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Proof step 211 from proof inv-rmdir (previous step)

(entries0[str] = m5 ⊃ mkdir(m0 - 1, md1, # links(entries0[str], dirs0), m2 - 1, entries0 -- str) ;mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅) ) = mkdir(m3, md2, m7 + 1, m6, entries), (entries0[str] = m5 ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)) = mkdir(m, md4, m8, m9, entries1), (m5 = entries0[str] ⊃ mkdir(m3, md0, m7, m6, entries);mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str)) = mkdir(m10, md5, m11, m12, entries2), dirs0[entries0[str]] = mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅), dirs0[m5] = mkdir(m0, md1, # links(m5, dirs0), m2, entries0), icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m))][m5, mkientry(false, mkinode(m5, md5, true, m11, m12, m10))] [ino ] = mkientry(boolvar0, mkinode(m13, md6, boolvar, m14, m15, m16)), icache0[ino] = mkientry(boolvar2, mkinode(m17, md7, boolvar1, m18, m19, m20)), afs-cons(dirs0, files), afs-cons (dirs0[m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], mkdir(m, md0, m8, m9, entries1) ], files), synced(dirs0, icache0, pcache), entries0[str] ∈ dirs0, str ∈ entries0, m5 ∈ dirs0, 1 ≤ m2, 1 ≤ m0, ino ∈ icache0 → m17 = ino ∧ (boolvar2 ⊃ ino ∈ files ∧ m18 = files[ino].nlink ∧ m19 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs0 ∨ ino ∈ files) ∧ mkinode(ino, md7, boolvar1, m18, m19, m20) = (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) ) ), asynced1 → 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(m5, dirs0) ≠ ∅ ∨ m5 = ROOT_INO, ino = m5 ∨ ino ∈ icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m))] ⊦ entries0[str] = ROOT_INO, m0 = 0, m2 = 0, m13 = ino ∧ (boolvar0 ⊃ ino ∈ files ∧ m14 = files[ino].nlink ∧ m15 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino ∈ files) ∧ mkinode(ino, md6, boolvar, m14, m15, m16) = (ino ∈ dirs0 ⊃ mkinode (ino, (ino = entries0[str] ⊃ mkdir(m, md0, m8, m9, entries1) ;(ino = m5 ⊃ mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str);dirs0[ino]) ) .meta, true, (ino = entries0[str] ⊃ mkdir(m, md0, m8, m9, entries1) ;(ino = m5 ⊃ mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str);dirs0[ino]) ) .nlink, (ino = entries0[str] ⊃ mkdir(m, md0, m8, m9, entries1) ;(ino = m5 ⊃ mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str);dirs0[ino]) ) .nsubdirs, (ino = entries0[str] ⊃ mkdir(m, md0, m8, m9, entries1) ;(ino = m5 ⊃ mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str);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 212:
(m5 = entries0[str] ⊃ mkdir(m3, md0, m7, m6, entries);mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str)) = mkdir(m10, md5, m11, m12, entries2), (entries0[str] = m5 ⊃ mkdir(m3, md, m7, m6, entries);mkdir(m3, md2, m7, m6, entries)) = mkdir(m, md4, m8, m9, entries1), (entries0[str] = m5 ⊃ mkdir(m0 - 1, md1, # links(entries0[str], dirs0), m2 - 1, entries0 -- str) ;mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅) ) = mkdir(m3, md2, m7 + 1, m6, entries), icache0[ino] = mkientry(boolvar2, mkinode(m17, md7, boolvar1, m18, m19, m20)), icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m))][m5, mkientry(false, mkinode(m5, md5, true, m11, m12, m10))] [ino ] = mkientry(boolvar0, mkinode(m13, md6, boolvar, m14, m15, m16)), dirs0[m5] = mkdir(m0, md1, # links(m5, dirs0), m2, entries0), dirs0[entries0[str]] = mkdir(m1, md3, # links(entries0[str], dirs0), m4, ∅), afs-cons (dirs0[m5, (m5 = entries0[str] ⊃ mkdir(m3, md2, m7, m6, entries);mkdir(m0 - 1, md1, # links(m5, dirs0), m2 - 1, entries0 -- str)).meta:= md] [entries0[str], mkdir(m, md0, m8, m9, entries1) ], files), afs-cons(dirs0, files), synced(dirs0, icache0, pcache), m5 ∈ dirs0, str ∈ entries0, entries0[str] ∈ dirs0, 1 ≤ m0, 1 ≤ m2, asynced1 → synced(files, icache0, pcache), ino ∈ icache0 → m17 = ino ∧ (boolvar2 ⊃ ino ∈ files ∧ m18 = files[ino].nlink ∧ m19 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs0 ∨ ino ∈ files) ∧ mkinode(ino, md7, boolvar1, m18, m19, m20) = (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 = m5 ∨ ino ∈ icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m))], links(m5, dirs0) ≠ ∅ ∨ m5 = ROOT_INO ⊦ entries0[str] = ROOT_INO, entries0[str] = m5, m0 = 0, m2 = 0, m13 = ino ∧ (boolvar0 ⊃ ino ∈ files ∧ m14 = files[ino].nlink ∧ m15 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino ∈ files) ∧ mkinode(ino, md6, boolvar, m14, m15, m16) = (ino ∈ dirs0 ⊃ mkinode (ino, (ino = entries0[str] ⊃ mkdir(m, md0, m8, m9, entries1) ;(ino = m5 ⊃ mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str);dirs0[ino]) ) .meta, true, (ino = entries0[str] ⊃ mkdir(m, md0, m8, m9, entries1) ;(ino = m5 ⊃ mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str);dirs0[ino]) ) .nlink, (ino = entries0[str] ⊃ mkdir(m, md0, m8, m9, entries1) ;(ino = m5 ⊃ mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str);dirs0[ino]) ) .nsubdirs, (ino = entries0[str] ⊃ mkdir(m, md0, m8, m9, entries1) ;(ino = m5 ⊃ mkdir(m0 - 1, md, # links(m5, dirs0), m2 - 1, entries0 -- str);dirs0[ino]) ) .size) ;mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ) )

Rule argument

fma: entries0[str] = m5

Additional information

Used simplifier rules: ⊦ icache[ino, ie][ino, ie0] = icache[ino, ie0]; (s)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)%⊦ mkdir(m, md, m0, m1, entries).meta:= md0 = mkdir(m, md0, m0, m1, entries); (s)% ⊦ dirs[ino, ad][ino, ad0] = dirs[ino, ad0]; (s)%⊦ p_ino ∈ dirs ∧ dirs[p_ino] = mkdir(m, md, n, n0, entries) ∧ str ∈ entries → links(entries[str], dirs) ≠ ∅; (s)% ⊦ ino ≠ ino0 → (ino ∈ icache[ino0, ie] ↔ ino ∈ icache); (s)%afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base% ⊦ ¬ str ∈ ∅; (s) Used formulas: entries0[str] = m5