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Proof step 15 from proof ubi-io-initial-valid-sqns-h (previous step)

n0 < # apebs, ubi-io-initial(apebs), ∀ apebs, v, m. ubi-io-initial(apebs) ∧ n0 ≤ # apebs → valid-sqns(v, m, apebs, n0) = ∅ ⊦ valid-sqns(v, m, apebs, n0) ∪ ∅ = ∅, valid-peb(v, m, apebs[n0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
n0 < # apebs, ubi-io-initial(apebs), ∀ apebs, v, m. ubi-io-initial(apebs) ∧ n0 ≤ # apebs → valid-sqns(v, m, apebs, n0) = ∅ ⊦ valid-sqns(v, m, apebs, n0) = ∅, valid-peb(v, m, apebs[n0])

Rule argument

Additional information

Used simplifier rules: union-com: ⊦ bag ∪ bag2 = bag2 ∪ bag; from specification bag-union[nat-bag]%union-ass: ⊦ bag ∪ bag3 ∪ bag4 = (bag ∪ bag3) ∪ bag4; from specification bag-union[nat-bag]% ⊦ ∅ ∪ bag0 = bag0; (s)