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Proof step 5 from proof in-prefixn-pos-smaller (previous step)

a ∈ firstn(n, a0 + x0), n ≤ pos(a, a0 + x0), ∀ a, n. ¬(a ∈ firstn(n, x0) ∧ n ≤ pos(a, x0)) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
a ∈ firstn(n, a0 ' + x0), n ≤ pos(a, a0 ' + x0), ∀ a1, n0. ¬ a1 ∈ firstn(n0, x0) ∨ ¬ n0 ≤ pos(a1, x0) ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ a + x = a ' + x; (s)