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Proof step 21 from proof valid-wl-erasing-invalidate0 (previous step)

# apebs = # wlar, avhdr0.sqn = valid-sqns(v, m0, apebs).max, apebs[m] = mkpeb(aehdr0, avhdr1, buf1, m1, boolvar), wlar[n] = wl-entry(m5, used), apebs[n] = mkpeb(aechdr(m5), avhdr0, buf0, m3, false), n < # wlar, m < # wlar, valid-peb(v, m0, mkpeb(aehdr0, avhdr1, buf1, m1, boolvar)), valid-peb(v, m0, mkpeb(aechdr(m5), avhdr0, buf0, m3, false)) ⊦ avhdr0.sqn = (valid-sqns(v, m0, apebs) -- avhdr1.sqn).max, n = m, valid-peb(mkpeb(aehdr, avhdr, buf, m2, false))

User applied rule apply lemma

And obtained the following new goals

Proof step 22:
⊦ n0 < # apebs ∧ n1 < # apebs ∧ n0 ≠ n1 ∧ valid-peb(v, m, apebs[n0]) ∧ valid-peb(v, m, apebs[n1]) → (∃ bag. valid-sqns(v, m, apebs) = bag ++ apebs[n0].vidhdr.sqn ++ apebs[n1].vidhdr.sqn)
Proof step 23:
# apebs = # wlar, avhdr0.sqn = valid-sqns(v, m0, apebs).max, apebs[n] = mkpeb(aechdr(m5), avhdr0, buf0, m3, false), wlar[n] = wl-entry(m5, used), apebs[m] = mkpeb(aehdr0, avhdr1, buf1, m1, boolvar), m < # wlar, n < # wlar, valid-peb(v, m0, mkpeb(aechdr(m5), avhdr0, buf0, m3, false)), valid-peb(v, m0, mkpeb(aehdr0, avhdr1, buf1, m1, boolvar)), m < # apebs ∧ n < # apebs ∧ m ≠ n ∧ valid-peb(v, m0, apebs[m]) ∧ valid-peb(v, m0, apebs[n]) → (∃ bag. valid-sqns(v, m0, apebs) = bag ++ apebs[m].vidhdr.sqn ++ apebs[n].vidhdr.sqn) ⊦ avhdr0.sqn = (valid-sqns(v, m0, apebs) -- avhdr1.sqn).max, n = m, valid-peb(mkpeb(aehdr, avhdr, buf, m2, false))

Rule argument

spec: sqns name: valid-sqns-extract2-sqn seq: ⊦ n0 < # apebs ∧ n1 < # apebs ∧ n0 ≠ n1 ∧ valid-peb(v, m, apebs[n0]) ∧ valid-peb(v, m, apebs[n1]) → (∃ bag. valid-sqns(v, m, apebs) = bag ++ apebs[n0].vidhdr.sqn ++ apebs[n1].vidhdr.sqn) subst: [n0, apebs, n1, v, m] → [m, apebs, n, v, m0]

Additional information

Used terms: m, apebs, n, v, m0