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Proof step 15 from proof unique-prefix (previous step)

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) = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
⊦ depths(t, i) ≠ []
Proof step 14:
depths(t, d + 1) = d ' + y ⊦

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ d ∈ d0 ' ↔ d = d0], [CSIMPSEQ : ⊦ d ∈ x + y ↔ ¬ ¬ (d ∈ x ∨ d ∈ y)], [CSIMPSEQ : ⊦ d ' + x ≠ []], [CSIMPSEQ : ⊦ (x + y) + z = x + y + z], [CSIMPFORWARD : ⊦ d ' + x = y → d ∈ y], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ d + x = d ' + x])]]