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Proof step 3 from proof valid-sqns-subarray-h (previous step)

n ≤ # apebs, n0 ≤ n, n0 ≤ # apebs ⊦ valid-sqns(v, m, subarray(apebs, 0, n), n0) = valid-sqns(v, m, apebs, n0)

User applied rule structural induction

And obtained the following new goals

Proof step 4:
n1 +1 ≤ # apebs, n1 +1 ≤ n, n ≤ # apebs, ∀ n, apebs, v, m. n ≤ # apebs ∧ n1 ≤ n ∧ n1 ≤ # apebs → valid-sqns(v, m, subarray(apebs, 0, n), n1) = valid-sqns(v, m, apebs, n1) ⊦ valid-sqns(v, m, subarray(apebs, 0, n), n1 +1) = valid-sqns(v, m, apebs, n1 +1)

Rule argument

indvar: n0

Additional information

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