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Proof step 4 from proof min-com (previous step)

∀ x1, x2. #(x1 + x2) < #(x + x0) → true → x1 + x2 = [] ∨ min(x1 + x2) = min(x2 + x1) ⊦ x + x0 = [], min(x + x0) = min(x0 + x)

User applied rule constructor cut

And obtained the following new goals

Proof step 5:
x = a + x3, ∀ x1, x2. #(x1 + x2) < #(x + x0) → true → x1 + x2 = [] ∨ min(x1 + x2) = min(x2 + x1) ⊦ x + x0 = [], min(x + x0) = min(x0 + x)

Rule argument

var: x

Additional information

Used simplifier rules: list freely generated by [], +;;%Nil: ⊦ [] + x = x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%app: ⊦ x + [] = x; from specification list