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Proof step 14 from proof min-in (previous step)

∀ x0. # x0 < # (i + i0 + x) → (true → x0 = [] ∨ min(x0) ∈ x0) ⊦ min(min(i, i0), min(max(i, i0) ' + x)) = i, min(min(i, i0), min(max(i, i0) ' + x)) = i0, min(min(i, i0), min(max(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 8:
¬ i < i0, ∀ x0. # x0 < # (i + i0 + x) → (true → x0 = [] ∨ min(x0) ∈ x0) ⊦ min(min(i, i0), min(max(i, i0) ' + x)) = i, min(min(i, i0), min(max(i, i0) ' + x)) = i0, min(min(i, i0), min(max(i, i0) ' + x)) ∈ x
Proof step 13:
i < i0, ∀ x0. # x0 < # (i + i0 + x) → (true → x0 = [] ∨ min(x0) ∈ x0) ⊦ min(i, min(max(i, i0) ' + x)) = i, min(i, min(max(i, i0) ' + x)) = i0, min(i, min(max(i, i0) ' + 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, 1, 1, 0, 1, 0)) dummy: () ]

Additional information

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