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Proof step 21 from proof max-com (previous step)

∀ x1, x2. # x1 + # x2 < #(a + []) + #(a0 + []) → true → x1 + x2 = [] ∨ max(x1 + x2) = max(x2 + x1) ⊦ (a0 < a ⊃ a;a0) = (a < a0 ⊃ a0;a)

User applied rule case distinction

And obtained the following new goals

Proof step 22:
¬ a0 < a, ∀ x1, x2. # x1 + # x2 < #(a + []) + #(a0 + []) → true → x1 + x2 = [] ∨ max(x1 + x2) = max(x2 + x1) ⊦ a0 = (a < a0 ⊃ a0;a)

Rule argument

pos: right 1

Additional information

Used simplifier rules: ls-le: ⊦ a < b → (¬ b < a ↔ true); from specification oelem