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Proof step 269 from proof inv-rename-file-negdentry (previous step)

# links (entries[str], dirs0 [m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0 ] [m, mkdir(m12, md5, m13, m14, entries3) ]) = # links(entries[str], dirs0), (m = m8 ⊃ mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str);mkdir(m7, md4, # links(m, dirs0), m9, entries2)) = mkdir(m1, md2, m4, m6, entries1), (m8 = m ⊃ mkdir(m1 + 1, md5, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str)) = mkdir(m0, md1, m10, m11, entries0), (m = m8 ⊃ mkdir(m1 + 1, md0, m4, m6, entries1[str0, entries[str]]);mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]])) = mkdir(m12, md6, m13, m14, entries3), icache0[ino] = mkientry(boolvar2, mkinode(m19, md8, boolvar1, m20, m21, m22)), icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))][ino] = mkientry(boolvar0, mkinode(m15, md7, boolvar, m16, m17, m18)), dirs0[m8] = mkdir(m2 + 1, md3, # links(m8, dirs0), m5, entries), files[entries[str]] = mkfile(m3, md, # links(entries[str], dirs0), content0), dirs0[m] = mkdir(m7, md4, # links(m, dirs0), m9, entries2), afs-cons(dirs0, files), afs-cons (dirs0[m8, (m8 = m ⊃ mkdir(m1 + 1, md2, m4, m6, entries1[str0, entries[str]]);mkdir(m2, md3, # links(m8, dirs0), m5, entries -- str)).meta:= md0] [m, mkdir(m12, md5, m13, m14, entries3) ], files), synced(dirs0, icache0, pcache), str ∈ entries, entries[str] ∈ files, m ∈ dirs0, m8 ∈ dirs0, ino ∈ icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))][m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))], asynced2 → synced(files, icache0, pcache), m = m8 → md5 = md0, ino ∈ icache0 → m19 = ino ∧ (boolvar2 ⊃ ino ∈ files ∧ m20 = files[ino].nlink ∧ m21 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs0 ∨ ino ∈ files) ∧ mkinode(ino, md8, boolvar1, m20, m21, m22) = (ino ∈ dirs0 ⊃ mkinode(ino, dirs0[ino].meta, true, dirs0[ino].nlink, dirs0[ino].nsubdirs, dirs0[ino].size) ;mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ) ), ∀ ino0. ino0 ∈ icache0 → icache0[ino0].inode.ino = ino0 ∧ (icache0[ino0].dirty ⊃ icache0[ino0].inode.ino ∈ files ∧ icache0[ino0].inode.nlink = files[icache0[ino0].inode.ino].nlink ∧ icache0[ino0].inode.nsubdirs = 0 ∧ ¬ icache0[ino0].inode.directory ; (ino0 ∈ dirs0 ∨ ino0 ∈ files) ∧ icache0[ino0].inode = (icache0[ino0].inode.ino ∈ dirs0 ⊃ mkinode (icache0[ino0].inode.ino, dirs0[icache0[ino0].inode.ino].meta, true, dirs0[icache0[ino0].inode.ino].nlink, dirs0[icache0[ino0].inode.ino].nsubdirs, dirs0[icache0[ino0].inode.ino].size) ;mkinode (icache0[ino0].inode.ino, files[icache0[ino0].inode.ino].meta, false, files[icache0[ino0].inode.ino].nlink, 0, files[icache0[ino0].inode.ino].size) ) ), links(m8, dirs0) ≠ ∅ ∨ m8 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries[str] ∈ dirs0, str0 ∈ entries2, m15 = ino ∧ (boolvar0 ⊃ ino ∈ files ∧ m16 = files[ino].nlink ∧ m17 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino ∈ files) ∧ mkinode(ino, md7, boolvar, m16, m17, m18) = (ino ∈ dirs0 ⊃ mkinode (ino, (ino = m ⊃ mkdir(m12, md5, m13, m14, entries3);(ino = m8 ⊃ mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str);dirs0[ino])).meta, true, (ino = m ⊃ mkdir(m12, md5, m13, m14, entries3);(ino = m8 ⊃ mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str);dirs0[ino])).nlink, (ino = m ⊃ mkdir(m12, md5, m13, m14, entries3);(ino = m8 ⊃ mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str);dirs0[ino])) .nsubdirs, (ino = m ⊃ mkdir(m12, md5, m13, m14, entries3);(ino = m8 ⊃ mkdir(m2, md0, # links(m8, dirs0), m5, entries -- str);dirs0[ino])).size) ;mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ) )

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: store, inst: icache name: In-insert seq: ⊦ ino ∈ icache[ino0, ie] ↔ ino = ino0 ∨ ino ∈ icache subst: [ino, icache, ino0, ie] → [ino, icache0 [m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0)) ], m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))] flags: <all paths>

Additional information

Used terms: ino, icache0[m8, mkientry(false, mkinode(m8, md1, true, m10, m11, m0))], m, mkientry(false, mkinode(m, md5, true, m13, m14, m12))