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Proof step 8 from proof depths-max (previous step)

depths(t0, i + 1) ≠ [] ∧ depths(t1, i + 1) ≠ [], max(max(depths(t0, i + 1)), max(depths(t1, i + 1))) < i, ∀ i. ¬ max(depths(t0, i)) < i, ∀ i. ¬ max(depths(t1, i)) < i ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
⊦ depths(t, i) ≠ []
Proof step 7:
max(depths(t0, i + 1)) < i, max(depths(t1, i + 1)) < i, ∀ i. ¬ max(depths(t0, i)) < i, ∀ i. ¬ max(depths(t1, i)) < i ⊦

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ max(i, j) = max(j, i)], [CSIMPSEQ : ⊦ max(i, max(j, j0)) = max(max(i, j), j0)], [CSIMPSEQ : ⊦ max(i, j) < j0 ↔ i < j0 ∧ j < j0])]]