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Proof step 87 from proof inv-rmdir (previous step)

(entries0[str] = m5 ⊃ mkdir(m0 - 1, md1, # links(entries0[str], dirs0), m2 - 1, entries0 -- str) ;mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅) ) = mkdir(m3, md2, m7 + 1, m6, entries), (entries0[str] = m5 ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)) = mkdir(m, md4, m8, m9, entries1), asynced ↔ false, dirs0[entries0[str]] = mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅), dirs0[m5] = mkdir(m0, md1, # links(m5, dirs0), m2, entries0), err = ESUCCESS, icache = icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m))], inode = ( m5 ∈ dirs0[m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md] ⊃ mkinode (m5, dirs0[m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= md0 ] [m5 ] .meta, true, dirs0[m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= md0 ] [m5 ] .nlink, dirs0[m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= md0 ] [m5 ] .nsubdirs, dirs0[m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], dirs0[entries0[str], mkdir(m3, md2, m7, m6, entries)] [m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str] ] .meta:= md0 ] [m5 ] .size) ;mkinode(m5, files[m5].meta, false, files[m5].nlink, 0, files[m5].size) ), afs-cons(dirs0, files), afs-cons (dirs0[m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], mkdir(m, md0, m8, m9, entries1) ], files), dcache-cons(dcache, dirs0, files), icache-cons(icache0, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), entries0[str] ∈ dirs0, str ∈ entries0, m5 ∈ dirs0, 1 ≤ m2, 1 ≤ m0, asynced1 → synced(files, icache0, pcache), (m5 ∈ dirs0[m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md] ⊃ ( (str ∈ entries0 ∧ (m5 = entries0[str] ⊃ true;m0 ≥ 1 ∧ m2 ≥ 1)) ∧ str ∈ entries0 ∧ (str ∈ entries0 ∧ str ∈ entries0 ∧ (m5 = entries0[str] ⊃ true;m0 ≥ 1 ∧ m2 ≥ 1)) ∧ str ∈ entries0) ∧ ( (str ∈ entries0 ∧ (m5 = entries0[str] ⊃ true;m0 ≥ 1 ∧ m2 ≥ 1)) ∧ str ∈ entries0 ∧ (str ∈ entries0 ∧ str ∈ entries0 ∧ (m5 = entries0[str] ⊃ true;m0 ≥ 1 ∧ m2 ≥ 1)) ∧ str ∈ entries0) ∧ ( (str ∈ entries0 ∧ (m5 = entries0[str] ⊃ true;m0 ≥ 1 ∧ m2 ≥ 1)) ∧ str ∈ entries0 ∧ (str ∈ entries0 ∧ str ∈ entries0 ∧ (m5 = entries0[str] ⊃ true;m0 ≥ 1 ∧ m2 ≥ 1)) ∧ str ∈ entries0) ∧ (str ∈ entries0 ∧ (m5 = entries0[str] ⊃ true;m0 ≥ 1 ∧ m2 ≥ 1)) ∧ str ∈ entries0 ∧ (str ∈ entries0 ∧ str ∈ entries0 ∧ (m5 = entries0[str] ⊃ true;m0 ≥ 1 ∧ m2 ≥ 1)) ∧ str ∈ entries0 ;true ), (m5 = entries0[str] ⊃ true;m0 ≥ 1 ∧ m2 ≥ 1), links(m5, dirs0) ≠ ∅ ∨ m5 = ROOT_INO ⊦ ⟪dcache_delete#(m5, mkdentry(str, entries0[str]).name; err, dcache)⟫ ( icache-cons (icache[inode.ino, mkientry(asynced, inode)], dirs0 [m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str], (entries0[str] = m5 ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)).meta:= md0 ], files) ∧ dcache-cons (dcache, dirs0 [m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str], (entries0[str] = m5 ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)).meta:= md0 ], files) ∧ pcache-cons (pcache, dirs0 [m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str], (entries0[str] = m5 ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)).meta:= md0 ], files) ∧ synced (dirs0 [m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str], (entries0[str] = m5 ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)).meta:= md0 ], icache[inode.ino, mkientry(asynced, inode)], pcache) ∧ (asynced1 → synced(files, icache[inode.ino, mkientry(asynced, inode)], pcache))), entries0[str] = ROOT_INO, m0 = 0, m2 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 88:
(entries0[str] = m5 ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)) = mkdir(m, md4, m8, m9, entries1), (entries0[str] = m5 ⊃ mkdir(m0 - 1, md1, # links(entries0[str], dirs0), m2 - 1, entries0 -- str) ;mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅) ) = mkdir(m3, md2, m7 + 1, m6, entries), dirs0[m5] = mkdir(m0, md1, # links(m5, dirs0), m2, entries0), dirs0[entries0[str]] = mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅), err = ESUCCESS, entries0[str] ≠ ROOT_INO, m0 ≠ 0, m2 ≠ 0, afs-cons (dirs0[m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], mkdir(m, md0, m8, m9, entries1) ], files), afs-cons(dirs0, files), dcache-cons(dcache, dirs0, files), icache-cons(icache0, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), m5 ∈ dirs0, str ∈ entries0, entries0[str] ∈ dirs0, 1 ≤ m0, 1 ≤ m2, asynced1 → synced(files, icache0, pcache), links(m5, dirs0) ≠ ∅ ∨ m5 = ROOT_INO ⊦ ⟪dcache_delete#(m5, str; err, dcache)⟫ ( icache-cons (icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m))] [m5, mkientry (false, mkinode (m5, (m5 = entries0[str] ⊃ mkdir(m3, md0, m7, m6, entries);mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta, true, (m5 = entries0[str] ⊃ mkdir(m3, md0, m7, m6, entries);mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str)).nlink, (m5 = entries0[str] ⊃ mkdir(m3, md0, m7, m6, entries);mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str)).nsubdirs, (m5 = entries0[str] ⊃ mkdir(m3, md0, m7, m6, entries);mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str)).size)) ], dirs0 [m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str], (entries0[str] = m5 ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)).meta:= md0 ], files) ∧ dcache-cons (dcache, dirs0 [m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str], (entries0[str] = m5 ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)).meta:= md0 ], files) ∧ pcache-cons (pcache, dirs0 [m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str], (entries0[str] = m5 ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)).meta:= md0 ], files) ∧ synced (dirs0 [m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md ] [entries0[str], (entries0[str] = m5 ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)).meta:= md0 ], icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m))] [m5, mkientry (false, mkinode (m5, (m5 = entries0[str] ⊃ mkdir(m3, md0, m7, m6, entries);mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta, true, (m5 = entries0[str] ⊃ mkdir(m3, md0, m7, m6, entries);mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str)).nlink, (m5 = entries0[str] ⊃ mkdir(m3, md0, m7, m6, entries);mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str)).nsubdirs, (m5 = entries0[str] ⊃ mkdir(m3, md0, m7, m6, entries);mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str)).size)) ], pcache) ∧ ( asynced1 → synced (files, icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m))] [m5, mkientry (false, mkinode (m5, (m5 = entries0[str] ⊃ mkdir(m3, md0, m7, m6, entries);mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta, true, (m5 = entries0[str] ⊃ mkdir(m3, md0, m7, m6, entries);mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str)).nlink, (m5 = entries0[str] ⊃ mkdir(m3, md0, m7, m6, entries);mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str)).nsubdirs, (m5 = entries0[str] ⊃ mkdir(m3, md0, m7, m6, entries);mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str)).size)) ], pcache)))

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ mkdir(m, md, m0, m1, entries).meta:= md0 = mkdir(m, md0, m0, m1, entries); (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)