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Proof step 35 from proof unique-prefix (previous step)

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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 34:
depths(t2, i + 1) + x = depths(t3, i + 1) + y, ∀ i, x, t1, y. depths(t2, i) + x = depths(t1, i) + y → x = y ∧ t2 = t1, ∀ i, x, t1, y. depths(t0, i) + x = depths(t1, i) + y → x = y ∧ t0 = t1 ⊦ x = y ∧ t2 = t3

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ Node(t, t0) = Node(t1, t2) ↔ t = t1 ∧ t0 = t2], [CSIMPSEQ : ⊦ (x + y) + z = x + y + z], [CSIMPSEQ : ⊦ i + j = j + i])]]