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Proof step 154 from proof inv-rename-file-dentry (previous step)

# links(entries1[str], dirs0) = m16 + 1, (m15 = m0 ⊃ mkdir(m6, md1, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md2, # links(m15, dirs0), m7, entries -- str0)) = mkdir(m12, md7, m13, m14, entries2), (m0 = m15 ⊃ mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0);mkdir(m4, md4, # links(m0, dirs0), m8, entries1)) = mkdir(m6, md3, m9, m10, entries0), (m0 = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])) = mkdir(m2, md, m11, m17, entries3), dirs0[m0] = mkdir(m4, md4, # links(m0, dirs0), m8, entries1), files0[entries1[str]] = mkfile(m5, md5, m16 + 1, content1), files0[entries[str0]] = mkfile(m3, md0, # links(entries[str0], dirs0), content), dirs0[m15] = mkdir(m1 + 1, md6, # links(m15, dirs0), m7, entries), err = ESUCCESS, name = str0, p_ino = m15, afs-cons(dirs0, files0), afs-cons (dirs0 [m15, (m15 = m0 ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0)).meta:= md2 ] [m0, mkdir(m2, md1, m11, m17, entries3) ], files0[entries1[str], mkfile(m, md8, m16, content1)]), dcache-cons(dcache, dirs0, files0), icache-cons(icache0, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache0, pcache), entries1[str] ∈ files0, m0 ∈ dirs0, str ∈ entries1, m15 ∈ dirs0, entries[str0] ∈ files0, str0 ∈ entries, asynced2 → synced(files0, icache0, pcache), m0 = m15 → md1 = md2, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m15, dirs0) ≠ ∅ ∨ m15 = ROOT_INO ⊦ ⟪let key = dentrykey(p_ino, name) in dcache := dcache -- key; dcache_set# (m0, mkdentry(mkdentry(str, entries1[str]).name, mkdentry(str0, entries[str0]).ino).name, mkdentry(mkdentry(str, entries1[str]).name, mkdentry(str0, entries[str0]).ino) ; err, dcache)⟫ ( icache-cons (icache0[m15, mkientry(false, mkinode(m15, md7, true, m13, m14, m12))][m0, mkientry(false, mkinode(m0, md1, true, m11, m17, m2))] [entries1[str], mkientry(false, mkinode(entries1[str], md8, false, m16, 0, m)) ], dirs0 [m15, (m15 = m0 ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0)).meta:= md2 ] [m0, (m0 = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ], files0[entries1[str], mkfile(m, md8, m16, content1)]) ∧ dcache-cons (dcache, dirs0 [m15, (m15 = m0 ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0)).meta:= md2 ] [m0, (m0 = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ], files0[entries1[str], mkfile(m, md8, m16, content1)]) ∧ pcache-cons (pcache, dirs0 [m15, (m15 = m0 ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0)).meta:= md2 ] [m0, (m0 = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ], files0[entries1[str], mkfile(m, md8, m16, content1)]) ∧ synced (dirs0 [m15, (m15 = m0 ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0)).meta:= md2 ] [m0, (m0 = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ], icache0[m15, mkientry(false, mkinode(m15, md7, true, m13, m14, m12))][m0, mkientry(false, mkinode(m0, md1, true, m11, m17, m2))] [entries1[str], mkientry(false, mkinode(entries1[str], md8, false, m16, 0, m)) ], pcache) ∧ ( asynced2 → synced (files0[entries1[str], mkfile(m, md8, m16, content1)], icache0[m15, mkientry(false, mkinode(m15, md7, true, m13, m14, m12))][m0, mkientry(false, mkinode(m0, md1, true, m11, m17, m2))] [entries1[str], mkientry(false, mkinode(entries1[str], md8, false, m16, 0, m)) ], pcache))), entries[str0] ∈ dirs0, entries1[str] ∈ dirs0, m15 = m0 ∧ mkdentry(str, entries1[str]) = mkdentry(str0, entries[str0])

