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

apebs[m] = mkpeb(aehdr, avhdr, buf0, m0, boolvar0), m < # apebs, ( (valid-sqns(v, m2, apebs) \ (valid-peb(v, m2, mkpeb(aehdr, avhdr, buf0, m0, boolvar0)) ⊃ {avhdr.sqn} ;∅)) ∪ (valid-peb(v, m2, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)) ⊃ {avhdr.sqn} ;∅) ).max < n, valid-peb(mkpeb(aehdr, avhdr, buf1, m1, boolvar1)), valid-peb(mkpeb(aehdr, avhdr, buf0, m0, boolvar0)), n ≤ valid-sqns(v, m2, apebs).max ⊦ valid-sqns(v, m2, apebs) = ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
apebs[m] = mkpeb(aehdr, avhdr, buf0, m0, boolvar0), ( (valid-sqns(v, m2, apebs) \ (valid-peb(v, m2, mkpeb(aehdr, avhdr, buf0, m0, boolvar0)) ⊃ {avhdr.sqn} ;∅)) ∪ (valid-peb(v, m2, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)) ⊃ {avhdr.sqn} ;∅) ).max < n, m < # apebs, ( (valid-sqns(v, m2, apebs) \ (valid-peb(v, m2, mkpeb(aehdr, avhdr, buf0, m0, boolvar0)) ⊃ {avhdr.sqn} ;∅)) ∪ (valid-peb(v, m2, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)) ⊃ {avhdr.sqn} ;∅) ).max < valid-sqns(v, m2, apebs).max, valid-peb(mkpeb(aehdr, avhdr, buf0, m0, boolvar0)), valid-peb(mkpeb(aehdr, avhdr, buf1, m1, boolvar1)), n ≤ valid-sqns(v, m2, apebs).max ⊦ valid-sqns(v, m2, apebs) = ∅

Rule argument

Additional information

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