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Proof step 16 from proof unique-prefix (previous step)

i = head(depths(t, i + 1)), i ∈ depths(t, i + 1) ⊦ depths(t, i + 1) + depths(t0, i + 1) = []

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
⊦ depths(t, i) ≠ []
Proof step 15:
depths(t, i + 1) = d + y ∧ depths(t, i + 1) ≠ [], i = d, i ∈ depths(t, i + 1) ⊦ depths(t, i + 1) + depths(t0, i + 1) = []

Rule argument

[x0lemmaarg: spec-name: list-data instance-name: intlist lemma-name: elim-list-c antecedent: x ≠ [] succedent: d = head(x) ∧ y = pop(x) ↔ x = d + y substlist: [x, d, y] → [depths(t, i + 1), d, y] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : x ≠ [] ⊦ d = head(x) ∧ y = pop(x) ↔ x = d + y])], [EXTRATERMS : (depths(t, i + 1), d, y)]]