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Proof step 41 from proof unique-prefix (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
⊦ depths(Node(t0, t1), i) = depths(t0, i + 1) + depths(t1, i + 1)
Proof step 40:
(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

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]