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Proof step 461 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[entries0[str0]] = mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅), dirs0[m7] = mkdir(m1, md1, # links(m7, dirs0), m4, entries0), dcache = dcache0 -- dentrykey(m7, str0), err = ESUCCESS, entries0[str0] ≠ ROOT_INO, afs-cons(dirs0[m7, mkdir(m1, md2, # links(m7, dirs0), m4, entries0)][entries0[str0], mkdir(m, md4, m8, m9, entries1)], files), afs-cons(dirs0, files), dcache-cons(dcache0, dirs0, files), icache-cons(icache0, dirs0, files), pcache-cons(pcache, dirs0, files), synced(dirs0, icache0, pcache), m7 ∈ dirs0, str0 ∈ entries0, entries0[str0] ∈ dirs0, asynced2 → synced(files, icache0, pcache), links(m7, dirs0) ≠ ∅ ∨ m7 = ROOT_INO ⊦ ⟪dcache_set#(m7, mkdentry(str0, mkdentry(str0, entries0[str0]).ino).name, mkdentry(str0, mkdentry(str0, entries0[str0]).ino); err, dcache)⟫ ( 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, 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 unfold applied rule call right

And obtained the following new goals

Proof step 462:
(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, 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 ⊦ ⟪let key = dentrykey(p_ino, name) in dcache[key] := dent⟫ ( 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, 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))), entries0[str0] = ROOT_INO

Rule argument

pos: right 1

Additional information

Used simplifier rules: dcache_set#(P_INO, NAME, DENT; ERR, DCACHE) {let KEY = dentrykey(P_INO, NAME) in DCACHE[KEY] := DENT};% ⊦ mkdentry(str, m).dentry?; (s)