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Proof step 40 from proof unique-prefix (previous step)

(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

User applied rule constructor cut

And obtained the following new goals

Proof step 30:
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
Proof step 39:
t1 = Node(t0, t3), (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

Rule argument

[var-arg: t1]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : tree generated by leaf, node;])]]