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Proof step 464 from proof inv-rename-dir-dentry (previous step)

(entries0[str0] = m7 ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0) ;mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅) ) .meta:= md0 = mkdir(m, md4, m8, m9, entries1), (m7 = entries0[str0] ⊃ mkdir(m1, md0, # links(entries0[str0], dirs0), m4, entries0);mkdir(m1, md2, # links(m7, dirs0), m4, entries0)) = mkdir(m0, md, m2, m5, entries), dirs0[m7] = mkdir(m1, md1, # links(m7, dirs0), m4, entries0), dirs0[entries0[str0]] = mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅), dcache = dcache0 -- dentrykey(m7, str0), dent = mkdentry(str0, mkdentry(str0, entries0[str0]).ino), err = ESUCCESS, key = dentrykey(p_ino, name), name = mkdentry(str0, mkdentry(str0, entries0[str0]).ino).name, p_ino = m7, mkdentry(str0, entries0[str0]).dentry?, afs-cons(dirs0, files), afs-cons(dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)][entries0[str0], mkdir(m, md4, m8, m9, entries1)], files), dcache-cons(dcache0, dirs0, files), icache-cons(icache0, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), entries0[str0] ∈ dirs0, str0 ∈ entries0, m7 ∈ dirs0, asynced2 → synced(files, icache0, pcache), links(m7, dirs0) ≠ ∅ ∨ m7 = ROOT_INO ⊦ entries0[str0] = ROOT_INO, icache-cons (icache0[m7, mkientry(false, mkinode(m7, md, true, m2, m5, m0))][entries0[str0], mkientry(false, mkinode(entries0[str0], md4, true, m8, m9, m))], dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m7 ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0);dirs0[entries0[str0]]).meta:= md0 ], files) ∧ dcache-cons (dcache[key, dent], dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m7 ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0);dirs0[entries0[str0]]).meta:= md0 ], files) ∧ pcache-cons (pcache, dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m7 ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0);dirs0[entries0[str0]]).meta:= md0 ], files) ∧ synced (dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)] [entries0[str0], (entries0[str0] = m7 ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0);dirs0[entries0[str0]]).meta:= md0 ], icache0[m7, mkientry(false, mkinode(m7, md, true, m2, m5, m0))][entries0[str0], mkientry(false, mkinode(entries0[str0], md4, true, m8, m9, m))], pcache) ∧ ( asynced2 → synced (files, icache0[m7, mkientry(false, mkinode(m7, md, true, m2, m5, m0))] [entries0[str0], mkientry(false, mkinode(entries0[str0], md4, true, m8, m9, m)) ], pcache))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 465:
(entries0[str0] = m7 ⊃ mkdir(m1, md2, # links(entries0[str0], dirs0), m4, entries0) ;mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅) ) .meta:= md0 = mkdir(m, md4, m8, m9, entries1), (m7 = entries0[str0] ⊃ mkdir(m1, md0, # links(entries0[str0], dirs0), m4, entries0);mkdir(m1, md2, # links(m7, dirs0), m4, entries0)) = mkdir(m0, md, m2, m5, entries), dirs0[m7] = mkdir(m1, md1, # links(m7, dirs0), m4, entries0), dirs0[entries0[str0]] = mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅), afs-cons(dirs0, files), afs-cons(dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)][entries0[str0], mkdir(m, md4, m8, m9, entries1)], files), dcache-cons(dcache0, dirs0, files), icache-cons(icache0, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), entries0[str0] ∈ dirs0, str0 ∈ entries0, m7 ∈ dirs0, asynced2 → synced(files, icache0, pcache), links(m7, dirs0) ≠ ∅ ∨ m7 = ROOT_INO ⊦ entries0[str0] = ROOT_INO, icache-cons (icache0[m7, mkientry(false, mkinode(m7, md, true, m2, m5, m0))][entries0[str0], mkientry(false, mkinode(entries0[str0], md4, true, m8, m9, m))], dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)][entries0[str0], mkdir(m, md4, m8, m9, entries1)], files) ∧ dcache-cons (dcache0[dentrykey(m7, str0), mkdentry(str0, entries0[str0])], dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)][entries0[str0], mkdir(m, md4, m8, m9, entries1)], files) ∧ pcache-cons(pcache, dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)][entries0[str0], mkdir(m, md4, m8, m9, entries1)], files) ∧ synced (dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)][entries0[str0], mkdir(m, md4, m8, m9, entries1)], icache0[m7, mkientry(false, mkinode(m7, md, true, m2, m5, m0))][entries0[str0], mkientry(false, mkinode(entries0[str0], md4, true, m8, m9, m))], pcache) ∧ ( asynced2 → synced (files, icache0[m7, mkientry(false, mkinode(m7, md, true, m2, m5, m0))] [entries0[str0], mkientry(false, mkinode(entries0[str0], md4, true, m8, m9, m)) ], pcache))

Rule argument

Additional information

Used simplifier rules: ⊦ (dcache -- key)[key, dent] = dcache[key, dent]; (s)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ mkdentry(str, m).ino = m; (s)% ⊦ mkdentry(str, m).dentry?; (s)