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Proof step 29 from proof unique-prefix (previous step)

(depths(t, i + 1) + depths(t2, i + 1)) + x = i ' + y, i ∈ 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 25:
⊦ i ≤ min(depths(t, i))
Proof step 28:
i + 1 ≤ min(depths(t, i + 1)), (depths(t, i + 1) + depths(t2, i + 1)) + x = i ' + y, i ∈ 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 ⊦

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (i + 1, t)]]