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Proof step 25 from proof valid-global-sqn-write-valid (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 26:
apebs[m] = mkpeb(aehdr, avhdr, buf0, m0, boolvar0), m < # apebs, valid-peb(mkpeb(aehdr, avhdr, buf1, m1, boolvar1)), valid-peb(mkpeb(aehdr, avhdr, buf0, m0, boolvar0)), n ≤ valid-sqns(v, m2, apebs).max, ∀ v, m2. valid-sqns(v, m2, apebs) ≠ ∅ → valid-sqns(v, m2, apebs).max < n ⊦ valid-sqns(v, m2, apebs) = ∅, v = avhdr.vol ∧ m2 = avhdr.leb

Rule argument

Additional information

Used simplifier rules: ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)%⊦ valid-peb(apeb) → (valid-peb(v, m, apeb) ↔ v = apeb.vidhdr.vol ∧ m = apeb.vidhdr.leb); (ss)%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)