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Proof step 6 from proof min-com (previous step)

∀ x1, x2. #(x1 + x2) < #((a + x3) + x0) → true → x1 + x2 = [] ∨ min(x1 + x2) = min(x2 + x1) ⊦ min((a ' + x3) + x0) = min(x0 + a ' + x3)

User applied rule constructor cut

And obtained the following new goals

Proof step 7:
x0 = a0 + x, ∀ x1, x2. #(x1 + x2) < #((a + x3) + x0) → true → x1 + x2 = [] ∨ min(x1 + x2) = min(x2 + x1) ⊦ min((a ' + x3) + x0) = min(x0 + a ' + x3)

Rule argument

var: x0

Additional information

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