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Proof step 116 from proof fsync-inode-overwrite (previous step)

icache[m2] = mkientry(false, mkinode(m2, md, false, m3, m4, m5)), files0[m2] = mkfile(m0, md0, m1, content), mkinode(m2, md, false, m3, m4, m5) = (m2 ∈ dirs ⊃ mkinode(m2, dirs[m2].meta, true, dirs[m2].nlink, dirs[m2].nsubdirs, dirs[m2].size);mkinode(m2, md0, false, m1, 0, m0)), m2 ∈ icache, m2 ∈ files0, ∀ ino. ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ icache[ino].inode.ino ∈ files0 ∧ icache[ino].inode.nlink = files0[icache[ino].inode.ino].nlink ∧ icache[ino].inode.nsubdirs = 0 ∧ ¬ icache[ino].inode.directory ; (ino ∈ dirs ∨ ino ∈ files0) ∧ icache[ino].inode = (icache[ino].inode.ino ∈ dirs ⊃ mkinode (icache[ino].inode.ino, dirs[icache[ino].inode.ino].meta, true, dirs[icache[ino].inode.ino].nlink, dirs[icache[ino].inode.ino].nsubdirs, dirs[icache[ino].inode.ino].size) ;mkinode (icache[ino].inode.ino, files0[icache[ino].inode.ino].meta, false, files0[icache[ino].inode.ino].nlink, 0, files0[icache[ino].inode.ino].size) ) ) ⊦ mkfile(m0, md0, m1, content) = mkfile(m5, md, m3, content)

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: m2 ∈ dirs

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: m2 ∈ dirs