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Proof step 98 from proof min-com (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 99:
min(x + a ' + x3) = min(x3 + x), min(x3 + a0 ' + x) = min(x + x3), ∀ x1, x2. #(x1 + x2) < #((a + x3) + (a0 + x)) → true → x1 + x2 = [] ∨ min(x1 + x2) = min(x2 + x1) ⊦ x3 + x = [], x + x3 = [], min(x + x3) = min(x3 + x), a0 < min(x3 + x), a0 < min(x + x3), a < min(x + x3), a < min(x3 + x)

Rule argument

Additional information

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