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Proof step 31 from proof valid-wl-next-valid-update (previous step)

# apebs = # wlar, avhdr1.sqn = avhdr0.sqn, avhdr0.sqn = valid-sqns(v0, m1, apebs, m).max, 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), n0 < m, m0 < # wlar, m < # wlar, avhdr0.sqn < avhdr.sqn, m0 < m, n0 < # wlar, m0 + 1 < # wlar, n0 + 1 < # wlar, 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)) ⊦ avhdr0.sqn = avhdr.sqn, n0 = m0, n0 = m

User applied rule apply lemma

And obtained the following new goals

Proof step 32:
⊦ n0 < m0 ∧ n1 < m0 ∧ m0 ≤ # apebs ∧ n0 ≠ n1 ∧ valid-peb(v, m, apebs[n0]) ∧ valid-peb(v, m, apebs[n1]) → (∃ bag. valid-sqns(v, m, apebs, m0) = bag ++ apebs[n0].vidhdr.sqn ++ apebs[n1].vidhdr.sqn)
Proof step 33:
# apebs = # wlar, avhdr0.sqn = valid-sqns(v0, m1, apebs, m).max, 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), n0 + 1 < # wlar, m0 + 1 < # wlar, n0 < # wlar, m0 < m, avhdr0.sqn < avhdr.sqn, m < # wlar, m0 < # wlar, n0 < m, 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)), m0 < m ∧ n0 < m ∧ m ≤ # apebs ∧ m0 ≠ n0 ∧ valid-peb(v0, m1, apebs[m0]) ∧ valid-peb(v0, m1, apebs[n0]) → (∃ bag. valid-sqns(v0, m1, apebs, m) = bag ++ apebs[m0].vidhdr.sqn ++ apebs[n0].vidhdr.sqn) ⊦ avhdr0.sqn = avhdr.sqn, n0 = m, n0 = m0

Rule argument

spec: sqns name: valid-sqns-extract2-sqn-h seq: ⊦ n0 < m0 ∧ n1 < m0 ∧ m0 ≤ # apebs ∧ n0 ≠ n1 ∧ valid-peb(v, m, apebs[n0]) ∧ valid-peb(v, m, apebs[n1]) → (∃ bag. valid-sqns(v, m, apebs, m0) = bag ++ apebs[n0].vidhdr.sqn ++ apebs[n1].vidhdr.sqn) subst: [n0, m0, n1, apebs, v, m] → [m0, m, n0, apebs, v0, m1]

Additional information

Used terms: m0, m, n0, apebs, v0, m1