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Proof step 9 from proof max-ge-every (previous step)

a0 < a, max(x0) < a0, a ∈ x0, ∀ a1. ¬ max(x0) < a1 ∨ ¬ a1 ∈ x0 ⊦ a = a0, x0 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
max(x0) < a0, a0 < a, max(x0) < a, a ∈ x0, ∀ a1. ¬ max(x0) < a1 ∨ ¬ a1 ∈ x0 ⊦ a = a0, x0 = []

Rule argument

Additional information

Used simplifier rules: transitivity: ⊦ a < b ∧ b < c → a < c; (forward) from specification oelem