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Proof step 12 from proof unique-sqns-update (previous step)

m < # apebs, unique-elems(valid-sqns(v, m0, apebs)), unique-elems(valid-sqns(v, m0, apebs[m, mkpeb(aehdr, avhdr, buf, m1, boolvar)])), valid-peb(v, m0, mkpeb(aehdr, avhdr, buf, m1, boolvar)), avhdr.sqn ∈ valid-sqns(v, m0, apebs) \ (valid-peb(v, m0, apebs[m]) ⊃ {apebs[m].vidhdr.sqn} ;∅) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: sqns name: valid-sqns-write seq: ⊦ n < # apebs → valid-sqns(v, m, apebs[n, apeb]) = ( valid-sqns(v, m, apebs) \ (valid-peb(v, m, apebs[n]) ⊃ {apebs[n].vidhdr.sqn} ;∅)) ∪ (valid-peb(v, m, apeb) ⊃ {apeb.vidhdr.sqn} ;∅) subst: [apeb, n, apebs, m, v] → [mkpeb(aehdr, avhdr, buf, m1, boolvar), m, apebs, m0, v] flags: <all paths>

Additional information

Used simplifier rules: ⊦ valid-peb(v0, m0, apeb) → (valid-peb(v1, m1, apeb) ↔ v0 = v1 ∧ m0 = m1); (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ bag ∪ {n} = bag ++ n; (s)%union-ass: ⊦ bag ∪ bag3 ∪ bag4 = (bag ∪ bag3) ∪ bag4; from specification bag-union[nat-bag]%union-com: ⊦ bag ∪ bag2 = bag2 ∪ bag; from specification bag-union[nat-bag]% ⊦ unique-elems(bag ++ m) ↔ unique-elems(bag) ∧ ¬ m ∈ bag; (s)% ⊦ bag \ ∅ = bag; (s) Used terms: mkpeb(aehdr, avhdr, buf, m1, boolvar), m, apebs, m0, v