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Proof step 8 from proof transitivity (previous step)

key0 = inodekey(ino0), key0 < key1, key1.ino ≤ ino, ino < key0.ino ∨ ¬ key0.inode? ∧ ino = key0.ino ⊦ ¬ key1.inode? ∧ ino = key1.ino

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
key1.ino < ino0, ino < ino0, inodekey(ino0) < key1, key1.ino ≤ ino ⊦ ¬ key1.inode? ∧ ino = key1.ino

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ inodekey(m).inode?; (s)% ⊦ inodekey(m).ino = m; (s)