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Proof step 30 from proof unique-prefix (previous step)

t1 = Leaf, (depths(t, i + 1) + depths(t2, i + 1)) + x = depths(t1, i) + y, ∀ i, x, t1, y. depths(t, i) + x = depths(t1, i) + y → x = y ∧ t = t1, ∀ i, x, t1, y. depths(t2, i) + x = depths(t1, i) + y → x = y ∧ t2 = t1 ⊦ x = y ∧ Node(t, t2) = t1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
⊦ depths(Leaf, i) = i '
Proof step 24:
⊦ depths(t, i) + x = d ' + y → d ∈ depths(t, i)
Proof step 29:
(depths(t, i + 1) + depths(t2, i + 1)) + x = i ' + y, i ∈ depths(t, i + 1), ∀ i, x, t1, y. depths(t2, i) + x = depths(t1, i) + y → x = y ∧ t2 = t1, ∀ i, x, t1, y. depths(t, i) + x = depths(t1, i) + y → x = y ∧ t = 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], [CSIMPSEQ : ⊦ Leaf ≠ Node(t, t0)])]]