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Proof step 66 from proof min-com (previous step)

¬ a0 < min(x + x3), min(x + a ' + x3) = min((a ' + x3) + x), min(x3 + a0 ' + x) = min(x + x3), a0 < min((a ' + x3) + x), ∀ x1, x2. #(x1 + x2) < #((a + x3) + (a0 + x)) → true → x1 + x2 = [] ∨ min(x1 + x2) = min(x2 + x1) ⊦ min(x + x3) = a0, x + x3 = [], a < min(x + x3)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 67:
min(x + a ' + x3) = min((a ' + x3) + x), min(x3 + a0 ' + x) = min(x + x3), a0 < min((a ' + x3) + x), min(x + x3) < a0, min(x + x3) < min((a ' + x3) + x), ∀ x1, x2. #(x1 + x2) < #((a + x3) + (a0 + x)) → true → x1 + x2 = [] ∨ min(x1 + x2) = min(x2 + x1) ⊦ min(x + x3) = a0, x + x3 = [], a < min(x + x3)

Rule argument

Additional information

Used simplifier rules: lel: ⊦ a < b ∧ a = c → c < b; (forward) from specification oelem%transitivity: ⊦ a < b ∧ b < c → a < c; (forward) from specification oelem%sls: ⊦ a ≠ b → (¬ a < b ↔ b < a); from specification oelem