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Proof step 3 from proof shift-02 (previous step)

(∀ a. #oc(a, x) + #oc(a, x0) ≤ #oc(a, y)) ∧ (∀ a. #oc(a, y) ≤ #oc(a, x) + #oc(a, x0)) ⊦ (∀ a. #oc(a, x0) + #oc(a, x) ≤ #oc(a, y)) ∧ (∀ a. #oc(a, y) ≤ #oc(a, x0) + #oc(a, x))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
∀ a. #oc(a, x) + #oc(a, x0) ≤ #oc(a, y), ∀ a. #oc(a, y) ≤ #oc(a, x) + #oc(a, x0) ⊦ #oc(a, x0) + #oc(a, x) ≤ #oc(a, y) ∧ #oc(a0, y) ≤ #oc(a0, x0) + #oc(a0, x)

Proof step 3 from proof shift-02 (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information