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Proof step 219 from proof inv-rmdir (previous step)

# links(entries0[str], dirs0) = m8 + 1, dirs0[m5] = mkdir(m1 + 1, md1, # links(m5, dirs0), m0 + 1, entries0), dirs0[entries0[str]] = mkdir(m, md3, m8 + 1, m9, ∅), icache0[ino] = mkientry(boolvar2, mkinode(m17, md7, boolvar1, m18, m19, m20)), icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m))][ino] = mkientry(boolvar0, mkinode(m13, md6, boolvar, m14, m15, m16)), afs-cons(dirs0[m5, mkdir(m1, md5, # links(m5, dirs0), m0, 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, ino ∈ icache0[entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m))], 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) ) ), links(m5, dirs0) ≠ ∅ ∨ m5 = ROOT_INO ⊦ entries0[str] = ROOT_INO, entries0[str] = m5, ino = m5, 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, ∅);dirs0[ino]).meta, true, (ino = entries0[str] ⊃ mkdir(m, md0, m8, m9, ∅);dirs0[ino]).nlink, (ino = entries0[str] ⊃ mkdir(m, md0, m8, m9, ∅);dirs0[ino]).nsubdirs, (ino = entries0[str] ⊃ mkdir(m, md0, m8, m9, ∅);dirs0[ino]).size) ;mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ) )

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: ino = entries0[str]

Additional information

Used simplifier rules: ⊦ ino ≠ ino0 → icache[ino0, ie][ino] = icache[ino]; (s)% ⊦ ino ≠ ino0 → (ino ∈ icache[ino0, ie] ↔ ino ∈ icache); (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)% ⊦ icache[ino, ie][ino] = ie; (s)% ⊦ ino ∈ icache[ino, ie]; (s)% ⊦ 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[str]