, ∅), cache_dirs[m6] = mkdir(m0 + 1, md6, # links(m6, cache_dirs), m1 + 1, entries3), boolvar, afs-cons (cache_dirs[m6, (m6 = entries3[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md6, # links(m6, cache_dirs), m1, entries3 -- str)).meta:= md] [entries3[str], mkdir(m, md0, m8, m9, entries1) ], cache_files), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons (cache_dcache -- dentrykey(m6, str), cache_dirs[m6, (m6 = entries3[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md6, # links(m6, cache_dirs), m1, entries3 -- str)).meta:= md] [entries3[str], mkdir(m, md0, m8, m9, entries1) ], cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons (cache_icache[entries3[str], mkientry(false, mkinode(entries3[str], md0, true, m8, m9, m))][m6, mkientry(false, mkinode(m6, md3, true, m14, m15, m4))], cache_dirs[m6, (m6 = entries3[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md6, # links(m6, cache_dirs), m1, entries3 -- str)).meta:= md] [entries3[str], mkdir(m, md0, m8, m9, entries1) ], cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons (cache_pcache, cache_dirs[m6, (m6 = entries3[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md6, # links(m6, cache_dirs), m1, entries3 -- str)).meta:= md] [entries3[str], mkdir(m, md0, m8, m9, entries1) ], cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), synced (cache_dirs[m6, (m6 = entries3[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md6, # links(m6, cache_dirs), m1, entries3 -- str)).meta:= md] [entries3[str], mkdir(m, md0, m8, m9, entries1) ], cache_icache[entries3[str], mkientry(false, mkinode(entries3[str], md0, true, m8, m9, m))][m6, mkientry(false, mkinode(m6, md3, true, m14, m15, m4))], cache_pcache), ino ∈ cache_icache[entries3[str], mkientry(false, mkinode(entries3[str], md0, true, m8, m9, m))] [m6, mkientry(false, mkinode(m6, md3, true, m14, m15, m4)) ], m6 ∈ cache_dirs, entries3[str] ∈ cache_dirs, str ∈ entries3, ino ∈ cache_files, cache_sync → synced (cache_files, cache_icache[entries3[str], mkientry(false, mkinode(entries3[str], md0, true, m8, m9, m))] [m6, mkientry(false, mkinode(m6, md3, true, m14, m15, m4)) ], cache_pcache), cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m6, cache_dirs) ≠ ∅ ∨ m6 = ROOT_INO ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino] = mkfile(cache_files[ino].size, cache_files[ino].meta, cache_files[ino].nlink, cache_files[ino].content ⊕ mkcontent(ino, cache_pcache)), entries3[str] = ROOT_INO

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] → [cache_icache [entries3[str], mkientry (false, mkinode(entries3[str], md0, true, m8, m9, m)) ] [m6, mkientry(false, mkinode(m6, md3, true, m14, m15, m4)) ] [ino ] .inode, m10, md5, boolvar, m11, m12, m16]

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: cache_icache [entries3[str], mkientry(false, mkinode(entries3[str], md0, true, m8, m9, m)) ] [m6, mkientry(false, mkinode(m6, md3, true, m14, m15, m4)) ] [ino ] .inode, m10, md5, boolvar, m11, m12, m16