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Proof step 30 from proof transitivity (previous step)

key0 = dentrykey(ino1, str), key0 < key1, key1.ino ≤ ino, ino < key0.ino ∨ key0.data? ∧ ino = key0.ino ∧ ino0 < key0.part ⊦ key1.data? ∧ ino = key1.ino ∧ ino0 < key1.part

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
key1.ino < ino1, ino < ino1, dentrykey(ino1, str) < key1, key1.ino ≤ ino ⊦ key1.data? ∧ ino = key1.ino ∧ ino0 < key1.part

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% ⊦ ¬ dentrykey(m, str).data?; (s)% ⊦ dentrykey(m, str).ino = m; (s)