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Proof step 11 from proof depths-min (previous step)

min(depths(t0, i + 1) + depths(t1, i + 1)) < i, ∀ i. ¬ min(depths(t0, i)) < i, ∀ i. ¬ min(depths(t1, i)) < i ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ x ≠ [] ∧ y ≠ [] → min(x + y) = min(min(x), min(y))
Proof step 5:
⊦ depths(t, i) ≠ []
Proof step 10:
depths(t0, i + 1) ≠ [] ∧ depths(t1, i + 1) ≠ [], min(min(depths(t0, i + 1)), min(depths(t1, i + 1))) < i, ∀ i. ¬ min(depths(t0, i)) < i, ∀ i. ¬ min(depths(t1, i)) < i ⊦

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: min-concat antecedent: succedent: x ≠ [] ∧ y ≠ [] → min(x + y) = min(min(x), min(y)) substlist: [y, x] → [depths(t1, i + 1), depths(t0, i + 1)] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 0, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (depths(t1, i + 1), depths(t0, i + 1))]]