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Proof step 145 from proof inv-rename-file-dentry (previous step)

# links(entries1[str], dirs0) = m11 + 1, (m15 = m ⊃ mkdir(m6, md1, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md2, # links(m15, dirs0), m7, entries -- str0)) = mkdir(m12, md7, m13, m14, entries2), (m = m15 ⊃ mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0);mkdir(m4, md4, # links(m, dirs0), m8, entries1)) = mkdir(m6, md3, m9, m10, entries0), ( m ∈ dirs0 [m15, (m15 = m ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0)).meta:= md2 ] [m, (m = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ] ⊃ mkinode (m, dirs0 [m15, (m15 = m ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0)).meta:= md2 ] [m, (m = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ] [m ] .meta, true, dirs0 [m15, (m15 = m ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0)).meta:= md2 ] [m, (m = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ] [m ] .nlink, dirs0 [m15, (m15 = m ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0)).meta:= md2 ] [m, (m = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ] [m ] .nsubdirs, dirs0 [m15, (m15 = m ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0)).meta:= md2 ] [m, (m = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ] [m ] .size) ;mkinode (m, (m = entries1[str] ∧ entries1[str] ∈ files0 ⊃ ( files0[entries1[str], mkfile(m5, md5, m11, content1)][entries1[str]] .size:= mkinode(entries1[str], md, false, # links(entries1[str], dirs0), 0, m2).size) .meta:= mkinode(entries1[str], md, false, # links(entries1[str], dirs0), 0, m2).meta ;files0[entries1[str], mkfile(m5, md5, m11, content1)][m] ) .meta, false, (m = entries1[str] ∧ entries1[str] ∈ files0 ⊃ ( files0[entries1[str], mkfile(m5, md5, m11, content1)][entries1[str]] .size:= mkinode(entries1[str], md, false, # links(entries1[str], dirs0), 0, m2).size) .meta:= mkinode(entries1[str], md, false, # links(entries1[str], dirs0), 0, m2).meta ;files0[entries1[str], mkfile(m5, md5, m11, content1)][m] ) .nlink, 0, (m = entries1[str] ∧ entries1[str] ∈ files0 ⊃ ( files0[entries1[str], mkfile(m5, md5, m11, content1)][entries1[str]] .size:= mkinode(entries1[str], md, false, # links(entries1[str], dirs0), 0, m2).size) .meta:= mkinode(entries1[str], md, false, # links(entries1[str], dirs0), 0, m2).meta ;files0[entries1[str], mkfile(m5, md5, m11, content1)][m] ) .size) ) = mkinode(m0, md8, boolvar, m16, m17, m18), dirs0[m] = mkdir(m4, md4, # links(m, dirs0), m8, entries1), files0[entries1[str]] = mkfile(m5, md5, m11 + 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, icache = icache0[m15, mkientry(false, mkinode(m15, md7, true, m13, m14, m12))] [m, mkientry (false, mkinode (m, md1, true, (m = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).nlink, (m = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).nsubdirs, (m = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).size)) ], afs-cons (dirs0[m15, (m15 = m ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0)).meta:= md2] [m, (m = 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(m2, md, m11, content1)]), afs-cons(dirs0, files0), dcache-cons(dcache, dirs0, files0), icache-cons(icache0, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache0, pcache), entries1[str] ∈ files0, m ∈ dirs0, str ∈ entries1, m15 ∈ dirs0, entries[str0] ∈ files0, str0 ∈ entries, asynced2 → synced(files0, icache0, pcache), m = m15 → md1 = md2, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m15, dirs0) ≠ ∅ ∨ m15 = ROOT_INO ⊦ ⟪icache_set# (mkinode (entries1[str], files0[entries1[str], (files0[entries1[str], mkfile(m5, md5, m11, content1)][entries1[str]].size:= m2).meta:= md][entries1[str]].meta, false, files0[entries1[str], (files0[entries1[str], mkfile(m5, md5, m11, content1)][entries1[str]].size:= m2).meta:= md][entries1[str]].nlink, 