Heuristic symbolic execution applied rule let right

And obtained the following new goals

Proof step 155:
# links(entries1[str], dirs0) = m16 + 1, (m0 = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])) = mkdir(m2, md, m11, m17, entries3), (m0 = m15 ⊃ mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0);mkdir(m4, md4, # links(m0, dirs0), m8, entries1)) = mkdir(m6, md3, m9, m10, entries0), (m15 = m0 ⊃ mkdir(m6, md1, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md2, # links(m15, dirs0), m7, entries -- str0)) = mkdir(m12, md7, m13, m14, entries2), dirs0[m15] = mkdir(m1 + 1, md6, # links(m15, dirs0), m7, entries), files0[entries[str0]] = mkfile(m3, md0, # links(entries[str0], dirs0), content), files0[entries1[str]] = mkfile(m5, md5, m16 + 1, content1), dirs0[m0] = mkdir(m4, md4, # links(m0, dirs0), m8, entries1), err = ESUCCESS, key = dentrykey(p_ino, name), name = str0, p_ino = m15, afs-cons (dirs0 [m15, (m15 = m0 ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0)).meta:= md2 ] [m0, mkdir(m2, md1, m11, m17, entries3) ], files0[entries1[str], mkfile(m, md8, m16, content1)]), afs-cons(dirs0, files0), dcache-cons(dcache, dirs0, files0), icache-cons(icache0, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache0, pcache), str0 ∈ entries, entries[str0] ∈ files0, m15 ∈ dirs0, str ∈ entries1, m0 ∈ dirs0, entries1[str] ∈ files0, m0 = m15 → md1 = md2, asynced2 → synced(files0, icache0, pcache), links(m15, dirs0) ≠ ∅ ∨ m15 = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪dcache := dcache -- key; dcache_set# (m0, mkdentry(mkdentry(str, entries1[str]).name, mkdentry(str0, entries[str0]).ino).name, mkdentry(mkdentry(str, entries1[str]).name, mkdentry(str0, entries[str0]).ino) ; err, dcache)⟫ ( icache-cons (icache0[m15, mkientry(false, mkinode(m15, md7, true, m13, m14, m12))][m0, mkientry(false, mkinode(m0, md1, true, m11, m17, m2))] [entries1[str], mkientry(false, mkinode(entries1[str], md8, false, m16, 0, m)) ], dirs0 [m15, (m15 = m0 ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0)).meta:= md2 ] [m0, (m0 = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ], files0[entries1[str], mkfile(m, md8, m16, content1)]) ∧ dcache-cons (dcache, dirs0 [m15, (m15 = m0 ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0)).meta:= md2 ] [m0, (m0 = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ], files0[entries1[str], mkfile(m, md8, m16, content1)]) ∧ pcache-cons (pcache, dirs0 [m15, (m15 = m0 ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0)).meta:= md2 ] [m0, (m0 = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ], files0[entries1[str], mkfile(m, md8, m16, content1)]) ∧ synced (dirs0 [m15, (m15 = m0 ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0)).meta:= md2 ] [m0, (m0 = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ], icache0[m15, mkientry(false, mkinode(m15, md7, true, m13, m14, m12))][m0, mkientry(false, mkinode(m0, md1, true, m11, m17, m2))] [entries1[str], mkientry(false, mkinode(entries1[str], md8, false, m16, 0, m)) ], pcache) ∧ ( asynced2 → synced (files0[entries1[str], mkfile(m, md8, m16, content1)], icache0[m15, mkientry(false, mkinode(m15, md7, true, m13, m14, m12))][m0, mkientry(false, mkinode(m0, md1, true, m11, m17, m2))] [entries1[str], mkientry(false, mkinode(entries1[str], md8, false, m16, 0, m)) ], pcache))), entries1[str] ∈ dirs0, entries[str0] ∈ dirs0, m15 = m0 ∧ mkdentry(str, entries1[str]) = mkdentry(str0, entries[str0])

Proof step 154 from proof inv-rename-file-dentry (previous step)

Heuristic symbolic execution applied rule let right

And obtained the following new goals

Rule argument

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