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Proof step 17 from proof unique-prefix (previous step)

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) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
i = head(depths(t, i + 1)), i ∈ depths(t, i + 1) ⊦ depths(t, i + 1) + depths(t0, i + 1) = []

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (x + y) + z = x + y + z], [CSIMPSEQ : ⊦ d ∈ x → head(x + y) = head(x)], [CSIMPSEQ : ⊦ i + j = j + i])]]