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

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ j < i → min(j, i) = j
Proof step 5:
¬ i < i0, i0 < max(min(i, i0) ' + x), i < max(min(i, i0) ' + x), ∀ x0. # x0 < # (i + i0 + x) → (true → x0 = [] ∨ max(x0) ∈ x0) ⊦ max(min(i, i0) ' + x) ∈ x
Proof step 6:
i < i0, i0 < max(i ' + x), i < max(i ' + x), ∀ x0. # x0 < # (i + i0 + x) → (true → x0 = [] ∨ max(x0) ∈ x0) ⊦ max(i ' + x) ∈ x

Rule argument

[x0lemmaarg: spec-name: int-min instance-name: lemma-name: Min-left antecedent: succedent: j < i → min(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, 0, 1, 0, 1, 0)) dummy: () ]

Additional information

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