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Proof step 11 from proof max-ge (previous step)

x1 ≠ [], max(x1 + x0) < (max(x1) < a ⊃ a;max(x1)), a < (max(x1) < a ⊃ a;max(x1)), max(x1 + x0) < a ⊦ x1 + x0 = [], x1 = [], ∃ x0. max(x1 + x0) < max(x1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
max(x1 + x0) < a, a < (max(x1) < a ⊃ a;max(x1)), max(x1 + x0) < max(x1) ⊦ x1 = [], x1 + x0 = [], ∃ x0. max(x1 + x0) < max(x1)

Rule argument

Additional information

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