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Proof step 3 from proof ubi-io-initial-valid-sqns-h (previous step)

ubi-io-initial(apebs), n ≤ # apebs ⊦ valid-sqns(v, m, apebs, n) = ∅

User applied rule structural induction

And obtained the following new goals

Proof step 4:
ubi-io-initial(apebs), n0 +1 ≤ # apebs, ∀ apebs, v, m. ubi-io-initial(apebs) ∧ n0 ≤ # apebs → valid-sqns(v, m, apebs, n0) = ∅ ⊦ valid-sqns(v, m, apebs, n0 +1) = ∅

Rule argument

indvar: n

Additional information

Used simplifier rules: nat freely generated by 0, +1;;% ⊦ valid-sqns(v, m, apebs, 0) = ∅; (s)