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Proof step 329 from proof inv-write_inode (previous step)

icache[m0] = mkientry(boolvar, mkinode(m0, md0, boolvar0, m1, m3, m4)), icache[ino] = mkientry(boolvar2, mkinode(m5, md1, boolvar1, m6, m7, m8)), afs-cons(dirs, files[m0, (files[m0].meta:= md).size:= m2]), afs-cons(dirs, files), synced(dirs, icache, pcache), synced(files, icache, pcache), m0 ∈ files, m0 ∈ icache, ino ∈ icache, (boolvar ⊃ m1 = files[m0].nlink ∧ m3 = 0 ∧ ¬ boolvar0 ;mkinode(m0, md0, boolvar0, m1, m3, m4) = mkinode(m0, files[m0].meta, false, files[m0].nlink, 0, files[m0].size) ), ∀ ino0. ino0 ∈ icache → icache[ino0].inode.ino = ino0 ∧ (icache[ino0].dirty ⊃ icache[ino0].inode.ino ∈ files ∧ icache[ino0].inode.nlink = files[icache[ino0].inode.ino].nlink ∧ icache[ino0].inode.nsubdirs = 0 ∧ ¬ icache[ino0].inode.directory ; (ino0 ∈ dirs ∨ ino0 ∈ files) ∧ icache[ino0].inode = (icache[ino0].inode.ino ∈ dirs ⊃ mkinode (icache[ino0].inode.ino, dirs[icache[ino0].inode.ino].meta, true, dirs[icache[ino0].inode.ino].nlink, dirs[icache[ino0].inode.ino].nsubdirs, dirs[icache[ino0].inode.ino].size) ;mkinode (icache[ino0].inode.ino, files[icache[ino0].inode.ino].meta, false, files[icache[ino0].inode.ino].nlink, 0, files[icache[ino0].inode.ino].size) ) ) ⊦ ino = m0, m5 = ino ∧ (boolvar2 ⊃ ino ∈ files ∧ m6 = files[ino].nlink ∧ m7 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs ∨ ino ∈ files) ∧ mkinode(ino, md1, boolvar1, m6, m7, m8) = (ino ∈ dirs ⊃ mkinode(ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[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 330:
icache[ino] = mkientry(boolvar2, mkinode(m5, md1, boolvar1, m6, m7, m8)), icache[m0] = mkientry(boolvar, mkinode(m0, md0, boolvar0, m1, m3, m4)), m1 = files[m0].nlink, afs-cons(dirs, files), afs-cons(dirs, files[m0, (files[m0].meta:= md).size:= m2]), synced(files, icache, pcache), synced(dirs, icache, pcache), ino ∈ icache, m0 ∈ icache, m0 ∈ files, (boolvar ⊃ m1 = files[m0].nlink ∧ m3 = 0 ∧ ¬ boolvar0 ;mkinode(m0, md0, boolvar0, m1, m3, m4) = mkinode(m0, files[m0].meta, false, files[m0].nlink, 0, files[m0].size) ), ∀ ino0. ino0 ∈ icache → icache[ino0].inode.ino = ino0 ∧ (icache[ino0].dirty ⊃ icache[ino0].inode.ino ∈ files ∧ icache[ino0].inode.nlink = files[icache[ino0].inode.ino].nlink ∧ icache[ino0].inode.nsubdirs = 0 ∧ ¬ icache[ino0].inode.directory ; (ino0 ∈ dirs ∨ ino0 ∈ files) ∧ icache[ino0].inode = (icache[ino0].inode.ino ∈ dirs ⊃ mkinode (icache[ino0].inode.ino, dirs[icache[ino0].inode.ino].meta, true, dirs[icache[ino0].inode.ino].nlink, dirs[icache[ino0].inode.ino].nsubdirs, dirs[icache[ino0].inode.ino].size) ;mkinode (icache[ino0].inode.ino, files[icache[ino0].inode.ino].meta, false, files[icache[ino0].inode.ino].nlink, 0, files[icache[ino0].inode.ino].size) ) ) ⊦ ino = m0, m5 = ino ∧ (boolvar2 ⊃ ino ∈ files ∧ m6 = files[ino].nlink ∧ m7 = 0 ∧ ¬ boolvar1 ; (ino ∈ dirs ∨ ino ∈ files) ∧ mkinode(ino, md1, boolvar1, m6, m7, m8) = (ino ∈ dirs ⊃ mkinode(ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode(ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ) )

Rule argument

fma: m1 = files[m0].nlink

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) Used formulas: m1 = files[m0].nlink