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Proof step 18 from proof unique-prefix (previous step)

i ' + x = (depths(t, i + 1) + depths(t0, i + 1)) + y, i ∈ depths(t, i + 1) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
y ≠ [] ⊦ d ' + x = y + z ↔ d = head(y) ∧ x = pop(y) + z
Proof step 7:
⊦ depths(t, i) ≠ []
Proof step 17:
depths(t, i + 1) + depths(t0, i + 1) ≠ [], i = head(depths(t, i + 1) + depths(t0, i + 1)) ∧ x = pop(depths(t, i + 1) + depths(t0, i + 1)) + y, i ∈ depths(t, i + 1) ⊦

Rule argument

[x0lemmaarg: spec-name: list instance-name: intlist lemma-name: firsteq antecedent: y ≠ [] succedent: d ' + x = y + z ↔ d = head(y) ∧ x = pop(y) + z substlist: [z, y, x, d] → [y, depths(t, i + 1) + depths(t0, i + 1), x, i] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ x + y ≠ [] ↔ x = [] ∧ y = []], [CSIMPSEQ : ⊦ (x + y) + z = x + y + z])], [EXTRATERMS : (y, depths(t, i + 1) + depths(t0, i + 1), x, i)]]