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Proof step 204 from proof inv-mkdir (previous step)

icache0[ino] = mkientry(boolvar2, mkinode(m6, md3, boolvar1, m7, m8, m9)), dirs0[m0] = mkdir(m3, md1, # links(m0, dirs0), m5, entries0), icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))][ino] = mkientry(boolvar0, mkinode(m, md0, boolvar, m1, m2, m4)), afs-cons(dirs0, files), afs-cons ((dirs0[m0, mkdir(m3 + 1, md1, # links(m0, dirs0), m5 + 1, entries0[str, ino0])] ++ ino0)[ino0, mkdir(0, md, 1, 0, ∅)] [m0, mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]) ], files), synced(dirs0, icache0, pcache), m0 ∈ dirs0, ino ∈ icache0[m0, mkientry(false, mkinode(m0, md2, true, # links(m0, dirs0), m5 + 1, m3 + 1))], ino ∈ icache0 → m6 = ino ∧ (boolvar2 ⊃ ino ∈ files ∧ m7 = files[ino].nlink ∧ m8 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs0 ∨ ino ∈ files) ∧ mkinode(ino, md3, boolvar1, m7, m8, m9) = (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), ∀ ino1. ino1 ∈ icache0 → icache0[ino1].inode.ino = ino1 ∧ (icache0[ino1].dirty ⊃ icache0[ino1].inode.ino ∈ files ∧ icache0[ino1].inode.nlink = files[icache0[ino1].inode.ino].nlink ∧ icache0[ino1].inode.nsubdirs = 0 ∧ ¬ icache0[ino1].inode.directory ; (ino1 ∈ dirs0 ∨ ino1 ∈ files) ∧ icache0[ino1].inode = (icache0[ino1].inode.ino ∈ dirs0 ⊃ mkinode (icache0[ino1].inode.ino, dirs0[icache0[ino1].inode.ino].meta, true, dirs0[icache0[ino1].inode.ino].nlink, dirs0[icache0[ino1].inode.ino].nsubdirs, dirs0[icache0[ino1].inode.ino].size) ;mkinode (icache0[ino1].inode.ino, files[icache0[ino1].inode.ino].meta, false, files[icache0[ino1].inode.ino].nlink, 0, files[icache0[ino1].inode.ino].size) ) ), links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ino = ino0, ino0 = 0, ino0 ∈ dirs0, ino0 ∈ files, str ∈ entries0, m = ino ∧ (boolvar0 ⊃ ino ∈ files ∧ m1 = files[ino].nlink ∧ m2 = 0 ∧ ¬ boolvar ; (ino ∈ dirs0 ∨ ino ∈ files) ∧ mkinode(ino, md0, boolvar, m1, m2, m4) = (ino ∈ dirs0 ⊃ mkinode (ino, (ino = m0 ⊃ mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]);dirs0[ino]).meta, true, (ino = m0 ⊃ mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]);dirs0[ino]).nlink, (ino = m0 ⊃ mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]);dirs0[ino]).nsubdirs, (ino = m0 ⊃ mkdir(m3 + 1, md2, # links(m0, dirs0), m5 + 1, entries0[str, ino0]);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 = m0

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 = m0