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Proof step 7 from proof min-concat (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ ¬ j < i → max(j, i) = j
Proof step 6:
⊦ min(i ') = i

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ j < i → min(j, i) = j], [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 : ⊦ min(i, j) = min(j, i)], [CSIMPSEQ : ⊦ ¬ j < i → min(j, i) = i], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ x + [] = x], [CSIMPSEQ : ⊦ (x + y) + z = x + y + z], [CSIMPSEQ : ⊦ j ≤ i → min(i, j) = j])], [EXTRATERMS : (i0, i)]]