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Proof step 19 from proof min-concat (previous step)

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))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
⊦ min(i ') = i
Proof step 18:
∀ x0, y0. # x0 + # y0 < # (i + i0 + []) + # y → (true → x0 = [] ∨ y0 = [] ∨ min(x0 + y0) = min(min(x0), min(y0))) ⊦ y = [], min(min(max(i, i0) ' + y), min(i, i0)) = min(min(y), min(max(i, i0), min(i, i0)))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ x + [] = x], [CSIMPSEQ : ⊦ (x + y) + z = x + y + z], [CSIMPSEQ : ⊦ [] + x = x])]]