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Proof step 20 from proof unique-sqns-update (previous step)

m < # apebs, unique-elems(valid-sqns(v, m0, apebs)), valid-peb(v, m0, apebs[m]), ¬ valid-peb(mkpeb(aehdr, avhdr, buf, m1, boolvar)) ∨ ¬ avhdr.sqn ∈ valid-sqns(avhdr.vol, avhdr.leb, apebs) \ (valid-peb(avhdr.vol, avhdr.leb, apebs[m]) ⊃ {apebs[m].vidhdr.sqn} ;∅) ⊦ unique-elems((valid-sqns(v, m0, apebs) \ {apebs[m].vidhdr.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 21:
m < # apebs, unique-elems(valid-sqns(v, m0, apebs)), valid-peb(v, m0, apebs[m]), ¬ valid-peb(mkpeb(aehdr, avhdr, buf, m1, boolvar)) ∨ ¬ avhdr.sqn ∈ valid-sqns(avhdr.vol, avhdr.leb, apebs) \ (v = avhdr.vol ∧ m0 = avhdr.leb ⊃ {apebs[m].vidhdr.sqn} ;∅) ⊦ unique-elems((valid-sqns(v, m0, apebs) -- apebs[m].vidhdr.sqn) ∪ (valid-peb(v, m0, mkpeb(aehdr, avhdr, buf, m1, boolvar)) ⊃ {avhdr.sqn} ;∅))

Rule argument

Additional information

Used simplifier rules: ⊦ valid-peb(v0, m0, apeb) → (valid-peb(v1, m1, apeb) ↔ v0 = v1 ∧ m0 = m1); (s)% ⊦ bag \ {n} = bag -- n; (s)