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Proof step 15 from proof unique-sqns-update (previous step)

m < # apebs, ∀ v, m. unique-elems(valid-sqns(v, m, 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[m, mkpeb(aehdr, avhdr, buf, m1, boolvar)]))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ 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} ;∅)
Proof step 17:
m < # apebs, ∀ v, m. unique-elems(valid-sqns(v, m, 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, apebs[m]) ⊃ {apebs[m].vidhdr.sqn} ;∅)) ∪ (valid-peb(v, m0, mkpeb(aehdr, avhdr, buf, m1, boolvar)) ⊃ {mkpeb(aehdr, avhdr, buf, m1, boolvar).vidhdr.sqn} ;∅))

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 terms: mkpeb(aehdr, avhdr, buf, m1, boolvar), m, apebs, m0, v