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Proof step 34 from proof valid-wl-next-valid-update (previous step)

# apebs = # wlar, avhdr1.sqn = avhdr0.sqn, wlar[n0] = wl-entry(m7, used), apebs[m0] = mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0), apebs[m] = mkpeb(aehdr, avhdr, buf, m3, boolvar), apebs[n0] = mkpeb(aechdr(m7), avhdr1, buf1, m5, false), valid-sqns(v0, m1, apebs, m) = bag ++ avhdr0.sqn ++ avhdr0.sqn, (bag ++ avhdr0.sqn ++ avhdr0.sqn).max < avhdr.sqn, n0 < m, m0 < # wlar, m < # wlar, avhdr0.sqn < avhdr.sqn, m0 < m, n0 < # wlar, m0 + 1 < # wlar, n0 + 1 < # wlar, (bag ++ avhdr0.sqn).max < avhdr.sqn, unique-elems(valid-sqns(v0, m1, apebs)), valid-peb(v0, m1, mkpeb(aechdr(m7), avhdr1, buf1, m5, false)), valid-peb(v0, m1, mkpeb(aehdr, avhdr, buf, m3, boolvar)), valid-peb(v0, m1, mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0)), (bag ++ avhdr0.sqn).max ≤ avhdr0.sqn ⊦ avhdr0.sqn = avhdr.sqn, n0 = m0, n0 = m

User applied rule apply lemma

And obtained the following new goals

Proof step 35:
⊦ bag0 ⊆ bag1 ∧ unique-elems(bag1) → unique-elems(bag0)
Proof step 36:
# apebs = # wlar, avhdr1.sqn = avhdr0.sqn, apebs[n0] = mkpeb(aechdr(m7), avhdr1, buf1, m5, false), apebs[m] = mkpeb(aehdr, avhdr, buf, m3, boolvar), apebs[m0] = mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0), wlar[n0] = wl-entry(m7, used), valid-sqns(v0, m1, apebs, m) = bag ++ avhdr0.sqn ++ avhdr0.sqn, (bag ++ avhdr0.sqn).max < avhdr.sqn, n0 + 1 < # wlar, m0 + 1 < # wlar, n0 < # wlar, m0 < m, avhdr0.sqn < avhdr.sqn, m < # wlar, m0 < # wlar, n0 < m, (bag ++ avhdr0.sqn ++ avhdr0.sqn).max < avhdr.sqn, unique-elems(valid-sqns(v0, m1, apebs)), valid-peb(v0, m1, mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0)), valid-peb(v0, m1, mkpeb(aehdr, avhdr, buf, m3, boolvar)), valid-peb(v0, m1, mkpeb(aechdr(m7), avhdr1, buf1, m5, false)), (bag ++ avhdr0.sqn).max ≤ avhdr0.sqn, valid-sqns(v0, m1, apebs, m) ⊆ valid-sqns(v0, m1, apebs) ∧ unique-elems(valid-sqns(v0, m1, apebs)) → unique-elems(valid-sqns(v0, m1, apebs, m)) ⊦ avhdr0.sqn = avhdr.sqn, n0 = m, n0 = m0

Rule argument

spec: bag-max name: unique-elems-subset seq: ⊦ bag0 ⊆ bag1 ∧ unique-elems(bag1) → unique-elems(bag0) subst: [bag0, bag1] → [valid-sqns(v0, m1, apebs, m), valid-sqns(v0, m1, apebs)]

Additional information

Used terms: valid-sqns(v0, m1, apebs, m), valid-sqns(v0, m1, apebs)