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Proof step 4 from proof ubi-io-initial-valid-sqns-h (previous step)

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) = ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
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]) ⊃ {apebs[n0].vidhdr.sqn} ;∅) = ∅

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%⊦ n < # apebs → valid-sqns(v, m, apebs, n + 1) = valid-sqns(v, m, apebs, n) ∪ (valid-peb(v, m, apebs[n]) ⊃ {apebs[n].vidhdr.sqn} ;∅); (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ m +1 = m + 1; (s)