0, files0[entries1[str], (files0[entries1[str], mkfile(m5, md5, m11, content1)][entries1[str]].size:= m2).meta:= md][entries1[str]].size), false ; err, icache); dcache_delete#(m15, mkdentry(str0, entries[str0]).name; err, dcache); 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 (icache, dirs0 [m15, (m15 = m ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0)).meta:= md2 ] [m, (m = 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(m2, md, m11, content1)]) ∧ dcache-cons (dcache, dirs0 [m15, (m15 = m ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0)).meta:= md2 ] [m, (m = 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(m2, md, m11, content1)]) ∧ pcache-cons (pcache, dirs0 [m15, (m15 = m ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0)).meta:= md2 ] [m, (m = 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(m2, md, m11, content1)]) ∧ synced (dirs0 [m15, (m15 = m ⊃ mkdir(m6, md3, m9, m10, entries0[str, entries[str0]]);mkdir(m1, md6, # links(m15, dirs0), m7, entries -- str0)).meta:= md2 ] [m, (m = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).meta:= md1 ], icache, pcache) ∧ (asynced2 → synced(files0[entries1[str], mkfile(m2, md, m11, content1)], icache, pcache))), entries[str0] ∈ dirs0, entries1[str] ∈ dirs0, m15 = m ∧ mkdentry(str, entries1[str]) = mkdentry(str0, entries[str0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 146:
# links(entries1[str], dirs0) = m11 + 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), dirs0[m0] = mkdir(m4, md4, # links(m0, dirs0), m8, entries1), files0[entries1[str]] = mkfile(m5, md5, m11 + 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, icache = icache0[m15, mkientry(false, mkinode(m15, md7, true, m13, m14, m12))] [m0, mkientry (false, mkinode (m0, md1, true, (m0 = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).nlink, (m0 = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).nsubdirs, (m0 = m15 ⊃ mkdir(m6, md2, m9, m10, entries0[str, entries[str0]]);mkdir(m6, md3, m9, m10, entries0[str, entries[str0]])).size)) ], 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, (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(m2, md, m11, content1)]), afs-cons(dirs0, files0), 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, ¬ entries[str0] ∈ dirs0, ¬ entries1[str] ∈ dirs0, asynced2 → synced(files0, icache0, pcache), m0 = m15 → md1 = md2, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m15, dirs0) ≠ ∅ ∨ m15 = ROOT_INO ⊦ ⟪icache_set# (mkinode (entries1[str], files0[entries1[str], (files0[entries1[str], mkfile(m5, md5, m11, content1)][entries1[str]].size:= m2).meta:= md][entries1[str]].meta, false, files0[entries1[str], (files0[entries1[str], mkfile(m5, md5, m11, content1)][entries1[str]].size:= m2).meta:= md][entries1[str]].nlink, 0, files0[entries1[str], (files0[entries1[str], mkfile(m5, md5, m11, content1)][entries1[str]].size:= m2).meta:= md][entries1[str]].size), false ; err, icache); dcache_delete#(m15, mkdentry(str0, entries[str0]).name; err, dcache); 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 (icache, 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(m2, md, m11, 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(m2, md, m11, 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(m2, md, m11, 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 ], icache, pcache) ∧ (asynced2 → synced(files0[entries1[str], mkfile(m2, md, m11, content1)], icache, pcache))), m15 = m0 ∧ mkdentry(str, entries1[str]) = mkdentry(str0, entries[str0])

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2) = mkinode(m3, md0, boolvar0, m4, m5, m6) ↔ m = m3 ∧ md = md0 ∧ (boolvar ↔ boolvar0) ∧ m0 = m4 ∧ m1 = m5 ∧ m2 = m6; (ws)% ⊦ (ad.meta:= md).size = ad.size; (s)% ⊦ (ad.meta:= md).nsubdirs = ad.nsubdirs; (s)% ⊦ (ad.meta:= md).nlink = ad.nlink; (s)% ⊦ (ad.meta:= md).meta = md; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)