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Proof step 23 from proof min-concat (previous step)

∀ x0, y0. # x0 + # y0 < # (i + i0 + x) + # y → (true → x0 = [] ∨ y0 = [] ∨ min(x0 + y0) = min(min(x0), min(y0))) ⊦ y = [], min(min(i, i0), min(max(i, i0) ' + x + y)) = min(min(min(i, i0), min(max(i, i0) ' + x)), min(y))

User applied rule constructor cut

And obtained the following new goals

Proof step 19:
x = [], ∀ x0, y0. # x0 + # y0 < # (i + i0 + x) + # y → (true → x0 = [] ∨ y0 = [] ∨ min(x0 + y0) = min(min(x0), min(y0))) ⊦ y = [], min(min(i, i0), min(max(i, i0) ' + x + y)) = min(min(min(i, i0), min(max(i, i0) ' + x)), min(y))
Proof step 22:
x = i1 + x2, ∀ x0, y0. # x0 + # y0 < # (i + i0 + x) + # y → (true → x0 = [] ∨ y0 = [] ∨ min(x0 + y0) = min(min(x0), min(y0))) ⊦ y = [], min(min(i, i0), min(max(i, i0) ' + x + y)) = min(min(min(i, i0), min(max(i, i0) ' + x)), min(y))

Rule argument

[var-arg: x]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : list generated by [], +;])]]