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Proof step 19 from proof unique-prefix (previous step)

t1 = Node(t, t0), i ' + x = depths(t1, i) + y, i ∈ depths(t1, i) ⊦ x = y ∧ Leaf = t1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ depths(Node(t0, t1), i) = depths(t0, i + 1) + depths(t1, i + 1)
Proof step 5:
⊦ depths(t, i) + x = d ' + y → d ∈ depths(t, i)
Proof step 18:
i ' + x = (depths(t, i + 1) + depths(t0, i + 1)) + y, i ∈ depths(t, i + 1) ⊦

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ d ∈ x → d ∈ x + y], [CSIMPFORWARD : ⊦ d ' + x = y → d ∈ y], [CSIMPSEQ : ⊦ Leaf ≠ Node(t, t0)], [CSIMPSEQ : ⊦ (x + y) + z = x + y + z], [CSIMPSEQ : ⊦ d ∈ x + y ↔ ¬ ¬ (d ∈ x ∨ d ∈ y)], [CSIMPSEQ : ⊦ i + j = j + i])]]