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Proof step 21 from proof unique-prefix (previous step)

depths(Leaf, i) + x = depths(t1, i) + y ⊦ x = y ∧ Leaf = t1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 1:
⊦ depths(Leaf, i) = i '
Proof step 2:
⊦ depths(t, i) + x = d ' + y → d ∈ depths(t, i)
Proof step 20:
i ' + x = depths(t1, i) + y, i ∈ depths(t1, i) ⊦ x = y ∧ Leaf = t1

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ d ∈ x → d ∈ x + y], [CSIMPFORWARD : ⊦ d ' + x = y → d ∈ y], [CSIMPSEQ : ⊦ (x + y) + z = x + y + z])]]