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Proof step 24 from proof unique-sqns-update (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
m < # apebs, unique-elems(valid-sqns(v, m0, apebs)), ¬ 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) ∪ (valid-peb(v, m0, mkpeb(aehdr, avhdr, buf, m1, boolvar)) ⊃ {avhdr.sqn} ;∅)), valid-peb(v, m0, apebs[m])

Rule argument

Additional information

Used simplifier rules: ⊦ bag \ ∅ = bag; (s)