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Proof step 27 from proof unique-prefix (previous step)

(depths(t, i + 1) + depths(t2, i + 1)) + x = i ' + y, i ∈ depths(t, i + 1), i < min(depths(t, i + 1)), ∀ i, x, t1, y. depths(t2, i) + x = depths(t1, i) + y → x = y ∧ t2 = t1, ∀ i, x, t1, y. depths(t, i) + x = depths(t1, i) + y → x = y ∧ t = t1 ⊦

User applied rule insert lemma

And obtained the following new goals

Proof step 26:
⊦ i ∈ x → min(x) ≤ i

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: min-le antecedent: succedent: i ∈ x → min(x) ≤ i substlist: [i, x] → [i, depths(t, i + 1)] add preconditions?: F is rewrite lemma?: F current spec?: T rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)])], [EXTRATERMS : (i, depths(t, i + 1))]]