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Proof step 42 from proof valid-wl-use (previous step)

# apebs = # wlar, avhdr1.sqn = valid-sqns(v, m, apebs).max, apebs[n] = mkpeb(aehdr0, avhdr0, buf0, m1, boolvar0), wlar[n0] = wl-entry(m3, used), apebs[n0] = mkpeb(aechdr(m3), avhdr1, buf1, m2, false), n0 < # wlar, n < # wlar, valid-peb(v, m, mkpeb(aehdr0, avhdr0, buf0, m1, boolvar0)), valid-peb(v, m, mkpeb(aechdr(m3), avhdr1, buf1, m2, false)), valid-peb(mkpeb(aehdr, avhdr, buf, m0, boolvar)), valid-sqns(avhdr.vol, avhdr.leb, apebs) ≠ ∅ → valid-sqns(avhdr.vol, avhdr.leb, apebs).max < avhdr.sqn, v ≠ avhdr.vol ∨ m ≠ avhdr.leb ⊦ avhdr1.sqn = (valid-sqns(v, m, apebs) -- avhdr0.sqn).max, n0 = n, v = avhdr.vol ∧ m = avhdr.leb

User applied rule apply lemma

And obtained the following new goals

Proof step 43:
⊦ 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 44:
# apebs = # wlar, avhdr1.sqn = valid-sqns(v, m, apebs).max, apebs[n0] = mkpeb(aechdr(m3), avhdr1, buf1, m2, false), wlar[n0] = wl-entry(m3, used), apebs[n] = mkpeb(aehdr0, avhdr0, buf0, m1, boolvar0), n < # wlar, n0 < # wlar, valid-peb(mkpeb(aehdr, avhdr, buf, m0, boolvar)), valid-peb(v, m, mkpeb(aechdr(m3), avhdr1, buf1, m2, false)), valid-peb(v, m, mkpeb(aehdr0, avhdr0, buf0, m1, boolvar0)), valid-sqns(avhdr.vol, avhdr.leb, apebs) ≠ ∅ → valid-sqns(avhdr.vol, avhdr.leb, apebs).max < avhdr.sqn, n < # apebs ∧ n0 < # apebs ∧ n ≠ n0 ∧ valid-peb(v, m, apebs[n]) ∧ valid-peb(v, m, apebs[n0]) → (∃ bag. valid-sqns(v, m, apebs) = bag ++ apebs[n].vidhdr.sqn ++ apebs[n0].vidhdr.sqn), v ≠ avhdr.vol ∨ m ≠ avhdr.leb ⊦ avhdr1.sqn = (valid-sqns(v, m, apebs) -- avhdr0.sqn).max, n0 = n, v = avhdr.vol ∧ m = avhdr.leb

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] → [n, apebs, n0, v, m]

Additional information

Used terms: n, apebs, n0, v, m