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Proof step 214 from proof inv-rmdir (previous step)

# links(entries0[str], dirs0) = m8 + 1, dirs0[entries0[str]] = mkdir(m, md3, m8 + 1, m9, ∅), 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, # links(m5, dirs0), m2 - 1, m1)) ] [ino ] = mkientry(boolvar0, mkinode(m13, md6, boolvar, m14, m15, m16)), icache0[ino] = mkientry(boolvar2, mkinode(m17, md7, boolvar1, m18, m19, m20)), m0 = m1 + 1, afs-cons(dirs0, files), afs-cons(dirs0[m5, mkdir(m1, md5, # links(m5, dirs0), m2 - 1, entries0 -- str)][entries0[str], mkdir(m, md0, m8, m9, ∅)], 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] = m5, 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, ∅);(ino = m5 ⊃ mkdir(m1, md5, # links(m5, dirs0), m2 - 1, entries0 -- str);dirs0[ino])) .meta, true, (ino = entries0[str] ⊃ mkdir(m, md0, m8, m9, ∅);(ino = m5 ⊃ mkdir(m1, md5, # links(m5, dirs0), m2 - 1, entries0 -- str);dirs0[ino])) .nlink, (ino = entries0[str] ⊃ mkdir(m, md0, m8, m9, ∅);(ino = m5 ⊃ mkdir(m1, md5, # links(m5, dirs0), m2 - 1, entries0 -- str);dirs0[ino])) .nsubdirs, (ino = entries0[str] ⊃ mkdir(m, md0, m8, m9, ∅);(ino = m5 ⊃ mkdir(m1, md5, # links(m5, dirs0), m2 - 1, entries0 -- str);dirs0[ino])) .size) ;mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ) )

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 215:
# links(entries0[str], dirs0) = m8 + 1, 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, # links(m5, dirs0), m2 - 1, m1)) ] [ino ] = mkientry(boolvar0, mkinode(m13, md6, boolvar, m14, m15, m16)), dirs0[m5] = mkdir(m1 + 1, md1, # links(m5, dirs0), m2, entries0), dirs0[entries0[str]] = mkdir(m, md3, m8 + 1, m9, ∅), afs-cons(dirs0[m5, mkdir(m1, md5, # links(m5, dirs0), m2 - 1, entries0 -- str)][entries0[str], mkdir(m, md0, m8, m9, ∅)], files), afs-cons(dirs0, files), synced(dirs0, icache0, pcache), m5 ∈ dirs0, str ∈ entries0, entries0[str] ∈ dirs0, 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, 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, ∅);(ino = m5 ⊃ mkdir(m1, md5, # links(m5, dirs0), m2 - 1, entries0 -- str);dirs0[ino])) .meta, true, (ino = entries0[str] ⊃ mkdir(m, md0, m8, m9, ∅);(ino = m5 ⊃ mkdir(m1, md5, # links(m5, dirs0), m2 - 1, entries0 -- str);dirs0[ino])) .nlink, (ino = entries0[str] ⊃ mkdir(m, md0, m8, m9, ∅);(ino = m5 ⊃ mkdir(m1, md5, # links(m5, dirs0), m2 - 1, entries0 -- str);dirs0[ino])) .nsubdirs, (ino = entries0[str] ⊃ mkdir(m, md0, m8, m9, ∅);(ino = m5 ⊃ mkdir(m1, md5, # 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

Additional information

Used simplifier rules: ⊦ m ≤ m + n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)