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Proof step 5 from proof in-depths-gt (previous step)

d ∈ depths(t, i), d < i ⊦

User applied rule insert lemma

And obtained the following new goals

Proof step 1:
⊦ i ∈ x → min(x) ≤ i
Proof step 4:
d ∈ depths(t, i) → min(depths(t, i)) ≤ d, d ∈ depths(t, i), d < i ⊦

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: min-le antecedent: succedent: i ∈ x → min(x) ≤ i substlist: [i, x] → [d, depths(t, i)] add preconditions?: F is rewrite lemma?: F current spec?: T rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (d, depths(t, i))]]