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Proof step 51 from proof eq-io-evict (previous step)

⟨afs_evict#(p_inode, asynced0; err, dirs1, files1)⟩ (err = err0 ∧ dirs1 = dirs0 ∧ files1 = files0), files[ino].nlink = 0, asynced ↔ boolvar0, dirs = dirs1, files = files1, ino = inode.ino, inode = p_inode, pre-evict(inode, dirs, files) ⊦ ino ∈ dirs, ESUCCESS = err0 ∧ dirs = dirs0 ∧ files -- ino = files0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 52:
⟨afs_evict#(p_inode, asynced0; err, dirs1, files1)⟩ (err = err0 ∧ dirs1 = dirs0 ∧ files1 = files0), p_inode.nlink = 0, p_inode.nsubdirs = 0, 0 = files1[p_inode.ino].nlink, p_inode.ino ≠ ROOT_INO, p_inode.ino ∈ files1, ¬ p_inode.directory, ¬ p_inode.ino ∈ dirs1 ⊦ ESUCCESS = err0 ∧ dirs1 = dirs0 ∧ files1 -- p_inode.ino = files0

Rule argument

Additional information

Used simplifier rules: ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)%⊦ valid-dir-inode(inode, dirs, files) ↔ valid-dir-ino(inode.ino, dirs, files) ∧ inode.nlink = dirs[inode.ino].nlink ∧ inode.size = dirs[inode.ino].size ∧ inode.nsubdirs = dirs[inode.ino].nsubdirs ∧ inode.directory; (s)%⊦ valid-wb-inode(inode, dirs, files) ↔ valid-dir-inode(inode, dirs, files) ∨ valid-file-inode(inode, dirs, files); (s)%⊦ pre-evict(inode, dirs, files) ↔ valid-wb-inode(inode, dirs, files) ∧ inode.ino ≠ ROOT_INO; (s)