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Proof step 21 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) \ (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} ;∅))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 22:
apebs[m] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), 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 ⊃ {avhdr0.sqn} ;∅) ⊦ unique-elems((valid-sqns(v, m0, apebs) -- avhdr0.sqn) ∪ (valid-peb(v, m0, mkpeb(aehdr, avhdr, buf, m1, boolvar)) ⊃ {avhdr.sqn} ;∅))

Rule argument

spec: apeb name: elim seq: ⊦ ( ( (aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar) subst: [apeb, aehdr, avhdr, buf, m, boolvar] → [apebs[m], aehdr0, avhdr0, buf0, m2, boolvar0]

Additional information

Used simplifier rules: ⊦ ( ((aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar); (elim) Used terms: apebs[m], aehdr0, avhdr0, buf0, m2, boolvar0