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Proof step 7 from proof max-ge (previous step)

i0 < i, i1 < i, max(min(i0, i1) ' + x) < i, i ∈ x, ∀ x0, i. # x0 < # (i0 + i1 + x) → (i ∈ x0 ∧ max(x0) < i → false) ⊦ i = i1, i = i0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ j < i → min(j, i) = j
Proof step 5:
¬ i0 < i1, i0 < i, i1 < i, max(min(i0, i1) ' + x) < i, i ∈ x, ∀ x0, i. # x0 < # (i0 + i1 + x) → (i ∈ x0 ∧ max(x0) < i → false) ⊦ i = i1, i = i0
Proof step 6:
i0 < i1, i0 < i, i1 < i, max(i0 ' + x) < i, i ∈ x, ∀ x0, i. # x0 < # (i0 + i1 + x) → (i ∈ x0 ∧ max(x0) < i → false) ⊦ i = i1, i = i0

Rule argument

[x0lemmaarg: spec-name: int-min instance-name: lemma-name: Min-left antecedent: succedent: j < i → min(j, i) = j substlist: [i, j] → [i1, i0] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 2, 1, 0, 1, 0, 1, 0, 1, 0)) dummy: () ]

Additional information

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