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Proof step 36 from proof unique-prefix (previous step)

depths(t, i + 1) + depths(t2, i + 1) + x = depths(t0, i + 1) + depths(t3, i + 1) + 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) = Node(t0, t3)

User applied rule all left

And obtained the following new goals

Proof step 35:
depths(t, i + 1) + depths(t2, i + 1) + x = depths(t0, i + 1) + depths(t3, i + 1) + y, depths(t, i + 1) + depths(t2, i + 1) + x = depths(t0, i + 1) + depths(t3, i + 1) + y → depths(t2, i + 1) + x = depths(t3, i + 1) + y ∧ t = t0, ∀ 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) = Node(t0, t3)

Rule argument

[EXRARG : pos: left 2, [extquanttermlist: (i + 1, depths(t2, i + 1) + x, t0, depths(t3, i + 1) + y) abort:F , discard:F , computed:T ]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (i + 1, depths(t2, i + 1) + x, t0, depths(t3, i + 1) + y)]]