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Proof step 579 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, ∅), icache0[m7, mkientry(false, mkinode(m7, md, true, m2, m5, m0))][entries0[str0], mkientry(false, mkinode(entries0[str0], md4, true, m8, m9, m))][ino] = mkientry(boolvar0, mkinode(m10, md5, boolvar, m11, m12, m13)), icache0[ino] = mkientry(boolvar2, mkinode(m14, md6, boolvar1, m15, m16, m17)), 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), synced(dirs0, icache0, pcache), entries0[str0] ∈ dirs0, str0 ∈ entries0, m7 ∈ dirs0, ino ∈ icache0 → m14 = ino ∧ (boolvar2 ⊃ ino ∈ files ∧ m15 = files[ino].nlink ∧ m16 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs0 ∨ ino ∈ files) ∧ mkinode(ino, md6, boolvar1, m15, m16, m17) = (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) ) ), asynced2 → synced(files, icache0, pcache), ∀ 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(m7, dirs0) ≠ ∅ ∨ m7 = ROOT_INO, ino = entries0[str0] ∨ ino ∈ icache0[m7, mkientry(false, mkinode(m7, md, true, m2, m5, m0))] ⊦ entries0[str0] = ROOT_INO, m10 = ino ∧ (boolvar0 ⊃ ino ∈ files ∧ m11 = files[ino].nlink ∧ m12 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino ∈ files) ∧ mkinode(ino, md5, boolvar, m11, m12, m13) = (ino ∈ dirs0 ⊃ mkinode (ino, (ino = entries0[str0] ⊃ mkdir(m, md4, m8, m9, entries1);(ino = m7 ⊃ mkdir(m1, md2, # links(m7, dirs0), m4, entries0);dirs0[ino])).meta, true, (ino = entries0[str0] ⊃ mkdir(m, md4, m8, m9, entries1);(ino = m7 ⊃ mkdir(m1, md2, # links(m7, dirs0), m4, entries0);dirs0[ino])) .nlink, (ino = entries0[str0] ⊃ mkdir(m, md4, m8, m9, entries1);(ino = m7 ⊃ mkdir(m1, md2, # links(m7, dirs0), m4, entries0);dirs0[ino])) .nsubdirs, (ino = entries0[str0] ⊃ mkdir(m, md4, m8, m9, entries1);(ino = m7 ⊃ mkdir(m1, md2, # links(m7, dirs0), m4, entries0);dirs0[ino])).size) ;mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ) )

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 580:
(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), icache0[ino] = mkientry(boolvar2, mkinode(m14, md6, boolvar1, m15, m16, m17)), icache0[m7, mkientry(false, mkinode(m7, md, true, m2, m5, m0))][entries0[str0], mkientry(false, mkinode(entries0[str0], md4, true, m8, m9, m))][ino] = mkientry(boolvar0, mkinode(m10, md5, boolvar, m11, m12, m13)), dirs0[entries0[str0]] = mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅), dirs0[m7] = mkdir(m1, md1, # links(m7, dirs0), m4, entries0), 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), synced(dirs0, icache0, pcache), m7 ∈ dirs0, str0 ∈ entries0, entries0[str0] ∈ dirs0, asynced2 → synced(files, icache0, pcache), ino ∈ icache0 → m14 = ino ∧ (boolvar2 ⊃ ino ∈ files ∧ m15 = files[ino].nlink ∧ m16 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs0 ∨ ino ∈ files) ∧ mkinode(ino, md6, boolvar1, m15, m16, m17) = (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) ) ), ino = entries0[str0] ∨ ino ∈ icache0[m7, mkientry(false, mkinode(m7, md, true, m2, m5, m0))], links(m7, dirs0) ≠ ∅ ∨ m7 = ROOT_INO ⊦ entries0[str0] = ROOT_INO, ino = entries0[str0], m10 = ino ∧ (boolvar0 ⊃ ino ∈ files ∧ m11 = files[ino].nlink ∧ m12 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino ∈ files) ∧ mkinode(ino, md5, boolvar, m11, m12, m13) = (ino ∈ dirs0 ⊃ mkinode (ino, (ino = entries0[str0] ⊃ mkdir(m, md4, m8, m9, entries1);(ino = m7 ⊃ mkdir(m1, md2, # links(m7, dirs0), m4, entries0);dirs0[ino])).meta, true, (ino = entries0[str0] ⊃ mkdir(m, md4, m8, m9, entries1);(ino = m7 ⊃ mkdir(m1, md2, # links(m7, dirs0), m4, entries0);dirs0[ino])) .nlink, (ino = entries0[str0] ⊃ mkdir(m, md4, m8, m9, entries1);(ino = m7 ⊃ mkdir(m1, md2, # links(m7, dirs0), m4, entries0);dirs0[ino])) .nsubdirs, (ino = entries0[str0] ⊃ mkdir(m, md4, m8, m9, entries1);(ino = m7 ⊃ mkdir(m1, md2, # links(m7, dirs0), m4, entries0);dirs0[ino])).size) ;mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ) )

Rule argument

fma: ino = entries0[str0]

Additional information

Used simplifier rules: ⊦ icache[ino, ie][ino] = ie; (s)%⊦ mkientry(boolvar, inode) = mkientry(boolvar0, inode0) ↔ (boolvar ↔ boolvar0) ∧ inode = inode0; (ws)%⊦ 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)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)% ⊦ mkdir(m, md, m0, m1, entries).meta = md; (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)% ⊦ mkdir(m, md, m0, m1, entries).nsubdirs = m1; (s)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (s) Used formulas: ino = entries0[str0]