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Proof step 24 from proof transitivity (previous step)

key1.ino < ino1, ino < ino1, inodekey(ino1) < key1, key1.ino ≤ ino ⊦ key1.data? ∧ ino = key1.ino ∧ ino0 < key1.part

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: key-order-def name: inode-less seq: ⊦ inodekey(ino) < key ↔ ino < key.ino ∨ ¬ key.inode? ∧ ino = key.ino subst: [key, ino] → [key1, ino1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < n → ¬ n < m; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ m ≤ n → (n < m ↔ false); (s) Used terms: key1, ino1