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Proof step 21 from proof max-app (previous step)

min(i, i0) ' = [] ∨ x2 + y = [] ∨ max(min(i, i0) ' + x2 + y) = max(max(min(i, i0) '), max(x2 + y)), min(i, i0) < i1, x2 = [] ∨ max(min(i, i0) ' + x2) = max(max(x2), min(i, i0)), ∀ 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))))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
⊦ max(i ') = i
Proof step 20:
max(min(i, i0) ' + x2) = max(max(x2), min(i, i0)), max(min(i, i0) ' + x2 + y) = max(max(x2 + y), min(i, i0)), min(i, i0) < i1, ∀ x0, y0. # x0 + # y0 < # (i + i0 + i1 + x2) + # y → (true → x0 = [] ∨ y0 = [] ∨ max(x0 + y0) = max(max(x0), max(y0))) ⊦ x2 + y = [], y = [], x2 = [], max(i1, max(max(x2 + y), max(i, i0))) = max(i1, max(max(x2), max(max(y), max(i, i0))))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ x + [] = x], [CSIMPSEQ : ⊦ [] + x = x], [CSIMPSEQ : ⊦ j < i → max(j, i) = i], [CSIMPSEQ : ⊦ (x + y) + z = x + y + z], [CSIMPSEQ : ⊦ ¬ x + y ≠ [] ↔ x = [] ∧ y = []], [CSIMPSEQ : ⊦ min(i, j) = min(j, i)], [CSIMPSEQ : ⊦ d ' ≠ []], [CSIMPSEQ : ⊦ max(i, j) = max(j, i)], [CSIMPSEQ : ⊦ max(i, max(j, j0)) = max(max(i, j), j0)])]]