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Proof step 2 from proof prefix-trans (previous step)

∀ x, y. x ⊑ y ∧ y ⊑ z0 → x ⊑ z0 ⊦ x ⊑ y ∧ y ⊑ a + z0 → x ⊑ a + z0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
x ⊑ y, y ⊑ a ' + z0, ∀ x, y. x ⊑ y ∧ y ⊑ z0 → x ⊑ z0 ⊦ x ⊑ a ' + z0

Rule argument

Additional information

Used simplifier rules: c: ⊦ a + x = a ' + x; from specification list