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Proof step 22 from proof valid-wl-erasing-invalidate (previous step)

# apebs = # wlar, avhdr1.sqn = valid-sqns(v, m1, apebs).max, apebs[m] = mkpeb(aehdr0, avhdr0, buf0, m3, boolvar), wlar[m] = wl-entry(m0, erasing), wlar[n] = wl-entry(m5, used), apebs[n] = mkpeb(aechdr(m5), avhdr1, buf1, m4, false), n < # wlar, m < # wlar, valid-peb(v, m1, mkpeb(aehdr0, avhdr0, buf0, m3, boolvar)), valid-peb(v, m1, mkpeb(aechdr(m5), avhdr1, buf1, m4, false)) ⊦ avhdr1.sqn = (valid-sqns(v, m1, apebs) -- avhdr0.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 23:
⊦ 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 24:
# apebs = # wlar, avhdr1.sqn = valid-sqns(v, m1, apebs).max, apebs[n] = mkpeb(aechdr(m5), avhdr1, buf1, m4, false), wlar[n] = wl-entry(m5, used), wlar[m] = wl-entry(m0, erasing), apebs[m] = mkpeb(aehdr0, avhdr0, buf0, m3, boolvar), m < # wlar, n < # wlar, valid-peb(v, m1, mkpeb(aechdr(m5), avhdr1, buf1, m4, false)), valid-peb(v, m1, mkpeb(aehdr0, avhdr0, buf0, m3, boolvar)), n < # apebs ∧ m < # apebs ∧ n ≠ m ∧ valid-peb(v, m1, apebs[n]) ∧ valid-peb(v, m1, apebs[m]) → (∃ bag. valid-sqns(v, m1, apebs) = bag ++ apebs[n].vidhdr.sqn ++ apebs[m].vidhdr.sqn) ⊦ avhdr1.sqn = (valid-sqns(v, m1, apebs) -- avhdr0.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] → [n, apebs, m, v, m1]

Additional information

Used terms: n, apebs, m, v, m1