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Proof step 14 from proof valid-global-sqn-add-valid (previous step)

apebs[m] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), avhdr.sqn < ((valid-sqns(v, m0, apebs) -- avhdr0.sqn) ++ avhdr.sqn).max, valid-sqns(v, m0, apebs).max < n, m < # apebs, avhdr.sqn < n, valid-sqns(v, m0, apebs).max < (valid-sqns(v, m0, apebs) -- avhdr0.sqn).max, avhdr.sqn < (valid-sqns(v, m0, apebs) -- avhdr0.sqn).max, valid-peb(mkpeb(aehdr, avhdr, buf, m1, boolvar)), valid-peb(v, m0, apebs[m]), n ≤ (valid-sqns(v, m0, apebs) -- avhdr0.sqn).max ⊦ (valid-sqns(v, m0, apebs) -- avhdr0.sqn) ∪ (valid-peb(v, m0, mkpeb(aehdr, avhdr, buf, m1, boolvar)) ⊃ {avhdr.sqn} ;∅) = ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
apebs[m] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), valid-sqns(v, m0, apebs).max < (valid-sqns(v, m0, apebs) -- avhdr0.sqn).max, avhdr.sqn < (valid-sqns(v, m0, apebs) -- avhdr0.sqn).max, avhdr.sqn < ((valid-sqns(v, m0, apebs) -- avhdr0.sqn) ++ avhdr.sqn).max, valid-sqns(v, m0, apebs).max < n, m < # apebs, avhdr.sqn < n, valid-peb(mkpeb(aehdr, avhdr, buf, m1, boolvar)), valid-peb(v, m0, mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0)), n ≤ (valid-sqns(v, m0, apebs) -- avhdr0.sqn).max ⊦ (valid-sqns(v, m0, apebs) -- avhdr0.sqn) ∪ (valid-peb(v, m0, mkpeb(aehdr, avhdr, buf, m1, boolvar)) ⊃ {avhdr.sqn} ;∅) = ∅

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)% ⊦ m < (bag ++ m).max → (bag ++ m).max = bag.max; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic