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Proof step 28 from proof max-concat (previous step)

∀ 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)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ ¬ j < i → max(j, i) = j
Proof step 25:
¬ ¬ 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)))
Proof step 27:
¬ 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(min(i, i0), max(min(min(i, i0), i1) ' + x2 + y)), max(i, i0)) = max(max(y), max(max(min(i, i0), max(min(min(i, i0), i1) ' + x2)), max(i, i0)))

Rule argument

[x0lemmaarg: spec-name: int-min instance-name: lemma-name: Max-left antecedent: succedent: ¬ j < i → max(j, i) = j substlist: [i, j] → [i1, min(i, i0)] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (i1, min(i, i0))]]