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Proof step 179 from proof inv-create (previous step)

dirs0[m1] = mkdir(m0, md2, # links(m1, dirs0), m4, entries1), icache0[ino] = mkientry(boolvar2, mkinode(ino, md3, boolvar1, m7, m8, m9)), afs-cons(dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]), afs-cons(dirs0, files0), synced(dirs0, icache0, pcache), m1 ∈ dirs0, ino ∈ icache0, asynced1 → synced(files0, icache0, pcache), (boolvar2 ⊃ ino ∈ files0 ∧ m7 = files0[ino].nlink ∧ m8 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs0 ∨ ino ∈ files0) ∧ 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, files0[ino].meta, false, files0[ino].nlink, 0, files0[ino].size) ) ), ∀ ino1. ino1 ∈ icache0 → icache0[ino1].inode.ino = ino1 ∧ (icache0[ino1].dirty ⊃ icache0[ino1].inode.ino ∈ files0 ∧ icache0[ino1].inode.nlink = files0[icache0[ino1].inode.ino].nlink ∧ icache0[ino1].inode.nsubdirs = 0 ∧ ¬ icache0[ino1].inode.directory ; (ino1 ∈ dirs0 ∨ ino1 ∈ files0) ∧ 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, files0[icache0[ino1].inode.ino].meta, false, files0[icache0[ino1].inode.ino].nlink, 0, files0[icache0[ino1].inode.ino].size) ) ), links(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ino = m1, ino = ino0, ino0 = 0, str ∈ entries1, ino0 ∈ files0, ino0 ∈ dirs0, (boolvar2 ⊃ ino ∈ files0 ∧ m7 = files0[ino].nlink ∧ m8 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs0 ∨ ino ∈ files0) ∧ 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, (files0 ++ ino0)[ino].meta, false, (files0 ++ ino0)[ino].nlink, 0, (files0 ++ ino0)[ino].size) ) )

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 180:
icache0[ino] = mkientry(boolvar2, mkinode(ino, md3, boolvar1, m7, m8, m9)), dirs0[m1] = mkdir(m0, md2, # links(m1, dirs0), m4, entries1), afs-cons(dirs0, files0), afs-cons(dirs0[m1, mkdir(m0 + 1, md1, # links(m1, dirs0), m4, entries1[str, ino0])], (files0 ++ ino0)[ino0, mkfile(0, md, 1, ∅)]), synced(dirs0, icache0, pcache), ino ∈ icache0, m1 ∈ dirs0, ino ∈ files0, asynced1 → synced(files0, icache0, pcache), (boolvar2 ⊃ ino ∈ files0 ∧ m7 = files0[ino].nlink ∧ m8 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs0 ∨ ino ∈ files0) ∧ 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, files0[ino].meta, false, files0[ino].nlink, 0, files0[ino].size) ) ), ∀ ino1. ino1 ∈ icache0 → icache0[ino1].inode.ino = ino1 ∧ (icache0[ino1].dirty ⊃ icache0[ino1].inode.ino ∈ files0 ∧ icache0[ino1].inode.nlink = files0[icache0[ino1].inode.ino].nlink ∧ icache0[ino1].inode.nsubdirs = 0 ∧ ¬ icache0[ino1].inode.directory ; (ino1 ∈ dirs0 ∨ ino1 ∈ files0) ∧ 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, files0[icache0[ino1].inode.ino].meta, false, files0[icache0[ino1].inode.ino].nlink, 0, files0[icache0[ino1].inode.ino].size) ) ), links(m1, dirs0) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ino = ino0, ino = m1, ino0 = 0, ino0 ∈ dirs0, ino0 ∈ files0, str ∈ entries1, (boolvar2 ⊃ ino ∈ files0 ∧ m7 = files0[ino].nlink ∧ m8 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs0 ∨ ino ∈ files0) ∧ 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, (files0 ++ ino0)[ino].meta, false, (files0 ++ ino0)[ino].nlink, 0, (files0 ++ ino0)[ino].size) ) )

Rule argument

fma: ino ∈ files0

Additional information

Used simplifier rules: ⊦ 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) Used formulas: ino ∈ files0