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Proof step 25 from proof max-app (previous step)

¬ ¬ min(i, i0) < i1, ∀ x0, y0. # x0 + # y0 < # (i + i0 + i1 + x2) + # y → (true → x0 = [] ∨ y0 = [] ∨ max(x0 + y0) = max(max(x0), max(y0))) ⊦ y = [], max(max(max(min(i, i0), i1), max(min(min(i, i0), i1) ' + x2 + y)), max(i, i0)) = max(max(y), max(max(max(min(i, i0), i1), max(min(min(i, i0), i1) ' + x2)), max(i, i0)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
min(i, i0) < i1, ∀ x0, y0. # x0 + # y0 < # (i + i0 + i1 + x2) + # y → (true → x0 = [] ∨ y0 = [] ∨ max(x0 + y0) = max(max(x0), max(y0))) ⊦ y = [], max(i1, max(max(min(i, i0) ' + x2 + y), max(i, i0))) = max(i1, max(max(min(i, i0) ' + x2), max(max(y), max(i, i0))))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ max(i, j) = max(j, i)], [CSIMPSEQ : ⊦ max(i, max(j, j0)) = max(max(i, j), j0)], [CSIMPSEQ : ⊦ j < i → max(j, i) = i], [CSIMPSEQ : ⊦ min(i, min(j, j0)) = min(min(i, j), j0)], [CSIMPSEQ : ⊦ j < i → min(j, i) = j], [CSIMPSEQ : ⊦ min(i, j) = min(j, i)])]]